arXiv subjects

Lubomir Kostal

Publications and source records attributed to Lubomir Kostal.

6 recordsLinked to original sources

arXiv2026

Modular memristor model with synaptic-like plasticity and volatile memory

Compact models of memristors are essential for simulating large-scale neuromorphic systems, yet they often do not include description of complex dynamics like volatile relaxation and synaptic plasticity. We introduce a modular, computationally efficient memristor model that bridges this gap by integrating principles from physics and computational neuroscience. The model defines a framework consisting of a standard formulation of memristive device dynamics, a functional rule mapping state variables to cumulative conductance, a volatility module inspired by the theory of linear viscoelasticity and a saturation module implementing a linear-nonlinear technique. Additionally, we develop a formulation of synaptic-like plasticity inspired by a biological spike-timing-dependent plasticity (STDP) rule, which is compatible with the general framework for memristive devices. Finally, we propose a Laplace transform-based technique to derive the precise form of the mapping from state variables to cumulative conductance, replacing ad hoc voltage-current relationships with principled construction. We quantitatively validate the complete model against a rich set of experimental data from polymeric memristors exhibiting potentiation, synaptic-like plasticity and volatile decay. Our work presents a new paradigm for memristor modeling that is both practical for large-scale simulation and rich in explanatory power, providing a principled tool for the design of next-generation neuromorphic hardware.

physics.app-ph↗

arXiv2025

Polymer-based probabilistic bits for thermodynamic computing

Probabilistic bits (p-bits) are stochastic hardware elements whose output probability can be tuned by an input bias, offering a route to energy-efficient architectures that exploit, rather than suppress, fluctuations. Here we report p-bit generation in an organic memristive device, establishing polymers as the first class of soft-matter systems to realize probabilistic hardware. The active element is a dithieno[3,2-b:2',3'-d]pyrrole (DTP)-backbone polymer with pendant triphenylamine (TPA) groups, whose stochastic resistance fluctuations are converted into binary outputs by a simple voltage-divider/comparator circuit. The resulting probability distributions follow logistic transfer functions, characteristic of stochastic binary neurons. Separately, ensembles of pulsed IV measurements were analyzed to construct binned current distributions, from which the discrete Shannon entropy was calculated. Peaks in this entropy coincide with bias conditions that maximize variability in the memristor voltage drop, directly linking device-level stochasticity to intrinsic material properties. Dielectric analysis shows that pendant TPA units provide dynamically active relaxation modes, while energy-resolved electrochemical impedance spectroscopy and density functional theory calculations indicate that the frontier orbitals of DTP, TPA and ITO align within the transport gap to produce a bifurcated percolation network. The correspondence between microscopic relaxation dynamics, electronic energetics and macroscopic probabilistic response highlights how organic semiconductors can serve as chemically tunable entropy sources, opening a polymer-based pathway toward thermodynamic computing.

cond-mat.soft↗

arXiv2021

Regular spiking in high conductance states: the essential role of inhibition

Strong inhibitory input to neurons, which occurs in balanced states of neural networks, increases synaptic current fluctuations. This has led to the assumption that inhibition contributes to the high spike-firing irregularity observed in vivo. We used single compartment neuronal models with time-correlated (due to synaptic filtering) and state-dependent (due to reversal potentials) input to demonstrate that inhibitory input acts to decrease membrane potential fluctuations, a result that cannot be achieved with simplified neural input models. To clarify the effects on spike-firing regularity, we used models with different spike-firing adaptation mechanisms and observed that the addition of inhibition increased firing regularity in models with dynamic firing thresholds and decreased firing regularity if spike-firing adaptation was implemented through ionic currents or not at all. This novel fluctuation-stabilization mechanism provides a new perspective on the importance of strong inhibitory inputs observed in balanced states of neural networks and highlights the key roles of biologically plausible inputs and specific adaptation mechanisms in neuronal modeling.

q-bio.NC↗

arXiv2020

An Optimal Gauss-Markov Approximation for a Process with Stochastic Drift and Applications

We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein-Uhlenbeck type process, by using direct methods of calculus of variations. We show that general power cost functionals satisfy the conditions for existence and uniqueness of the approximation. We provide some examples of general interest and we give bounds on the goodness of the corresponding approximations. Finally, we focus on a model of a neuron embedded in a simple network and we study the approximation of its activity, by exploiting the aforementioned results.

math.PR↗

arXiv2010

Information transfer with small-amplitude signals

We study the optimality conditions of information transfer in systems with memory in the low signal-to-noise ratio regime of vanishing input amplitude. We find that the optimal mutual information is represented by a maximum-variance of the signal time course, with correlation structure determined by the Fisher information matrix. We provide illustration of the method on a simple biologically-inspired model of electro-sensory neuron. Our general results apply also to the study of information transfer in single neurons subject to weak stimulation, with implications to the problem of coding efficiency in biological systems.

q-bio.NC↗

arXiv2010

Information capacity in the weak-signal approximation

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.

cs.IT↗