# gst: phase transition of inertial self-propelled agents, a ‘inverse modeling’ approach.

AA << formulate and analyze a kinetic MFG (Mean-field Game) model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. >>️️

The << ‘inverse modelling’ approach is to stipulate that the collective behavior of a population of decision-making agents is a solution to a collective optimization or optimal control problem. (..) In a MFG system, the collective behavior is the result of each agent solving an optimal control problem that depends on its own state and control as well as the collective state. MFGs formulated in continuous state space and time are described by coupled set of forward-backward in time nonlinear partial differential equations (PDEs). >>

<< While standard kinetic or hydrodynamic equations used for modelling collective behavior are initial value problems (IVP or evolution PDEs), the MFG systems have a forward-backward in time structure, and hence consist of boundary value problem (BVP in time PDEs). >>

<< By analyzing the associated coupled forward-backward in time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, (AA) obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, (AA) show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a traveling wave solution. >>️

️

Piyush Grover, Mandy Huo. Phase transition in a kinetic mean-field game model of inertial self-propelled agents. arXiv: 2407.18400v1 [math.OC]. Jul 25, 2024. 

https://arxiv.org/abs/2407.18400

Also: transition, wave, game, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, criticality, bifurcations, wave, games

# game: noise-induced Parrondo's paradox in discrete-time qu-walks

<< Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. >>

AA << show that noise can induce Parrondo's paradox in one-dimensional discrete-time quantum walks with deterministic periodic as well as aperiodic sequences of two-state quantum coins where this paradox does not occur in the absence of noise. >>️

Zbigniew Walczak, Jarosław H. Bauer. Noise-induced Parrondo's paradox in discrete-time quantum walks. Phys. Rev. E 108, 044212. Oct 11, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.044212

Also: parrondo, walk, noise, in: https://www.inkgmr.net/kwrds.html

Keywords: games, parrondo, walk, noise

# jazz: a 'Trombiverse' approach, 'hear Beethoven like you've never heard it before'

<< Trombone Champ is the world's first trombone-based rhythm music game. Unlike most music games, you can freely play any note at any time. You're not just following along with the music, you're actually playing the music! >>️

Holy Wow. Trombone Champ. Sep 15, 2022. 

https://store.steampowered.com/app/1059990/Trombone_Champ

https://twitter.com/pcgamer/status/1572372646012260353

Christopher Livingston. The world's first trombone rhythm game is instantly a GOTY contender. Sep21, 2022.

https://www.pcgamer.com/the-worlds-first-trombone-rhythm-game-is-instantly-a-goty-contender

cit. @RhiannonJudithW. The Download. MIT. Sep 22, 2022.

https://mailchi.mp/technologyreview.com/1ys7rzr55b

FonT

a working hypothesis: anyone could summarize, filtering life-data through an artificial intelligence, the salient episodes of one's own existence through an approach of this type ... 

Also

'jazz' in FonT

https://flashontrack.blogspot.com/search?q=jazz

'jazz' | 'jazzy' | 'funky' |  in FonT (twitter)

https://twitter.com/flashontrack

'jazz' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=jazz

'ai' | 'bot' in FonT

https://flashontrack.blogspot.com/search?q=ai

https://flashontrack.blogspot.com/search?q=bot

'ia' | 'ai' | 'robota' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=ia

https://inkpi.blogspot.com/search?q=ai

https://inkpi.blogspot.com/search?q=robota

Keywords: jazz, life, music, trombone,  games, ai, artificial intelligence

# gst: switch to three players within the Parrondo game

<< Parrondo's paradox indicates a paradoxical situation in which a winning expectation may occur in sequences of losing games. There are many versions of the original Parrondo's games in the literature, but the games are played by two players in all of them. (AA) introduce a new extended version of games played by three players and a three-sided biased dice instead of two players and a biased coin in this work.  >>️

<< Figure 11 shows the result of combination switches A and B for the fair probabilities in set S_5. The simulation results are performed so on until 100 steps were done, and each step is averaged over 10000 repeats. This strategy, different from the others and even the original Parrondo's paradox, produces a fair expectation from two noisy switches in which the combination of two fair switches is fair. >>

️

Atiyeh Fotoohinasab. A new generalization of Parrondo's games to three players and its application in genetic switches.  arXiv: 2101.11401v2 [q-bio.PE]. Feb 2, 2021. 

https://arxiv.org/abs/2101.11401 

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

keyword 'three-body' in FonT

https://flashontrack.blogspot.com/search?q=three-body

Keywords: gst, games, parrondo, three-body

# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

Also

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach

# game: inject irrationality into a game scenario; when a player will be their own worst enemy

<< in game theory, a game is defined as any type of scenario where there's an interaction between different decision-makers, or players, each of whom has well-defined preferences. >>

<< previous analyses assume the decision-makers always do what is best for them-they are fully rational-which is not always realistic. >>

<< So SFI Professor David Wolpert and economist Justin Grana, a former SFI postdoctoral scholar, wanted to inject some humanity into the players. They analyzed games with players who were subject to error, or "boundedly rational." >>

<< Our analysis shows that in many of these situations, a player will be their own worst enemy; >> David Wolpert.

Jenna Marshall. How much would you pay to change a game before playing it? Santa Fe Institute. Aug13, 2019.    https://m.phys.org/news/2019-08-game.html  

David Wolpert, Justin Grana. How Much Would You Pay to Change a Game before Playing It? Entropy 2019, 21, 686. doi: 10.3390/ e21070686. July 13, 2019.   https://www.mdpi.com/1099-4300/21/7/686  

# game: 'pulsing' Parrondo to jump (and win) between two losing games

<< Parrondo’s paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; >>

<< In this review paper, the authors examine a large range of recent developments of Parrondo’s paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. >>

Kang Hao Cheong, Jin Ming Koh, Michael C. Jones. Paradoxical Survival: Examining the Parrondo Effect across Biology. BioEssays. Volume 41, Issue 6. doi: 10.1002/bies.201900027. May 27,  2019.   https://onlinelibrary.wiley.com/doi/abs/10.1002/bies.201900027  

Paradoxical Survival: Examining the Parrondo effect across biology. Singapore University of Technology and Design. Aug 5, 2019.   https://www.sciencedaily.com/releases/2019/08/190805134043.htm 

Also

"Parrondo" in: "Notes" & "FonT"

https://inkpi.blogspot.com/search?q=parrondo

https://flashontrack.blogspot.com/search?q=parrondo