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### A Pluto.jl notebook ###
# v0.19.39
using Markdown
using InteractiveUtils
# ╔═╡ d3b7f59a-712b-4520-a413-c5f5eb71a12f
begin
using PlutoUI
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using Plots
using LinearAlgebra
# using JuMP, Cbc
using Optim, LineSearches
using Statistics # for mean...
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end
# ╔═╡ 29893d76-8153-4b84-89ac-289e41327205
md"""
# Acoustic Localization Using Carrier-Phase Measurements
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# Introduction
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TODO!
## Problem Statment
!!! info "This text is copied from the provided document."
We assume an acoustic localization system with $M$ beacons transmitting signals of a certain carrier frequency. The signals are received by a mobile device (MD) located at ``x = [x, y, z]^T``, while the beacons are located at ``b_i = v = [x_i, y_i, z_i]^T``, ``i = 1, 2, \ldots, M``. The beacons and the MD are all synchronized.
By processing the received signal from each beacon, the MD estimates its range from each beacon. In addition, the MD can also obtain the phase of the carrier signal received from each beacon. The range measurements for beacon ``i`` can be modelled as
```math
r_i =\|x −
```
where wi is additive noise and ``\|\cdot\|_2`` is the Euclidean norm. On the other hand, the phase data can be described as
```math
\varphi_i = \|x −
```
where ``v_i`` is additive noise and ``n_i \in \mathbb{Z}`` is an integer phase ambiguity. In (1) and (2), we assume that the range and phase are
measured in units of cycles or wavelengths. Hence, ``\varphi_i \in [−
The objective of this work is to use both sets of measurements in (1) and (2) to estimate the MD position ``x``. To motivate the
use of the carrier phase data, we assume generally that ``\|v_i\|_2 \ll \|w_i\|_2,\, \forall i \in {1, 2, · · · , M}``. However, this is not a necessary condition for the carrier-phase use to be beneficial. To proceed further, we assume that ``w_i`` and ``v_i`` are independent for all ``i``
values, and that these noise processes are of zero mean and variances ``\alpha_i^2`` and ``\sigma_i^2``, respectively.
"""
# ╔═╡ 835ef9c7-727a-4672-bba4-58aa6766b9e6
md"""
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## Outline of The Solution
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!!! info "This text is copied from the provided document."
To formulate the estimation problem, we can define the objective function:
```math
f(\mathbf{x}, \mathbf{n}) = \sum_{i=1}^M
\alpha_i^{-2} (r_i - \|x-b_i\|_2)^2
+ \sigma_i^{-2} (\varphi_i - \|x-b_i\|_2 - n_i)^2
```
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where ``\mathbf{n} \triangleq [n_1, n_2, · · · , n_M]^T``. Hence, we can obtain a MD position estimate by solving the following mixed integer optimization problem:
```math
\hat x,\, \hat n =
\operatorname*{arg\,min}_{x\in R^3,\, n\in\mathbb{Z}^M}f(x, n)
```
We can solve (4) through the following steps:
1. Obtain a float solution (FS) of (4) by ignoring the integer constraints.
2. Find a decomposition of the objective function around the FS.
3. Develop a search algorithm using the FS and the decomposition.
"""
# ╔═╡ 57546347-5dc6-4f59-9e61-d57bc3bee3e5
b = [[1 1 10]
[2 6 10]
[7 7 10]
[7 3 10]]'
# ╔═╡ 428c1a49-2825-43a2-920d-46d9a9950455
begin
_, M = size(b)
md"""
# An Attempt to Solve this Problem...
> Note: I try to solve the problem generally, the examples are for demonstration purposes.
Lets assume that we have `b` beacons as follows, of size ``M=``**$(M)**:
"""
end
# ╔═╡ 4d9c23f1-4544-4b4b-ac59-26d534be10a9
md"""
And our mobile device ``x`` is:
"""
# ╔═╡ b089c934-de4f-483f-a2a7-96aa0d26f29d
x = [3 5 3]'
# ╔═╡ fdb7ab79-4715-4ed7-92d2-81b4f6ba2734
md"""
*Global Variable* such as ``\alpha^2`` and ``\sigma^2`` are defined here for convenience. To help debugging, we force a `seed` to keep things consistant.
"""
# ╔═╡ 51b790fc-887a-4d05-b9cc-288c6ee22b11
begin
import Random
Random.seed!(123)
end
# ╔═╡ f62bb0be-9891-4670-93c8-bd3207fc49fb
alpha = 0.1;
# ╔═╡ fbd815c1-994d-4673-a4e6-3501d190edc0
range_noise = randn(M) * alpha;
# ╔═╡ a5c5c885-a8d2-4b5b-84a6-26d1220bb89e
sigma = 0.1;
# ╔═╡ 4063cc32-a506-47f9-af52-07fe7594bcd9
phase_noise = randn(M) * sigma;
# ╔═╡ 11f45a3f-d773-4d20-95fb-c9843b18da62
phase_n = 0;
# ╔═╡ bdba2216-b866-4b53-9032-50af0b3eec0f
md"""
---
"""
# ╔═╡ 20ba966c-7f63-4e9c-9513-3d217c7b2b77
md"""
In the next steps, we try to find ``x`` in the most optimal/efficient method..
"""
# ╔═╡ 44ad3946-c1f8-4485-9db2-41d862fb41a2
md"""
We can Visualize this configuration in 3D space:
"""
# ╔═╡ 9a74694b-54f9-4a7e-8777-4d732034f53b
begin
scatter( b[1,:], b[2,:], b[3,:], label="Beacons", markersize = 10)
scatter!(x[1,:], x[2,:], x[3,:], label="MD", markersize = 10)
end
# ╔═╡ 3f34e354-137f-4614-bea9-ea3110715cae
md"""
## Using range measurments only
If we ignore the noise and the phase measurments, we notice that our solution can be solved analytically in the form:
```math
\begin{eqnarray}
(x - x_1)^2 + (y - y_1)^2 + (z - z_1)^2 &= r_1^2 \\
(x - x_2)^2 + (y - y_2)^2 + (z - z_2)^2 &= r_2^2 \\
(x - x_3)^2 + (y - y_3)^2 + (z - z_3)^2 &= r_3^2
\end{eqnarray}
```
Where ``x_i,\, y_i,\, z_i`` are the locations of the beacon ``b_i``, and ``r_i`` is the distance from the beacon to the MD.
*However this method neither scalas well when we increase the number of beacons, nor can it be solved if there is noise withen the data.*
Nevertheless, solving this problem numerically is trivial.
We know that that distance ``r`` from each beacon is `r_no_phase_or_noise`:
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"""
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# ╔═╡ 985f2cfb-1965-49de-ad1a-787fe11e9394
md"""
we can see that the result of `x_no_phase_or_noise` is very similar to the MD's original position = `x`, as expected.
"""
# ╔═╡ b239dd0a-5527-4f74-b2fb-d15ff3caa011
md"""
## Using Range and Phase
We now add a noise process of zero mean and variance ``\alpha^2`` to our equation.
"""
# ╔═╡ a7f1e580-fcb0-4833-b463-d97cf918c4f3
# ╔═╡ 786f3a79-424d-4e42-a6af-0624ecc87ff3
# Acoustic Localization Using Carrier Phase Measurments
# Give beacons located at trasmitting signals which are recieved by a mobile device (MD) located at
# clear; clc;
# Starting values...
# x = [1 2 3]'; % Mobile Device
# b = [4 3 4;
# 5 4 6;
# 7 8 9;
# 10 11 12]';
# [~, M] = size(b); % Number of Beacons
# sigma = 0.1;
# w = rand(1, M) * sigma; % White Noise
# The range measurments for the beacons can be modelled as:
# (PS: We use a search algorithm because noise would cause us to not have a numerical solution)
# r = vecnorm(b - x) + w
# Outline of The Solution
# To formulate the estimation problem. We have and , we need to find .
# f1 = @(point) mean((r - vecnorm(point - b)).^2);
# fminsearch(f1,x)'
# Adding Phase
# The phase data can be described as:
# n = rand(1, M) * 0;
# v = rand(1, M) * 0.01;
# phi = vecnorm(b-x) + n + v
# Soln W/ Phase
# f2 = @(point) mean((r - vecnorm(point(1:3) - b)).^2) ...
# + mean((phi - vecnorm(point(1:3) - b) - point(4)).^2);
# initial_guess = [x; 5]; % (1:3) => point. (4) => n.
# fminsearch(f2, initial_guess)'
# ╔═╡ f9e80776-0c5e-4ae5-b9ed-e0896bec970d
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# ╔═╡ 6040b344-d338-11ee-256a-67ae4cb673c6
md"""
# Appendex
"""
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# ╔═╡ ed6a19ef-fd4f-43b2-aa09-aa7fe38f52ed
TableOfContents()
# ╔═╡ 1929d137-dcc9-4208-992d-71001f976466
vecnorm(v) = norm.(eachcol(v))
# ╔═╡ 67c2acf3-52ea-4132-9372-d50d2c837ce8
r_no_phase_or_noise = vecnorm(b .- x)
# ╔═╡ 6abf7266-8ef4-43e7-a7ec-ced409129ced
r = vecnorm(b .- x) + range_noise
# ╔═╡ 48843f6a-cda7-4a34-b459-da1b66a48e06
phi = vecnorm(b .- x) + phase_noise .+ phase_n
# ╔═╡ 3a61a22c-07a4-4cd2-91ad-b573d8b01f30
function minimize(f, x0)
result = optimize(f,
x0,
LBFGS(linesearch = LineSearches.HagerZhang()),Optim.Options(extended_trace=true,show_every=0,store_trace = true,show_trace = false))
end
# ╔═╡ 9d567a1b-4c56-42f9-9762-a9f226bb6a51
x_no_phase_or_noise = begin
f_no_phase_or_noise(point) = # Define the minimization function LSE
mean((r_no_phase_or_noise - vecnorm(point .- b)).^2);
local x = [0.0, 0.0, 0.0] # First Guess
local res = minimize(f_no_phase_or_noise, x)
local vals = map(x-> x.value, res.trace)
local iterations = map(x-> x.iteration, res.trace)
plot(iterations, vals)
local points = map(x-> x.metadata["x"], res.trace)
end
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git-tree-sha1 = "e5becd4411063bdcac16be8b66fc2f9f6f1e8fe5"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.0.10+1"
[[deps.Xorg_libSM_jll]]
deps = ["Libdl", "Pkg", "Xorg_libICE_jll"]
git-tree-sha1 = "4a9d9e4c180e1e8119b5ffc224a7b59d3a7f7e18"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.3+0"
[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"
[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"
[[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"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"
[[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"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"
[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"
[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"
[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.4+0"
[[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", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"
[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"
[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"
2024-02-24 20:08:50 +00:00
[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"
2024-02-24 23:41:34 +00:00
[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"
[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"
[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.43.0+0"
[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+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"
2024-02-24 20:08:50 +00:00
[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"
2024-02-24 23:41:34 +00:00
[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+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.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"
[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "873b4f805771d3e4bafe63af759a26ea8ca84d14"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.42+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.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"
2024-02-24 20:08:50 +00:00
[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"
[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"
2024-02-24 23:41:34 +00:00
[[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 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
2024-02-24 20:08:50 +00:00
"""
# ╔═╡ Cell order:
# ╟─29893d76-8153-4b84-89ac-289e41327205
2024-02-24 23:41:34 +00:00
# ╟─835ef9c7-727a-4672-bba4-58aa6766b9e6
# ╟─428c1a49-2825-43a2-920d-46d9a9950455
# ╟─57546347-5dc6-4f59-9e61-d57bc3bee3e5
# ╟─4d9c23f1-4544-4b4b-ac59-26d534be10a9
# ╟─b089c934-de4f-483f-a2a7-96aa0d26f29d
# ╟─fdb7ab79-4715-4ed7-92d2-81b4f6ba2734
# ╟─51b790fc-887a-4d05-b9cc-288c6ee22b11
# ╠═f62bb0be-9891-4670-93c8-bd3207fc49fb
# ╠═fbd815c1-994d-4673-a4e6-3501d190edc0
# ╠═a5c5c885-a8d2-4b5b-84a6-26d1220bb89e
# ╠═4063cc32-a506-47f9-af52-07fe7594bcd9
# ╠═11f45a3f-d773-4d20-95fb-c9843b18da62
# ╟─bdba2216-b866-4b53-9032-50af0b3eec0f
# ╟─20ba966c-7f63-4e9c-9513-3d217c7b2b77
# ╟─44ad3946-c1f8-4485-9db2-41d862fb41a2
# ╟─9a74694b-54f9-4a7e-8777-4d732034f53b
# ╟─3f34e354-137f-4614-bea9-ea3110715cae
# ╠═67c2acf3-52ea-4132-9372-d50d2c837ce8
# ╠═9d567a1b-4c56-42f9-9762-a9f226bb6a51
# ╟─985f2cfb-1965-49de-ad1a-787fe11e9394
# ╟─b239dd0a-5527-4f74-b2fb-d15ff3caa011
# ╠═6abf7266-8ef4-43e7-a7ec-ced409129ced
# ╠═48843f6a-cda7-4a34-b459-da1b66a48e06
# ╠═a7f1e580-fcb0-4833-b463-d97cf918c4f3
# ╠═786f3a79-424d-4e42-a6af-0624ecc87ff3
# ╠═f9e80776-0c5e-4ae5-b9ed-e0896bec970d
2024-02-24 20:08:50 +00:00
# ╟─6040b344-d338-11ee-256a-67ae4cb673c6
2024-02-24 23:41:34 +00:00
# ╠═d3b7f59a-712b-4520-a413-c5f5eb71a12f
# ╠═ed6a19ef-fd4f-43b2-aa09-aa7fe38f52ed
# ╠═1929d137-dcc9-4208-992d-71001f976466
# ╠═3a61a22c-07a4-4cd2-91ad-b573d8b01f30
2024-02-24 20:08:50 +00:00
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
