Vladimir G. Ivancevic

Neuro-fuzzy associative machinery for comprehensive brain and cognition modelling

to Brain and Cognition.- Various Approaches (Functors) to Brain and Cognition Modeling.- Neuro-Dynamics, Synergetics and Synchronization.- Fuzzy Systems.

Applied differential geometry : a modern introduction

Technical Preliminaries: Tensors, Actions and Functors Applied Manifold Geometry Applied Bundle Geometry Applied Jet Geometry Geometrical Path Integrals and Their Applications.

Path planning and obstacle avoidance for autonomous mobile robots: a review

Recent advances in the area of mobile robotics caused growing attention of the armed forces, where the necessity for unmanned vehicles being able to carry out the “dull and dirty” operations, thus avoid endangering the life of the military personnel. UAV offers a great advantage in supplying reconnaissance data to the military personnel on the ground, thus lessening the life risk of the troops. In this paper we analyze various techniques for path planning and obstacle avoidance and cooperation issues for multiple mobile robots. We also present a generic dynamics and control model for steering a UAV along a collision free path from a start to a goal position.

Quantum Neural Computation

Quantum Neural Computation is a graduatelevel monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brains nonlinear complexity, in order to perform a superhighspeed and errorfree computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence.

Adaptive-Wave Alternative for the Black-Scholes Option Pricing Model

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing controlled Brownian behavior of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock price and time. The model includes two parameters: volatility (playing the role of dispersion frequency coefficient), which can be either fixed or stochastic, and adaptive market potential that depends on the interest rate. The wave function represents quantum probability amplitude, whose absolute square is probability density function. Four types of analytical solutions of the NLS equation are provided in terms of Jacobi elliptic functions, all starting from de Broglie’s plane-wave packet associated with the free quantum-mechanical particle. The best agreement with the Black-Scholes model shows the adaptive shock-wave NLS-solution, which can be efficiently combined with adaptive solitary-wave NLS-solution. Adjustable ‘weights’ of the adaptive market-heat potential are estimated using either unsupervised Hebbian learning or supervised Levenberg–Marquardt algorithm. In the case of stochastic volatility, it is itself represented by the wave function, so we come to the so-called Manakov system of two coupled NLS equations (that admits closed-form solutions), with the common adaptive market potential, which defines a bidirectional spatio-temporal associative memory.

New mechanics of traumatic brain injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton–Euler dynamics of brain’s micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain’s rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain’s dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model.

Life-space foam: A medium for motivational and cognitive dynamics

General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field-theoretic psychodynamics [K. Lewin, Field Theory in Social Science, University of Chicago Press, Chicago, 1951; K. Lewin, Resolving Social Conflicts, and, Field Theory in Social Science, American Psychological Association, Washington, 1997; M. Gold, A Kurt Lewin Reader, the Complete Social Scientist, American Psychological Association, Washington, 1999], resulting in the development of a new concept of life-space foam (LSF) as a natural medium for motivational and cognitive psychodynamics. According to LSF formalisms, the classic Lewinian life space can be macroscopically represented as a smooth manifold with steady force fields and behavioral paths, while at the microscopic level it is more realistically represented as a collection of wildly fluctuating force fields, (loco)motion paths and local geometries (and topologies with holes). A set of least-action principles is used to model the smoothness of global, macro-level LSF paths, fields and geometry. To model the corresponding local, micro-level LSF structures, an adaptive path integral is used, defining a multi-phase and multi-path (multi-field and multi-geometry) transition process from intention to goal-driven action. Application examples of this new approach include (but are not limited to) information processing, motivational fatigue, learning, memory and decision making.

HUMAN VERSUS HUMANOID ROBOT BIODYNAMICS

In this paper we compare and contrast modern dynamical methodologies common to both humanoid robotics and human biomechanics. While the humanoid robots motion is defined on the system of constrained rotational Lie groups SO(3) acting in all major robot joints, human motion is defined on the corresponding system of constrained Euclidean groups SE(3) of the full (rotational + translational) rigid motions acting in all synovial human joints. In both cases the smooth configuration manifolds, Qrob and Qhum, respectively, can be constructed. The autonomous Lagrangian dynamics are developed on the corresponding tangent bundles, TQrob and TQhum, respectively, which are themselves smooth Riemannian manifolds. Similarly, the autonomous Hamiltonian dynamics are developed on the corresponding cotangent bundles, T*Qrob and T*Qhum, respectively, which are themselves smooth symplectic manifolds. In this way a full rotational + translational biodynamics simulator has been created with 270 DOFs in total, called the Human Biodynamics Engine, which is currently in its validation stage. Finally, in both the human and the humanoid case, the time-dependent biodynamics generalizing the autonomous Lagrangian (of Hamiltonian) dynamics is naturally formulated in terms of jet manifolds.

Dynamics of confined crowds modelled using Entropic Stochastic Resonance and Quantum Neural Networks

We present a new approach to modelling dynamics of confined crowds driven by Entropic Stochastic Resonance (ESR). The standard approach is to model confined Brownian particles using overdamped Langevin equations and corresponding linear, real-time, Fokker-Planck equations for Probability Density Functions (PDFs). Instead, we propose a new approach based on a set of (weakly or strongly) coupled Quantum Neural Networks (QNNs), which are self-organised, complex-valued nonlinear Schrodinger equations with unsupervised Hebbian-type learning. Utilising the full power of nonlinear analysis in the complex-plane, the new approach promises to be ideal for any kind of two-dimensional terrains. Besides, instead of over-simplistic Brownian particles, the new approach allows us to model crowds consisting of rigid-body-type agents.

Complexity and control : towards a rigorous behavioral theory of complex dynamical systems

The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory.This book contains 11 chapters and is designed as a one-semester course for engineers, applied and pure mathematicians, theoretical and experimental physicists, computer and economic scientists, theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.