Related papers: Continuous-time DC kernel --- a stable generalized…

We develop an idea of fixed exit double-crystal monochromator of general position, in which the lines of entering and exit beams (both being fixed) do not lie in one plane, i.e., are in general position. Both cases of identical and not…

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically forced quantum many-body systems. Spontaneous modification of discrete time translation symmetry in a periodically driven…

Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry.…

Spiking Neural Networks (SNNs) offer a promising alternative to traditional deep learning frameworks, since they provide higher computational efficiency due to event-driven information processing. SNNs distribute the analog values of pixel…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Recent works indicate that convolutional neural networks (CNN) need large receptive fields (RF) to compete with visual transformers and their attention mechanism. In CNNs, RFs can simply be enlarged by increasing the convolution kernel…

Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of…

Doppler-free spectroscopy using two counter-propagating dual-frequency laser beams in alkali vapor cells has been demonstrated recently, providing the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances.…

In this work, we will give proper estimates for the discrete convolution complementary (DCC) kernels, which leads to the asymptotically compatible fractional Gr\"onwall inequality. The consequence can be applied in the analysis of the…

Classification of long sequential data is an important Machine Learning task and appears in many application scenarios. Recurrent Neural Networks, Transformers, and Convolutional Neural Networks are three major techniques for learning from…

The biggest challenge when using DNA as a storage medium is maintaining its stability. The relative occurrence of Guanine (G) and Cytosine (C) is essential for the longevity of DNA. In addition to that, reverse complementary base pairs…

Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…

Different families of generalized CS for one-dimensional systems with general time dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension.…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…

We demonstrate the realization of a Discrete Time-Crystal (DTC) phase in a family of periodically driven, one-dimensional quadratic lattice Hamiltonians that can be obtained using spin chains. These interactions preserve integrability while…

For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated…

Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems…

We propose a continuous-time formulation of persistent contrastive divergence (PCD) for maximum likelihood estimation (MLE) of unnormalised densities. Our approach expresses PCD as a coupled, multiscale system of stochastic differential…