In this appendix, we follow all the same notation in Section 9. Our aim is to prove that the constant δ(Λ) does not appear in the lower bound, showing also that the frame inequality in (4.9) in Theorem 4.4 is indeed the Parseval identity.

Let $R$ be an expanding matrix with integer entries and let $B,L$ be finite integer digit sets so that $(R,B,L)$ form a Hadamard triple on ${\br}^d$ …

For the rest of the paper g will be an even integer g≥4 and m will be an odd integer m≥1.

We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore …

The Long Short-Term Memory (LSTM) recurrent neural network is capable of processing complex sequential information since it utilizes special gating s…

The long short-term memory (LSTM) neural network is capable of processing complex sequential information since it utilizes special gating schemes for…

The planar Tur\'an number of a given graph $F$, denoted $ex_{_\mathcal{P}}(n,F)$, is the maximum number of edges in a planar graph on $n$ vertices wi…

Experiments using ARPES, which is based on the photoelectric effect, show that the surface states in 3D topological insulators (TI) are helical. Here…

In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. …

In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these index structur…

Analytic expressions of the spatial coherence of partially coherent fields propagating in the Fresnel regime in all but the simplest of scenarios are…

Transition metal dichalcogenides (TMDs) are quasi-two-dimensional layered compounds exhibiting strongly competing charge-density wave (CDW) and super…

Recent studies have shown that deep neural networks (DNNs) are vulnerable to adversarial attacks. To this end, many defense approaches that attempt t…

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allow…

We report a detailed study of upper critical field in superconducting topological semimetal CaSn$_{3}$ with the AuCu$_{3}$-type cubic structure (poin…

With Von-Neumann computing architectures struggling to address computationally- and memory-intensive big data analytic task today, Processing-in-Memo…

If A1,…,An are finite spectral sets in G1,…,Gn respectively, with corresponding spectra Λ1,…,Λn, then A1×⋯×An is spectral in G1×⋯×Gn with spectrum Λ1×⋯×Λn.

Based on tiles and on the Coven-Meyerowitz property, we present some examples and some general constructions of spectral subsets of integers.

We consider the electron transport in single molecule magnet transistors in the presence of Zeeman spin splitting and magnetic quantum coherence (MQC…

Social coding platforms, such as GitHub, can serve as natural laboratories for studying the diffusion of innovation through tracking the pattern of c…

The normal matrix model with a cubic potential is ill-defined and it develops a critical behavior in finite time. We follow the approach of Bleher an…

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we conside…

In the past years, Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous mod…

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