Luca Innocenti lucainnocenti
lucainnocenti
/ bibitem-sorter.py
Last active
December 13, 2023 06:17
Python script to sort the bibitem entries according to the citation order in the text. Useful when one has for some reason to not use bibtex and .bib files. Usage is as `python bibitem-sorter.py file.tex sorted_file.tex`
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| import argparse | |
| import os | |
| import sys | |
| import re | |
| def printBold(msg): | |
| HEADER = '\033[95m' | |
| BOLD = '\033[1m' | |
| print(HEADER + BOLD + msg + '\x1b[0m') |
lucainnocenti
/ scramblingDynamics.m
Last active
July 28, 2022 09:40
Examples of scrambling (cit) dynamics
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| (* this one gives maximally negative tripartite *) | |
| superScrambling2qutritsUnitary := Table[ | |
| Normal @ Flatten @ KroneckerProduct[ | |
| SparseArray[{Mod[i + j, 3] + 1 -> 1}, 3], | |
| SparseArray[{Mod[i - j, 3] + 1 -> 1}, 3] | |
| ], | |
| {i, {0, 1, 2}}, {j, {0, 1, 2}} | |
| ] // ArrayReshape[#, {9, 9}] & // Transpose; | |
| (* unitary changing local bases to Fourier bases *) |
lucainnocenti
/ weirdPauliMatricesDecomposition.m
Created
June 7, 2022 16:22
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| generatePair[pauliIndices_List, tuple_List] := { | |
| BitXor[ | |
| ReplaceAll[ | |
| pauliIndices, {3 -> 0, 2 -> 1} | |
| ], | |
| tuple | |
| ], | |
| (-1)^Total@tuple[[Flatten@Position[pauliIndices, 2 | 3]]] | |
| }; |
lucainnocenti
/ shannonEntropy.m
Created
November 15, 2021 02:44
Two-dimensional visualisation of Shannon entropy
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| ShannonEntropy[probs_] := -Total[# * Log @ #] & @ DeleteCases[probs, _?PossibleZeroQ]; | |
| par[t_, s_] = {1, 0, 0} + t / Sqrt@2 {-1, 1, 0} + s/Sqrt[3/2] {-1/2, -1/2, 1} // Simplify; | |
| par[pars_List] := par @@ pars; | |
| ContourPlot[ | |
| ShannonEntropy@par[t, s], {t, 0, Sqrt@2}, {s, 0, Sqrt[3/2]}, | |
| PlotRange -> All, | |
| ColorFunction -> "TemperatureMap", PlotRangePadding -> None, | |
| Contours -> 10, | |
| FrameStyle -> Directive[Large, Black, FontFamily -> "Latin Modern Math"], | |
| FrameLabel -> (MaTeX[#, Magnification -> 2] & /@ {"t", "s"}), |
lucainnocenti
/ visualiseDualFrames.m
Last active
November 11, 2021 16:53
Dynamically visualise dual and parseval frames
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| getDualBasis[vecs_List] := With[{ | |
| sMatrix = Total[KroneckerProduct[#, Conjugate@#] & /@ vecs] | |
| }, | |
| Dot[Inverse@sMatrix, #] & /@ vecs | |
| ]; | |
| getParsevalFrame[vecs_List] := With[{ | |
| sMatrix = Total[KroneckerProduct[#, Conjugate@#] & /@ vecs] | |
| }, | |
| Dot[MatrixFunction[Sqrt, Inverse@sMatrix], #] & /@ vecs | |
| ]; |
lucainnocenti
/ dynamicStereographicProjectionIn3D.m
Created
August 8, 2021 23:29
Dynamic visualisation of stereographic projection of the sphere
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| stereoTo3D[x_, y_] := 1/(1 + x^2 + y^2) {2 x, 2 y, 1 - x^2 - y^2}; | |
| DynamicModule[ | |
| {pt = {0, 0}}, | |
| Row @ { | |
| LocatorPane[Dynamic @ pt, | |
| Graphics[{Gray, Disk[]}, Frame -> True, ImageSize -> 200] | |
| ], | |
| Graphics3D[ | |
| { |
lucainnocenti
/ euclideanAlgorithm.m
Created
April 29, 2021 17:38
Perform and visualise Euclidean algorithm on a pair of integers
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| euclideanAlgorithmList[a_Integer, b_Integer] := NestWhileList[ | |
| With[{newSortedPair = {Max@# - Floor[Max@#/Min@#] Min@#, Min@#}}, | |
| If[#[[1]] > #[[2]], newSortedPair, Reverse@newSortedPair] | |
| ] &, | |
| {a, b}, | |
| Min @ # > 1 & | |
| ]; | |
| DynamicModule[{a = 17, b = 10}, | |
| EventHandler[ |
lucainnocenti
/ pointPlanesDualityInR2.m
Last active
August 29, 2020 22:03
Dynamic visualisation of point-plane duality in convex geometry
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| DynamicModule[{pts={{1,1}}, activePoint=None}, | |
| EventHandler[ | |
| Dynamic @ Show[ | |
| Graphics[{ | |
| PointSize@0.04,Dynamic@Point@pts, | |
| Circle[], | |
| If[activePoint =!= None, | |
| {Blue, Point @ pts[[activePoint]]}, {} | |
| ], | |
| InfiniteLine[# / Norm[#]^2, Cross @ #] & /@ pts // Dynamic |
lucainnocenti
/ interpolationLinearApprox.m
Created
July 31, 2020 12:34
linear approximation of function in MMA
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| xMax = 1.4; | |
| numPartitions = 10; dx = xMax/numPartitions; | |
| pointsAndLines[pts_] := {Point@pts, Line@pts}; | |
| fun[x_] := x^2; | |
| Plot[fun@x, {x, 0, xMax}, | |
| PlotRange -> All, PlotStyle -> Directive[Thick], Frame -> True, | |
| GridLines -> Automatic, | |
| FrameStyle -> Directive[Black, Thick, Large], | |
| PlotLegends -> "Expressions", | |
| ImageSize -> 500 |
lucainnocenti
/ distribute.m
Last active
May 17, 2020 20:18
Replacement rules implementing a noncommutative algebra, and functions to show how expressions are written in terms of nested commutators
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| << MaTeX` | |
| distribute[args_] := (args //. { | |
| HoldPattern[nc[l___, Plus[m__], r___]] :> Total[nc[l, #, r] & /@ {m}], | |
| nc[l___, c_*nc[m__], r___] :> c nc[l, m, r], | |
| nc[l___, nc[m__], r___] :> nc[l, m, r], | |
| nc[-a_, b_] :> -nc[a, b], | |
| nc[a_, -b_] :> -nc[a, b], | |
| nc[nc[l : __], r_] :> nc[l, r], nc[l_, nc[r : __]] :> nc[l, r], | |
| nc[a_] :> a |
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