Ihor Lubashevsky

• PhD
• Professor (Full) at National Research University Higher School of Economics

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, de...

We put forward a novel model for self-organized criticality in the dynamics of systems controlled by human actions. The model is based on two premises. First, without human control, the system in issue undergoes supercritical instability. Second, the subject’s actions are aimed at preventing the occurrence of critical fluctuations when the risk of...

Detection of significant edges maintaining the connectivity in complex networks is essential in many applications such as attack vulnerability analysis, the spread of epidemic diseases, and information spreading patterns discovery. There are many existing methods enabling us to evaluate the criticality ranking of links in networks, which are based...

The finalizing chapter presents our account of the self which is essential in constructing the theory of human temporality. The modern concepts of the self taking a central position in philosophy of mind, psychology, neuroscience are briefly outlined. The proposed concept of the self does not contradict the available accounts but has other roots. O...

This chapter finalizes the qualitative description of the complex present and two main issues are the focus of attention. First, our approach to describing intentional, goal-oriented actions is elucidated. The proposed multi-component time formalism of human actions contains two constituent components: the human temporality with complex temporal st...

The present chapter is devoted to the experiential now as an individual fundamental entity of the complex present that plays the pivot role in dynamics of the human temporality. In our theory, the implementation cost of action strategies is determined by effort. For this reason, we elucidate its essential properties and develop the multi-component...

The present chapter is devoted to a qualitative description of the human temporality and the complex present as its constituent component. Special attention is focused on action strategies representing intentional, goal-oriented actions. The concept of space-time clouds is elaborated in detail in order to describe the mental representation of perce...

This chapter is the final part of our constructions of mathematical formalism for human goal-oriented actions within the complex present. The proposed concept of action strategy cloud is the gist of formalism. The developed description comprises several constituent components: temporal extension of the complex present; fuzziness of the complex pres...

In the present chapter, we discuss the main milestones in the history of philosophy of time from the days of ancient Greece up to the beginning of the XX century. We pay special attention to the crucial concepts put forward in the philosophy of time and related branches of physics in the XX century except for the issues related to the Theories of R...

In this chapter, we discuss the problems of the human now, that attracted much attention in the XX century, and a number of their comprehensive accounts proposed at the beginning of the XXI century. We combine these accounts under the term temporal experience or temporal consciousness and analyze them in detail. During this analysis, in parallel, w...

This book presents a novel account of the human temporal dimension called the “human temporality” and develops a special mathematical formalism for describing such an object as the human mind. One of the characteristic features of the human mind is its temporal extent. For objects of physical reality, only the present exists, which may be conceived...

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., visual...

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 us to speak about psychological space as an indiv...

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-st...

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 individu...

According to the modern theory of adaption of socioeconomic systems to unknown environments only the interaction between agents can be responsible for various emergent phenomena governed by decision-making and agent learning. Previously we advocated the idea that adopting a more complex model for the agent individual behavior including rational and...

We present the results of our experiments on studying the probabilistic properties of human response delay in balancing virtual pendulum (stick) with over-damped dynamics. The overdamping eliminates the effects of inertia and, thereby, reduces the dimensionality of the system under control. Two types simulators were employed for studying human resp...

Archetypal stick balancing task represents a wide class of unstable processes under human control. The currently dominant theory of human control in stick balancing is based on the concept of discontinuous, or intermittent control. Traditionally, intermittent control models involve threshold-driven control activation, however, recently it has been...

The results of conducted experiments on categorical perception with respect to gray color categorization into three classes are reported. Namely, the subjects were instructed to categorize shades of gray generated in a random sequence into three classes: light-gray, gray, and dark-gray. The collected data are analyzed employing (i) the asymptotics...

Within the paradigm of human intermittent control over unstable systems human behavior admits the interpretation as a sequence of point-like moments when the operator makes decision on activating or deactivating the control. These decision-making events are assumed to be governed by the information about the state of system under control which the...

In this chapter I discuss various systems where human mind plays a crucial role. I think that the description of such systems cannot be reduced to the paradigm of modern physics and propose to consider a number of problem where it becomes apparent. To justify this proposition it will be necessary to analyze in detail several particular systems.

Jerry Alan Fodor (born 1935) is an American philosopher and cognitive scientist, developed, in particular, the concept of multiple realizability arguing for nonreductive physicalism. Jaegwon Kim (born 1934) is a Korean American philosopher, in his works he, in particular, posed the famous exclusion problem arguing against nonreductive physicalism....

Rather often I met situations when my friends and colleagues being specialists in various branches of physics and mathematics became puzzled if I asked for their opinion about whether physics can describe human behavior. Some of them replied that physic is a science about the inanimate world, from elementary particles up to stars and galaxies. Howe...

In the previous chapter I have proposed the concept of attractor-caused supervenience of the mental upon the physical. This type supervenience does not possess causal power, which gives freedom for the mental to cause mental as well as physical events. In its turn, the physical also have causal power to affect physical and mental events. Therefore...

In Chap. 1 (Sect. 1. 7) I have introduced the concept of effective dualism as a useful approach to developing mathematical models of human behavior. Within this approach the human person is considered to be composed of two complementary components, objective and subjective ones, which possess their own properties and are governed by their own laws....

This chapter is devoted to the detailed analysis of the relationship between the principle of microscopic level reducibility and the formalism of classical physics, which has been used in Chap. 1 Initially I had no intention of writing this chapter and included its materials in Sect. 1. 6 There, however, they turned out to be in conflict in style n...

A considerable progress in modeling human actions and social phenomena achieved at the beginning of twenty-first century demonstrates that the notions and formalism developed in modern physics are really efficient in describing systems and phenomena where human role is crucial. It turns our that a wide variety of fundamental notions such as dynamic...

This book tackles the challenging question which mathematical formalisms and possibly new physical notions should be developed for quantitatively describing human cognition and behavior, in addition to the ones already developed in the physical and cognitive sciences. Indeed, physics is widely used in modeling social systems, where, in particular,...

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 ove...

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, namel...

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 cur...

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 a...

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...

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...

Within the rigor typical for physical models a new type non-symmetric diffusion problem is considered and the corresponding Brownian motion implementing such diffusion processes is constructed. As a particular example, random walks with internal causality on a square lattice are studied in detail. By construction, one elementary step of a random wa...

Recent progress in motor control suggests that in controlling unstable systems humans switch intermittently between the passive and active behavior instead of controlling the system in a continuous manner. Traditionally, the models of intermittent control employ the notion of threshold to mimic control switching mechanisms in humans. The notion of...

The present work reports the results of our experiments aimed at estimating the distribution of the response delay time in human intermittent control over unstable mechanical systems. A novel experimental paradigm: balancing an overdamped inverted pendulum was used; the overdamping eliminates the effects of inertia and, therefore, reduces the dimen...

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 int...

In controlling unstable systems humans switch intermittently between the passive and active behavior instead of controlling the system in a continuous manner. The notion of noise-driven control activation provides a richer alternative to the conventional threshold-based models of intermittent motor control. The present study represents the control...

Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Much evidence appears in favor of event-driven control hypothesis: human operators are passive by default and only start actively controling the system when the discrepancy between the current an...

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 m...

The work is devoted to possible generalizations of the Langevin equation based on the notion of the intermediate point determining the contribution of nonlinear random forces and different channels of noise action.

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 are passive by default and only start actively controlling the system when the discrepancy between...

The results of experiments on balancing a virtual inverted pendulum with over-damped dynamics are reported. Three types of pendulum, namely, an inverted stick, a triangle pendulum, and a vibrating spring were used in experiments and subjects of different age, gender, and skill of balancing participated in these experiments. It is demonstrated that...

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 be...

Dynamical traps as a new emergence mechanism related to the bounded capacity of human cognition is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. This is...

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...

A new emergence mechanism related to the bounded capacity of human cognition is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them, which is called human fuzz...

We conduct a theoretical analysis of the effects of intrinsic motivation on learning dynamics. We study a simple example of a single agent adapting to unknown environment; the agent is biased by the desire to take those actions she has little information about. We show that the intrinsic motivation may induce the instability (namely, periodic oscil...

We consider the dynamical traps model of human fuzzy rationality which describes the behavior of human controling a dynamical system near an equilibrium point. The basic dynamical trap model describes the behavior of human operator neglecting small deviations from the equilubrium point. We propose the extended model that takes into account the effe...

For describing irregular movement of animals in random search as well as patterns of human travel during daily activity an original model of Brownian nonlinear motion is proposed. The wandering particle is represented as a point in the extended phase space comprising its position, velocity, and, in addition, the acceleration. The acceleration is as...

Human behavior during the process of virtual inverted pendulum balancing in viscous environment is analyzed. The results of the virtual experiments are compared to the results of previous studies on so called dynamical trap effect. It is shown that the phase trajectories and phase variables distributions of the virtual stick motion under human cont...

We present the experimental evidence of the dynamical traps model describing the human fuzzy rationality in the dynamical systems framework. The results of the experiments on virtual stick balancing are compared to the results of the previous studies on the dynamical trap effect. According to the results obtained, we suggest that the dynamical trap...

A new emergence mechanism related to the bounded capacity of human cognition is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. The main attention is focu...

We develop a mathematical description of human fuzzy rationality. Human operators controlling dynamical systems are often incapable of precisely identifying and implementing the desired control strategy. The operator of a dynamical system treats the current value of the control effort as acceptable if it deviates insignificantly from the desired, o...

We propose the dynamical model describing the effect of boredom in the human learning process. It is shown numerically that the instability may appear in the dynamics of the system corresponding to the simple case of the single agent performing repeated choice between two alternatives. The discovered patterns of the periodic preference oscillations...

An original classification of random trajectories formed by a Brownian particle whose motion is governed by stochastic self-acceleration is constructed. In particular, it enables us to elucidate the mechanism endowing the analyzed continuous Markovian random walks with the characteristic properties of Lévy flights or Lévy walks. Lévy flights appear...

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...

We analyze data collected during the series of experiments aimed at elucidation of basic properties of human perception, namely, the limited capacity of ordering events, actions, etc. according to their preference. Previously it was shown that in a wide class of human-controlled systems small deviations from the equilibrium position do not cause an...

In the present paper we discuss the basic methodological aspects of studying social systems and attract attention to the fact that hybrid human-computer simulation referred to as "virtual experiments" should be one its cornerstones. The special attention is paid to systems with motivation that can be treated as a characteristic representative of st...

Phase transitions in a chain of oscillators with dynamical traps is studied numerically. The notion of dynamical traps mimics the basic features caused by the bounded capacity of human cognition in decision-making. In mathematical terms the dynamical traps form a "low" dimensional region in the phase space of a given system where its dynamics is st...

We discuss a new approach to describing Lévy flights in terms of continuous Markovian processes admitting the introduction of continuous trajectories of particle motion.

A new emergence mechanism related to the human fuzzy rationality is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. The main attention is focused on the s...

A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity depen...

A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for nonlinear friction in wondering particle motion and saturation of the noise intensity depending on the particl...

We discuss fundamental problems of mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human societies that distinguish social and natural systems from each other are listed to make it clear that individual math...

We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously only the superdiffusive regime has been analyzed. In this model the walker ve...

Oscillatory zoning (OZ) occurs in all major classes of minerals and also in a wide range of geological environments. It is caused by self-organization and describes fluctuations of the spatial chemical composition profile of the crystal. We present here a two-dimensional model of OZ based on our previous one-dimensional (1D) analysis and investigat...

The present paper is devoted to mathematical description of the vascular network response to local perturbations in the cellular tissue state, being one of the basic mechanisms controlling the inner environment of human body. Keeping in mind individual organs we propose a model for distributed self-regulation of living tissue, which is regarded as...

Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations. In addition, applications from different fields are included so as to strengthen t...

Drift–Diffusion Equation with Natural BoundariesDrift–Diffusion Problem with Absorbing and Reflecting BoundariesDimensionless Drift–Diffusion EquationSolution in Terms of Orthogonal EigenfunctionsFirst-Passage Time Probability DensityCumulative Breakdown ProbabilityThe Limiting Case for Large Positive Values of the Control ParameterA Brief Survey o...

Dynamics of First-Order Phase Transitions in Finite SystemsCondensation of Supersaturated VaporThe General Multi-Droplet ScenarioDetailed Balance and Free EnergyRelaxation to the Free Energy MinimumChemical PotentialsExercises

Definitions and PropertiesThe Ornstein–Uhlenbeck Process and its SolutionThe Ornstein–Uhlenbeck Process with Linear PotentialThe Exponential Ornstein–Uhlenbeck ProcessOutlook on EconophysicsExercises

Hopping Models with Zero-Range InteractionThe Zero-Range Model of Traffic FlowTransition Rates and Phase SeparationMetastabilityMonte Carlo Simulations of the Hopping ModelFundamental Diagram of the Zero-Range ModelPolarization Kinetics in Ferroelectrics with FluctuationsExercises

Equilibrium and Nonequilibrium Phase TransitionsTypes of Stochastic Differential EquationsTransformation of Random VariablesForms of the Fokker–Planck EquationThe Verhulst Model of Third OrderThe Genetic ModelNoise-Induced Instability in Geometric Brownian MotionSystem Dynamics with StagnationOscillator with Dynamical TrapsDynamics with Traps in a...

The Car-Following TheoryThe Optimal Velocity Model and its Langevin ApproachTraffic Jam Formation on a Circular RoadMetastability Near Phase Transitions in Traffic FlowCar Cluster Formation as First-Order Phase TransitionThermodynamics of Traffic FlowExercises

Random Walk on a Line and Diffusion: Main ResultsA Drunken Sailor as Random WalkerDiffusion with Natural BoundariesDiffusion in a Finite Interval with Mixed BoundariesThe Mirror Method and Time LagMaximum Value DistributionSummary of Results for Diffusion in a Finite IntervalExercises

A System of Many Brownian ParticlesA Traditional View of the Langevin EquationAdditive White NoiseSpectral AnalysisBrownian Motion in Three-Dimensional Velocity SpaceStochastic Differential EquationsThe Standard Wiener ProcessArithmetic Brownian MotionGeometric Brownian MotionExercises

Markovian Stochastic ProcessesThe Master EquationOne-Step Processes in Finite SystemsThe First-Passage Time ProblemThe Poisson Process in Closed and Open SystemsThe Two-Level SystemThe Three-Level SystemExercises

General Fokker–Planck EquationsBounded Drift–Diffusion in One DimensionThe Escape Problem and its SolutionDerivation of the Fokker–Planck EquationFokker–Planck Dynamics in Finite State SpaceFokker–Planck Dynamics with Coordinate-Dependent Diffusion CoefficientAlternative Method of Solving the Fokker–Planck EquationExercises

Bounded Multidimensional RegionFrom Chapman–Kolmogorov Equation to Fokker–Planck DescriptionDifferent Types of BoundariesEquivalent Lattice Representation of Random Walks Near the BoundaryExpression for Boundary SingularitiesDerivation of Singular Boundary Scaling PropertiesBoundary Condition for the Backward Fokker–Planck EquationBoundary Conditio...

Wiener Process, Adapted Processes and Quadratic VariationThe Space of Square Integrable Random VariablesThe Ito Integral and the Ito FormulaThe Kolmogorov Differential Equation and the Fokker–Planck EquationSpecial Diffusion ProcessesExercises

Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any governing center and, thereby, their self-regulation is based on a cooperative interaction of all the elements. T...

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtain...

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtain...

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff’s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes cal...

The studies of traffic flows are reviewed and different approaches in the analysis of the phase states of flows and the fundamental diagram are described. A comparison with the experimental results is performed. The attention is focused on the analysis of the empirical data collected on the linear branch of the Lefortovo tunnel (Moscow’s third ring...

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to t...

The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human societies that distinguish social and natural systems from each other are listed to make it clear that indivi...