pwc-archive/papers-with-abstracts huggingface dataset:
The k-statistics approach to epidemiology
Authors: Giorgio Kaniadakis, Mauro M. Baldi, Thomas S. Deisboeck, Giulia Grisolia, Dionissios T. Hristopulos, Antonio M. Scarfone, Amelia Sparavigna, Tatsuaki Wada, Umberto Lucia
Date: 2020-11-25 00:00:00
Tasks: Epidemiology

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $\kappa$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $\kappa$-statistics in fitting empirical data. In this paper, we use $\kappa$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $\kappa$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $\kappa$-Weibull model has universal features.
Open Quasispecies Systems: New Approach to Evolutionary Adaptation
Authors: Igor Samokhin, Tatiana Yakushkina, Alexander S. Bratus
Date: 2020-11-23 00:00:00

Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We assume that evolutionary parameters of mutation and selection processes vary in a way to maximize the mean fitness of the system. From this standpoint, Fisher's theorem of natural selection is being rethought and discussed. Another assumption is that system dynamics has two significant timescales. According to our central hypothesis, major evolutionary transitions happen in the steady-state of the corresponding dynamical system, so the evolutionary time is much slower than the one of internal dynamics. For the specific cases of quasispecies systems, we show how our premises form the fitness landscape adaptation process.
Senescence, change, and competition: when the desire to pick one model harms our understanding
Authors: André C. R. Martins
Date: 2020-11-09 00:00:00

The question of why we age is a fundamental one. It is about who we are, and it also might have critical practical aspects as we try to find ways to age slower. Or to not age at all. Different reasons point at distinct strategies for the research of anti-ageing drugs. While the main reason why biological systems work as they do is evolution, for quite a while, it was believed that aging required another explanation. Aging seems to harm individuals so much that even if it has group benefits, those benefits were unlikely to be enough. That has led many scientists to propose non-evolutionary explanations as to why we age. But those theories seem to fail at explaining all the data on how species age. Here, I will show that the insistence of finding the one idea that explains it all might be at the root of the difficulty of getting a full picture. By exploring an evolutionary model of aging where locality and temporal changes are fundamental aspects of the problem, I will show that environmental change causes the barrier for group advantages to become much weaker. That weakening might help small group advantages to add up to the point they could make an adaptive difference. To answer why we age, we might have to abandon asking which models are correct. The full answer might come from considering how much each hypothesis behind each existing model, evolutionary and non-evolutionary ones, contributes to the real world's solution.
Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
Authors: Filippo Palombi, Stefano Ferriani, Simona Toti
Date: 2019-05-14 00:00:00

We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species develops through cooperative predation. Its rate equations in a well-mixed environment display a degenerate Hopf bifurcation, occurring as reactions involving two predators plus one prey have the same rate as reactions involving two preys plus one predator. We estimate the magnitude of the stochastic noise at the bifurcation point, where finite size effects turn neutrally stable orbits into erratically diverging trajectories. In particular, we compare analytic predictions for the extinction probability, derived in the Fokker-Planck approximation, with numerical simulations based on the Gillespie stochastic algorithm. We then extend the analysis of the phase portrait to heterogeneous rates. In a well-mixed environment, we observe a continuum of degenerate Hopf bifurcations, generalizing the above one. Neutral stability ensues from a complex equilibrium between different reactions. Remarkably, on a two-dimensional lattice, all bifurcations disappear as a consequence of the spatial locality of the interactions. In the second part of the paper, we investigate the effects of mobility in a lattice metapopulation model with patches hosting several agents. We find that strategies propagate along the arms of rotating spirals, as they usually do in models of cyclic dominance. We observe propagation instabilities in the regime of large wavelengths. We also examine three-agent interactions inducing nonlinear diffusion.
A Review of Complex Systems Approaches to Cancer Networks
Authors: Abicumaran Uthamacumaran
Date: 2020-09-26 00:00:00
Tasks: BIG-bench Machine Learning, Decision Making

Cancers remain the lead cause of disease-related, pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system with intractable algorithmic complexity. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple, strange attractors. Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction. Deep Learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.
Macroscopic Fluctuations Emerge in Balanced Networks with Incomplete Recurrent Alignment
Authors: Itamar Daniel Landau, Haim Sompolinsky
Date: 2021-03-11 00:00:00

Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal vectors, these networks generate large-scale coherent fluctuations. Although a striking phenomenon, that result depended on a fine-tuned choice of low-rank structure. Here we extend that work by generalizing the theory of excitation-inhibition balance to networks with arbitrary low-rank structure and show that low-dimensional variability emerges intrinsically through what we call incomplete recurrent alignment. We say that a low-rank connectivity structure exhibits incomplete alignment if its row-space is not contained in its column-space. In the setting of incomplete alignment, recurrent connectivity can be decomposed into a subspace-recurrent component and an effective-feedforward component. We show that high-dimensional, microscopic fluctuations are propagated via the effective-feedforward component to a low-dimensional subspace where they are dynamically balanced by macroscopic fluctuations. We present biologically plausible examples from excitation-inhibition networks and networks with heterogeneous degree distributions. Finally, we define the alignment matrix as the overlap between left and right-singular vectors of the structured connectivity, and show that the singular values of the alignment matrix determine the amplitude of macroscopic variability, while its singular vectors determine the structure. Our work shows how macroscopic fluctuations can emerge generically in strongly-coupled networks with low-rank structure. Furthermore, by generalizing excitation-inhibition balance to arbitrary low-rank structure our work may find relevance in any setting with strongly interacting units, whether in biological, social, or technological networks.
Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
Authors: Kestutis Pyragas, Augustinas P. Fedaravičius, Tatjana Pyragienė
Date: 2021-03-01 00:00:00

Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
On the stability of equilibria of the physiologically-informed dynamic causal model
Authors: Sayan Nag
Date: 2021-01-14 00:00:00

Experimental manipulations perturb the neuronal activity. This phenomenon is manifested in the fMRI response. Dynamic causal model and its variants can model these neuronal responses along with the BOLD responses [1, 2, 3, 4, 5] . Physiologically-informed DCM (P-DCM) [5] gives state-of-the-art results in this aspect. But, P-DCM has more parameters compared to the standard DCM model and the stability of this particular model is still unexplored. In this work, we will try to explore the stability of the P-DCM model and find the ranges of the model parameters which make it stable.
Signal anticipation and delay in excitable media: group delay of the FitzHugh-Nagumo model
Authors: Akke Mats Houben
Date: 2021-01-02 00:00:00

An expression for the group delay of the FitzHugh-Nagumo model in response to low amplitude input is obtained by linearisation of the cubic term of the voltage equation around its stable fixed-point. It is found that a negative group delay exists for low frequencies, indicating that the evolution of slowly fluctuating signals are anticipated by the voltage dynamics. The effects of the group delay for different types of signals are shown numerically for the non-linearised FitzHugh-Nagumo model, and some observations on the signal aspects that are anticipated are stated.
Human Social Cycling Spectrum
Authors: Wang Zhijian, Yao Qingmei
Date: 2020-12-06 00:00:00

This paper investigates the reality and accuracy of evolutionary game dynamics theory in human game behavior experiments. In classical game theory, the central concept is Nash equilibrium, which reality and accuracy has been well known since the firstly illustration by the O'Neill game experiment in 1987. In game dynamics theory, the central approach is dynamics equations, however, its reality and accuracy is rare known, especially in high dimensional games. By develop a new approach, namely the eigencycle approach, with the eigenvectors from the game dynamics equations, we discover the fine structure of the cycles in the same experiments. We show that, the eigencycle approach can increase the accuracy by an order of magnitude in the human dynamic hehavior data. As the eigenvector is fundamental in dynamical systems theory which has applications in natural, social, and virtual worlds, the power of the eigencycles is expectedly. Inspired by the high dimensional eigencycles, we suggest that, the mathematical concept, namely 'invariant manifolds', could be a candidate as the central concept for the game dynamics theory, like the fixed point concept for classical game theory.
Boom-bust population dynamics can increase diversity in evolving competitive communities
Authors: Michael Doebeli, Eduardo Cancino Jaque, Iaroslav Ispolatov
Date: 2020-11-30 00:00:00
Tasks: Diversity

The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is limited by the number of resources, or by the species' similarity in resource use. Natural systems such as the extreme diversity of unicellular life in the oceans provide counter examples. It is known that mathematical models incorporating population fluctuations can lead to violations of the exclusion principle. Here we use simple eco-evolutionary models to show that a certain type of population dynamics, boom-bust dynamics, can allow for the evolution of much larger amounts of diversity than would be expected with stable equilibrium dynamics. Boom-bust dynamics are characterized by long periods of almost exponential growth (boom) and a subsequent population crash due to competition (bust). When such ecological dynamics are incorporated into an evolutionary model that allows for adaptive diversification in continuous phenotype spaces, desynchronization of the boom-bust cycles of coexisting species can lead to the maintenance of high levels of diversity.
Synchronization within synchronization: transients and intermittency in ecological networks
Authors: Huawei Fan, Ling-Wei Kong, Xingang Wang, Alan Hastings, Ying-Cheng Lai
Date: 2020-11-20 00:00:00
Tasks: Management

Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e., synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry - henceforth the phenomenon of "synchronization within synchronization." Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.
Modelling strong control measures for epidemic propagation with networks -- A COVID-19 case study
Authors: Michael Small, David Cavanagh
Date: 2020-04-22 00:00:00

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions. Contact between individuals in the community is characterised by a contact graph, the structure of that contact graph is selected to mimic community control measures. Our model of city-level transmission of an infectious agent (SEIR model) characterises spread via a (a) scale-free contact network (no control); (b) a random graph (elimination of mass gatherings); and (c) small world lattice (partial to full lockdown -- "social" distancing). This model exhibits good qualitative agreement between simulation and data from the 2020 pandemic spread of coronavirus. Estimates of the relevant rate parameters of the SEIR model are obtained and we demonstrate the robustness of our model predictions under uncertainty of those estimates. The social context and utility of this work is identified, contributing to a highly effective pandemic response in Western Australia.
Predictive modelling of disease propagation in a mobile, connected community
Authors: Ishant Tiwari, Pradeep Sarin, Punit Parmananda
Date: 2020-03-19 00:00:00

We present numerical results obtained from the modelling of a stochastic, highly connected and mobile community. The spread of attributes like health, disease among the community members is simulated using cellular automata on a planar 2 dimensional bounded space. With remarkably few assumptions, we are able to predict the future course of propagation of such disease as a function of time and the fine-tuning of parameters related to the interaction among the automata.
A Survey of the Individual-Based Model applied in Biomedical and Epidemiology
Authors: E. G. Nepomuceno, D. F. Resende, M. J. Lacerda
Date: 2019-02-07 00:00:00
Tasks: Articles, Epidemiology

Individual-based model (IBM) has been used to simulate and to design control strategies for dynamic systems that are subject to stochasticity and heterogeneity, such as infectious diseases. In the IBM, an individual is represented by a set of specific characteristics that may change dynamically over time. This feature allows a more realistic analysis of the spread of an epidemic. This paper presents a literature survey of IBM applied to biomedical and epidemiology research. The main goal is to present existing techniques, advantages and future perspectives in the development of the model. We evaluated 89 articles, which mostly analyze interventions aimed at endemic infections. In addition to the review, an overview of IBM is presented as an alternative to complement or replace compartmental models, such as the SIR (Susceptible-Infected-Recovered) model. Numerical simulations also illustrate the capabilities of IBM, as well as some limitations regarding the effects of discretization. We show that similar side-effects of discretization scheme for compartmental models may also occur in IBM, which requires careful attention.
Statistical dynamics of spatial-order formation by communicating cells
Authors: Eduardo P. Olimpio, Yiteng Dang, Hyun Youk
Date: 2017-06-16 00:00:00
Tasks: Form

Communicating cells can coordinate their gene expressions to form spatial patterns. 'Secrete-and-sense cells' secrete and sense the same molecule to do so and are ubiquitous. Here we address why and how these cells, from disordered beginnings, can form spatial order through a statistical mechanics-type framework for cellular communication. Classifying cellular lattices by 'macrostate' variables - 'spatial order paramete' and average gene-expression level - reveals a conceptual picture: cellular lattices act as particles rolling down on 'pseudo-energy landscapes' shaped by a 'Hamiltonian' for cellular communication. Particles rolling down represent cells' spatial order increasing. Particles trapped on the landscapes represent metastable spatial configurations. The gradient of the Hamiltonian and a 'trapping probability' determine the particle's equation of motion. This framework is extendable to more complex forms of cellular communication.
On a nonlinear electromechanical model of nerve
Authors: Alain M. Dikande
Date: 2021-02-20 00:00:00
Tasks: model

The generation of action potential brings into play specific mechanosensory stimuli manifest in the variation of membrane capacitance, resulting from the selective membrane permeability to ions exchanges and testifying to the central role of electromechanical processes in the buildup mechanism of nerve impulse. As well established [See e.g. D. Gross et al, Cellular and Molecular Neurobiology vol. 3, p. 89 (1983)], in these electromechanical processes the net instantaneous charge stored in the membrane is regulated by the rate of change of the net fluid density through the membrane, orresponding to the difference in densities of extacellular and intracellular fluids. An electromechanical model is proposed for which mechanical forces are assumed to result from the flow of ionic liquids through the nerve membrane, generating pressure waves stimulating the membrane and hence controlling the net charge stored in the membrane capacitor. The model features coupled nonlinear partial differential equations: the familiar Hodgkin-Huxley's cable equation for the transmembrane voltage in which the membrane capacitor is now a capacitive diode, and the Heimburg-Jackson's nonlinear hydrodynamic equation for the pressure wave controlling the total charge in the membrane capacitor. In the stationary regime, the Hodgkin-Huxley cable equation with variable capacitance reduces to a linear operator problem with zero eigenvalue, the bound states of which can be obtained exactly for specific values of characteristic parameters of the model. In the dynamical regime, numerical simulations of the modified Hodgkin-Huxley equation lead to a variety of typical figures for the transmembrane voltage, reminiscent of action potentials observed in real physiological contexts.
A General Model of Structured Cell Kinetics
Authors: Michael Grinfeld, Nigel Mottram, Jozsef Farkas
Date: 2021-02-12 00:00:00
Tasks: model

We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the molecule and apply this approach to models of silicosis, quorum sensing in Gram-negative bacteria and magnetic ion exchange.
A qualitative mathematical model of the immune response under the effect of stress
Authors: Maria Elena Gonzalez Herrero, Christian Kuehn
Date: 2021-02-10 00:00:00

In the last decades, the interest to understand the connection between brain and body has grown notably. For example, in psychoneuroimmunology many studies associate stress, arising from many different sources and situations, to changes in the immune system from the medical or immunological point of view as well as from the biochemical one. In this paper we identify important behaviours of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end we develop a differential equation model with two equations for infection level and immune system, which integrates the effects of stress as an additional parameter. We are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a "burn-out" or stable sick state for extremely high stress. The mechanism between the different dynamics is controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing before eventually reaching a burn-out state.