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A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with $n$ degrees of freedom (DOF) possesses $n$ nontrivial integrals of motion, and can…
This paper deals with characterizing the freeness and asymptotic freeness of free multiple integrals with respect to a free Brownian motion or a free Poisson process. We obtain three characterizations of freeness, in terms of contraction…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our…
Recent advances in human mobility research have revealed consistent pairwise characteristics in movement behavior, yet existing mobility models often overlook the spatial and topological structure of mobility networks. By analyzing millions…
An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In…
As the pace of AI technology continues to accelerate, more tools have become available to researchers to solve longstanding problems, Hybrid approaches available today continue to push the computational limits of efficiency and precision.…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Vibrations appearance, either unstability system, is the result of the dynamic interaction of the cutting process with the elastic system of machine tools in various working conditions. Our objective is to develop an experimental…
Autonomous robots must operate in complex and changing environments subject to requirements on their behaviour. Verifying absolute satisfaction (true or false) of these requirements is challenging. Instead, we analyse requirements that…
We define a new integer invariant of a finite graph G, the freeness index, that measures the extent to which G can be embedded in the 3-sphere so that it and its subgraphs have ``simple" complements, i.e., complements which are homeomorphic…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
We develop a method to evaluate the generalized degrees of freedom (GDF), which is a key quantity of a model selection criterion, for linear regression with sparse regularization. Using the replica method, GDF is expressed by the variables…
In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and…
Crawling is a common locomotion mechanism in soft robots and nonskeletal animals. In this work we propose modeling soft-robotic legged locomotion by approximating it with an equivalent articulated robot with elastic joints. For concreteness…