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We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully…
We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network…
Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used…
Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing…
Formal verification provides a powerful framework for proving that dynamical systems satisfy their specifications. However, these techniques face scalability challenges in high-dimensional settings, as they often rely on state-space…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…
This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to…
Models that involve extra dimensions have introduced completely new ways of looking up on old problems in theoretical physics. The aim of the present notes is to provide a brief introduction to the many uses that extra dimensions have found…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
The laws of quantum-critical scaling theory of quantum fidelity, dependent on the underlying system dimensionality $D$, have so far been verified in exactly solvable $1D$ models, belonging to or equivalent to interacting, quadratic…