Energy landscape analysis of neuroimaging data

Ezaki, Takahiro; Watanabe, Takamitsu; Ohzeki, Masayuki; Masuda, Naoki

doi:10.1098/rsta.2016.0287

Cited by 103 publications

(239 citation statements)

References 34 publications

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“…-better data analysis and diagnoses [9,12,16,17]; -better therapies or instrumentation [15,[19][20][21]; -better understanding of biological processes [10,13,14]; and -better understanding of medical disorders [11,18].…”

Section: Resultsmentioning

confidence: 99%

“…This theme issue on the applications of mathematics to medicine is composed of six papers belonging to the area of neuroscience [9][10][11][12][13][14], three papers belonging to cardiology [15][16][17] and four papers belonging to pathology [18][19][20][21], totalling 13 papers from collaborations among 55 scientists.…”

Section: This Issuementioning

confidence: 99%

“…The data analysed by Ezaki et al [9] are voxels obtained by functional magnetic resonance imaging of some regions of the brain. The scope is to represent that information in such a way that alterations in brain dynamics can be easily identified.…”

Section: (C) Data Processingmentioning

confidence: 99%

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Mathematical methods in medicine: neuroscience, cardiology and pathology

Amigó

Small

2017

Phil. Trans. R. Soc. A.

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The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

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Section: Resultsmentioning

confidence: 99%

Section: This Issuementioning

confidence: 99%

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Mathematical methods in medicine: neuroscience, cardiology and pathology

Amigó

Small

2017

Phil. Trans. R. Soc. A.

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“…Panel (a) shows the upper bound T u (ν, α) and lower bound T l (ν, α) computed from (19) and (20) if and only if 0 < ν < 3/4. Moreover, for 0 < ν < 3/4 fixed and increasing α, (22) is maintained as long as there are still three roots: the −α 2 ln R/2 dependence means that V (R min ) increases while V (R max ) decreases with α.…”

Section: Sequential Escape Times For Coupled Bistable Nodesmentioning

confidence: 99%

“…Panel (a) shows the lower and upper bound T l (ν, α) and T u (ν, α) also numerically estimated using Maple from (19) and (20) respectively. The Kramers asymptotic approximation of T (ν, α) from [6] is shown for comparison.…”

Section: Mean Escape Times For a Single Nodementioning

confidence: 99%

Sequential Noise-Induced Escapes for Oscillatory Network Dynamics

Creaser¹,

Tsaneva-Atanasova²,

Ashwin³

2018

SIAM J. Appl. Dyn. Syst.

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It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for potential systems in the presence of asymptotically low noise the well-known Kramers' escape time gives an expression for the mean escape time. This paper examines some general properties and examples of transitions between local steady and oscillatory attractors within networks: the transition rates at each node may be affected by the dynamics at other nodes. We use first passage time theory to explain some properties of scalings noted in the literature for an idealised model of initiation of epileptic seizures in small systems of coupled bistable systems with both steady and oscillatory attractors. We focus on the case of sequential escapes where a steady attractor is only marginally stable but all nodes start in this state. As the nodes escape to the oscillatory regime, we assume that the transitions back are very infrequent in comparison. We quantify and characterise the resulting sequences of noise-induced escapes. For weak enough coupling we show that a master equation approach gives a good quantitative understanding of sequential escapes, but for strong coupling this description breaks down.

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Energy landscape analysis elucidates the multistability of ecological communities across environmental gradients

Suzuki

Nakaoka

Fukuda

et al. 2021

Ecological Monographs

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Compositional multistability is widely observed in multispecies ecological communities. Since differences in community composition often lead to differences in community function, understanding compositional multistability is essential to comprehend the role of biodiversity in maintaining ecosystems. In community assembly studies, it has long been recognized that the order and timing of species migration and extinction influence structure and function of communities. The study of multistability in ecology has focused on the change in dynamical stability across environmental gradients, and was developed mainly for low‐dimensional systems. As a result, methodologies for studying the compositional stability of empirical multispecies communities are not well developed. Here, we show that models previously used in ecology can be analyzed from a new perspective, the energy landscape, to unveil compositional stability in observational data. To show that our method can be applicable to real‐world ecological communities, we simulated assembly dynamics driven by population‐level processes, and show that results were mostly robust to different simulation assumptions. Our method reliably captured the change in the overall compositional stability of multispecies communities over environmental change, and indicated a small fraction of community compositions that may be channels for transitions between stable states. When applied to murine gut microbiota, our method showed the presence of two alternative states whose relationship changes with age, and suggested mechanisms by which aging affects the compositional stability of the murine gut microbiota. Our method provides a practical tool to study the compositional stability of communities in a changing world, and will facilitate empirical studies that integrate the concept of multistability from different fields.

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Energy landscape analysis of neuroimaging data

Cited by 103 publications

References 34 publications

Mathematical methods in medicine: neuroscience, cardiology and pathology

Mathematical methods in medicine: neuroscience, cardiology and pathology

Sequential Noise-Induced Escapes for Oscillatory Network Dynamics

Energy landscape analysis elucidates the multistability of ecological communities across environmental gradients

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