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Boris Gutkin

Publications and source records attributed to Boris Gutkin.

At least 19 recordsLinked to original sources
arXiv2026

Local correlations in long-range dual-unitary kicked Hamiltonian chains

Many-body Floquet models with exact space--time symmetry, such as the kicked Ising spin chain (KIC), provide natural examples of systems with dual-unitary dynamics. The requirement of exact space--time symmetry is, however, highly restrictive, as it permits only nearest-neighbor interactions. Based on a pair of Hadamard matrices, we construct a wide family of dual-unitary kicked spin chains with long-range interactions. We show that local two-point correlations in such models propagate along the light-cone edges \( |n| = r|t| \), where \(r\) is the interaction range, and can be derived analytically for operators with local support. This approach is illustrated using the example of a kicked Ising spin chain with next-to-next-neighbor interactions.

quant-ph↗
arXiv2026

Chern numbers in quantum graphs

Quantum graphs provide an analytically tractable setting for the study of Chern numbers and band degeneracies in periodic systems. We study the Chern numbers of energy bands in a two-dimensional square lattice quantum graph. We approach the problem by mapping the lattice to a single-vertex quantum graph with two loops of equal lengths pierced by magnetic fluxes. By establishing the degeneracy condition for its energy levels, we show that the model possesses two topological phases: a trivial phase, where the Chern numbers of all energy bands are $0$, and the nontrivial one, where the Chern numbers of successive energy bands alternate between $\pm1$. By applying the degeneracy condition, we calculate Chern-number phase diagrams analytically as a function of the node scattering matrix parameters and compare the results with numerical calculations.

math-ph↗
arXiv2026

The role of classical periodic orbits in quantum many-body systems

Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an extension to $\textit{many}$-body systems result from the exponential proliferation of the number of classical orbits in chaotic systems and the exponential growth of the quantum Hilbert-space dimension with the particle number. To circumvent these problems, we apply here our recently developed duality relation. Considering the kicked spin chain as example for a many-body system, we show how the duality relation can be used to extract the classical orbits from the quantum spectrum. For coupled cat maps, we analyze the spectral statistics of chaotic many-body systems and discuss the double limit of large semiclassical parameter and large particle number.

quant-ph↗
arXiv2025

Linking Homeostasis to Reinforcement Learning: Internal State Control of Motivated Behavior

For living beings, survival depends on effective regulation of internal physiological states through motivated behaviors. In this perspective we propose that Homeostatically Regulated Reinforcement Learning (HRRL) as a framework to describe biological agents that optimize internal states via learned predictive control strategies, integrating biological principles with computational learning. We show that HRRL inherently produces multiple behaviors such as risk aversion, anticipatory regulation, and adaptive movement, aligning with observed biological phenomena. Its extension to deep reinforcement learning enables autonomous exploration, hierarchical behavior, and potential real-world robotic applications. We argue further that HRRL offers a biologically plausible foundation for understanding motivation, learning, and decision-making, with broad implications for artificial intelligence, neuroscience, and understanding the causes of psychiatric disorders, ultimately advancing our understanding of adaptive behavior in complex environments.

q-bio.NC↗
arXiv2025

Metric Framework of Coherent Activity Patterns Identification in Spiking Neuronal Networks

Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure of coherent activity patterns reflects the network's current state, developing automated tools to identify them is a key challenge in neurodynamics. Existing methods for analyzing neuronal dynamics tend to focus on global characteristics of the network, such as its aggregated synchrony level. While this approach can distinguish between the network's main dynamical states, it cannot reveal the localization or properties of distinct coherent patterns. In this work, we propose a new perspective on neural dynamics analysis that enables the study of network coherence at the single-neuron scale. We interpret the network as a metric space of neurons and represent its instantaneous state as an activity function on that space. We identify specific coherent activity clusters as regions where the activity function exhibits spatial continuity. Each cluster's activity is further characterized using the analytical properties of the activity function within that region. This approach yields a concise yet detailed algorithmic profile of the network's activity patterns.

q-bio.NC↗
arXiv2025

Neuro-oscillatory models of cortical speech processing

In this review, we examine computational models that explore the role of neural oscillations in speech perception, spanning from early auditory processing to higher cognitive stages. We focus on models that use rhythmic brain activities, such as gamma, theta, and delta oscillations, to encode phonemes, segment speech into syllables and words, and integrate linguistic elements to infer meaning. We analyze the mechanisms underlying these models, their biological plausibility, and their potential applications in processing and understanding speech in real time, a computational feature that is achieved by the human brain but not yet implemented in speech recognition models. Real-time processing enables dynamic adaptation to incoming speech, allowing systems to handle the rapid and continuous flow of auditory information required for effective communication, interactive applications, and accurate speech recognition in a variety of real-world settings. While significant progress has been made in modeling the neural basis of speech perception, challenges remain, particularly in accounting for the complexity of semantic processing and the integration of contextual influences. Moreover, the high computational demands of biologically realistic models pose practical difficulties for their implementation and analysis. Despite these limitations, these models provide valuable insights into the neural mechanisms of speech perception. We conclude by identifying current limitations, proposing future research directions, and suggesting how these models can be further developed to achieve a more comprehensive understanding of speech processing in the human brain.

q-bio.NC↗
arXiv2024

The role of gap junctions and clustered connectivity in emergent synchronisation patterns of inhibitory neuronal networks

Inhibitory interneurons, ubiquitous in the central nervous system, form networks connected through both chemical synapses and gap junctions. These networks are essential for regulating the activity of principal neurons, especially by inducing temporally patterned dynamic states. We aim to understand the dynamic mechanisms for synchronisation in networks of electrically and chemically coupled interneurons. We use the exact mean-field reduction to derive a neural mass model for both homogeneous and clustered networks. We first analyse a single population of neurons to understand how the two couplings interact with one another. We demonstrate that the network transitions from an asynchronous to a synchronous regime either by increasing the strength of the gap junction connectivity or the strength of the background input current. Conversely, the strength of inhibitory synapses affects the population firing rate, suggesting that electrical and chemical coupling strengths act as complementary mechanisms by which networks can tune synchronous oscillatory behavior. In line with previous work, we confirm that the depolarizing spikelet is crucial for the emergence of synchrony. Furthermore, find that the fast frequency component of the spikelet ensures robustness to heterogeneity. Next, inspired by the existence of multiple interconnected interneuron subtypes in the cerebellum, we analyse networks consisting of two clusters of cell types defined by differing chemical versus electrical coupling strengths. We show that breaking the electrical and chemical coupling symmetry between these clusters induces bistability, so that a transient external input can switch the network between synchronous and asynchronous firing. Together, our results shows the variety of cell-intrinsic and network properties that contribute to synchronisation of interneuronal networks with multiple types of coupling.

q-bio.NC↗
arXiv2024

Modelling crypto markets by multi-agent reinforcement learning

Building on a previous foundation work (Lussange et al. 2020), this study introduces a multi-agent reinforcement learning (MARL) model simulating crypto markets, which is calibrated to the Binance's daily closing prices of $153$ cryptocurrencies that were continuously traded between 2018 and 2022. Unlike previous agent-based models (ABM) or multi-agent systems (MAS) which relied on zero-intelligence agents or single autonomous agent methodologies, our approach relies on endowing agents with reinforcement learning (RL) techniques in order to model crypto markets. This integration is designed to emulate, with a bottom-up approach to complexity inference, both individual and collective agents, ensuring robustness in the recent volatile conditions of such markets and during the COVID-19 era. A key feature of our model also lies in the fact that its autonomous agents perform asset price valuation based on two sources of information: the market prices themselves, and the approximation of the crypto assets fundamental values beyond what those market prices are. Our MAS calibration against real market data allows for an accurate emulation of crypto markets microstructure and probing key market behaviors, in both the bearish and bullish regimes of that particular time period.

q-fin.CP↗
arXiv2024

Continuous Time Continuous Space Homeostatic Reinforcement Learning (CTCS-HRRL) : Towards Biological Self-Autonomous Agent

Homeostasis is a biological process by which living beings maintain their internal balance. Previous research suggests that homeostasis is a learned behaviour. Recently introduced Homeostatic Regulated Reinforcement Learning (HRRL) framework attempts to explain this learned homeostatic behavior by linking Drive Reduction Theory and Reinforcement Learning. This linkage has been proven in the discrete time-space, but not in the continuous time-space. In this work, we advance the HRRL framework to a continuous time-space environment and validate the CTCS-HRRL (Continuous Time Continuous Space HRRL) framework. We achieve this by designing a model that mimics the homeostatic mechanisms in a real-world biological agent. This model uses the Hamilton-Jacobian Bellman Equation, and function approximation based on neural networks and Reinforcement Learning. Through a simulation-based experiment we demonstrate the efficacy of this model and uncover the evidence linked to the agent's ability to dynamically choose policies that favor homeostasis in a continuously changing internal-state milieu. Results of our experiments demonstrate that agent learns homeostatic behaviour in a CTCS environment, making CTCS-HRRL a promising framework for modellng animal dynamics and decision-making.

cs.AI↗
arXiv2023

Local correlations in partially dual-unitary lattice models

We consider the problem of local correlations in the kicked, dual-unitary coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully dual-unitary systems exhibit ultra-local correlations: the correlations between any pair of operators with local support vanish in a finite number of time steps. In addition, for $D=2$, we consider the partially dual-unitary regime of the model, where the dual-unitarity applies to only one of the two spatial directions. For this case, we show that correlations generically decay exponentially and provide an explicit formula for the correlation function between the operators supported on two and four neighbouring sites.

cond-mat.stat-mech↗
arXiv2023

Dynamical manifold dimensionality as characterization measure of chimera states in bursting neuronal networks

Methods that distinguish dynamical regimes in networks of active elements make it possible to design the dynamics of models of realistic networks. A particularly salient example is partial synchronization, which may play a pivotal role in elucidating the dynamics of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly denoted as chimera states. While several methods for detecting chimeras in networks of spiking neurons have been proposed, these are less effective when applied to networks of bursting neurons. Here we introduce the correlation dimension as a novel approach to identifying dynamic network states. To assess the viability of this new method, we study a network of intrinsically Hindmarsh-Rose neurons with non-local connections. In comparison to other measures of chimera states, the correlation dimension effectively characterizes chimeras in burst neurons, whether the incoherence arises in spikes or bursts. The generality of dimensionality measures inherent in the correlation dimension renders this approach applicable to any dynamic system, facilitating the comparison of simulated and experimental data. We anticipate that this methodology will enable the tuning and simulation of when modelling intricate network processes, contributing to a deeper understanding of neural dynamics.

nlin.AO↗
arXiv2023

A new generation of reduction methods for networks of neurons with complex dynamic phenotypes

Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking networks have been developed. However, most of these efforts have been limited to networks of neurons with simple dynamics (e.g. the quadratic integrate and fire models). Here, we present an extension of ER to conductance-based networks of two-dimensional Izhikevich neuron models. We employ an adiabatic approximation, which allows us to analytically solve the continuity equation describing the evolution of the state of the neural population and thus to reduce model dimensionality. We validate our results by showing that the reduced mean-field description we derived can qualitatively and quantitatively describe the macroscopic behaviour of populations of two-dimensional QIF neurons with different electrophysiological profiles (regular firing, adapting, resonator and type III excitable). Most notably, we apply this technique to develop an ER for networks of neurons with bursting dynamics.

q-bio.NC↗
arXiv2023

A Universal Description of Stochastic Oscillators

Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here we introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function $Q^*_1(\textbf{x})$ that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function $Q^*_1(\textbf{x})$ is the eigenfunction of the Kolmogorov backward operator with the least negative (but non-vanishing) eigenvalue $λ_1=μ_1+iω_1$. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency $ω_1$ and half-width $μ_1$; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around $ω_1$; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

nlin.AO↗
arXiv2023

Order book regulatory impact on stock market quality: a multi-agent reinforcement learning perspective

Recent technological developments have changed the fundamental ways stock markets function, bringing regulatory instances to assess the benefits of these developments. In parallel, the ongoing machine learning revolution and its multiple applications to trading can now be used to design a next generation of financial models, and thereby explore the systemic complexity of financial stock markets in new ways. We here follow on a previous groundwork, where we designed and calibrated a novel agent-based model stock market simulator, where each agent autonomously learns to trade by reinforcement learning. In this Paper, we now study the predictions of this model from a regulator's perspective. In particular, we focus on how the market quality is impacted by smaller order book tick sizes, increasingly larger metaorders, and higher trading frequencies, respectively. Under our model assumptions, we find that the market quality benefits from the latter, but not from the other two trends.

q-fin.TR↗
arXiv2023

Spikebench: An open benchmark for spike train time-series classification

Modern well-performing approaches to neural decoding are based on machine learning models such as decision tree ensembles and deep neural networks. The wide range of algorithms that can be utilized to learn from neural spike trains, which are essentially time-series data, results in the need for diverse and challenging benchmarks for neural decoding, similar to the ones in the fields of computer vision and natural language processing. In this work, we propose a spike train classification benchmark, based on open-access neural activity datasets and consisting of several learning tasks such as stimulus type classification, animal's behavioral state prediction, and neuron type identification. We demonstrate that an approach based on hand-crafted time-series feature engineering establishes a strong baseline performing on par with state-of-the-art deep learning-based models for neural decoding. We release the code allowing to reproduce the reported results.

q-bio.NC↗
arXiv2021

Activity stabilization in a population model of working memory by sinusoidal and noisy inputs

According to mechanistic theories of working memory (WM), information is retained as persistent spiking activity of cortical neural networks. Yet, how this activity is related to changes in the oscillatory profile observed during WM tasks remains an open issue. We explore joint effects of input gamma-band oscillations and noise on the dynamics of several firing rate models of WM. The considered models have a metastable active regime, i.e. they demonstrate long-lasting transient post-stimulus firing rate elevation. We start from a single excitatory-inhibitory circuit and demonstrate that either gamma-band or noise input could stabilize the active regime, thus supporting WM retention. We then consider a system of two circuits with excitatory intercoupling. We find that fast coupling allows for better stabilization by common noise compared to independent noise and stronger amplification of this effect by in-phase gamma inputs compared to anti-phase inputs. Finally, we consider a multi-circuit system comprised of two clusters, each containing a group of circuits receiving a common noise input and a group of circuits receiving independent noise. Each cluster is associated with its own local gamma generator, so all its circuits receive gamma-band input in the same phase. We find that gamma-band input differentially stabilizes the activity of the "common-noise" groups compared to the "independent-noise" groups. If the inter-cluster connections are fast, this effect is more pronounced when the gamma-band input is delivered to the clusters in the same phase rather than in the anti-phase. Assuming that the common noise comes from a large-scale distributed WM representation, our results demonstrate that local gamma oscillations can stabilize the activity of the corresponding parts of this representation, with stronger effect for fast long-range connections and synchronized gamma oscillations.

q-bio.NC↗
arXiv2021

Robust universal approach to identify travelling chimeras and synchronized clusters in spiking networks

We propose a robust universal approach to identify multiple dynamical states, including stationary and travelling chimera states based on an adaptive coherence measure. Our approach allows automatic disambiguation of synchronized clusters, travelling waves, chimera states, and asynchronous regimes. In addition, our method can determine the number of clusters in the case of cluster synchronization. We further couple our approach with a new speed calculation method for travelling chimeras. We validate our approach by an example of a ring network of type II Morris-Lecar neurons with asymmetrical nonlocal inhibitory connections where we identify a rich repertoire of coherent and wave states. We propose that the method is robust for the networks of phase oscillators and extends to a general class of relaxation oscillator networks.

nlin.AO↗
arXiv2021

Adjoint Method for Macroscopic Phase-Resetting Curves of Generic Spiking Neural Networks

Brain rhythms emerge as a result of synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferring the macroscopic PRC and developing a systematic phase reduction theory for emerging rhythms remains an outstanding theoretical challenge. Here we present a practical theoretical framework to compute the PRC of generic spiking networks with emergent collective oscillations. To do so, we adopt a refractory density approach where neurons are described by the time since their last action potential. In the thermodynamic limit, the network dynamics are captured by a continuity equation known as the refractory density equation. We develop an appropriate adjoint method for this equation which in turn gives a semi-analytical expression of the infinitesimal PRC. We confirm the validity of our framework for specific examples of neural networks. Our theoretical findings highlight the relationship between key biological properties at the individual neuron scale and the macroscopic oscillatory properties assessed by the PRC.

q-bio.NC↗