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We study the problem of interpolating all values of a discrete signal f of length N when d<N values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set J; these comprise the…
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
We analyze several aspects of a class of simple counting processes, that can emerge in some fields of applications where the presence of a change-point occurs. Under simple conditions we, in particular, prove a significant inequality for…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
Diffusion models have enabled high-quality, conditional image editing capabilities. We propose to expand their arsenal, and demonstrate that off-the-shelf diffusion models can be used for a wide range of cross-domain compositing tasks.…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
We define a general framework that includes objects such as tilings, Delone sets, functions and measures. We define local derivability and mutual local derivability (MLD) between any two of these objects in order to describe their…
In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…
Diffusion models are typically trained using pointwise reconstruction objectives that are agnostic to the spectral and multi-scale structure of natural signals. We propose a loss-level spectral regularization framework that augments…
Diffusion models have demonstrated remarkable capabilities in synthesizing realistic images, spurring interest in using their representations for various downstream tasks. To better understand the robustness of these representations, we…
Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…
The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate,…
The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…
The static diffraction intensity distribution from large material system conceived as perfectly homogeneous system made inhomogeneous, though substitution of groups of atoms, small particles, by other groups of atoms, is explicitly…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
We exhibit new examples of regions of $M\setminus L$ where $M$ and $L$ denote the Markov and Lagrange spectra, respectively. These regions have a different nature from all known regions studied so far: they contain \emph{intruder sets}…
Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the…
Using a simple observation based on holomorphy, we argue that any model which spontaneously breaks supersymmetry for some range of a parameter will do so generically for all values of that parameter, modulo some isolated exceptional points.…
In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an…