arXiv subjects

Ihor Lubashevsky

Publications and source records attributed to Ihor Lubashevsky.

At least 19 recordsLinked to original sources

arXiv2026

A Non-Hermitian Potential Well Formalism for Conscious--Preconscious--Subliminal Processing

We propose a phenomenological model of the Global Neuronal Workspace (GNW) in which early sensory processing generates an effective complex-valued landscape governing the dynamics of high-level stimulus representations. This landscape provides a dynamical bridge between sensory encoding and conscious access, enabling both processes to be described within a unified framework. High-level representations are encoded in a cloud function defined on a Hilbert space over a perceptual state space, thereby combining the holistic structure of mental images with a neural implementation. Its dynamics is governed by a nonlinear Schrödinger-type equation in imaginary time with a non-Hermitian, non-normal Hamiltonian and a nonlinear Lotka--Volterra-type term that preserves norm and enables spatially nonlocal interactions. The Hermitian and anti-Hermitian parts of the Hamiltonian generate complementary processes: recognition via dissipative localization at minima of the GNW landscape and information broadcasting via spatial spreading across the state space. The resulting dynamics reproduces the subliminal--preconscious--conscious hierarchy of sensory processing. Conscious access corresponds to the emergence of a bound state, which occurs only when both the GNW landscape depth and the degree of top-down attention exceed threshold values. The resulting framework provides a tractable dynamical description linking sensory processing, attention, and conscious access within a unified dynamical setting.

q-bio.NC↗

arXiv2026

A Quantum-Analogue Formalism for Modeling Supraliminal Information Processing

We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment from the first-person perspective. The cloud function is characterized by two key features: (i) its spatial structure inherits properties of the perceived physical object, and (ii) its temporal evolution is governed by regularities reflecting intrinsic properties of large-scale neural activity. The governing equation for the cloud function is based on a neural-field model with polynomial nonlinearities and global phase-shift invariance of neural-pattern oscillations. Its structure may be interpreted as a Schrodinger-type equation with a nonlinear non-Hermitian Hamiltonian supplemented by terms analogous to those of the Lotka-Volterra model. The proposed approach is applied to the change-of-mind phenomenon in decision-making, in which an initial choice may be revised during its execution. Changes of mind are explained as arising from the interplay between fast preconscious sensory processing and slower conscious comparison of alternatives, consistent with neurophysiological evidence for continuous post-decisional evidence accumulation. The necessity of incorporating cloud-function self-interaction is also discussed.

q-bio.NC↗

arXiv2025

Oscillator Chain Model for Multi-Contour Systems With Priority in Conflict Resolution

We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring oscillators when their phases lie within defined interaction sectors. The size of the interaction sector can be seen as a measure of vehicle density within clusters moving along contours. The model assumes that oscillators can synchronize their dynamics, using concepts inherited from the Kuramoto model, which effectively accounts for the discrete state effects observed in Buslaev nets. The governing equation for oscillator dynamics incorporates four key factors: deceleration caused by conflicts with neighboring oscillators and the synchronization process, which induces additional acceleration or deceleration. Numerical analysis shows that the system exhibits both familiar properties from classic Buslaev nets, such as metastable synchronization, and novel behaviors, including phase transitions as the interaction sector size changes.

nlin.AO↗

arXiv2025

Stochastic Description of Dynamical Traps in Human Control

A novel model for dynamical traps in intermittent human control is proposed. It describes probabilistic, step-wise transitions between two modes of a subject's behavior - active and passive phases in controlling an object's dynamics - using an original stochastic differential equation. This equation governs time variations of a special variable, denoted as $ζ$, between two limit values, $ζ=0$ and $ζ=1$. The introduced trap function, $Ω(Δ)$, quantifies the subject's perception of the object's deviation from a desired state, thereby determining the relative priority of the two action modes. Notably, these transitions - referred to as the subject's action points - occur before the trap function reaches its limit values, $Ω(Δ)=0$ or $Ω(Δ)=1$. This characteristic enables the application of the proposed model to describe intermittent human control over real objects.

nlin.AO↗

arXiv2019

Phase Transitions in Binary Categorization: Evidence for Dual-System Decision Making

We report experiment results on binary categorization of (i) gray color, (ii) speech sounds, and (iii) number discrimination. Data analysis is based on constructing psychometric functions and focusing on asymptotics. We discuss the transitions between two types of subjects' response to stimuli presented for two-category classification, e.g., visualized shade of gray into "light-gray" or "dark-gray." Response types are (i) the conscious choice of non-dominant category, described by the deep tails of psychometric function, and (ii) subjects' physical errors in recording decisions in cases where the category choice is obvious. Explanation of results is based on the concept of dual-system decision making. When the choice is obvious, System 1 (fast and automatic) determines subjects' actions, with higher probability of physical errors than when subjects' decision-making is based on slow, deliberate analysis (System 2). Results provide possible evidence for hotly debated dual-system theories of cognitive phenomena.

physics.med-ph↗

arXiv2018

Complexity of human response delay in intermittent control: The case of virtual stick balancing

Response delay is an inherent and essential part of human actions. In the context of human balance control, the response delay is traditionally modeled using the formalism of delay-differential equations, which adopts the approximation of fixed delay. However, experimental studies revealing substantial variability, adaptive anticipation, and non-stationary dynamics of response delay provide evidence against this approximation. In this paper, we call for development of principally new mathematical formalism describing human response delay. To support this, we present the experimental data from a simple virtual stick balancing task. Our results demonstrate that human response delay is a widely distributed random variable with complex properties, which can exhibit oscillatory and adaptive dynamics characterized by long-range correlations. Given this, we argue that the fixed-delay approximation ignores essential properties of human response, and conclude with possible directions for future developments of new mathematical notions describing human control.

q-bio.NC↗

arXiv2018

Psychophysical laws as reflection of mental space properties

The paper is devoted to the relationship between psychophysics and physics of mind. The basic trends in psychophysics development are briefly discussed with special attention focused on Teghtsoonian's hypotheses. These hypotheses pose the concept of the universality of inner psychophysics and enable to speak about psychological space as an individual object with its own properties. Turning to the two-component description of human behavior (I. Lubashevsky, Physics of the Human Mind, Springer, 2017) the notion of mental space is formulated and human perception of external stimuli is treated as the emergence of the corresponding images in the mental space. On one hand, these images are caused by external stimuli and their magnitude bears the information about the intensity of the corresponding stimuli. On the other hand, the individual structure of such images as well as their subsistence after emergence is determined only by the properties of mental space on its own. Finally, the mental operations of image comparison and their scaling are defined in a way allowing for the bounded capacity of human cognition. As demonstrated, the developed theory of stimulus perception is able to explain the basic regularities of psychophysics, e.g., (i) the regression and range effects leading to the overestimation of weak stimuli and the underestimation of strong stimuli, (ii) scalar variability (Weber's and Ekman' laws), and (\textit{iii}) the sequential (memory) effects. As the final result, a solution to the Fechner-Stevens dilemma is proposed. This solution posits that Fechner's logarithmic law is not a consequences of Weber's law but stems from the interplay of uncertainty in evaluating stimulus intensities and the multi-step scaling required to overcome the stimulus incommensurability.

q-bio.NC↗

arXiv2016

Intermittent Control Properties of Car Following: Theory and Driving Simulator Experiments

A rather simple car driving simulator was created based on the available open source engine TORCS and used to analyze the basic features of human behavior in car driving within the car-following setups. Eight subjects with different skill in driving real cars participated in these experiments. They were instructed to drive a virtual car without overtaking the lead car driven by computer at a fixed speed and not to lose sight of it. Moreover, these experiments were conducted with four different speed including 60km/h, 80km/h, 100km/h, and 120km/h. Based on the collected data the distribution of the headway, velocity, acceleration, and jerk are constructed and compared with available experimental data collected previously by the analysis of the real traffic flow. A new model for car-following is proposed capture the found properties. As the main results we draw a conclusion that the human behavior in car driving should be categorized as a generalized intermittent control with noise-driven activation of the active phase. Besides, we hypothesize that the extended phase space required for modeling human actions in car driving has to comprise four phase variables, namely, the headway distance, the velocity of car, its acceleration, and the car jerk, i.e., the time derivative of the car acceleration. This time, the time pattern of pedal pushing and the distribution of time derivative of pedal was utilized in addition to previous variables. Moreover, all subjects' driving data were categorized as some styles with their shapes.

physics.soc-ph↗

arXiv2016

Noise-induced phase transition in the model of human virtual stick balancing

Humans face the task of balancing dynamic systems near an unstable equilibrium repeatedly throughout their lives. Much research has been aimed at understanding the mechanisms of intermittent control in the context of human balance control. The present paper deals with one of the recent developments in the theory of human intermittent control, namely, the double-well model of noise-driven control activation. We demonstrate that the double-well model can reproduce the whole range of experimentally observed distributions under different conditions. Moreover, we show that a slight change in the noise intensity parameter leads to a sudden shift of the action point distribution shape, that is, a phase transition is observed.

q-bio.NC↗

arXiv2016

Thick Presentism and Newtonian Mechanics

In the present paper I argue that the formalism of Newtonian mechanics stems directly from the general principle to be called the principle of microlevel reducibility which physical systems obey in the realm of classical physics. This principle assumes, first, that all the properties of physical systems must be determined by their states at the current moment of time, in a slogan form it is "only the present matters to physics." Second, it postulates that any physical system is nothing but an ensemble of structureless particles arranged in some whose interaction obeys the superposition principle. I substantiate this statement and demonstrate directly how the formalism of differential equations, the notion of forces in Newtonian mechanics, the concept of phase space and initial conditions, the principle of least actions, etc. result from the principle of microlevel reducibility. The philosophical concept of thick presentism and the introduction of two dimensional time---physical time and meta-time that are mutually independent on infinitesimal scales---are the the pivot points in these constructions.

physics.hist-ph↗

arXiv2015

Statistical Properties of Car Following: Theory and Driving Simulator Experiments

A fair simple car driving simulator was created based on the open source engine TORCS and used in car-following experiments aimed at studying the basic features of human behavior in car driving. Four subjects with different skill in driving real cars participated in these experiments. The subjects were instructed to drive a car without overtaking and losing sight of a lead car driven by computer at a fixed speed. Based on the collected data the distributions of the headway distance, the car velocity, acceleration, and jerk are constructed and compared with the available experimental data for the real traffic flow. A new model for the car-following is proposed to capture the found properties. As the main result, we draw a conclusion that human actions in car driving should be categorized as generalized intermittent control with noise-driven activation. Besides, we hypothesize that the car jerk together with the car acceleration are additional phase variables required for describing the dynamics of car motion governed by human drivers.

nlin.AO↗

arXiv2015

Statistical Properties of Gray Color Categorization: Asymptotics of Psychometric Function

The results of our experiments on categorical perception of different shades of gray are reported. A special color generator was created for conducting the experiments on categorizing a random sequence of colors into two classes, light-gray and dark-gray. The collected data are analyzed based on constructing (i) the asymptotics of the corresponding psychometric functions and (ii) the mean decision time in categorizing a given shade of gray depending on the shade brightness (shade number). Conclusions about plausible mechanisms governing categorical perception, at least for the analyzed system, are drawn.

q-bio.NC↗

arXiv2015

Bistable dynamics of control activation in human intermittent control

When facing a task of balancing a dynamic system near an unstable equilibrium, humans often adopt intermittent control strategy: instead of continuously controlling the system, they repeatedly switch the control on and off. Paradigmatic example of such a task is stick balancing. Despite the simplicity of the task itself, the complexity of human intermittent control dynamics in stick balancing still puzzles researchers in motor control. Here we attempt to model one of the key mechanisms of human intermittent control, control activation, using as an example the task of overdamped stick balancing. In so doing, we focus on the concept of noise-driven activation, a more general alternative to the conventional threshold-driven activation. We describe control activation as a random walk in an energy potential, which changes in response to the state of the controlled system. By way of numerical simulations, we show that the developed model captures the core properties of human control activation observed previously in the experiments on overdamped stick balancing. Our results demonstrate that the double-well potential model provides tractable mathematical description of human control activation at least in the considered task, and suggest that the adopted approach can potentially aid in understanding human intermittent control in more complex processes.

physics.bio-ph↗

arXiv2014

To react or not to react? Intrinsic stochasticity of human control in virtual stick balancing

Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidence appears in favor of event-driven control hypothesis: human operators only start actively controlling the system when the discrepancy between the current and desired system states becomes large enough. The event-driven models based on the concept of threshold can explain many features of the experimentally observed dynamics. However, much still remains unclear about the dynamics of human-controlled systems, which likely indicates that humans employ more intricate control mechanisms. The present paper argues that control activation in humans may be not threshold-driven, but instead intrinsically stochastic, noise-driven. Specifically, we suggest that control activation stems from stochastic interplay between the operator's need to keep the controlled system near the goal state on one hand and the tendency to postpone interrupting the system dynamics on the other hand. We propose a model capturing this interplay and show that it matches the experimental data on human balancing of virtual overdamped stick. Our results illuminate that the noise-driven activation mechanism plays a crucial role at least in the considered task, and, hypothetically, in a broad range of human-controlled processes.

physics.bio-ph↗

arXiv2014

Unstable Dynamics of Adaptation in Unknown Environment due to Novelty Seeking

Learning and adaptation play great role in emergent socio-economic phenomena. Complex dynamics has been previously found in the systems of multiple learning agents interacting via a simple game. Meanwhile, the single agent adaptation is considered trivially stable. We advocate the idea that adopting a more complex model of the individual behavior may result in a more diverse spectrum of macro-level behaviors. We develop an adaptation model based on the reinforcement learning framework extended by an additional processing channel. We scrutiny the dynamics of the single agent adapting to the unknown environment; the agent is biased by novelty seeking, the intrinsic inclination for exploration. We demonstrate that the behavior of the novelty-seeking agent may be inherently unstable. One of the surprising results is that under certain conditions the increase of the novelty-seeking level may cause the agent to switch from the non-rational to the strictly rational behavior. Our results give evidence to the hypothesis that the intrinsic motives of agents should be paid no less attention than the extrinsic ones in the models of complex socio-economic systems.

physics.soc-ph↗

arXiv2014

Extended phase space description of human-controlled systems dynamics

Humans are often incapable of precisely identifying and implementing the desired control strategy in controlling unstable dynamical systems. That is, the operator of a dynamical system treats the current control effort as acceptable even if it deviates slightly from the desired value, and starts correcting the actions only when the deviation has become evident. We argue that the standard Newtonian approach does not allow to model such behavior. Instead, the physical phase space of a controlled system should be extended with an independent phase variable characterizing the operator motivated actions. The proposed approach is illustrated via a simple non-Newtonian model capturing the operators fuzzy perception of their own actions. The properties of the model are investigated analytically and numerically; the results confirm that the extended phase space may aid in capturing the intricate dynamical properties of human-controlled systems.

nlin.AO↗

arXiv2014

Fractional Dynamics and Multi-Slide Model of Human Memory

We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of new memory traces caused by learning a certain fragment of information pattern and affected by the fragments of this pattern already retained by the current moment of time. Using the available psychological and physiological data these constructions are justified. The final equation governing the learning and forgetting processes is constructed in the form of the differential equation with the Caputo type fractional time derivative. Several characteristic situations of the learning (continuous and discontinuous) and forgetting processes are studied numerically. In particular, it is demonstrated that, first, the "learning" and "forgetting" exponents of the corresponding power laws of the memory fractional dynamics should be regarded as independent system parameters. Second, as far as the spacing effects are concerned, the longer the discontinuous learning process, the longer the time interval within which a subject remembers the information without its considerable lost. Besides, the latter relationship is a linear proportionality.

q-bio.NC↗

arXiv2012

Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle

The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of continuous time random walks. Our consideration is confined to the one-dimensional model for continuous random motion of a particle with inertia. Its dynamics governed by stochastic self-acceleration is described as motion on the phase plane {x,v} comprising the position x and velocity v=dx/dt of the given particle. A notion of random walks inside a certain neighbourhood L of the line v=0 (the x-axis) and outside it is developed. It enables us to represent a continuous trajectory of particle motion on the plane {x,v} as a collection of the corresponding discrete steps. Each of these steps matches one complete fragment of the velocity fluctuations originating and terminating at the "boundary" of L. As demonstrated, the characteristic length of particle spatial displacement is mainly determined by velocity fluctuations with large amplitude, which endows the derived random walks along the x-axis with the characteristic properties of Levy flights. Using the developed classification of random trajectories a certain parameter-free core stochastic process is constructed. Its peculiarity is that all the characteristics of Levy flights similar to the exponent of the Levy scaling law are no more than the parameters of the corresponding transformation from the particle velocity v to the related variable of the core process. In this way the previously found validity of the continuous Markovian model for all the regimes of Levy flights is explained.

cond-mat.stat-mech↗