Related papers: Topologically Modulated Signals and Predicate Gate…
In a recent paper, Bassett et al. (2011) have analyzed the static and dynamic organization of functional brain networks in humans. We here focus on the first claim made in this paper, which states that the static modular structure of such…
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
This article summarizes principles and ideas from the emerging area of applying \textit{conditional computation} methods to the design of neural networks. In particular, we focus on neural networks that can dynamically activate or…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
Mechanistic interpretability has transformed the analysis of transformer circuits by decomposing model behavior into competing algorithms, identifying phase transitions during training, and deriving closed-form predictions for when and why…
A tunable, multi-degree-of-freedom, parametrically excited amplifier is introduced as an apparatus capable of shifting slow, weak signals to higher frequencies, by exploiting the amplifier natural resonances via controlled parametric…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally establish…
Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…
Wave-domain processing is an emerging paradigm where signal processing operations are partially shifted from the digital to the electromagnetic (EM) domain. Leveraging reconfigurable EM devices, this approach aims to reduce complexity,…
Efficient technique of manipulation with phase prefactors in electronic Fock spaces is developed. Its power is demonstrated on example of both relatively simple classic configuration interaction matrix element evaluation and essentially…
The impact of an edge radial electric field on the particle orbits and the orbital spectrum in an axisymmetric toroidal magnetic equilibrium is investigated using a guiding center canonical formalism. Poloidal and bounce/transit-averaged…
Many music theoretical constructs (such as scale types, modes, cadences, and chord types) are defined in terms of pitch intervals---relative distances between pitches. Therefore, when computer models are employed in music tasks, it can be…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Vortices in electron beams can manifest several types of topological phenomena, such as the formation of exotic structures or interactions with topologically structured electromagnetic fields. For instance, the wavefunction of an electron…
During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…