Tijana T. 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.

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.

A new two-feature FAM-matrix classifier for breast cancer diagnosis

In this paper, a fuzzy-logic FAM (fuzzy associative memory) matrix classifier is used for the classification (diagnosis) of breast cancer. It is implemented in Mathematica 3.0 and tested on two features (radius and perimeter) from the Wisconsin breast cancer database. The sensitivity of the FAM-matrix classifier is 94.29%, and its specificity is 73.33%.

Control of the extension–flexion cycle of human knees during bicycle riding by a synergy of solitary muscular excitations and contractions

A Hill-type model is proposed for the extension–flexion cycle of human knees during bicycle riding. The extension–flexion cycle is controlled by a synergy of muscular excitations and contractions of the knee musculature. Muscular action potentials are modeled by sine-Gordon kinks, while titin-influenced actomyosin contractions are modeled by Korteweg-de Vries solitons. As an application, the total knee arthroplasty is discussed.

A new two-feature GBAM-neurodynamical classifier for breast cancer diagnosis

Like standard discrete artificial neural networks (ANNs), continual neurodynamical systems can be used for the classification and diagnosis of breast cancer. In this paper, a two-feature generalized bidirectional associative memory (GBAM) classifier is formulated in tensorial invariant form. It is implemented in Mathematica 3.0 and tested on two sample features (the radius and perimeter of cell nuclei in fine-needle aspiration slides) from the Wisconsin breast-cancer database. The classification accuracy obtained (86%), together with the invariance of the classification result upon the variation of the dimensions and output form of the neural activation fields, shows the potential classification ability of theoretical classifiers that are directly implemented in computer algebra systems.

JET-RICCI GEOMETRY OF TIME-DEPENDENT HUMAN BIOMECHANICS

We propose the time-dependent generalization of an ordinary autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold.

Dynamics and control of humanoid robots: A geometrical approach

This 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.

Non-linear dynamics, chaos and phase transitions in DNA molecule

DNA molecule is a complex dynamical system consisting of many atoms having a quasi-one-dimensional structure. In this paper, we first review non-linear Hamiltonian DNA dynamics in the form of several Peyrard-Bishoptype DNA models. Then, we explore Hamiltonian chaos and thermodynamical phase transitions related to Hamiltonian DNA dynamics. These second-order phase transitions are shown to have topological origin, rooted in the geometry of the DNA configuration manifold.

MACRO- AND MICROSCOPIC SELF-SIMILARITY IN NEURO- AND PSYCHO-DYNAMICS

The unique Hamiltonian description of neuro- and psycho-dynamics at the macroscopic, classical, inter-neuronal level of brains neural networks, and microscopic, quantum, intra-neuronal level of brains microtubules, is presented in the form of open Liouville equations. This implies the arrow of time in both neuro- and psycho-dynamic processes and shows the existence of the formal neuro-biological space-time self-similarity. nKeywords: Neuro- and psycho-dynamics, Brain microtubules, Hamiltonian and Liouville dynamics, Neuro-biological self-similarity