Multilinear Time Invariant System Theory

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are not amenable to the standard system and controls framework which requires the state to be in the form of a vector. In order to address this limitation, recently a new class of multiway dynamical systems has been introduced in which the states, inputs and outputs are tensors. We propose a new form of multilinear time invariant (MLTI) systems based on the Einstein product and even-order paired tensors. We extend classical linear time invariant (LTI) system notions including stability, reachability and observability for the new MLTI system representation by leveraging recent advances in tensor algebra.Comment: 8 pages, SIAM Conference on Control and its Applications 2019, accepted to appea

IMMANUEL WALLERSTEIN'S WORLD SYSTEM THEORY

World-systems analysis is not a theory, but an approach to social analysis and social change developed, among others by the Immanuel Wallerstein. Professor Wallerstein writes in three domains of world-systems analysis: the historical development of the modern world-system; the contemporary crisis of the capitalist world-economy; the structures of knowledge. The American anlyst rejects the notion of a "Third World", claiming there is only one world connected by a complex network of economic exchange relationship. Our world system is characterized by mechanisms which bring about a redistribution of resources from the periphery to the core. His analytical approach has made a significant impact and established an institutional base devoted to the general approach.World system, core, semi-periphery, periphery, external regions

Dynamical system theory of periodically collapsing bubbles

We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are mediated by the dependence of their "fundamental values" on past asset prices and bond themselves. The obtained nonlinear self-referencing price dynamics can induce, in a completely objective deterministic way, the appearance of periodically exploding bubbles ending in crashes. Technically, the periodically explosive bubbles arise due to the proximity of two types of bifurcations as a function of the two key control parameters $b$ and $g$, which represent, respectively, the sensitivity of the fundamental asset price on past asset and bond prices and of the fundamental bond price on past asset prices. One is a Hopf bifurcation, when a stable focus transforms into an unstable focus and a limit cycle appears. The other is a rather unusual bifurcation, when a stable node and a saddle merge together and disappear, while an unstable focus survives and a limit cycle develops. The lines, where the periodic bubbles arise, are analogous to the critical lines of phase transitions in statistical physics. The amplitude of bubbles and waiting times between them respectively diverge with the critical exponents $\gamma = 1$ and $\nu = 1/2$, as the critical lines are approached.Comment: Latex file, 35 pages, 16 figure

A Physiologically Based System Theory of Consciousness

A system which uses large numbers of devices to perform a complex functionality is forced to adopt a simple functional architecture by the needs to construct copies of, repair, and modify the system. A simple functional architecture means that functionality is partitioned into relatively equal sized components on many levels of detail down to device level, a mapping exists between the different levels, and exchange of information between components is minimized. In the instruction architecture functionality is partitioned on every level into instructions, which exchange unambiguous system information and therefore output system commands. The von Neumann architecture is a special case of the instruction architecture in which instructions are coded as unambiguous system information. In the recommendation (or pattern extraction) architecture functionality is partitioned on every level into repetition elements, which can freely exchange ambiguous information and therefore output only system action recommendations which must compete for control of system behavior. Partitioning is optimized to the best tradeoff between even partitioning and minimum cost of distributing data. Natural pressures deriving from the need to construct copies under DNA control, recover from errors, failures and damage, and add new functionality derived from random mutations has resulted in biological brains being constrained to adopt the recommendation architecture. The resultant hierarchy of functional separations can be the basis for understanding psychological phenomena in terms of physiology. A theory of consciousness is described based on the recommendation architecture model for biological brains. Consciousness is defined at a high level in terms of sensory independent image sequences including self images with the role of extending the search of records of individual experience for behavioral guidance in complex social situations. Functional components of this definition of consciousness are developed, and it is demonstrated that these components can be translated through subcomponents to descriptions in terms of known and postulated physiological mechanisms

A new breakthrough in linear-system theory: Kharitonov's result

Given a real coefficient polynomial D(s), there exist several procedures for testing whether it is strictly Hurwitz (i.e., whether it has all its zeros in the open left-half plane). If the coefficients of D(s) are uncertain and belong to a known interval, such testing becomes more complicated because there is an infinitely large family of polynomials to which D(s) now belongs. It was shown by Kharitonov that in this case it is necessary and sufficient to test only four polynomials in order to know whether every polynomial in the family is strictly Hurwitz. An interpretation of this result in terms of reactance functions (i.e., LC impedances) was recently proposed. These results were also extended recently for the testing of positive real property of rational transfer functions with uncertain denominators. In this paper we review these results along with detailed proofs and discuss extensions to the discrete-time case

Optimal relaxed causal sampler using sampled-date system theory

This paper studies the design of an optimal relaxed causal sampler using sampled data system theory. A lifted frequency domain approach is used to obtain the existence conditions and the optimal sampler. A state space formulation of the results is also provided. The resulting optimal relaxed causal sampler is a cascade of a linear continuous time system followed by a generalized sampler and a discrete system