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The interplay between the two fundamental concepts of topological order and reflection positivity allows one to characterize the ground states of certain many-body Hamiltonians. We define topological order in an appropriate fashion and show…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
The principles of the physical description of non-inertial frames of reference are analyzed. The systems of physical reality description (PhRD) are introduced on base of generalization of the relativistic principle in special and general…
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.
What is a systems approach? The first step towards answering this question is an understanding of the history of the systems movement, which includes a survey of contemporary systems discourse. In particular, I examine how systems…
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…