Search results

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

The cybernetic approach differs significantly from the conventional reductionist methods of natural and biological sciences. Norbert Wiener established the theory of cybernetics as a science of control and communication process in living beings (human and animals) and machines. Dutta Majumder in his Norbert Wiener Award winning paper extended the approach to include integrated complex human machine systems and functions with general systems theory as a unitary science laying the mathematical foundation for unifying observing systems, observed systems and the act of observing as indicated in von Foerster’s concept of second‐order cybernetics. Both from the point of view of ontology and that of epistemology the cybernetic approach now enables computer technology to incorporate artificial intelligence (AI) and expert system (ES) for knowledge based instrumentation for diagnostics and therapy planning. Presents the results of a project for development of a knowledge based framework for combining different modalities of medical image processing such as CT, MR(T₁), MR(T₂), SPECT, PET, USG etc. whichever is relevant for particular pathological investigation for diagnostics and therapeutic planning. Experiments were conducted with (a) Alzheimer’s patient data and (b) detection and grading of malignancy with oncological data for the cancer screening system.

To develop a mathematical and algorithmic approach of avoiding the limitations of deterministically computing the values of energy, time, position and momentum imposed by Heisenberg's uncertainity principle (HUP) which is of profound significance from the point of view of some emerging science and technology like quantum computing, nano scale technology and chaotic dynamical systems.

A parametric method of establishing deterministic solutions for energy and momentum on the basis of quantized energy limits (instead of HUP) if developed in the non‐infinite non‐zero quantized energy limits where hidden deterministic solutions can be obtained for micro/nano structures.

The philosophical foundations of quantum mechanics as developed by Max Planck, Neils Bohrz, Werner Heisenburg, Dirac and Edwein Schrodinger is based on a duality concept of complimentarity notions. In most general logical sense for any physical reality qualitative dualism have to have a quantitative dualism may be hidden or virtual. The upper and lower limits of the dynamical quantum mechanical observables are determined based on the dimensional considerations for the physical constants H, C, G and H₀. The conceptual basis and mathematical framework of the paper in based Norbert Wiener's work on theory of cybernetics and D. Dutta Majumdars' unified cybernetic and general dynamical systems theory.

The testability of the theory needs to be established.

Without challenging HUP this is a contribution of tremendous practical implications.

The historical perspective of the emergence of cybernetics as the science of control, communication and computation in machines and living tissues, and integrated and complex man‐machine systems as a unitary discipline of General Systems Theory is presented. In the second section both the theories of cybernetics and general systems are shown to be the same in motivation, requirements, characteristics, attributes and behaviour. In the third section cybernetic systems such as the class of finite state machines are established as a subclass of general dynamical systems. In the last section the cybernetics as a general and universal theory of action, including social praxis in general comprehending technical and moral praxis, is presented.

The approach of biocybernetics and non‐equilibrium systems dynamics is used to analyse biological, psychological, anthropological and cultural evolution. Using experimental data, positive feedback of biological activation and Prigogine‐Einstein fluctuation analysis, the energy dissipation equations for biological and anthropological evolution are developed.

Aims to investigate the causative factors and clinical applicability of spontaneous regression of malignant tumours without treatment, a really paradoxical phenomenon with many therapeutic potentialities. Analyses past cases to find that the commonest cause is a preceding episode of high fever‐induced thermal fluctuation which produces fluctuation of biochemical/immunological parameters. Using Prigogine‐Glansdorff‐Langevin stability theory and biocybernetic principles, develops the theoretical foundation of a tumour’s self‐control, homeostasis and regression induced by thermal, radiation or oxygenation fluctuations. Derives a threshold condition of perturbations for producing regression. Presents some striking confirmation of such fluctuation‐induced regression in Ewing tumour, Clear cell cancer and Lewis lung carcinoma. Using experimental data on patients, elucidates a novel therapeutic approach of multi‐modal hyper‐fluctuation utilizing radiotherapeutic hyper‐fractionation, temperature and immune‐status.