arXiv subjects

Vladimir G. Ivancevic

Publications and source records attributed to Vladimir G. Ivancevic.

At least 19 recordsLinked to original sources

arXiv2013

Sine-Gordon Solitons, Kinks and Breathers as Physical Models of Nonlinear Excitations in Living Cellular Structures

Nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine-Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living cellular structures, both intra-cellular (DNA, protein folding and microtubules) and inter-cellular (neural impulses and muscular contractions). Key words: Sine-Gordon solitons, kinks and breathers, DNA, Protein folding, Microtubules, Neural conduction, Muscular contraction

q-bio.OT↗

arXiv2011

Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics

This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction-diffusion processes in biology, chemistry and physics can be modelled by the combined geometric-diffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction-diffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow. Keywords: geometrical Ricci flow, nonlinear reaction-diffusion, dissipative solitons and breathers

nlin.PS↗

arXiv2011

Turbulence and Shock-Waves in Crowd Dynamics

In this paper we analyze crowd turbulence from both classical and quantum perspective. We analyze various crowd waves and collisions using crowd macroscopic wave function. In particular, we will show that nonlinear Schrödinger (NLS) equation is fundamental for quantum turbulence, while its closed-form solutions include shock-waves, solitons and rogue waves, as well as planar de Broglie's waves. We start by modeling various crowd flows using classical fluid dynamics, based on Navier-Stokes equations. Then, we model turbulent crowd flows using quantum turbulence in Bose-Einstein condensation, based on modified NLS equation. Keywords: Crowd behavior dynamics, classical and quantum turbulence, shock waves, solitons and rogue waves

nlin.AO↗

arXiv2011

Undergraduate Lecture Notes in De Rham-Hodge Theory

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The only necessary background for comprehensive reading of these notes is Green's theorem from multivariable calculus.

math.DG↗

arXiv2011

Dynamics and Control of Humanoid Robots: A Geometrical Approach

his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the `covariant force law', the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated `humanoid velocity phase space', while autonomous Hamiltonian dynamics is formulated on the associated `humanoid momentum phase space'. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples. Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like humanoid control, time-dependent biodynamics

nlin.AO↗

arXiv2011

Lecture Notes in Lie Groups

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. We give both physical and medical examples of Lie groups. The only necessary background for comprehensive reading of these notes are advanced calculus and linear algebra.

math.DG↗

arXiv2010

New Financial Research Program: General Option-Price Wave Modeling

Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schrödinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevic b]. Both the solitary and shock-wave solutions of the nonlinear model, as well as its linear (periodic) quantum simplification are shown to successfully fit the Black-Scholes data, and define the financial Greeks. This initial wave model (called the Ivancevic option pricing model) has been further extended in [Yan], by providing the new NLS solutions in the form of rogue waves (one-rogon and two-rogon solutions). In this letter, I propose a new financial research program, with a goal to develop a general wave-type model for realistic option-pricing prediction and control. Keywords: General option-price wave modeling, new financial research program

q-fin.PR↗

arXiv2010

Adaptive Wave Models for Option Pricing Evolution: Nonlinear and Quantum Schrödinger Approaches

Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equation. The nonlinear approach comes in two flavors: (i) for the case of constant volatility, it is defined by a single adaptive nonlinear Schrödinger (NLS) equation, while for the case of stochastic volatility, it is defined by an adaptive Manakov system of two coupled NLS equations. The linear quantum approach is defined in terms of de Broglie's plane waves and free-particle Schrödinger equation. In this approach, financial variables have quantum-mechanical interpretation and satisfy the Heisenberg-type uncertainty relations. Both models are capable of successful fitting of the Black--Scholes data, as well as defining Greeks. Keywords: Black--Scholes option pricing, adaptive nonlinear Schrödinger equation, adaptive Manakov system, quantum-mechanical option pricing, market-heat potential PACS: 89.65.Gh, 05.45.Yv, 03.65.Ge

q-fin.PR↗

arXiv2009

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. Keywords: Black-Scholes option pricing, adaptive nonlinear Schrödinger equation, market heat potential, controlled stochastic volatility, adaptive Manakov system, controlled Brownian behavior

q-fin.PR↗

arXiv2009

New Universal Theory of Injury Prediction and Prevention

The prediction and prevention of traumatic brain injury, spinal injury and general musculo-skeletal injury is a very important aspect of preventive medical science. Recently, in a series of papers, I have proposed a new coupled loading-rate hypothesis as a unique cause of all above injuries. This new hypothesis states that the main cause of all mechanical injuries is a Euclidean Jolt, which is an impulsive loading that strikes any part of the human body (head, spine or any bone/joint) - in several coupled degrees-of-freedom simultaneously. It never goes in a single direction only. Also, it is never a static force. It is always an impulsive translational and/or rotational force, coupled to some human mass eccentricity. Keywords: traumatic brain injury, spinal injury, musculo-skeletal injury, coupled loading-rate hypothesis, Euclidean jolt

q-bio.TO↗

arXiv2009

Extending Feynman's Formalisms for Modelling Human Joint Action Coordination

The recently developed Life-Space-Foam approach to goal-directed human action deals with individual actor dynamics. This paper applies the model to characterize the dynamics of co-action by two or more actors. This dynamics is modelled by: (i) a two-term joint action (including cognitive/motivatonal potential and kinetic energy), and (ii) its associated adaptive path integral, representing an infinite--dimensional neural network. Its feedback adaptation loop has been derived from Bernstein's concepts of sensory corrections loop in human motor control and Brooks' subsumption architectures in robotics. Potential applications of the proposed model in human--robot interaction research are discussed. Keywords: Psycho--physics, human joint action, path integrals

nlin.AO↗

arXiv2009

Crowd Behavior Dynamics: Entropic Path-Integral Model

We propose an entropic geometrical model of crowd behavior dynamics (with dissipative crowd kinematics), using Feynman action--amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor (order parameter) is crowd entropy $S$ that satisfies the Prigogine's extended second law of thermodynamics, $\partial_t S\geq 0$ (for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that \emph{goal-directed crowd movement} operates under entropy conservation, $\partial_t S = 0$, while \emph{naturally chaotic crowd dynamics} operates under (monotonically) increasing entropy function, $\partial_t S > 0$. Between these two distinct topological phases lies a phase transition with a chaotic inter-phase. Both inertial crowd dynamics and its dissipative kinematics represent diffusion processes on the crowd manifold governed by the Ricci flow. Keywords: Crowd behavior dynamics, action--amplitude formalism, entropic crowd manifold, crowd turbulence, Ricci flow, topological phase transitions.

nlin.AO↗

arXiv2009

Applied Categories and Functors for Undergraduates

These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of these notes are first-year calculus and linear algebra.

math.HO↗

arXiv2009

New Mechanics of Generic Musculo-Skeletal Injury

Prediction and prevention of musculo-skeletal injuries is an important aspect of preventive health science. Using as an example a human knee joint, this paper proposes a new coupled-loading-rate hypothesis, which states that a generic cause of any musculo-skeletal injury is a Euclidean jolt, or SE(3)-jolt, an impulsive loading that hits a joint in several coupled degrees-of-freedom simultaneously. Informally, it is a rate-of-change of joint acceleration in all 6-degrees-of-freedom simultaneously, times the corresponding portion of the body mass. In the case of a human knee, this happens when most of the body mass is on one leg with a semi-flexed knee -- and then, caused by some external shock, the knee suddenly `jerks'; this can happen in running, skiing, sports games (e.g., soccer, rugby) and various crashes/impacts. To show this formally, based on the previously defined covariant force law and its application to traumatic brain injury (Ivancevic, 2008), we formulate the coupled Newton--Euler dynamics of human joint motions and derive from it the corresponding coupled SE(3)-jolt dynamics of the joint in case. The SE(3)-jolt is the main cause of two forms of discontinuous joint injury: (i) mild rotational disclinations and (ii) severe translational dislocations. Both the joint disclinations and dislocations, as caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum joint model. Keywords: musculo-skeletal injury, coupled-loading--rate hypothesis, coupled Newton-Euler dynamics, Euclidean jolt dynamics, joint dislocations and disclinations

q-bio.TO↗

arXiv2009

Quantum Neural Computation for Option Price Modelling

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model for the Black--Scholes--like option price evolution, consisting of a pair of coupled NLS equations, one governing the stochastic volatility and the other governing the option price, both self-organizing in an adaptive `market heat potential', trained by continuous Hebbian learning. This stiff pair of NLS equations is numerically solved using the method of lines with adaptive step-size integrator. Keywords: Option price modelling, Quantum neural computation, nonlinear Schrödinger equations, leverage effect, bidirectional associative memory

q-fin.CP↗

arXiv2008

Undergraduate Lecture Notes in Topological Quantum Field Theory

These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory

math-ph↗

arXiv2008

Entropic Geometry of Crowd Dynamics

We propose an entropic geometrical model of psycho-physical crowd dynamics (with dissipative crowd kinematics), using Feynman action-amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor is crowd entropy $S$ that satisfies the Prigogine's extended second law of thermodynamics, $\partial_tS\geq 0$ (for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that goal-directed crowd movement operates under entropy conservation, $\partial_tS = 0$, while natural crowd dynamics operates under (monotonically) increasing entropy function, $\partial_tS > 0$. Between these two distinct topological phases lies a phase transition with a chaotic inter-phase. Both inertial crowd dynamics and its dissipative kinematics represent diffusion processes on the crowd manifold governed by the Ricci flow, with the associated Perelman entropy-action. Keywords: Crowd psycho-physical dynamics, action-amplitude formalism, crowd manifold, Ricci flow, Perelman entropy, topological phase transition

nlin.AO↗

arXiv2008

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. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinations

q-bio.TO↗