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Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear…
Process science is a highly interdisciplinary field of research. Despite numerous proposals, process science lacks an adequate understanding of the core concepts of the field, including notions such as process, event, and system. A more…
A general theory is developed for describing the nonlinear relaxation of spin systems from a strongly nonequilibrium initial state, when, in addition, the sample is coupled to a resonator. Such processes are characterized by nonlinear…
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Learning is traditionally studied in biological or computational systems. The power of learning frameworks in solving hard inverse-problems provides an appealing case for the development of `physical learning' in which physical systems…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Experiments that look for nonlinear quantum dynamics test the fundamental premise of physics that one of two separate systems can influence the physical behavior of the other only if there is a force between them, an interaction that…
Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
The brain is an intricately structured organ responsible for the rich emergent dynamics that support the complex cognitive functions we enjoy as humans. With around $10^{11}$ neurons and $10^{15}$ synapses, understanding how the human brain…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour…
There is a renewed interest to study spin-polarized transport and spin dynamics in various electronic materials. The motivation to examine the spin degrees of freedom (mostly in electrons, but also in holes and nuclei) comes from various…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…