pwc-archive/papers-with-abstracts huggingface dataset:
Radical Complexity
Authors: Jean-Philippe Bouchaud
Date: 2021-03-17 00:00:00

This is an informal and sketchy review of six topical, somewhat unrelated subjects in quantitative finance: rough volatility models; random covariance matrix theory; copulas; crowded trades; high-frequency trading & market stability; and "radical complexity" & scenario based (macro)economics. Some open questions and research directions are briefly discussed.
The field theoretical ABC of epidemic dynamics
Authors: Giacomo Cacciapaglia, Corentin Cot, Michele Della Morte, Stefan Hohenegger, Francesco Sannino, Shahram Vatani
Date: 2021-01-25 00:00:00
Tasks: Epidemiology

Infectious diseases are a threat for human health with tremendous impact on our society at large. The recent COVID-19 pandemic, caused by the SARS-CoV-2, is the latest example of a highly infectious disease ravaging the world, since late 2019. It is therefore imperative to develop efficient mathematical models, able to substantially curb the damages of a pandemic by unveiling disease spreading dynamics and symmetries. This will help inform (non)-pharmaceutical prevention strategies. For the reasons above we wrote this report that goes at the heart of mathematical modelling of infectious disease diffusion by simultaneously investigating the underlying microscopic dynamics in terms of percolation models, effective description via compartmental models and the employment of temporal symmetries naturally encoded in the mathematical language of critical phenomena. Our report reviews these approaches and determines their common denominators, relevant for theoretical epidemiology and its link to important concepts in theoretical physics. We show that the different frameworks exhibit common features such as criticality and self-similarity under time rescaling. These features are naturally encoded within the unifying field theoretical approach. The latter leads to an efficient description of the time evolution of the disease via a framework in which (near) time-dilation invariance is explicitly realised. As important test of the relevance of symmetries we show how to mathematically account for observed phenomena such as multi-wave dynamics. The models presented here are of immediate relevance for different realms of scientific enquiry from medical applications to the understanding of human behaviour. Our review offers novel perspectives on how to model, capture, organise and understand epidemiological data and disease dynamics for modelling real-world phenomena.
Isolating the impact of trading on grid frequency fluctuations
Authors: Benjamin Schäfer, Marc Timme, Dirk Witthaut
Date: 2021-03-24 00:00:00
Tasks: energy trading, Time Series, Time Series Analysis

To ensure reliable operation of power grids, their frequency shall stay within strict bounds. Multiple sources of disturbances cause fluctuations of the grid frequency, ranging from changing demand over volatile feed-in to energy trading. Here, we analyze frequency time series from the continental European grid in 2011 and 2017 as a case study to isolate the impact of trading. We find that trading at typical trading intervals such as full hours modifies the frequency fluctuation statistics. While particularly large frequency deviations in 2017 are not as frequent as in 2011, large deviations are more likely to occur shortly after the trading instances. A comparison between the two years indicates that trading at shorter intervals might be beneficial for frequency quality and grid stability, because particularly large fluctuations are substantially diminished. Furthermore, we observe that the statistics of the frequency fluctuations do not follow Gaussian distributions but are better described using heavy-tailed and asymmetric distributions, for example L\'evy-stable distributions. Comparing intervals without trading to those with trading instances indicates that frequency deviations near the trading times are distributed more widely and thus extreme deviations are orders of magnitude more likely. Finally, we briefly review a stochastic analysis that allows a quantitative description of power grid frequency fluctuations.
A data-driven epidemic model with social structure for understanding the COVID-19 infection on a heavily affected Italian Province
Authors: M. Zanella, C. Bardelli, G. Dimarco, S. Deandrea, P. Perotti, M. Azzi, S. Figini, G. Toscani
Date: 2021-03-10 00:00:00
Tasks: Uncertainty Quantification

In this work, using a detailed dataset furnished by National Health Authorities concerning the Province of Pavia (Lombardy, Italy), we propose to determine the essential features of the ongoing COVID-19 pandemic in term of contact dynamics. Our contribution is devoted to provide a possible planning of the needs of medical infrastructures in the Pavia Province and to suggest different scenarios about the vaccination campaign which possibly help in reducing the fatalities and/or reducing the number of infected in the population. The proposed research combines a new mathematical description of the spread of an infectious diseases which takes into account both age and average daily social contacts with a detailed analysis of the dataset of all traced infected individuals in the Province of Pavia. These information are used to develop a data-driven model in which calibration and feeding of the model are extensively used. The epidemiological evolution is obtained by relying on an approach based on statistical mechanics. This leads to study the evolution over time of a system of probability distributions characterizing the age and social contacts of the population. One of the main outcomes shows that, as expected, the spread of the disease is closely related to the mean number of contacts of individuals. The model permits to forecast thanks to an uncertainty quantification approach and in the short time horizon, the average number and the confidence bands of expected hospitalized classified by age and to test different options for an effective vaccination campaign with age-decreasing priority.
Antipredator behavior in the rock-paper-scissors model
Authors: J. Menezes
Date: 2021-02-28 00:00:00

When faced with an imminent risk of predation, many animals react to escape consumption. Antipredator strategies are performed by individuals acting as a group to intimidate predators and minimize the damage when attacked. We study the antipredator prey response in spatial tritrophic systems with cyclic species dominance using the rock-paper-scissors game. The impact of the antipredator behavior is local, with the predation probability reducing exponentially with the number of preys in the predator's neighborhood. In contrast to the standard Lotka-Volterra implementation of the rock-paper-scissors model, where no spiral waves appear, our outcomes show that the antipredator behavior leads to spiral patterns from random initial conditions. The results show that the predation risk decreases exponentially with the level of antipredator strength. Finally, we investigate the coexistence probability and verify that antipredator behavior may jeopardize biodiversity for high mobility. Our findings may help biologists to understand ecosystems formed by species whose individuals behave strategically to resist predation.
Characterising the Non-Equilibrium Dynamics of a Neural Cell
Authors: Dalton A R Sakthivadivel
Date: 2021-02-18 00:00:00

We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems theory to characterise the nature of the neural resting state, and its relationship to firing. The stereotypical shape of the action potential arises from this model, as well as bursting dynamics, and the non-equilibrium phase transition from resting to spiking. Geometric properties of the system are discussed, such as the birth and shape of the neural limit cycle, which provide a complementary understanding of these dynamics. This provides a multiscale model of the neural cell, from molecules to spikes, and explains various phenomena in a unified manner. Some more general notions for damped oscillators, birth-death processes, and stationary non-equilibrium systems are included.
Identification of Phase-Locked Loop System From Its Experimental Time Series
Authors: Mikhail A. Mishchenko, Denis I. Bolshakov, Alexander S. Vasin, Valery V. Matrosov, Ilya V. Sysoev
Date: 2021-02-17 00:00:00
Tasks: parameter estimation, Time Series, Time Series Analysis

Phase-locked loops (PLLs) are now widely used in communication systems and have been a classic system for more than 60 years. Well-known mathematical models of such systems are constructed in a number of approximations, so questions about how they describe the experimental dynamics qualitatively and quantitatively, and how the accuracy of the model description depends on the behavior mode, remain open. One of the most direct approaches to the verification of any model is its reconstruction from the time series obtained in experiment. If it is possible to fit the model to experimental data and the resulting parameter values are close to the expected values (calculated from the first principles), the quantitative correspondence between the model and the physical object is nearly proved. In this paper, for the first time, the equations of the PLL model with a bandpass filter are reconstructed from the experimental signals of the generator in various modes. The reconstruction showed that the model known in the literature generally describes the experimental dynamics in regular and chaotic regimes. The relative error of parameter estimation is between 2% and 50% for different regimes and parameters. The reconstructed nonlinear function of phase is not harmonic and highly asymmetric in contrary to the model one.
Toward an Effective Theory of Neurodynamics: Topological Supersymmetry Breaking, Network Coarse-Graining, and Instanton Interaction
Authors: Igor V. Ovchinnikov, Skirmantas Janusonis
Date: 2021-02-07 00:00:00
Tasks: STS

Experimental research has shown that the brain's fast electrochemical dynamics, or neurodynamics (ND), is strongly stochastic, chaotic, and instanton (neuroavalanche)-dominated. It is also partly scale-invariant which has been loosely associated with critical phenomena. It has been recently demonstrated that the supersymmetric theory of stochastics (STS) offers a theoretical framework that can explain all of the above ND features. In the STS, all stochastic models possess a topological supersymmetry (TS), and the "criticality" of ND and similar stochastic processes is associated with noise-induced, spontaneous breakdown of this TS (due to instanton condensation near the border with ordinary chaos in which TS is broken by non-integrability). Here, we propose a new approach that may be useful for the construction of low-energy effective theories of ND. Its centerpiece is a coarse-graining procedure of neural networks based on simplicial complexes and the concept of the "enveloping lattice." It represents a neural network as a continuous, high-dimensional base space whose rich topology reflects that of the original network. The reduced one-instanton state space is determined by the de Rham cohomology classes of this base space, and the effective ND dynamics can be recognized as interactions of the instantons in the spirit of the Segal-Atiyah formalism.
Collective dynamics in the presence of finite-width pulses
Authors: Afifurrahman, Ekkehard Ullner, Antonio Politi
Date: 2021-02-05 00:00:00

The idealisation of neuronal pulses as $\delta$-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire neurons with delay and type-I phase-response curves. By exploring the role of the pulse-widths for different coupling strengths we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e. the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for $\delta$-spikes is smoothed out for finite-width pulses.
Mechanistic models of cell-fate transitions from single-cell data
Authors: Gabriel Torregrosa, Jordi Garcia-Ojalvo
Date: 2021-02-05 00:00:00

Our knowledge of how individual cells self-organize to form complex multicellular systems is being revolutionized by a data outburst, coming from high-throughput experimental breakthroughs such as single-cell RNA sequencing and spatially resolved single-molecule FISH. This information is starting to be leveraged by machine learning approaches that are helping us establish a census and timeline of cell types in developing organisms, shedding light on how biochemistry regulates cell-fate decisions. In parallel, imaging tools such as light-sheet microscopy are revealing how cells self-assemble in space and time as the organism forms, thereby elucidating the role of cell mechanics in development. Here we argue that mathematical modeling can bring together these two perspectives, by enabling us to test hypotheses about specific mechanisms, which can be further validated experimentally. We review the recent literature on this subject, focusing on representative examples that use modeling to better understand how single-cell behavior shapes multicellular organisms.
Local homeostatic regulation of the spectral radius of echo-state networks
Authors: Fabian Schubert, Claudius Gros
Date: 2021-01-26 00:00:00

Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius towards the desired value under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols and the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using setpoint homeostatic feedback controls of neural firing.
Best-response dynamics, playing sequences, and convergence to equilibrium in random games
Authors: Torsten Heinrich, Yoojin Jang, Luca Mungo, Marco Pangallo, Alex Scott, Bassel Tarbush, Samuel Wiese
Date: 2021-01-11 00:00:00
Tasks: All

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games.
Microcircuit synchronization and heavy tailed synaptic weight distribution in preBötzinger Complex contribute to generation of breathing rhythm
Authors: Valentin M. Slepukhin, Sufyan Ashhad, Jack L. Feldman, Alex J. Levine
Date: 2020-12-23 00:00:00
Tasks: Decision Making, Rhythm

The preB\"otzinger Complex, the mammalian inspiratory rhythm generator, encodes inspiratory time as motor pattern. Spike synchronization throughout this sparsely connected network generates inspiratory bursts albeit with variable latencies after preinspiratory activity onset in each breathing cycle. Using preB\"otC rhythmogenic microcircuit minimal models, we examined the variability in probability and latency to burst, mimicking experiments. Among various physiologically plausible graphs of 1000 point neurons with experimentally determined neuronal and synaptic parameters, directed Erd\H{o}s-R\'enyi graphs best captured the experimentally observed dynamics. Mechanistically, preB\"otC (de)synchronization and oscillatory dynamics are regulated by the efferent connectivity of spiking neurons that gates the amplification of modest preinspiratory activity through input convergence. Furthermore, to replicate experiments, a lognormal distribution of synaptic weights was necessary to augment the efficacy of convergent coincident inputs. These mechanisms enable exceptionally robust yet flexible preB\"otC attractor dynamics that, we postulate, represent universal temporal-processing and decision-making computational motifs throughout the brain.
Phase-Amplitude Coupling in Neuronal Oscillator Networks
Authors: Yuzhen Qin, Tommaso Menara, Danielle S. Bassett, Fabio Pasqualetti
Date: 2020-12-08 00:00:00

Phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. We propose a model that explains the emergence of PAC in two commonly-accepted architectures in the brain, namely, a high-frequency neural oscillation driven by an external low-frequency input and two interacting local oscillations with distinct, locally-generated frequencies. We further propose an interconnection structure for brain regions and demonstrate that low-frequency phase synchrony can integrate high-frequency activities regulated by local PAC and control the direction of information flow across distant regions.
Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks
Authors: Xize Xu, Hermann Riecke
Date: 2020-12-03 00:00:00
Tasks: Rhythm

The synchronization of different $\gamma$-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of PING (pyramidal-interneuronal network gamma) and ING (interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determined the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC), using numerical simulation of all-to-all coupled networks of integrate-and-fire (IF) neurons exhibiting either PING or ING rhythms. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC. While the phase-response curve for the individual IF-neurons is strictly positive (type I), the fmPRC can be biphasic and exhibit both signs (type II). Thus, for PING rhythms, an external excitation to the excitatory cells can, in fact, delay the collective oscillation of the network, even though the same excitation would lead to an advance when applied to uncoupled neurons. This paradoxical delay arises when the external excitation modifies the internal dynamics of the network by causing additional spikes of inhibitory neurons, whose delaying within-network inhibition outweighs the immediate advance caused by the external excitation. These results explain how intrinsic heterogeneity allows the PING rhythm to become synchronized with a periodic forcing or another PING rhythm for a wider range in the mismatch of their frequencies. We demonstrate a similar mechanism for the synchronization of ING rhythms. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled $\gamma$-rhythms, which may play a role in neural information transfer via communication through coherence.
Tregs self-organize into a "computing ecosystem" and implement a sophisticated optimization algorithm for mediating immune response
Authors: Robert Marsland III, Owen Howell, Andreas Mayer, Pankaj Mehta
Date: 2020-12-01 00:00:00
Tasks: Diversity

Regulatory T cells (Tregs) play a crucial role in mediating immune response. Yet an algorithmic understanding of the role of Tregs in adaptive immunity remains lacking. Here, we present a biophysically realistic model of Treg mediated self-tolerance in which Tregs bind to self-antigens and locally inhibit the proliferation of nearby activated T cells. By exploiting a duality between ecological dynamics and constrained optimization, we show that Tregs tile the potential antigen space while simultaneously minimizing the overlap between Treg activation profiles. We find that for sufficiently high Treg diversity, Treg mediated self-tolerance is robust to fluctuations in self-antigen concentrations but lowering the Treg diversity results in a sharp transition -- related to the Gardner transition in perceptrons -- to a regime where changes in self-antigen concentrations can result in an auto-immune response. We propose a novel experimental test of this transition in immune-deficient mice and discuss potential implications for autoimmune diseases.