Games in Rigged Economies

Seoane, Luís F.

doi:10.1103/physrevx.11.031058

Cited by 4 publications

(5 citation statements)

References 35 publications

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“…We ran 1000 simulations with each fixed injury size, λ ∈ [1, 50], to find out emerging trends in spontaneous SOM reorganization after stroke. Focusing on λ = 45, we compare maps before and right after lesion (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Our work is part of an effort to ground neural plasticity in statistical mechanics [20, 47–50]. In classic thermodynamics, we subject a sample of matter (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Lesions around this area would muddle the characterization of contralesional representations, thus we avoided it. In this paper we report lesions starting always at unit l = 20 with λ ∈ [1, 50]. The largest injuries affect up to unit u 69 , thus damage is always confined to the first half of the SOM.…”

Section: Methodsmentioning

confidence: 99%

“…Our input signals and SOM were purposefully designed to resemble spins, which interactive dynamics are known to contain minimal, yet universal computational capabilities [45]. In our framework, phenomenology is often guided by phase transitions, critical points, symmetry or symmetry-breaking [20, 47–50], and other ingredients for which statistical mechanics offers a very solid bedrock. As we will show, some of these concepts constitute the key mechanisms that enable our model to reproduce clinical observations.…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions in a simple model of focal stroke imitate recovery and suggest neurorehabilitation strategies

Carballo-Castro¹,

Seoane

2022

Preprint

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A stroke is a brain insult that can take offline (often permanently) extended regions of the brain. As a consequence, cognitive tasks or representations implemented by the affected circuitry lose their computational substrate (they become {\em orphan}). The brain must adapt to attempt retaining such functions. The existing clinical literature offers a complex picture, often with conflicting observations, about how the brain gets reorganized after stroke. It also does little use of the few mathematical works on the topic. Can a minimal mathematical model of cortical plasticity shed light on this complex phenomenology? Here we explore such minimal model, and find a specific phenomenology: a lasting perilesional reorganization for small injuries, and a temporary contralesional reorganization for large injuries that is not always reverted to ipsilesional. We furthermore show the mechanisms behind these dynamics in our model: a second order phase transition with a critical point, as well as a delayed engagement of perilesional reorganization in large injuries. These dynamics emerge out of a fairly minimal modeling of plasticity, and they reproduce the story put together from clinical observations. We further explore neurorehabilitation strategies, and argue that increased tissue susceptibility (a property that diverges at critical points) can be crucial to manipulate plasticity in beneficial ways.

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Section: Resultsmentioning

confidence: 99%

“…Our work is part of an effort to ground neural plasticity in statistical mechanics [20, 47–50]. In classic thermodynamics, we subject a sample of matter (e.g.…”

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phase transitions in a simple model of focal stroke imitate recovery and suggest neurorehabilitation strategies

Carballo-Castro¹,

Seoane

2022

Preprint

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“…Second, seemingly unrelated problems across disciplines can be cast in terms of the unifying framework of spin models on random networks [7,8]. Models of scalar spins on networks have a vast number of applications in a variety of research fields, such as opinion dynamics [9,10], models of socio-economic phenomena [11], artificial neural networks [12][13][14], agent-based models of the market behavior [15][16][17], dynamics of biological neural networks [18][19][20], information theory and computer science [8], sparse random-matrix theory [21,22], and the stability of large dynamical systems [23,24]. Models of vector spins on networks are relevant for the study of synchronization phenomena [25][26][27][28], random lasers [29][30][31], vector spin-glasses (SGs) [32][33][34], and the collective dynamics of swarms [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Mean-field theory of vector spin models on networks with arbitrary degree distributions

Metz

Peron

2022

J. Phys. Complex.

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Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-ﬁeld theories of spin models on networks constitute a fundamental tool to tackle this problem and a cornerstone of statistical physics, with an impressive number of applications in condensed matter, biology, and computer science. In this work we derive the mean-ﬁeld equations for the equilibrium behavior of vector spin models on high-connectivity random networks with an arbitrary degree distribution and with randomly weighted links. We demonstrate that the high-connectivity limit of spin models on networks is not universal in that it depends on the full degree distribution. Such nonuniversal behavior is akin to a remarkable mechanism that leads to the breakdown of the central limit theorem when applied to the distribution of effective local ﬁelds. Traditional mean-ﬁeld theories on fully-connected models, such as the Curie-Weiss, the Kuramoto, and the Sherrington-Kirkpatrick model, are only valid if the network degree distribution is highly concentrated around its mean degree. We obtain a series of results that highlight the importance of degree ﬂuctuations to the phase diagram of mean-ﬁeld spin models by focusing on the Kuramoto model of synchronization and on the Sherrington-Kirkpatrick model of spin-glasses. Numerical simulations corroborate our theoretical ﬁndings and provide compelling evidence that the present mean-ﬁeld theory describes an intermediate regime of connectivity, in which the average degree $c$ scales as a power $c \propto N^{b}$ ($b < 1$) of the total number $N \gg 1$ of spins. Our ﬁndings put forward a novel class of spin models that incorporate the effects of degree ﬂuctuations and, at the same time, are amenable to exact analytic solutions.

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From Coordination to Collapse in Rigged Economies

Sinha

2021

Physics

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Games in Rigged Economies

Cited by 4 publications

References 35 publications

Phase transitions in a simple model of focal stroke imitate recovery and suggest neurorehabilitation strategies

Phase transitions in a simple model of focal stroke imitate recovery and suggest neurorehabilitation strategies

Mean-field theory of vector spin models on networks with arbitrary degree distributions

From Coordination to Collapse in Rigged Economies

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