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We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…
In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of…
Defect inspection is paramount within the closed-loop manufacturing system. However, existing datasets for defect inspection often lack precision and semantic granularity required for practical applications. In this paper, we introduce the…
We approach the following question: if supersymmetry is discovered, how can we select among different supersymmetric extensions of the Standard Model? In particular, we perform an analysis of the sparticle spectrum in low-energy string…
Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…
The Short-Time Fourier Transform (STFT) has been a staple of signal processing, often being the first step for many audio tasks. A very familiar process when using the STFT is the search for the best STFT parameters, as they often have…
There are several high-performance adaptive optics systems that deliver diffraction-limited imaging on ground-based telescopes, which renewed the interest of single-mode fiber (SMF) spectroscopy for exoplanet characterization. However, the…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
The paper aims at removing the aliasing effects of the whole focal stack generated from a sparse-sampled {4D} light field, while keeping the consistency across all the focal layers. We first explore the structural characteristics embedded…
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…
The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and analyzed under highly simplified…
We introduce the relative Matsui spectrum, a new invariant associated with a stable \(\infty\)-category equipped with an action. This construction generalizes both Balmer's tensor triangular spectra and Matsui's triangular spectra, and…
We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a…
Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits…
Our main observation is that the contravariant functor Spec on the category of commutative monoids is representable. We discuss a few consequences of this fact. In particular, we give an efficient way of calculating the Spec(M) of a…
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…
We give a proof avoiding spectral sequences of Deligne's decomposition theorem for objects in a triangulated category admitting a Lefschetz homomorphism.
Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable…
The fully convolutional network (FCN) has achieved tremendous success in dense visual recognition tasks, such as scene segmentation. The last layer of FCN is typically a global classifier (1x1 convolution) to recognize each pixel to a…
In this paper we study the $\nu$-continuity of the spectrum and some of its parts. We show that the approximate point spectrum $\sigma_{ap}$ is upper semi-$\nu$-continuous at every Fredholm operator, then we give sufficient conditions to…