Related papers: Trace and antitrace maps for aperiodic sequences, …
Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the…
By using antitrace map method, we investigate the light transmission for a generalized Fibonacci multilayers. Analytical results are obtained for transmission coefficients in some special cases. We find that the transmission coefficients…
The structure of type A and B trace anomalies is reanalyzed in terms of the universal behaviour of dimension -2 invariant amplitudes. Based on it a general argument for trace anomaly matching between the unbroken and broken phases of a CFT…
We characterize the graphs with loops whose degree sequences have no repeated values and find their adjacency spectrum. In the case of simple graphs, such graphs are called anti-regular graphs and are examples of threshold graphs. The…
We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…
Understanding the periodic and structural properties of permutation maps over residue rings such as $\mathbb{Z}_{p^k}$ is a foundational challenge in algebraic dynamics and pseudorandom sequence analysis. Despite notable progress in…
An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the arcs alternate between forward and backward arcs. An antidirected path is an antidirected trail where no vertex is repeated. We show that it is…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…
Time series anomaly detection is crucial for maintaining stable systems. Existing methods face two main challenges. First, it is difficult to directly model the dependencies of diverse and complex patterns within the sequences. Second, many…
In this work we study the Silver mean sequence based on substitution rules by means of a transfer-matrix approach. Using transfer-matrix method we find a recurrence relation for the traces of general transfer-matrices which characterizes…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We…
We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal $\alpha$-Family of Maps depending on a single parameter $\alpha > 0$ which is the order of the fractional derivative in the nonlinear…
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ("traces") among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose…
Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ("traces") among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…