All posts under tag "System"
A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras, the (classical and quantum) q-oscillator algebra and the Re
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra. This type of recursive sequences are frequently used in appl
We view Digital Ecosystems to be the digital counterparts of biological ecosystems, exploiting the self-organising properties of biological ecosystems, which are considered to be robust, self-organising and scalable architectures that can automatically solve complex, dynamic problems. Digital Ecosys
This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite Programming (SDP). The strength of the proposed method lies in a n
We study restricted multiple three wave interaction system by the inverse scattering method. We develop the algebraic approach in terms of classical $r$-matrix and give an interpretation of the Poisson brackets as linear $r$-matrix algebra. The solutions are expressed in terms of polynomials of thet
We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a
We review results on scattering observables for $^4$He--$^4$He$_2$ and $^3$He--$^4$He$_2$ collisions. We also study the effect of varying the coupling constant of the atom-atom interaction on the scattering length.
We consider a real-time communication system with noisy feedback consisting of a Markov source, a forward and a backward discrete memoryless channels, and a receiver with finite memory. The objective is to design an optimal communication strategy (that is, encoding, decoding, and memory update strat
We start with elementary algebraic theory of factorization of linear ordinary differential equations developed in the period 1880-1930. After exposing these classical results we sketch more sophisticated algorithmic approaches developed in the last 20 years. The main part of this paper is devoted
The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting close
As the volume of published scholarly literature continues to grow, finding relevant literature becomes increasingly difficult. With the rise of generative Artificial Intelligence (AI), and particularly Large Language Models (LLMs), new possibilities emerge to find and explore literature. We introduc
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