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Overparameterized neural networks often contain many removable neurons, yet what makes a neuron redundant remains poorly understood. Existing pruning criteria commonly rely on local quantities such as weight magnitude, activation strength,…
The advancements in stellar spectroscopy data acquisition have made it necessary to accomplish similar improvements in efficient data analysis techniques. Current automated methods for analyzing spectra are either (a) data-driven, which…
SAR despeckling is a key tool for Earth Observation. Interpretation of SAR images are impaired by speckle, a multiplicative noise related to interference of backscattering from the illuminated scene towards the sensor. Reducing the noise is…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…
This paper presents a significant improvement for the synthesis of texture images using convolutional neural networks (CNNs), making use of constraints on the Fourier spectrum of the results. More precisely, the texture synthesis is…
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a…
Spectral projectors of Hermitian matrices play a key role in many applications, and especially in electronic structure computations. Linear scaling methods for gapped systems are based on the fact that these special matrix functions are…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
We analyze bipartite quantum states that admit a symmetric extension. Any such state can be decomposed into a convex combination of states that allow a _pure_ symmetric extension. A necessary condition for a state to admit a pure symmetric…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
We expand on the method of sequential filtering for calculating spectra of inhomogeneous fields. Sadek & Aluie [Phys. Rev. Fluids, 3, 124610 (2018)] showed that the kernel has to have at least $p$ vanishing moments to extract a power-law…
Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary…
In this article we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work we do not assume that convergence occurs to an isolated attractor but instead allow…
We develop a framework of parametrized semiadditivity and stability with respect to so-called atomic orbital subcategories of an indexing $\infty$-category $T$, extending work of Nardin. Specializing this framework, we introduce global…
Spread-spectrum signals are increasingly adopted in fields including communications, testing of electronic systems, Electro-Magnetic Compatibility (EMC) enhancement, ultrasonic non-destructive testing. This paper considers the synthesis of…
The local spectrum of a vertex set in a graph has been proven to be very useful to study some of its metric properties. It also has applications in the area of pseudo-distance-regularity around a set and can be used to obtain quasi-spectral…
We propose occupying guard-bands in closely-spaced WDM systems with redundant signal spectral components, to increase tolerance to frequency misalignment and channel shaping from multiplexing elements. By cyclically repeating the spectrum…
We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark…
For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain…