13 Landscapes and Complex Systems.jl

### A Pluto.jl notebook ###
# v0.19.24

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 30b13841-97f1-47ab-a5c9-346ea8261f03
using Plots, PlutoUI, ParameterizedFunctions, DifferentialEquations

# ╔═╡ 3aee4ef3-15bc-435f-89bb-c07a17c72021
using CairoMakie

# ╔═╡ 64b8c8d1-91d2-4cb7-bf20-84fa04eeb738
begin
	#using Gadfly
	using Random
	
	function F(x,parms)
	  (S,I,R) = x
	  (beta,gamma) = parms
	  infection = beta*S*I
	  recovery = gamma*I
	  [infection,recovery]
	end
	
	x0 = [999,1,0]
	nu = [[-1 1 0];[0 -1 1]]
	parms = [0.1/1000.0,0.01]
	tf = 250.0
	Random.seed!(1234)
	
	result = ssa(x0,F,nu,parms,tf)
	
	data = ssa_data(result)
	
	plot_theme = Theme(
	    panel_fill=colorant"white",
	    default_color=colorant"black"
	)
	pppp=plot(data,
	    layer(x=:time,y=:x1,Geom.step,Theme(default_color=colorant"red")),
	    layer(x=:time,y=:x2,Geom.step,Theme(default_color=colorant"orange")),
	    layer(x=:time,y=:x3,Geom.step,Theme(default_color=colorant"blue")),
	    Guide.xlabel("Time"),
	    Guide.ylabel("Number"),
	    Guide.title("SSA simulation"),
	    Guide.manual_color_key("Subpopulation",["S","I","R"],["red","orange","blue"]),
	    plot_theme
	)
end

# ╔═╡ c8765318-d2d1-4af4-8604-c363038018b7
html"<button onclick='present()'>present</button>"

# ╔═╡ 01bab882-2588-4d5d-8808-cdd4aaa23a47
#Pkg.add("Gillespie")

# ╔═╡ 3878c1bf-64fd-403a-aab1-dd5364588744
#import Pkg; Pkg.add("Gillespie")

# ╔═╡ 190cc65b-0fad-4150-98f8-0494cc018636
html"<button onclick='present()'>present</button>"

# ╔═╡ 7c9d5d2d-9d2f-4490-a891-eaffa42e6cca
begin
	struct Foldable{C}
	    title::String
	    content::C
	end
	
	function Base.show(io, mime::MIME"text/html", fld::Foldable)
	    write(io,"<details><summary>$(fld.title)</summary><p>")
	    show(io, mime, fld.content)
	    write(io,"</p></details>")
	end
end

# ╔═╡ 24a0dea7-bbd3-4eaa-8d69-c78e2a484534
md"## Other tools

Often times, the linearization approach does not succesfully recovers the dynamcis of teh system of interest, maybe becausde we are not close to a steady state (where perturbations behave as in the linear system). In thsi case, we can use other mathematical tools,. Apart from linear stability analysis and other mathematical tools, there are other common approaches. 


- Lyapunov exponents
- Poincaré maps
- Numerical simulations
- Agent base models
- Null Clines, Phase potraits and lansdcapes


### Lyapunov exponents 

Lyapunov stability theory is a standard tool and one of the most important tools in the analysis of nonlinear systems. The Lyapunov exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.

### Poincaré maps 

Poincaré map represents the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace (a 3D orbit and a plane), called the Poincaré section, transversal to the flow of the system. A Poincaré maps can be interpreted as a discrete dynamical system with a state space that is one dimension smaller than the original continuous dynamical system. Because it preserves many properties of periodic and quasiperiodic orbits of the original system and has a lower-dimensional state space, it is often used for analyzing the original system in a simpler way.

### Numerical simulations

If we do have teh differential equations, but these are not analitically solvable, a common approac is to simulate the dynamics just by intergrating the differential equations numerically. For instance, in this model of interactions between two species (cubic autocatalator model) 

```math
\begin{eqnarray}
\frac{\partial x}{\partial t} = x^2 y -x \\
\frac{\partial y}{\partial t} = \mu - x^2 y 
\end{eqnarray}
```
we need the initial conditions


"

# ╔═╡ 95aa2183-e03c-41a7-98f9-1ad074ba3baa
Cubic! = @ode_def Cubic begin
    dX = µ - X * Y^2 - r * X 
    dY =  X * Y^2 - Y + r * X
end µ r

# ╔═╡ 52b75ad6-d1ad-4f33-ad7d-2089f02ca6a7
 begin
	µ_slide = @bind µ html"<input type=range min=0.0 max=3.0 step=.1>"
	r_slide = @bind r html"<input type=range min=0.0 max=3.0 step=.1>"
	
	md"""
	**Set the values of the kinetic constants**
	
	value of µ: $(µ_slide)

	value of r: $(r_slide)

	
	"""
end

# ╔═╡ 43f4f9de-a09a-43ae-8383-06d3a3be3589
begin
	prob3 = ODEProblem(Cubic!,[0.0,0.0],(0.0,50.0),[µ,r])
	sol3 = solve(prob3)
	Plots.plot(sol3,label=["X" "Y"])
	title!("Cubic Autocatalator")
	Plots.xlabel!("Time [s]")
	Plots.ylabel!("Concentration [a.u]")
end

# ╔═╡ de58d9dd-dc03-44b0-bc6a-6068d3ff9d28
md" ### Models of partial differential equations 
(reaction-diffusion-flow)

The Diffusion Equation is a partial differential equation which describes changes in concentratio
n of a substance that diffusing in a spatial system. When the diffusion coefficient `D` of the substance `u` is constant throughout  the system, the diffusion equation takes the form. 


```math
\begin{equation} 
\frac{\partial u}{\partial t} = D \frac{ \partial^2 u}{\partial x^2} \tag{1}
\end{equation}
```

This equation is also called the Heat Equation, since it also describes the distribution of a heat in a given region over time. It is also Fick’s second law. To solve these type of equations, we need to now the initial conditions, as well as the boundary condition, i.e., the value of `u` at the two edges of the system: `u(0)` and `u(L)`. Let’s assume that the value of `u` is constant in one of the edges with a value `u_0`. This is equivalent to assume that our substance `u` is being produced at one side of the system. Let's also assume that at the other edge, `u` disappears or is being consumed, so `u(L)=0`. Therefore, our boundary conditions are $u(0,t)=u_0$ and $u(L,t)=0$.

If we want to find the steady state solution we obtain:


```math
\begin{equation} 
\frac{\partial u}{\partial t} = D \frac{ \partial^2 u}{\partial x^2} =0 \tag{2}
\end{equation}
```

In this condition, Fick’s second law is reduced to Laplace’s equation, $\nabla^2 u= 0$. It follows that $u=C_1 x +  C_2$, where  $C_1$ and $C_2$ are intergration constants that we can find using the boundary conditions. 

```math
\begin{equation} 
u(0)=C_1 \cdot 0 + C_2 = C_2\\
u(L)= 0 = C_1 \cdot L + C_2 = C_1 \cdot L + u(0) \\
C_1 = -\frac{u(0)}{L} \tag{3}
\end{equation} 
```

so the solution of the gradient is simply a straight line when the system is stable, such as:

```math
u_{ss}(x)=  - \frac{u(0)}{L} x + u(0)=u(0)(1-\frac{x}{L}) \tag{4}
```




"

# ╔═╡ 40bac874-8e71-4a45-9fd6-fd6b5f673b16
md"

Quite often in biology, these diffusing substances or morphogens interact with other substances or receptor molecules, or are being internalized by cells, or simply degraded constantly in the systems. To study this type of systems we use a class of partial differential equations (PDE's) called Reaction-Diffusion Equations. These type of equations are used to describe the diffusion (spreading out) and reaction of one or several chemical species.

In the simplest one-dimensional case and one single substance, let `u(x,t)` be the concentration of `u` at location `x` at time `t`. Then, the reaction-diffusion equation has the form:

```math
\begin{equation} \frac{\partial u}{\partial t} = \underbrace{D_u \frac{\partial^2 u} 
{\partial x^2}}_{\text{Diffusion}} + \overbrace{f(u)}^{\text{Reaction}}  \tag{5} 
\end{equation}
```

where `D`  is a coefficient associated with the diffusive properties of `u`, and `f(u)` is a function that describes how `u` grows or decays depending on its current state.

## Degradation or clearance

Lets for now consider the simplest reaction where `u` is simply being consumed in the extended system with a constant rate. This is a very common scenario for morphogens, that are consumed by the cells as they process the information:

```math  
u \overset{k}{\longrightarrow} 0 \tag{6}
```

so, the reaction term is $f(u) = - k \cdot u$. In this case, in a a-dimensional system, (no diffusion), the system is described by a single first order differential equation. 


```math
\frac{\mathrm{d} u}{\mathrm{d} t} =  - k \cdot u \tag{7}
```
 
 with a solution
 
```math
u (t)= u (0) \cdot e^{- k t}  \tag{8}
```


 
When we combine both diffusion and degradation we have the following equation: 


```math
\begin{equation} 
\frac{\partial u(x,t)}{\partial t} = D \frac{ \partial^2u(x,t)}{\partial x^2} - k \cdot u(x,t) \tag{9}
\end{equation}
```


if we look for the steady state solution 

```math
\begin{equation} 
\frac{ \partial^2u(x,t)}{\partial x^2} = \frac{k}{D} u(x,t) \tag{10}
\end{equation}
```


where, the second derivative of `u` with respect to `x` is proportional to itself. The only functions for `u` with this property are exponential functions. Therefore, one can propose a general solution for `u` :

```math
u=  C_1 \cdot e^{-x/\lambda} + C_2 e^{+x/\lambda} \tag{11}
```

if we test if the previous equation is a solution, the first derivative:

```math
\frac{ \partial u(x,t)}{\partial x}=-\frac{C_1}{\lambda} \cdot e^{-x/\lambda} + \frac{C_2}{\lambda} e^{+x/\lambda} \tag{12}
```


and the second derivative

```math
\frac{ \partial^2 u(x,t)}{\partial^2 x}=\frac{C_1}{\lambda^2} \cdot e^{-x/\lambda} + \frac{C_2}{\lambda^2} e^{+x/\lambda} \tag{13}
```

rearranging terms 

```math
\frac{ \partial^2 u(x,t)}{\partial^2 x}=\frac{1}{\lambda^2}(C_1 \cdot e^{-x/\lambda} + C_2 e^{+x/\lambda})=\frac{u}{\lambda^2} \tag{4}
```

using the Eq 10. we arrive at the condition for the solution

```math
\frac{u(x,t)}{\lambda^2}=\frac{k}{D} u(x,t) \tag{15}
```
so, the characteristic length of the exponential 

```math
\lambda = \sqrt{\frac{D}{k}} \tag{16}
```

To determine the constants $C_1$ and $C_2$, we need two equations. We use the two boundary conditions used for the case of only diffusion. 

```math
u(0,t)_{ss}=  C_1 \cdot e^{-0/\lambda} + C_2 e^{+0/\lambda}= C_1 + C_2 = u_0 \tag{17}
```

```math
u(L,t)_{ss}=  C_1 \cdot e^{-L/\lambda} + C_2 e^{+L/\lambda}= 0 \tag{18}
```
for the case that the dimensions are much larger than the characteristic length of the exponential, the second term of the equation goes to infinite, so $C_2$ has to be zero. Therefore $ C_1=u_0 $ and the solution of the stable gradient is a single exponential:

```math
\begin{equation}  u(x,t)_{ss} = u_0 e^{-x\sqrt{\frac{k}{D}}} \tag{19}
 \end{equation}
```





"

# ╔═╡ dad48b2a-201f-40d1-a515-347b5fbc15bc
begin
	## spatial scaling
	number_of_steps=100;
	size_of_system=100;
	space_step=size_of_system/number_of_steps;
	x_vector = LinRange(0,size_of_system,number_of_steps)
	
	## temporal scaling
	number_of_iterations=1000;
	total_time=70;
	time_step=total_time/number_of_iterations;
	
	## Parameters and initial conditions
	Diff=10; # ?m^2/min 
	k=0.1
	u=zeros(1,number_of_steps)
	u[1]=1;
	u_=u; 

plt2=Plots.plot(x_vector,u')
	
end

# ╔═╡ e6b6aa9f-f3c6-4f4a-92dd-b881c61f7df9
begin
	for ii=1:number_of_iterations
	    for i=2:number_of_steps-1
	       u[i]= u_[i] + time_step *(-k*u_[i]+ Diff * (u_[i-1]-2*u_[i]+u_[i+1])/(space_step*space_step));  
	    end
	    
	    u[1]=1; # fixed boundary conditions
	    u[number_of_steps]=0; # fixed boundary conditions
	    
	    #u[1]=u[2]; # zero flux boundary conditions
	    #u[number_of_steps]=u[number_of_steps-1]; # zero flux boundary conditions
	    
	    #u[1]=u[number_of_steps]; # periodic boundary conditions
	    
	    u_=u;
	    if   ii% 10 == 0
	        plt2=Plots.plot!(x_vector,u',legend=false)
	        
	        
	    end
	end
	#show(plt2)
	#Plots.plot!(x_vector,u')
end

# ╔═╡ 903e68f4-7766-43bd-bfa0-018140101606
Plots.plot!(x_vector,x_vector->1*exp(-x_vector*sqrt(k/Diff)),label="Theory",seriestype=:scatter,
    xaxis = ("Space", (-1,100), 0:25:100,  font(15, "Futura")),
    yaxis = ("Concentration of u", (-0.015,1.05), 0:0.2:1,  font(15, "Futura")),
title=("Diffusion and degradation system"))

# ╔═╡ 46ed8542-733c-4a0d-9f60-c2bc1df955b4


	md"This shows that the simulation and the analytical solution produce the same output"
	


# ╔═╡ de723296-d4e4-4762-ade7-add5e2b8c79c
md" ### Stochastic numerical simulations

Gillespies simulations, in situatiosn where the number of particles is small, so we cannot assume a continumm system. Collisions between players are so rare that we see jumps. 


"

# ╔═╡ 14994f78-8f03-4e5e-bfb6-533ac0f2c289


# ╔═╡ 2df1ebdd-1889-42c7-9617-5f445f206553
md"### Agent base models


If we dont even have the differential equations, we can use agent-based modeling: a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and what governs its outcomes.

We set entities and rules of behavior. 

"

# ╔═╡ aec8b317-d3d8-49d3-823f-14a1b16e9f58
md"https://agentscript.org"

# ╔═╡ c7304b77-70a5-444f-9199-eff5539e65bc
md" # 5 Representation of Dynamical Systems 

When the solution is known (analytically or numerically), the optimal way to represent the dynamics is by directly plotting the value of the variables against time. In these plots, to observe the dynamics, we just need to follow the change of the curve as time progresses. We can see where the system moves and how fast or slow the dynamics is. 

We will illustrate this by solving the pendulum problem. In the physics class, we often solve this problem by small angle approximation, i.e. sin(\theta) \approx \theta, because otherwise, we get an elliptic integral which doesn't have an analytic solution. The linearized form is

```math
\ddot{\theta} + \frac{g}{L}{\theta} = 0
```


But we have numerical ODE solvers! Why not solve the real pendulum?
```math
\ddot{\theta} + \frac{g}{L}{\sin(\theta)} = 0
```





"



# ╔═╡ e3dd377a-a26d-400e-867b-ffb037dd1c5b
begin
	L_slider = @bind 😺 html"<input type=range min=0.1 max=2.0 step=0.5>"
	
	md"""
	**slide to change the length of the pendulum**
	
	Length : $(L_slider)
	
	
	"""
end

# ╔═╡ 1ee73b45-192d-4a9d-8a89-d2199cb99dae
begin
	# Simple Pendulum Problem
	# Constants
	const g = 9.81
	const L = 😺
	
	#Initial Conditions
	
	#Define the problem
	function simplependulum(du,u,p,t)
	    θ  = u[1]
	    dθ = u[2]
	    du[1] = dθ
	    du[2] = -(g/L)*sin(θ)
	end
	
	#Pass to solvers
	prob = ODEProblem(simplependulum,[0,π/2], (0.0,6.3))
	sol = solve(prob,Tsit5())
	
	#Plot
	Plots.plot(sol,linewidth=2,
	     title ="Simple Pendulum Problem", 
	     xaxis = "Time", 
	     yaxis = "Height", 
	     label = ["Angle" "Speed"])
end

# ╔═╡ 1703658a-7b64-4e4a-a8ed-c953dfa11f81
md"
But, what if we do not have the full solution, which is often the case when dealing with complex systems, researches often  represet their dynamcis and response using graphicall representations. The two most common and useful ones are phase potraits and landscapes. 
"

# ╔═╡ 64063f3d-4f4f-4923-82c6-73f387732944
md" ## 5.1 Phase potraits

A first approximation is to represent a plot where the value of the variables are in each of the axis. This is called a _phase potrait_. In this representation, each point a posible state of the system. A phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different curve, or point.

Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the state space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value. The concept of topological equivalence is important in classifying the behaviour of systems by specifying when two different phase portraits represent the same qualitative dynamic behavior. An attractor is a stable point which is also called _sink_. The repeller is considered as an unstable point, which is also known as _source_.


The dynamcis of the system is then represented by a trajectory in this representation. In two dimensional systems we can see
plane is called the _phase plane_.





"

# ╔═╡ c4089458-3561-439a-9285-f2d9e0f7cb13
md"So now we know that behavior of the position versus time. However, it will be useful to us to look at the phase space of the pendulum, i.e., and representation of all possible states of the system in question (the pendulum) by looking at its velocity and position. Phase space analysis is ubiquitous in the analysis of dynamical systems, and thus we will provide a few facilities for it."

# ╔═╡ b3b3db0d-196e-4f6f-b297-873e908caabb
begin
	pp = Plots.plot(sol, idxs = (1,2), xlims = (-9,9), 
	         title = "Phase Space Plot", 
	         xaxis = "Velocity", 
	         yaxis = "Position", 
	         leg=false)
	function phase_plot(prob, u0, p, tspan=2pi)
	    _prob = ODEProblem(prob.f,u0,(0.0,tspan))
	    sol = solve(_prob) # Use Vern9 solver for higher accuracy
	    Plots.plot!(pp, sol, idxs = (1,2))
	end
	
	for i in -4pi:pi:4π
	    for j in -4pi:pi:4π
	        phase_plot(prob, [j,i], pp)
	    end
	end
	Plots.plot(pp,xlims = (-9,9))
end

# ╔═╡ 30a4eca5-511c-41f1-832e-897f1e755f0c
md"In The typical buterfly in the Lorenz atractor is the phase representation of the three variables. "

# ╔═╡ 7c288433-e782-4f2e-97c0-b70c7c2d3748
# define the Lorenz attractor
	Base.@kwdef mutable struct Lorenz
	    dt::Float64 = 0.02
	    σ::Float64 = 10
	    ρ::Float64 = 28
	    β::Float64 = 8/3
	    x::Float64 = 1
	    y::Float64 = 1
	    z::Float64 = 1
	end

# ╔═╡ fd7d91f0-b58b-4600-b39e-288ed09bbe34
function step!(l::Lorenz)
	    dx = l.σ * (l.y - l.x)
	    dy = l.x * (l.ρ - l.z) - l.y
	    dz = l.x * l.y - l.β * l.z
	    l.x += l.dt * dx
	    l.y += l.dt * dy
	    l.z += l.dt * dz
	end

# ╔═╡ 821963b2-a6d2-45e4-bff0-247fe75f8852
attractor = Lorenz()

# ╔═╡ 6b5c3ff9-57ed-4801-ae9b-2691102e0db7
begin	
	plt = plot3d(
		    1,
		    xlim = (-30, 30),
		    ylim = (-30, 30),
		    zlim = (0, 60),
		    title = "Lorenz Attractor",
		    marker = 2,
		    xlabel="x [a.u.]",
		    ylabel="y [a.u.]",
		    zlabel="z [a.u.]",
		    legend=false
		)
	# build an animated gif by pushing new points to the plot, saving every 10th frame
	@gif for i=1:1500
	    step!(attractor)
	    push!(plt, attractor.x, attractor.y, attractor.z)
	end every 10
end

# ╔═╡ a68f4047-b934-4e56-a70b-f99e640afb9f
md" In nonlinear systems, we do not have the full trajectory, but the have the dynamics in the vicinity of the fixed points (thanks to our linear stability analysis, that calculates the dynamcis of perturbation if we aproximate our system and linearize around each steady state). By looking at trajectories, we can ask whether or not the solution will approach the equilibrium solution as 

An example of the null-clines for the _Cubic Autocatalor Model_. The equations for this specific model are:

```math
\begin{eqnarray}
\frac{\partial x}{\partial t} = x^2 y -x \\
\frac{\partial y}{\partial t} = \mu - x^2 y 
\end{eqnarray}
```

The steady state for this model is ($x_0,y_0$)= ($\mu, 1/\mu$)."

# ╔═╡ 836e1653-4f3e-4043-96c3-38a5616d2f89
begin
	Plots.plot(sol3,idxs=(1,2),label="limit cycle plot")
	title!("Cubic Autocatalator")
	Plots.xlabel!("X [a.u.]")
	Plots.ylabel!("Y [a.u.]")
end

# ╔═╡ 8ad14cbb-2737-4142-b52b-2a22a3b8352a
md"Static landscapes: no not change z(x,y) do not depend on is not $z$"

# ╔═╡ 64c9dbd0-edfd-4b1c-b14d-5e9875ea4f33
html"""<iframe width="700" height="400" src="https://www.youtube.com/embed/4pdiAneMMhU?start=83" title="static" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>"""

# ╔═╡ 1822e04a-9986-42e0-9235-06ef0e486a74
html"""<iframe width="700" height="400" src="https://www.youtube.com/embed/4pdiAneMMhU?start=26" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>"""

# ╔═╡ 9db87f92-f361-465a-8841-fac3fc078343
md"Moving landscapes: z(x,y,z) feedback

A complex system is not the one that has several maxima, minima, are systems where the landscape moves, it depends on variables of the system. The landscape changes depending on the state of the system (Feedback). 

Imagine that the landscape is a mountain, that you want to climb, and that the peak moves to another location as you approach, this is a complex system. 

-  Feedback between you (position) and the mountain (value).
-  Adaptation, you need to change your direction if you want to go up. 

Examples of these landscapes that move:
- Living making decisions
- Evolution: evolutionary landscape
- Development: Fittness landscapes"

# ╔═╡ 7e6ae3bb-e518-4b15-80fb-e853eceef96c
begin
	x=-1:0.01:1
	y=-1:0.01:1
	h(x,y)=x^2-y^2;
	
	Plots.surface(x,y,h, title= "A saddle node landscape")
end

# ╔═╡ 42924ebd-0bc9-4bd2-9e22-daba975b19e2
html"""<iframe width="700" height="400" src="https://www.youtube.com/embed/iaq_Fpr4KZc?start=83" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>"""

# ╔═╡ 0e68a81f-d628-40e4-a56f-1dc386247946
md" ## Landscapes in Biology:

Exploration + Exploitation: 

Exploration = Mutations, Genetic  recombination (mix of genes of mother and father in sexual reproduction), (increased variability in a population of bacteria)

Exploitation: natural selection 
(Reduces de variability in a population of bacteria)

Imaging these with feedbacks, with moving landscapes

In moving landscapes, the system never stops exploring, if the system stops exploring, a shitf in the landscape, can convert a peak on a valley, and if you are not exploring you are done

So, complex systems have to always balance between exploring and exploiting

So, here it is the cool thing: complexity itself is an emerging property!
Generated by the need of a system to balance exploitation and exploration. 
"




# ╔═╡ 5b77331c-adfa-4df2-9fb8-c1d14785cc2b
html"""
<iframe width="700" height="400" src="https://www.youtube.com/embed/KUvuv74_E1U" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
"""


# ╔═╡ c87ffaca-cec4-4aef-8fa8-9d8608941284
md"In this second rendition of Wadington's 'epigenetic landscape', we introduce two variations which we believe reflect some important developmental processes. The first one is that the valleys and the hills, the actual landscape that cells will traverse, are not predermined, that the cells make them as they move along the developmental landscape. The second notion is that at every bifurcation of the landscape there is a binary decision (green or red)"

# ╔═╡ e23af05f-d125-4798-918f-8a20c0f55065
html"""<iframe width="700" height="400" src="https://www.youtube.com/embed/PRmWBBnWfdA" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>"""

# ╔═╡ 6bd76627-d6f0-4adb-af46-203f21f95d27

annealing_url = "https://www.researchgate.net/profile/Omid_Ghasemalizadeh/publication/308786233/figure/fig1/AS:412751978614791@1475419148801/Simulated-Annealing-optimization-of-a-one-dimensional-objective-function.png"

# ╔═╡ 0aa7e21a-255c-4fcc-8ee6-8b3ef96a82b9
md" ## Dynamical systems in lanscape: 

Systems evolve dynamically in a landscape towards the point of minimal energy. They do so by exploring locally in small steps (using pertubrbation and noise).

- Small perturbations, (finds local minima)
- Large perturbations (global minimum, but risky, the system can move too fat away from optimal, and dies)

The process of moving in a landscape is often compared to the process of __Annealing__: a treatment that alters the physical and sometimes chemical properties of a material. It involves heating above recrystallization temperature,  followed by cooling. Heat increases the rate of diffusion, which results in redistributing and eradicating the dislocations in metals. Cooling is then perfomed gradually to reduce gradually the excursions and more local exploration. 

So intially the system can explore larger regions, and then smaller regions to find local minimum.

- $(Resource(annealing_url)) simulated annealing

 This process has inspired many algoritms and optimization methdos, called __Simulated anhealing__: a probabilistic method for finding the minimum of a complex functions using computers. 
"


# ╔═╡ b5174a24-428e-4a41-9b85-fccc7bcf8d32
path_url = "https://cdncontribute.geeksforgeeks.org/wp-content/uploads/exampleFigure-1.png"

# ╔═╡ 6c11b041-72c9-41c7-9fdb-f3257fea0fd9
waddington_url = "https://www.researchgate.net/profile/Vladimir-Kovac/publication/230718157/figure/fig1/AS:300417280954380@1448636469781/The-epigenetic-landscape-proposed-by-C-H-Waddington-1940-in-Organisers-genes.png"

# ╔═╡ 08ff363a-a0e9-4eb2-a118-5374869fc0da
md" ## Waddington epigenetic landscape: Stem cell differentiation

In 1957, Conrad Waddington described that mammalian development is unidirectional, which means that embryonic stem cells develop into a more mature differentiated state. This idea has been depicted as a ball rolling down from the top of Waddington’s mountain to the bottom of a valley (Figure 1a). It demonstrates visually the natural restriction of cell differentiation potential during normal development. 

$(Resource(waddington_url)) Waddington

In this short animation we take the original idea of the 'epigenetic landscape' by CH Waddington and put it into motion, as he probably conceived it in his mind. Waddington saw cells as pebbles rolling down a mountain with hills and valleys. The bottom of the valleys represents cell or differentiation states. Our rendition keeps close to the notions of Waddington except that it looks at the starting point not as a summit but rather as the crater of a volcano"

# ╔═╡ 02c540f7-cdf8-428d-88c0-64ae6cb905c5
fuji_url = "https://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Mount_Fuji_and_Shinkansen_100_from_Fuji_River.jpg/1200px-Mount_Fuji_and_Shinkansen_100_from_Fuji_River.jpg"

# ╔═╡ 6be4813b-fb90-4fcb-bc93-314971a7b50d
ireland_url = "https://images.ireland.com/media/Images/Down/3e656c481c7a49a2b366d4f8696b17b2.jpg"

# ╔═╡ e25205ff-a4fa-4a54-8a6c-1f94c9dd9ac3
discrete_url = "https://reference.wolfram.com/language/ref/Files/DiscretePlot3D.en/O_3.png"

# ╔═╡ 52f9023e-fb67-43ca-8548-46dfeeb7fb86
continuum_url = "https://i.stack.imgur.com/jGmh5.png"

# ╔═╡ 40804fce-7a1e-420e-94cc-2b1dbdf6e357
md" ## 5.2 Fittness Landscapes

In many cases, the rather abstract and mathematically complex structure of a system of attractors and basins can be replaced by the more intuitive model of a fitness landscape. Under certain mathematical conditions, the deterministic dynamics of a system can be represented by a potential function F on the state space, which attaches a certain number to each state: F: S -> R: s -> F(s), such that trajectory of the system through the state space will always follow the path of steepest descent, i.e. move from a given state s to that neighboring state for which F is minimal. In mechanics, this function corresponds to the potential energy of the system. More generally, the function represents the degree to which a certain state is __preferable__ to another state: the lower the value of F, the __better__ or the more __fit__ the state. Thus, the potential can be seen as the negative of the fitness function. 

The fitness function transforms the state space into a fitness landscape, where every point in the space has a certain __height__ corresponding to its fitness value. This landscape has peaks and valleys. The attractors of the dynamics will now correspond to the local minima of the potential function (potential valleys), or, equivalently, to the maxima of the fitness function (fitness peaks). This can be understood by noting that the system will always move downward in the potential landscape. 

Landscapes are potential functions that define the behavior of the system. Plotting and analyzing landscapes is a great tool to approach a system (for instance , find maximums, minimums of energy, equilibrium points., local versus global maxima on minima...) 

z = z (x, y) 

the state of a system is its position in the _xy_ plane (teh pase plane), 
the elevation _z_ is the value of a given property of the system (for instance, temperature…)

usually lanscapes are drawn in such a way that moving up in _z_ (potential function) represents a change in state that requires energy, while moving down is spontaneous. 


### 5.2.1 Types of landscapes


$(Resource(fuji_url)) Mount Fuji landscapes: One peak
   
$(Resource(ireland_url)) Ripple landscapes: many peaks and valleys
   
$(Resource(discrete_url)) Discrete landscapes: a finite numer of states

$(Resource(continuum_url)) Continuum landscapes: infinite number of states

"

# ╔═╡ 99b02d20-8596-4b56-bda8-30d671d9f098

Plots.wireframe(x,y,h)

# ╔═╡ f88f76e6-2b7a-4feb-88e4-34fb62a4ebe7
NoFeedback! = @ode_def ab2 begin
   dM = -γ_M*M+α_M*T^n/(K^n +T^n)
   dP =   α_P * M - γ_P * P
    end α_M γ_M T n α_P γ_P K

# ╔═╡ 00c2793d-2414-48e6-9946-c4211428d649
PositiveFeedback! = @ode_def ab begin
   dM = -γ_M*M+α_M*P^n/(K^n +P^n)
   dP =   α_P * M - γ_P * P
    end α_M γ_M T n α_P γ_P K

# ╔═╡ 68184209-041c-4e78-9d29-1ba56f21a7fd
begin
	dog_slide = @bind 🐶 html"<input type=range min=0.01 max=0.5 step=0.1>"
	cat_slide = @bind 🐱 html"<input type=range min=0.01 max=0.5 step=0.1>"
	
	md"""
	**How many molecules do you have?**
	
	Initial concentration of a: $(dog_slide)
	
	Initial concentration of b: $(cat_slide)
	"""
end

# ╔═╡ af5781a8-73f3-4ab4-bf20-38d41e5274e1
begin
	u₀ = [🐶,🐱]
	tspan = (0.0,50.0)
	n=3
	K=1
	k_m=1
	D=1
	T=3
	α_M=k_m*D
	γ_M=0.1
	α_P=0.6
	γ_P=0.5
	p=[α_M,γ_M,T,n,α_P,γ_P,K];
	
	prob1 = ODEProblem(PositiveFeedback!,u₀,tspan,p)
prob2 = ODEProblem(NoFeedback!,u₀,tspan,p)

sol1 = solve(prob1)
P1=plot(sol1,label=["mRNA","Protein"],ylims = (0,12))
title!("Positive feedback")
xlabel!("Time [s]")
ylabel!("Concentration [M]")

sol2 = solve(prob2)
P2=plot(sol2,label=["mRNA","Protein"],ylims = (0,12))
title!("Linear")
xlabel!("Time [s]")
ylabel!("Concentration [M]")

plot(P1,P2,layout=(1,2),legend=true)
end

# ╔═╡ bcfe0e20-c93b-41b7-8291-3f4f9792ba64
pendulum_url="https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Pendulum_phase_portrait.svg/618px-Pendulum_phase_portrait.svg.png"

# ╔═╡ d22c55f9-d8a0-443b-804e-4cb9976a0ac3


# ╔═╡ 25fcbb57-f3ec-4cce-b22c-2503c9bb36e5


# ╔═╡ ce8ccbe5-2637-43df-906a-ce6a71e9b918


# ╔═╡ 87e78056-fecc-4b15-a723-16f51fa19353


# ╔═╡ 0162ae2a-c19c-4700-9c87-4c76f1169d06


# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
ParameterizedFunctions = "65888b18-ceab-5e60-b2b9-181511a3b968"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[compat]
CairoMakie = "~0.10.4"
DifferentialEquations = "~7.7.0"
ParameterizedFunctions = "~5.15.0"
Plots = "~1.38.11"
PlutoUI = "~0.7.51"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.8.5"
manifest_format = "2.0"
project_hash = "8844f899021d17492dbfb56ccc751377ac8eb45e"

[[deps.AbstractAlgebra]]
deps = ["GroupsCore", "InteractiveUtils", "LinearAlgebra", "MacroTools", "Random", "RandomExtensions", "SparseArrays", "Test"]
git-tree-sha1 = "3ee5c58774f4487a5bf2bb05e39d91ff5022b4cc"
uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
version = "0.29.4"

[[deps.AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "16b6dbc4cf7caee4e1e75c49485ec67b667098a0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.3.1"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"

[[deps.AbstractTrees]]
git-tree-sha1 = "faa260e4cb5aba097a73fab382dd4b5819d8ec8c"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.4.4"

[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "cc37d689f599e8df4f464b2fa3870ff7db7492ef"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.6.1"

[[deps.Animations]]
deps = ["Colors"]
git-tree-sha1 = "e81c509d2c8e49592413bfb0bb3b08150056c79d"
uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
version = "0.4.1"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

[[deps.ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "62e51b39331de8911e4a7ff6f5aaf38a5f4cc0ae"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.2.0"

[[deps.ArrayInterface]]
deps = ["Adapt", "LinearAlgebra", "Requires", "SnoopPrecompile", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "38911c7737e123b28182d89027f4216cfc8a9da7"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "7.4.3"

[[deps.ArrayInterfaceCore]]
deps = ["LinearAlgebra", "SnoopPrecompile", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "e5f08b5689b1aad068e01751889f2f615c7db36d"
uuid = "30b0a656-2188-435a-8636-2ec0e6a096e2"
version = "0.1.29"

[[deps.ArrayLayouts]]
deps = ["FillArrays", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "4aff5fa660eb95c2e0deb6bcdabe4d9a96bc4667"
uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
version = "0.8.18"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[deps.Automa]]
deps = ["Printf", "ScanByte", "TranscodingStreams"]
git-tree-sha1 = "d50976f217489ce799e366d9561d56a98a30d7fe"
uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b"
version = "0.8.2"

[[deps.AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.1"

[[deps.AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "1dd4d9f5beebac0c03446918741b1a03dc5e5788"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.6"

[[deps.BandedMatrices]]
deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "SnoopPrecompile", "SparseArrays"]
git-tree-sha1 = "6ef8fc1d77b60f41041d59ce61ef9eb41ed97a83"
uuid = "aae01518-5342-5314-be14-df237901396f"
version = "0.17.18"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[deps.Bijections]]
git-tree-sha1 = "fe4f8c5ee7f76f2198d5c2a06d3961c249cce7bd"
uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
version = "0.1.4"

[[deps.BitFlags]]
git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.7"

[[deps.BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b"
uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
version = "0.1.5"

[[deps.BoundaryValueDiffEq]]
deps = ["BandedMatrices", "DiffEqBase", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "NLsolve", "Reexport", "SciMLBase", "SparseArrays"]
git-tree-sha1 = "ed8e837bfb3d1e3157022c9636ec1c722b637318"
uuid = "764a87c0-6b3e-53db-9096-fe964310641d"
version = "2.11.0"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[deps.CEnum]]
git-tree-sha1 = "eb4cb44a499229b3b8426dcfb5dd85333951ff90"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.4.2"

[[deps.CPUSummary]]
deps = ["CpuId", "IfElse", "Static"]
git-tree-sha1 = "2c144ddb46b552f72d7eafe7cc2f50746e41ea21"
uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
version = "0.2.2"

[[deps.CRC32c]]
uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc"

[[deps.CSTParser]]
deps = ["Tokenize"]
git-tree-sha1 = "3ddd48d200eb8ddf9cb3e0189fc059fd49b97c1f"
uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
version = "3.3.6"

[[deps.Cairo]]
deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
version = "1.0.5"

[[deps.CairoMakie]]
deps = ["Base64", "Cairo", "Colors", "FFTW", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "Makie", "SHA", "SnoopPrecompile"]
git-tree-sha1 = "2aba202861fd2b7603beb80496b6566491229855"
uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
version = "0.10.4"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[deps.Calculus]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
version = "0.5.1"

[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c6d890a52d2c4d55d326439580c3b8d0875a77d9"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.15.7"

[[deps.ChangesOfVariables]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "f84967c4497e0e1955f9a582c232b02847c5f589"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.7"

[[deps.CloseOpenIntervals]]
deps = ["Static", "StaticArrayInterface"]
git-tree-sha1 = "70232f82ffaab9dc52585e0dd043b5e0c6b714f1"
uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9"
version = "0.1.12"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "9c209fb7536406834aa938fb149964b985de6c83"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.1"

[[deps.ColorBrewer]]
deps = ["Colors", "JSON", "Test"]
git-tree-sha1 = "61c5334f33d91e570e1d0c3eb5465835242582c4"
uuid = "a2cac450-b92f-5266-8821-25eda20663c8"
version = "0.4.0"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "be6ab11021cd29f0344d5c4357b163af05a48cba"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.21.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.4"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.10"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.10"

[[deps.Combinatorics]]
git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
version = "1.0.2"

[[deps.CommonMark]]
deps = ["Crayons", "JSON", "PrecompileTools", "URIs"]
git-tree-sha1 = "532c4185d3c9037c0237546d817858b23cf9e071"
uuid = "a80b9123-70ca-4bc0-993e-6e3bcb318db6"
version = "0.8.12"

[[deps.CommonSolve]]
git-tree-sha1 = "9441451ee712d1aec22edad62db1a9af3dc8d852"
uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
version = "0.2.3"

[[deps.CommonSubexpressions]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.0"

[[deps.Compat]]
deps = ["Dates", "LinearAlgebra", "UUIDs"]
git-tree-sha1 = "7a60c856b9fa189eb34f5f8a6f6b5529b7942957"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.6.1"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.0.1+0"

[[deps.CompositeTypes]]
git-tree-sha1 = "02d2316b7ffceff992f3096ae48c7829a8aa0638"
uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
version = "0.1.3"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "b306df2650947e9eb100ec125ff8c65ca2053d30"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.1.1"

[[deps.ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "89a9db8d28102b094992472d333674bd1a83ce2a"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.5.1"

[[deps.Contour]]
git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.2"

[[deps.CpuId]]
deps = ["Markdown"]
git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406"
uuid = "adafc99b-e345-5852-983c-f28acb93d879"
version = "0.3.1"

[[deps.Crayons]]
git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.1.1"

[[deps.DataAPI]]
git-tree-sha1 = "e8119c1a33d267e16108be441a287a6981ba1630"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.14.0"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.13"

[[deps.DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[deps.DelayDiffEq]]
deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "LinearAlgebra", "Logging", "OrdinaryDiffEq", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SimpleNonlinearSolve", "SimpleUnPack"]
git-tree-sha1 = "89f3fbfe78f9d116d1ed0721d65b0b2cf9b36169"
uuid = "bcd4f6db-9728-5f36-b5f7-82caef46ccdb"
version = "5.42.0"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[deps.DensityInterface]]
deps = ["InverseFunctions", "Test"]
git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
version = "0.4.0"

[[deps.DiffEqBase]]
deps = ["ArrayInterface", "ChainRulesCore", "DataStructures", "Distributions", "DocStringExtensions", "EnumX", "FastBroadcast", "ForwardDiff", "FunctionWrappers", "FunctionWrappersWrappers", "LinearAlgebra", "Logging", "Markdown", "MuladdMacro", "Parameters", "PreallocationTools", "Printf", "RecursiveArrayTools", "Reexport", "Requires", "SciMLBase", "Setfield", "SparseArrays", "Static", "StaticArraysCore", "Statistics", "Tricks", "TruncatedStacktraces", "ZygoteRules"]
git-tree-sha1 = "988bbd7283aaee5c34cd3cc09e78e7c45a931c5b"
uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
version = "6.123.0"

[[deps.DiffEqCallbacks]]
deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "Markdown", "NLsolve", "Parameters", "RecipesBase", "RecursiveArrayTools", "SciMLBase", "StaticArraysCore"]
git-tree-sha1 = "63b6be7b396ad395825f3cc48c56b53bfaf7e69d"
uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def"
version = "2.26.1"

[[deps.DiffEqNoiseProcess]]
deps = ["DiffEqBase", "Distributions", "GPUArraysCore", "LinearAlgebra", "Markdown", "Optim", "PoissonRandom", "QuadGK", "Random", "Random123", "RandomNumbers", "RecipesBase", "RecursiveArrayTools", "Requires", "ResettableStacks", "SciMLBase", "StaticArrays", "Statistics"]
git-tree-sha1 = "2c4ed3eedb87579bfe9f20ecc2440de06b9f3b89"
uuid = "77a26b50-5914-5dd7-bc55-306e6241c503"
version = "5.16.0"

[[deps.DiffResults]]
deps = ["StaticArraysCore"]
git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "1.1.0"

[[deps.DiffRules]]
deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "a4ad7ef19d2cdc2eff57abbbe68032b1cd0bd8f8"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.13.0"

[[deps.DifferentialEquations]]
deps = ["BoundaryValueDiffEq", "DelayDiffEq", "DiffEqBase", "DiffEqCallbacks", "DiffEqNoiseProcess", "JumpProcesses", "LinearAlgebra", "LinearSolve", "NonlinearSolve", "OrdinaryDiffEq", "Random", "RecursiveArrayTools", "Reexport", "SciMLBase", "SteadyStateDiffEq", "StochasticDiffEq", "Sundials"]
git-tree-sha1 = "ac145e3d718157c679fc4febf2fcef73ec77b067"
uuid = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
version = "7.7.0"

[[deps.Distances]]
deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "49eba9ad9f7ead780bfb7ee319f962c811c6d3b2"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.8"

[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[deps.Distributions]]
deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
git-tree-sha1 = "180538ef4e3aa02b01413055a7a9e8b6047663e1"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.88"

[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"

[[deps.DomainSets]]
deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays", "Statistics"]
git-tree-sha1 = "698124109da77b6914f64edd696be8dccf90229e"
uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
version = "0.6.6"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.DualNumbers]]
deps = ["Calculus", "NaNMath", "SpecialFunctions"]
git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566"
uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
version = "0.6.8"

[[deps.DynamicPolynomials]]
deps = ["DataStructures", "Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Pkg", "Reexport", "Test"]
git-tree-sha1 = "8b84876e31fa39479050e2d3395c4b3b210db8b0"
uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
version = "0.4.6"

[[deps.EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e3290f2d49e661fbd94046d7e3726ffcb2d41053"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.4+0"

[[deps.EnumX]]
git-tree-sha1 = "bdb1942cd4c45e3c678fd11569d5cccd80976237"
uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
version = "1.0.4"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.8+0"

[[deps.ExponentialUtilities]]
deps = ["Adapt", "ArrayInterface", "GPUArraysCore", "GenericSchur", "LinearAlgebra", "Printf", "SnoopPrecompile", "SparseArrays", "libblastrampoline_jll"]
git-tree-sha1 = "fb7dbef7d2631e2d02c49e2750f7447648b0ec9b"
uuid = "d4d017d3-3776-5f7e-afef-a10c40355c18"
version = "1.24.0"

[[deps.ExprTools]]
git-tree-sha1 = "c1d06d129da9f55715c6c212866f5b1bddc5fa00"
uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
version = "0.1.9"

[[deps.Extents]]
git-tree-sha1 = "5e1e4c53fa39afe63a7d356e30452249365fba99"
uuid = "411431e0-e8b7-467b-b5e0-f676ba4f2910"
version = "0.1.1"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.2+2"

[[deps.FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "f9818144ce7c8c41edf5c4c179c684d92aa4d9fe"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.6.0"

[[deps.FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.10+0"

[[deps.FastBroadcast]]
deps = ["ArrayInterface", "LinearAlgebra", "Polyester", "Static", "StaticArrayInterface", "StrideArraysCore"]
git-tree-sha1 = "d1248fceea0b26493fd33e8e9e8c553270da03bd"
uuid = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
version = "0.2.5"

[[deps.FastClosures]]
git-tree-sha1 = "acebe244d53ee1b461970f8910c235b259e772ef"
uuid = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
version = "0.3.2"

[[deps.FastLapackInterface]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c1293a93193f0ae94be7cf338d33e162c39d8788"
uuid = "29a986be-02c6-4525-aec4-84b980013641"
version = "1.2.9"

[[deps.FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "299dc33549f68299137e51e6d49a13b5b1da9673"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.16.1"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"

[[deps.FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
git-tree-sha1 = "7072f1e3e5a8be51d525d64f63d3ec1287ff2790"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.13.11"

[[deps.FiniteDiff]]
deps = ["ArrayInterface", "LinearAlgebra", "Requires", "Setfield", "SparseArrays", "StaticArrays"]
git-tree-sha1 = "03fcb1c42ec905d15b305359603888ec3e65f886"
uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
version = "2.19.0"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[deps.Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[deps.ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "00e252f4d706b3d55a8863432e742bf5717b498d"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.35"

[[deps.FreeType]]
deps = ["CEnum", "FreeType2_jll"]
git-tree-sha1 = "cabd77ab6a6fdff49bfd24af2ebe76e6e018a2b4"
uuid = "b38be410-82b0-50bf-ab77-7b57e271db43"
version = "4.0.0"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[deps.FreeTypeAbstraction]]
deps = ["ColorVectorSpace", "Colors", "FreeType", "GeometryBasics"]
git-tree-sha1 = "38a92e40157100e796690421e34a11c107205c86"
uuid = "663a7486-cb36-511b-a19d-713bb74d65c9"
version = "0.10.0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[deps.FunctionWrappers]]
git-tree-sha1 = "d62485945ce5ae9c0c48f124a84998d755bae00e"
uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
version = "1.1.3"

[[deps.FunctionWrappersWrappers]]
deps = ["FunctionWrappers"]
git-tree-sha1 = "b104d487b34566608f8b4e1c39fb0b10aa279ff8"
uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf"
version = "0.1.3"

[[deps.Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.8+0"

[[deps.GPUArraysCore]]
deps = ["Adapt"]
git-tree-sha1 = "1cd7f0af1aa58abc02ea1d872953a97359cb87fa"
uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
version = "0.1.4"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
git-tree-sha1 = "efaac003187ccc71ace6c755b197284cd4811bfe"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.72.4"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4486ff47de4c18cb511a0da420efebb314556316"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.72.4+0"

[[deps.GenericSchur]]
deps = ["LinearAlgebra", "Printf"]
git-tree-sha1 = "fb69b2a645fa69ba5f474af09221b9308b160ce6"
uuid = "c145ed77-6b09-5dd9-b285-bf645a82121e"
version = "0.5.3"

[[deps.GeoInterface]]
deps = ["Extents"]
git-tree-sha1 = "0eb6de0b312688f852f347171aba888658e29f20"
uuid = "cf35fbd7-0cd7-5166-be24-54bfbe79505f"
version = "1.3.0"

[[deps.GeometryBasics]]
deps = ["EarCut_jll", "GeoInterface", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "659140c9375afa2f685e37c1a0b9c9a60ef56b40"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.7"

[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.74.0+2"

[[deps.Glob]]
git-tree-sha1 = "97285bbd5230dd766e9ef6749b80fc617126d496"
uuid = "c27321d9-0574-5035-807b-f59d2c89b15c"
version = "1.3.1"

[[deps.Graphics]]
deps = ["Colors", "LinearAlgebra", "NaNMath"]
git-tree-sha1 = "d61890399bc535850c4bf08e4e0d3a7ad0f21cbd"
uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
version = "1.1.2"

[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[deps.Graphs]]
deps = ["ArnoldiMethod", "Compat", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
git-tree-sha1 = "1cf1d7dcb4bc32d7b4a5add4232db3750c27ecb4"
uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
version = "1.8.0"

[[deps.GridLayoutBase]]
deps = ["GeometryBasics", "InteractiveUtils", "Observables"]
git-tree-sha1 = "678d136003ed5bceaab05cf64519e3f956ffa4ba"
uuid = "3955a311-db13-416c-9275-1d80ed98e5e9"
version = "0.9.1"

[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[deps.Groebner]]
deps = ["AbstractAlgebra", "Combinatorics", "Logging", "MultivariatePolynomials", "Primes", "Random", "SnoopPrecompile"]
git-tree-sha1 = "b6c3e9e1eb8dcc6fd9bc68fe08dcc7ab22710de6"
uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
version = "0.3.4"

[[deps.GroupsCore]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "9e1a5e9f3b81ad6a5c613d181664a0efc6fe6dd7"
uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
version = "0.4.0"

[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "69182f9a2d6add3736b7a06ab6416aafdeec2196"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.8.0"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"

[[deps.HostCPUFeatures]]
deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
git-tree-sha1 = "734fd90dd2f920a2f1921d5388dcebe805b262dc"
uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
version = "0.1.14"

[[deps.HypergeometricFunctions]]
deps = ["DualNumbers", "LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
git-tree-sha1 = "432b5b03176f8182bd6841fbfc42c718506a2d5f"
uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
version = "0.3.15"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "c47c5fa4c5308f27ccaac35504858d8914e102f9"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.4"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"

[[deps.IfElse]]
git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.1"

[[deps.ImageAxes]]
deps = ["AxisArrays", "ImageBase", "ImageCore", "Reexport", "SimpleTraits"]
git-tree-sha1 = "c54b581a83008dc7f292e205f4c409ab5caa0f04"
uuid = "2803e5a7-5153-5ecf-9a86-9b4c37f5f5ac"
version = "0.6.10"

[[deps.ImageBase]]
deps = ["ImageCore", "Reexport"]
git-tree-sha1 = "b51bb8cae22c66d0f6357e3bcb6363145ef20835"
uuid = "c817782e-172a-44cc-b673-b171935fbb9e"
version = "0.1.5"

[[deps.ImageCore]]
deps = ["AbstractFFTs", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Graphics", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "Reexport"]
git-tree-sha1 = "acf614720ef026d38400b3817614c45882d75500"
uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
version = "0.9.4"

[[deps.ImageIO]]
deps = ["FileIO", "IndirectArrays", "JpegTurbo", "LazyModules", "Netpbm", "OpenEXR", "PNGFiles", "QOI", "Sixel", "TiffImages", "UUIDs"]
git-tree-sha1 = "342f789fd041a55166764c351da1710db97ce0e0"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
version = "0.6.6"

[[deps.ImageMetadata]]
deps = ["AxisArrays", "ImageAxes", "ImageBase", "ImageCore"]
git-tree-sha1 = "36cbaebed194b292590cba2593da27b34763804a"
uuid = "bc367c6b-8a6b-528e-b4bd-a4b897500b49"
version = "0.9.8"

[[deps.Imath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "3d09a9f60edf77f8a4d99f9e015e8fbf9989605d"
uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
version = "3.1.7+0"

[[deps.IndirectArrays]]
git-tree-sha1 = "012e604e1c7458645cb8b436f8fba789a51b257f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "1.0.0"

[[deps.Inflate]]
git-tree-sha1 = "5cd07aab533df5170988219191dfad0519391428"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.3"

[[deps.IntegerMathUtils]]
git-tree-sha1 = "f366daebdfb079fd1fe4e3d560f99a0c892e15bc"
uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
version = "0.1.0"

[[deps.IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0cb9352ef2e01574eeebdb102948a58740dcaf83"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2023.1.0+0"

[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[deps.Interpolations]]
deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "721ec2cf720536ad005cb38f50dbba7b02419a15"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.14.7"

[[deps.IntervalSets]]
deps = ["Dates", "Random", "Statistics"]
git-tree-sha1 = "16c0cc91853084cb5f58a78bd209513900206ce6"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.7.4"

[[deps.InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "6667aadd1cdee2c6cd068128b3d226ebc4fb0c67"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.9"

[[deps.IrrationalConstants]]
git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.2.2"

[[deps.Isoband]]
deps = ["isoband_jll"]
git-tree-sha1 = "f9b6d97355599074dc867318950adaa6f9946137"
uuid = "f1662d9f-8043-43de-a69a-05efc1cc6ff4"
version = "0.1.1"

[[deps.IterTools]]
git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.4.0"

[[deps.IterativeSolvers]]
deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays"]
git-tree-sha1 = "1169632f425f79429f245113b775a0e3d121457c"
uuid = "42fd0dbc-a981-5370-80f2-aaf504508153"
version = "0.9.2"

[[deps.IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[deps.JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.5"

[[deps.JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.4"

[[deps.JpegTurbo]]
deps = ["CEnum", "FileIO", "ImageCore", "JpegTurbo_jll", "TOML"]
git-tree-sha1 = "106b6aa272f294ba47e96bd3acbabdc0407b5c60"
uuid = "b835a17e-a41a-41e7-81f0-2f016b05efe0"
version = "0.1.2"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6f2675ef130a300a112286de91973805fcc5ffbc"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.91+0"

[[deps.JuliaFormatter]]
deps = ["CSTParser", "CommonMark", "DataStructures", "Glob", "Pkg", "PrecompileTools", "Tokenize"]
git-tree-sha1 = "536ef70e17d2f5b0dcbe5411002721c9bbdfaa05"
uuid = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
version = "1.0.27"

[[deps.JumpProcesses]]
deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "DocStringExtensions", "FunctionWrappers", "Graphs", "LinearAlgebra", "Markdown", "PoissonRandom", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "StaticArrays", "TreeViews", "UnPack"]
git-tree-sha1 = "50bd271af7f6cc23be7d24c8c4804809bb5d05ae"
uuid = "ccbc3e58-028d-4f4c-8cd5-9ae44345cda5"
version = "9.6.3"

[[deps.KLU]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse_jll"]
git-tree-sha1 = "764164ed65c30738750965d55652db9c94c59bfe"
uuid = "ef3ab10e-7fda-4108-b977-705223b18434"
version = "0.4.0"

[[deps.KernelDensity]]
deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
git-tree-sha1 = "90442c50e202a5cdf21a7899c66b240fdef14035"
uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
version = "0.6.7"

[[deps.Krylov]]
deps = ["LinearAlgebra", "Printf", "SparseArrays"]
git-tree-sha1 = "dd90aacbfb622f898a97c2a4411ac49101ebab8a"
uuid = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
version = "0.9.0"

[[deps.KrylovKit]]
deps = ["ChainRulesCore", "GPUArraysCore", "LinearAlgebra", "Printf"]
git-tree-sha1 = "1a5e1d9941c783b0119897d29f2eb665d876ecf3"
uuid = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
version = "0.6.0"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[deps.LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[deps.LabelledArrays]]
deps = ["ArrayInterface", "ChainRulesCore", "ForwardDiff", "LinearAlgebra", "MacroTools", "PreallocationTools", "RecursiveArrayTools", "StaticArrays"]
git-tree-sha1 = "cd04158424635efd05ff38d5f55843397b7416a9"
uuid = "2ee39098-c373-598a-b85f-a56591580800"
version = "1.14.0"

[[deps.LambertW]]
git-tree-sha1 = "c5ffc834de5d61d00d2b0e18c96267cffc21f648"
uuid = "984bce1d-4616-540c-a9ee-88d1112d94c9"
version = "0.4.6"

[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
git-tree-sha1 = "8c57307b5d9bb3be1ff2da469063628631d4d51e"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.21"

[[deps.LayoutPointers]]
deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static", "StaticArrayInterface"]
git-tree-sha1 = "88b8f66b604da079a627b6fb2860d3704a6729a1"
uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
version = "0.1.14"

[[deps.Lazy]]
deps = ["MacroTools"]
git-tree-sha1 = "1370f8202dac30758f3c345f9909b97f53d87d3f"
uuid = "50d2b5c4-7a5e-59d5-8109-a42b560f39c0"
version = "0.15.1"

[[deps.LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[deps.LazyModules]]
git-tree-sha1 = "a560dd966b386ac9ae60bdd3a3d3a326062d3c3e"
uuid = "8cdb02fc-e678-4876-92c5-9defec4f444e"
version = "0.3.1"

[[deps.LevyArea]]
deps = ["LinearAlgebra", "Random", "SpecialFunctions"]
git-tree-sha1 = "56513a09b8e0ae6485f34401ea9e2f31357958ec"
uuid = "2d8b4e74-eb68-11e8-0fb9-d5eb67b50637"
version = "1.0.0"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.3"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.84.0+0"

[[deps.LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.10.2+0"

[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[deps.Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.6.0+0"

[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+2"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.4.0+0"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

[[deps.LineSearches]]
deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
git-tree-sha1 = "7bbea35cec17305fc70a0e5b4641477dc0789d9d"
uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
version = "7.2.0"

[[deps.LinearAlgebra]]
deps = ["Libdl", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[deps.LinearSolve]]
deps = ["ArrayInterface", "DocStringExtensions", "EnumX", "FastLapackInterface", "GPUArraysCore", "IterativeSolvers", "KLU", "Krylov", "KrylovKit", "LinearAlgebra", "Preferences", "RecursiveFactorization", "Reexport", "SciMLBase", "SciMLOperators", "Setfield", "SnoopPrecompile", "SparseArrays", "Sparspak", "SuiteSparse", "UnPack"]
git-tree-sha1 = "4a4f8cc7a59fadbb02d1852d1e0cef5dca3a9460"
uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
version = "1.42.0"

[[deps.LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "0a1b7c2863e44523180fdb3146534e265a91870b"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.23"

[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "cedb76b37bc5a6c702ade66be44f831fa23c681e"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.0.0"

[[deps.LoopVectorization]]
deps = ["ArrayInterface", "ArrayInterfaceCore", "CPUSummary", "ChainRulesCore", "CloseOpenIntervals", "DocStringExtensions", "ForwardDiff", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "PrecompileTools", "SIMDTypes", "SLEEFPirates", "SpecialFunctions", "Static", "StaticArrayInterface", "ThreadingUtilities", "UnPack", "VectorizationBase"]
git-tree-sha1 = "e7ce3cdc520da8135e73d7cb303e0617a19f582b"
uuid = "bdcacae8-1622-11e9-2a5c-532679323890"
version = "0.12.158"

[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"

[[deps.MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "2ce8695e1e699b68702c03402672a69f54b8aca9"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2022.2.0+0"

[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.10"

[[deps.Makie]]
deps = ["Animations", "Base64", "ColorBrewer", "ColorSchemes", "ColorTypes", "Colors", "Contour", "Distributions", "DocStringExtensions", "Downloads", "FFMPEG", "FileIO", "FixedPointNumbers", "Formatting", "FreeType", "FreeTypeAbstraction", "GeometryBasics", "GridLayoutBase", "ImageIO", "InteractiveUtils", "IntervalSets", "Isoband", "KernelDensity", "LaTeXStrings", "LinearAlgebra", "MakieCore", "Markdown", "Match", "MathTeXEngine", "MiniQhull", "Observables", "OffsetArrays", "Packing", "PlotUtils", "PolygonOps", "Printf", "Random", "RelocatableFolders", "Setfield", "Showoff", "SignedDistanceFields", "SnoopPrecompile", "SparseArrays", "StableHashTraits", "Statistics", "StatsBase", "StatsFuns", "StructArrays", "TriplotBase", "UnicodeFun"]
git-tree-sha1 = "74657542dc85c3b72b8a5a9392d57713d8b7a999"
uuid = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
version = "0.19.4"

[[deps.MakieCore]]
deps = ["Observables"]
git-tree-sha1 = "9926529455a331ed73c19ff06d16906737a876ed"
uuid = "20f20a25-4f0e-4fdf-b5d1-57303727442b"
version = "0.6.3"

[[deps.ManualMemory]]
git-tree-sha1 = "bcaef4fc7a0cfe2cba636d84cda54b5e4e4ca3cd"
uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667"
version = "0.1.8"

[[deps.MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[deps.Match]]
git-tree-sha1 = "1d9bc5c1a6e7ee24effb93f175c9342f9154d97f"
uuid = "7eb4fadd-790c-5f42-8a69-bfa0b872bfbf"
version = "1.2.0"

[[deps.MathTeXEngine]]
deps = ["AbstractTrees", "Automa", "DataStructures", "FreeTypeAbstraction", "GeometryBasics", "LaTeXStrings", "REPL", "RelocatableFolders", "Test", "UnicodeFun"]
git-tree-sha1 = "8f52dbaa1351ce4cb847d95568cb29e62a307d93"
uuid = "0a4f8689-d25c-4efe-a92b-7142dfc1aa53"
version = "0.5.6"

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
git-tree-sha1 = "03a9b9718f5682ecb107ac9f7308991db4ce395b"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.7"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.0+0"

[[deps.Measures]]
git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.2"

[[deps.MiniQhull]]
deps = ["QhullMiniWrapper_jll"]
git-tree-sha1 = "9dc837d180ee49eeb7c8b77bb1c860452634b0d1"
uuid = "978d7f02-9e05-4691-894f-ae31a51d76ca"
version = "0.4.0"

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.1.0"

[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[deps.ModelingToolkit]]
deps = ["AbstractTrees", "ArrayInterface", "Combinatorics", "Compat", "ConstructionBase", "DataStructures", "DiffEqBase", "DiffEqCallbacks", "DiffRules", "Distributed", "Distributions", "DocStringExtensions", "DomainSets", "ForwardDiff", "FunctionWrappersWrappers", "Graphs", "IfElse", "InteractiveUtils", "JuliaFormatter", "JumpProcesses", "LabelledArrays", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "Serialization", "Setfield", "SimpleNonlinearSolve", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "SymbolicUtils", "Symbolics", "UnPack", "Unitful"]
git-tree-sha1 = "e52b0337d18fd6ca8b1e1e3d801636dba203b966"
uuid = "961ee093-0014-501f-94e3-6117800e7a78"
version = "8.55.1"

[[deps.MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "7b86a5d4d70a9f5cdf2dacb3cbe6d251d1a61dbe"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.4"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.2.1"

[[deps.MuladdMacro]]
git-tree-sha1 = "cac9cc5499c25554cba55cd3c30543cff5ca4fab"
uuid = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
version = "0.2.4"

[[deps.MultivariatePolynomials]]
deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
git-tree-sha1 = "eaa98afe2033ffc0629f9d0d83961d66a021dfcc"
uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
version = "0.4.7"

[[deps.MutableArithmetics]]
deps = ["LinearAlgebra", "SparseArrays", "Test"]
git-tree-sha1 = "3295d296288ab1a0a2528feb424b854418acff57"
uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
version = "1.2.3"

[[deps.NLSolversBase]]
deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
git-tree-sha1 = "a0b464d183da839699f4c79e7606d9d186ec172c"
uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
version = "7.8.3"

[[deps.NLsolve]]
deps = ["Distances", "LineSearches", "LinearAlgebra", "NLSolversBase", "Printf", "Reexport"]
git-tree-sha1 = "019f12e9a1a7880459d0173c182e6a99365d7ac1"
uuid = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
version = "4.5.1"

[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.2"

[[deps.Netpbm]]
deps = ["FileIO", "ImageCore", "ImageMetadata"]
git-tree-sha1 = "5ae7ca23e13855b3aba94550f26146c01d259267"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.1.0"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.NonlinearSolve]]
deps = ["ArrayInterface", "DiffEqBase", "EnumX", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "LinearSolve", "RecursiveArrayTools", "Reexport", "SciMLBase", "SimpleNonlinearSolve", "SnoopPrecompile", "SparseArrays", "SparseDiffTools", "StaticArraysCore", "UnPack"]
git-tree-sha1 = "a6000c813371cd3cd9cbbdf8a356fc3a97138d92"
uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
version = "1.6.0"

[[deps.Observables]]
git-tree-sha1 = "6862738f9796b3edc1c09d0890afce4eca9e7e93"
uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
version = "0.5.4"

[[deps.OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "82d7c9e310fe55aa54996e6f7f94674e2a38fcb4"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.12.9"

[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.20+0"

[[deps.OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[deps.OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "a4ca623df1ae99d09bc9868b008262d0c0ac1e4f"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.4+0"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+0"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "7fb975217aea8f1bb360cf1dde70bad2530622d2"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.4.0"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9ff31d101d987eb9d66bd8b176ac7c277beccd09"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.20+0"

[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[deps.Optim]]
deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
git-tree-sha1 = "a89b11f0f354f06099e4001c151dffad7ebab015"
uuid = "429524aa-4258-5aef-a3af-852621145aeb"
version = "1.7.5"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "d321bf2de576bf25ec4d3e4360faca399afca282"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.0"

[[deps.OrdinaryDiffEq]]
deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DocStringExtensions", "ExponentialUtilities", "FastBroadcast", "FastClosures", "FiniteDiff", "ForwardDiff", "FunctionWrappersWrappers", "IfElse", "LinearAlgebra", "LinearSolve", "Logging", "LoopVectorization", "MacroTools", "MuladdMacro", "NLsolve", "NonlinearSolve", "Polyester", "PreallocationTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLNLSolve", "SimpleNonlinearSolve", "SimpleUnPack", "SnoopPrecompile", "SparseArrays", "SparseDiffTools", "StaticArrayInterface", "StaticArrays", "TruncatedStacktraces"]
git-tree-sha1 = "b639e192c0422c849aeda7240382375961d0cb4b"
uuid = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
version = "6.50.0"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.40.0+0"

[[deps.PDMats]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "67eae2738d63117a196f497d7db789821bce61d1"
uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
version = "0.11.17"

[[deps.PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "f809158b27eba0c18c269cf2a2be6ed751d3e81d"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
version = "0.3.17"

[[deps.Packing]]
deps = ["GeometryBasics"]
git-tree-sha1 = "ec3edfe723df33528e085e632414499f26650501"
uuid = "19eb6ba3-879d-56ad-ad62-d5c202156566"
version = "0.5.0"

[[deps.PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "0fac6313486baae819364c52b4f483450a9d793f"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.12"

[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "84a314e3926ba9ec66ac097e3635e270986b0f10"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.50.9+0"

[[deps.ParameterizedFunctions]]
deps = ["DataStructures", "DiffEqBase", "DocStringExtensions", "Latexify", "LinearAlgebra", "ModelingToolkit", "Reexport", "SciMLBase"]
git-tree-sha1 = "78ab7ecc18b307e00abba28bb29d7ed6bf11b9f7"
uuid = "65888b18-ceab-5e60-b2b9-181511a3b968"
version = "5.15.0"

[[deps.Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[deps.Parsers]]
deps = ["Dates", "SnoopPrecompile"]
git-tree-sha1 = "478ac6c952fddd4399e71d4779797c538d0ff2bf"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.5.8"

[[deps.Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"

[[deps.Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"

[[deps.PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "f6cf8e7944e50901594838951729a1861e668cb8"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
version = "0.3.2"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.1.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "f92e1315dadf8c46561fb9396e525f7200cdc227"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.3.5"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Preferences", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "6c7f47fd112001fc95ea1569c2757dffd9e81328"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.38.11"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "b478a748be27bd2f2c73a7690da219d0844db305"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.51"

[[deps.PoissonRandom]]
deps = ["Random"]
git-tree-sha1 = "a0f1159c33f846aa77c3f30ebbc69795e5327152"
uuid = "e409e4f3-bfea-5376-8464-e040bb5c01ab"
version = "0.4.4"

[[deps.Polyester]]
deps = ["ArrayInterface", "BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "ManualMemory", "PolyesterWeave", "Requires", "Static", "StaticArrayInterface", "StrideArraysCore", "ThreadingUtilities"]
git-tree-sha1 = "0fe4e7c4d8ff4c70bfa507f0dd96fa161b115777"
uuid = "f517fe37-dbe3-4b94-8317-1923a5111588"
version = "0.7.3"

[[deps.PolyesterWeave]]
deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"]
git-tree-sha1 = "240d7170f5ffdb285f9427b92333c3463bf65bf6"
uuid = "1d0040c9-8b98-4ee7-8388-3f51789ca0ad"
version = "0.2.1"

[[deps.PolygonOps]]
git-tree-sha1 = "77b3d3605fc1cd0b42d95eba87dfcd2bf67d5ff6"
uuid = "647866c9-e3ac-4575-94e7-e3d426903924"
version = "0.1.2"

[[deps.PositiveFactorizations]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
version = "0.2.4"

[[deps.PreallocationTools]]
deps = ["Adapt", "ArrayInterface", "ForwardDiff", "Requires"]
git-tree-sha1 = "f739b1b3cc7b9949af3b35089931f2b58c289163"
uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
version = "0.4.12"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "2e47054ffe7d0a8872e977c0d09eb4b3d162ebde"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.0.2"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.3.0"

[[deps.Primes]]
deps = ["IntegerMathUtils"]
git-tree-sha1 = "311a2aa90a64076ea0fac2ad7492e914e6feeb81"
uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
version = "0.5.3"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[deps.ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "d7a7aef8f8f2d537104f170139553b14dfe39fe9"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.2"

[[deps.QOI]]
deps = ["ColorTypes", "FileIO", "FixedPointNumbers"]
git-tree-sha1 = "18e8f4d1426e965c7b532ddd260599e1510d26ce"
uuid = "4b34888f-f399-49d4-9bb3-47ed5cae4e65"
version = "1.0.0"

[[deps.QhullMiniWrapper_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Qhull_jll"]
git-tree-sha1 = "607cf73c03f8a9f83b36db0b86a3a9c14179621f"
uuid = "460c41e3-6112-5d7f-b78c-b6823adb3f2d"
version = "1.0.0+1"

[[deps.Qhull_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "238dd7e2cc577281976b9681702174850f8d4cbc"
uuid = "784f63db-0788-585a-bace-daefebcd302b"
version = "8.0.1001+0"

[[deps.Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "0c03844e2231e12fda4d0086fd7cbe4098ee8dc5"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+2"

[[deps.QuadGK]]
deps = ["DataStructures", "LinearAlgebra"]
git-tree-sha1 = "6ec7ac8412e83d57e313393220879ede1740f9ee"
uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
version = "2.8.2"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[deps.Random123]]
deps = ["Random", "RandomNumbers"]
git-tree-sha1 = "552f30e847641591ba3f39fd1bed559b9deb0ef3"
uuid = "74087812-796a-5b5d-8853-05524746bad3"
version = "1.6.1"

[[deps.RandomExtensions]]
deps = ["Random", "SparseArrays"]
git-tree-sha1 = "062986376ce6d394b23d5d90f01d81426113a3c9"
uuid = "fb686558-2515-59ef-acaa-46db3789a887"
version = "0.4.3"

[[deps.RandomNumbers]]
deps = ["Random", "Requires"]
git-tree-sha1 = "043da614cc7e95c703498a491e2c21f58a2b8111"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.5.3"

[[deps.RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[deps.Ratios]]
deps = ["Requires"]
git-tree-sha1 = "6d7bb727e76147ba18eed998700998e17b8e4911"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.4"

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.12"

[[deps.RecursiveArrayTools]]
deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "Requires", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
git-tree-sha1 = "68078e9fa9130a6a768815c48002d0921a232c11"
uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
version = "2.38.4"

[[deps.RecursiveFactorization]]
deps = ["LinearAlgebra", "LoopVectorization", "Polyester", "SnoopPrecompile", "StrideArraysCore", "TriangularSolve"]
git-tree-sha1 = "9088515ad915c99026beb5436d0a09cd8c18163e"
uuid = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
version = "0.2.18"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "90bc7a7c96410424509e4263e277e43250c05691"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.0"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[deps.ResettableStacks]]
deps = ["StaticArrays"]
git-tree-sha1 = "256eeeec186fa7f26f2801732774ccf277f05db9"
uuid = "ae5879a3-cd67-5da8-be7f-38c6eb64a37b"
version = "1.1.1"

[[deps.Rmath]]
deps = ["Random", "Rmath_jll"]
git-tree-sha1 = "f65dcb5fa46aee0cf9ed6274ccbd597adc49aa7b"
uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
version = "0.7.1"

[[deps.Rmath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6ed52fdd3382cf21947b15e8870ac0ddbff736da"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
version = "0.4.0+0"

[[deps.RuntimeGeneratedFunctions]]
deps = ["ExprTools", "SHA", "Serialization"]
git-tree-sha1 = "f139e81a81e6c29c40f1971c9e5309b09c03f2c3"
uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
version = "0.5.6"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.SIMD]]
deps = ["SnoopPrecompile"]
git-tree-sha1 = "8b20084a97b004588125caebf418d8cab9e393d1"
uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
version = "3.4.4"

[[deps.SIMDTypes]]
git-tree-sha1 = "330289636fb8107c5f32088d2741e9fd7a061a5c"
uuid = "94e857df-77ce-4151-89e5-788b33177be4"
version = "0.1.0"

[[deps.SLEEFPirates]]
deps = ["IfElse", "Static", "VectorizationBase"]
git-tree-sha1 = "cda0aece8080e992f6370491b08ef3909d1c04e7"
uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
version = "0.6.38"

[[deps.ScanByte]]
deps = ["Libdl", "SIMD"]
git-tree-sha1 = "2436b15f376005e8790e318329560dcc67188e84"
uuid = "7b38b023-a4d7-4c5e-8d43-3f3097f304eb"
version = "0.3.3"

[[deps.SciMLBase]]
deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "Preferences", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SnoopPrecompile", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables", "TruncatedStacktraces"]
git-tree-sha1 = "392d3e28b05984496af37100ded94dc46fa6c8de"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "1.91.7"

[[deps.SciMLNLSolve]]
deps = ["DiffEqBase", "LineSearches", "NLsolve", "Reexport", "SciMLBase"]
git-tree-sha1 = "2e1606c282fae6bd9aed4f159695774a44b9c75f"
uuid = "e9a6253c-8580-4d32-9898-8661bb511710"
version = "0.1.4"

[[deps.SciMLOperators]]
deps = ["ArrayInterface", "DocStringExtensions", "Lazy", "LinearAlgebra", "Setfield", "SparseArrays", "StaticArraysCore", "Tricks"]
git-tree-sha1 = "e61e48ef909375203092a6e83508c8416df55a83"
uuid = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
version = "0.2.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "30449ee12237627992a99d5e30ae63e4d78cd24a"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.0"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "1.1.1"

[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.SignedDistanceFields]]
deps = ["Random", "Statistics", "Test"]
git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
version = "0.4.0"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.1.0"

[[deps.SimpleNonlinearSolve]]
deps = ["ArrayInterface", "DiffEqBase", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Reexport", "Requires", "SciMLBase", "SnoopPrecompile", "StaticArraysCore"]
git-tree-sha1 = "54c78ac3cc0343a16785adabe5bbf4063c737967"
uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
version = "0.1.14"

[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[deps.SimpleUnPack]]
git-tree-sha1 = "58e6353e72cde29b90a69527e56df1b5c3d8c437"
uuid = "ce78b400-467f-4804-87d8-8f486da07d0a"
version = "1.1.0"

[[deps.Sixel]]
deps = ["Dates", "FileIO", "ImageCore", "IndirectArrays", "OffsetArrays", "REPL", "libsixel_jll"]
git-tree-sha1 = "8fb59825be681d451c246a795117f317ecbcaa28"
uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
version = "0.1.2"

[[deps.SnoopPrecompile]]
deps = ["Preferences"]
git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c"
uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c"
version = "1.0.3"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "a4ada03f999bd01b3a25dcaa30b2d929fe537e00"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.1.0"

[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[deps.SparseDiffTools]]
deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "Graphs", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays", "VertexSafeGraphs"]
git-tree-sha1 = "e19ac47477c9a8fcca06dab5e5471417d5d9d723"
uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
version = "1.31.0"

[[deps.Sparspak]]
deps = ["Libdl", "LinearAlgebra", "Logging", "OffsetArrays", "Printf", "SparseArrays", "Test"]
git-tree-sha1 = "342cf4b449c299d8d1ceaf00b7a49f4fbc7940e7"
uuid = "e56a9233-b9d6-4f03-8d0f-1825330902ac"
version = "0.3.9"

[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "ef28127915f4229c971eb43f3fc075dd3fe91880"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.2.0"

[[deps.StableHashTraits]]
deps = ["CRC32c", "Compat", "Dates", "SHA", "Tables", "TupleTools", "UUIDs"]
git-tree-sha1 = "0b8b801b8f03a329a4e86b44c5e8a7d7f4fe10a3"
uuid = "c5dd0088-6c3f-4803-b00e-f31a60c170fa"
version = "0.3.1"

[[deps.StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[deps.Static]]
deps = ["IfElse"]
git-tree-sha1 = "08be5ee09a7632c32695d954a602df96a877bf0d"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.8.6"

[[deps.StaticArrayInterface]]
deps = ["ArrayInterface", "Compat", "IfElse", "LinearAlgebra", "Requires", "SnoopPrecompile", "SparseArrays", "Static", "SuiteSparse"]
git-tree-sha1 = "33040351d2403b84afce74dae2e22d3f5b18edcb"
uuid = "0d7ed370-da01-4f52-bd93-41d350b8b718"
version = "1.4.0"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "c262c8e978048c2b095be1672c9bee55b4619521"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.5.24"

[[deps.StaticArraysCore]]
git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.0"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "45a7769a04a3cf80da1c1c7c60caf932e6f4c9f7"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.6.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "d1bf48bfcc554a3761a133fe3a9bb01488e06916"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.21"

[[deps.StatsFuns]]
deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "f625d686d5a88bcd2b15cd81f18f98186fdc0c9a"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "1.3.0"

[[deps.SteadyStateDiffEq]]
deps = ["DiffEqBase", "DiffEqCallbacks", "LinearAlgebra", "NLsolve", "Reexport", "SciMLBase"]
git-tree-sha1 = "564451a262696334a3bab19108a99dd90d5a22c8"
uuid = "9672c7b4-1e72-59bd-8a11-6ac3964bc41f"
version = "1.15.0"

[[deps.StochasticDiffEq]]
deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqNoiseProcess", "DocStringExtensions", "FillArrays", "FiniteDiff", "ForwardDiff", "JumpProcesses", "LevyArea", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
git-tree-sha1 = "073da86200349ddf4ef8bc3e3f3acd62e1d554f7"
uuid = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
version = "6.60.0"

[[deps.StrideArraysCore]]
deps = ["ArrayInterface", "CloseOpenIntervals", "IfElse", "LayoutPointers", "ManualMemory", "SIMDTypes", "Static", "StaticArrayInterface", "ThreadingUtilities"]
git-tree-sha1 = "b3e9c174a9df77ed7b66fc0aa605def3351a0653"
uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
version = "0.4.13"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "GPUArraysCore", "StaticArraysCore", "Tables"]
git-tree-sha1 = "521a0e828e98bb69042fec1809c1b5a680eb7389"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.15"

[[deps.SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "5.10.1+0"

[[deps.Sundials]]
deps = ["CEnum", "DataStructures", "DiffEqBase", "Libdl", "LinearAlgebra", "Logging", "Reexport", "SciMLBase", "SnoopPrecompile", "SparseArrays", "Sundials_jll"]
git-tree-sha1 = "a4e8491c163d74fb92905c6443e59558f5e609a4"
uuid = "c3572dad-4567-51f8-b174-8c6c989267f4"
version = "4.16.0"

[[deps.Sundials_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg", "SuiteSparse_jll"]
git-tree-sha1 = "04777432d74ec5bc91ca047c9e0e0fd7f81acdb6"
uuid = "fb77eaff-e24c-56d4-86b1-d163f2edb164"
version = "5.2.1+0"

[[deps.SymbolicIndexingInterface]]
deps = ["DocStringExtensions"]
git-tree-sha1 = "f8ab052bfcbdb9b48fad2c80c873aa0d0344dfe5"
uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
version = "0.2.2"

[[deps.SymbolicUtils]]
deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TimerOutputs", "Unityper"]
git-tree-sha1 = "5cb1f963f82e7b81305102dd69472fcd3e0e1483"
uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
version = "1.0.5"

[[deps.Symbolics]]
deps = ["ArrayInterface", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "Groebner", "IfElse", "LaTeXStrings", "LambertW", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "Markdown", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TreeViews"]
git-tree-sha1 = "e23ec62c083ca8f15a4b7174331b3b8d1c511e47"
uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
version = "5.3.1"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "1544b926975372da01227b382066ab70e574a3ec"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.10.1"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.1"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.ThreadingUtilities]]
deps = ["ManualMemory"]
git-tree-sha1 = "c97f60dd4f2331e1a495527f80d242501d2f9865"
uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
version = "0.5.1"

[[deps.TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "8621f5c499a8aa4aa970b1ae381aae0ef1576966"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.6.4"

[[deps.TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "f548a9e9c490030e545f72074a41edfd0e5bcdd7"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.23"

[[deps.Tokenize]]
git-tree-sha1 = "90538bf898832b6ebd900fa40f223e695970e3a5"
uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
version = "0.5.25"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "9a6ae7ed916312b41236fcef7e0af564ef934769"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.13"

[[deps.TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"

[[deps.TriangularSolve]]
deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
git-tree-sha1 = "31eedbc0b6d07c08a700e26d31298ac27ef330eb"
uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
version = "0.1.19"

[[deps.Tricks]]
git-tree-sha1 = "aadb748be58b492045b4f56166b5188aa63ce549"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.7"

[[deps.TriplotBase]]
git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
version = "0.1.0"

[[deps.TruncatedStacktraces]]
deps = ["InteractiveUtils", "MacroTools", "Preferences"]
git-tree-sha1 = "7bc1632a4eafbe9bd94cf1a784a9a4eb5e040a91"
uuid = "781d530d-4396-4725-bb49-402e4bee1e77"
version = "1.3.0"

[[deps.TupleTools]]
git-tree-sha1 = "3c712976c47707ff893cf6ba4354aa14db1d8938"
uuid = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
version = "1.3.0"

[[deps.URIs]]
git-tree-sha1 = "074f993b0ca030848b897beff716d93aca60f06a"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.2"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "dba3eba51b9512695b59e0bd8263ac074c5ed2d9"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.13.1"

[[deps.Unityper]]
deps = ["ConstructionBase"]
git-tree-sha1 = "d5f4ec8c22db63bd3ccb239f640e895cfde145aa"
uuid = "a7c27f48-0311-42f6-a7f8-2c11e75eb415"
version = "0.1.2"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static", "StaticArrayInterface"]
git-tree-sha1 = "b182207d4af54ac64cbc71797765068fdeff475d"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.64"

[[deps.VertexSafeGraphs]]
deps = ["Graphs"]
git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.2.0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.10.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "977aed5d006b840e2e40c0b48984f7463109046d"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.3"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
# ╠═30b13841-97f1-47ab-a5c9-346ea8261f03
# ╟─c8765318-d2d1-4af4-8604-c363038018b7
# ╠═01bab882-2588-4d5d-8808-cdd4aaa23a47
# ╠═3878c1bf-64fd-403a-aab1-dd5364588744
# ╟─190cc65b-0fad-4150-98f8-0494cc018636
# ╟─7c9d5d2d-9d2f-4490-a891-eaffa42e6cca
# ╟─24a0dea7-bbd3-4eaa-8d69-c78e2a484534
# ╠═95aa2183-e03c-41a7-98f9-1ad074ba3baa
# ╟─52b75ad6-d1ad-4f33-ad7d-2089f02ca6a7
# ╟─43f4f9de-a09a-43ae-8383-06d3a3be3589
# ╟─de58d9dd-dc03-44b0-bc6a-6068d3ff9d28
# ╟─40bac874-8e71-4a45-9fd6-fd6b5f673b16
# ╟─dad48b2a-201f-40d1-a515-347b5fbc15bc
# ╟─e6b6aa9f-f3c6-4f4a-92dd-b881c61f7df9
# ╟─903e68f4-7766-43bd-bfa0-018140101606
# ╟─46ed8542-733c-4a0d-9f60-c2bc1df955b4
# ╟─de723296-d4e4-4762-ade7-add5e2b8c79c
# ╠═14994f78-8f03-4e5e-bfb6-533ac0f2c289
# ╠═64b8c8d1-91d2-4cb7-bf20-84fa04eeb738
# ╟─2df1ebdd-1889-42c7-9617-5f445f206553
# ╟─aec8b317-d3d8-49d3-823f-14a1b16e9f58
# ╟─c7304b77-70a5-444f-9199-eff5539e65bc
# ╟─e3dd377a-a26d-400e-867b-ffb037dd1c5b
# ╟─1ee73b45-192d-4a9d-8a89-d2199cb99dae
# ╟─1703658a-7b64-4e4a-a8ed-c953dfa11f81
# ╟─64063f3d-4f4f-4923-82c6-73f387732944
# ╟─c4089458-3561-439a-9285-f2d9e0f7cb13
# ╟─b3b3db0d-196e-4f6f-b297-873e908caabb
# ╟─30a4eca5-511c-41f1-832e-897f1e755f0c
# ╟─7c288433-e782-4f2e-97c0-b70c7c2d3748
# ╟─fd7d91f0-b58b-4600-b39e-288ed09bbe34
# ╠═821963b2-a6d2-45e4-bff0-247fe75f8852
# ╟─6b5c3ff9-57ed-4801-ae9b-2691102e0db7
# ╟─a68f4047-b934-4e56-a70b-f99e640afb9f
# ╠═836e1653-4f3e-4043-96c3-38a5616d2f89
# ╠═3aee4ef3-15bc-435f-89bb-c07a17c72021
# ╟─40804fce-7a1e-420e-94cc-2b1dbdf6e357
# ╟─8ad14cbb-2737-4142-b52b-2a22a3b8352a
# ╟─64c9dbd0-edfd-4b1c-b14d-5e9875ea4f33
# ╟─1822e04a-9986-42e0-9235-06ef0e486a74
# ╟─9db87f92-f361-465a-8841-fac3fc078343
# ╟─7e6ae3bb-e518-4b15-80fb-e853eceef96c
# ╟─0aa7e21a-255c-4fcc-8ee6-8b3ef96a82b9
# ╟─42924ebd-0bc9-4bd2-9e22-daba975b19e2
# ╟─0e68a81f-d628-40e4-a56f-1dc386247946
# ╟─08ff363a-a0e9-4eb2-a118-5374869fc0da
# ╟─5b77331c-adfa-4df2-9fb8-c1d14785cc2b
# ╟─c87ffaca-cec4-4aef-8fa8-9d8608941284
# ╟─e23af05f-d125-4798-918f-8a20c0f55065
# ╟─6bd76627-d6f0-4adb-af46-203f21f95d27
# ╠═b5174a24-428e-4a41-9b85-fccc7bcf8d32
# ╠═6c11b041-72c9-41c7-9fdb-f3257fea0fd9
# ╠═02c540f7-cdf8-428d-88c0-64ae6cb905c5
# ╠═6be4813b-fb90-4fcb-bc93-314971a7b50d
# ╠═e25205ff-a4fa-4a54-8a6c-1f94c9dd9ac3
# ╠═52f9023e-fb67-43ca-8548-46dfeeb7fb86
# ╟─99b02d20-8596-4b56-bda8-30d671d9f098
# ╠═f88f76e6-2b7a-4feb-88e4-34fb62a4ebe7
# ╠═00c2793d-2414-48e6-9946-c4211428d649
# ╟─68184209-041c-4e78-9d29-1ba56f21a7fd
# ╠═af5781a8-73f3-4ab4-bf20-38d41e5274e1
# ╟─bcfe0e20-c93b-41b7-8291-3f4f9792ba64
# ╠═d22c55f9-d8a0-443b-804e-4cb9976a0ac3
# ╠═25fcbb57-f3ec-4cce-b22c-2503c9bb36e5
# ╠═ce8ccbe5-2637-43df-906a-ce6a71e9b918
# ╠═87e78056-fecc-4b15-a723-16f51fa19353
# ╠═0162ae2a-c19c-4700-9c87-4c76f1169d06
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002