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It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a…

Numerical Analysis · Mathematics 2024-03-11 Heike Faßbender , Martin Halwaß

We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.

Complex Variables · Mathematics 2007-05-23 Debraj Chakrabarti

We present some new results on union ultrafilters. We characterize stability for union ultrafilters and, as the main result, we construct a new kind of unordered union ultrafilter.

Logic · Mathematics 2011-02-16 Peter Krautzberger

Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special ``neutrino'' symmetries. If not…

High Energy Physics - Phenomenology · Physics 2009-11-11 Alexei Yu. Smirnov

The ideal imaging system would efficiently capture information about all fundamental properties light: intensity, direction, wavelength, and polarization. Most common imaging systems only map the spatial degrees of freedom of light onto a…

Optics · Physics 2023-01-26 Conner Ballew , Gregory Roberts , Andrei Faraon

This paper introduces versatile filters to construct efficient convolutional neural networks that are widely used in various visual recognition tasks. Considering the demands of efficient deep learning techniques running on cost-effective…

Computer Vision and Pattern Recognition · Computer Science 2021-09-23 Kai Han , Yunhe Wang , Chang Xu , Chunjing Xu , Enhua Wu , Dacheng Tao

This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch width is a significant graph width parameter that measures the degree of connectivity in a graph using a branch decomposition and a symmetric submodular…

Combinatorics · Mathematics 2023-06-27 Takaaki Fujita

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter…

Commutative Algebra · Mathematics 2013-04-02 Franz-Viktor Kuhlmann

For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness…

Functional Analysis · Mathematics 2020-11-03 Ben De Bondt , Hans Vernaeve

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

Optimization and Control · Mathematics 2012-02-07 Marius Apetrii , Marius Durea , Radu Strugariu

For a set $S$ of (positive definite and integral) quadratic forms with bounded rank, a quadratic form $f$ is called $S$-universal if it represents all quadratic forms in $S$. A subset $S_0$ of $S$ is called an $S$-universality criterion set…

Number Theory · Mathematics 2020-09-10 Kyoungmin Kim , Jeongwon Lee , Byeong-Kweon Oh

Neural network-based collaborative filtering systems focus on designing network architectures to learn better representations while fixing the input to the user/item interaction vectors and/or ID. In this paper, we first show that the…

Information Retrieval · Computer Science 2022-03-16 Ramin Raziperchikolaei , Young-joo Chung

In order to relate nanoparticle properties to function, fast and detailed particle characterization, is needed. The ability to characterize nanoparticle samples using optical microscopy techniques has drastically improved over the past few…

CNNs have excelled at performing place recognition over time, particularly when the neural network is optimized for localization in the current environmental conditions. In this paper we investigate the concept of feature map filtering,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-03 Stephen Hausler , Adam Jacobson , Michael Milford

The paper deals with kernel density estimates of filtering densities in the particle filter. The convergence of the estimates is investigated by means of Fourier analysis. It is shown that the estimates converge to the theoretical filtering…

Computation · Statistics 2014-07-29 David Coufal

We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…

Logic · Mathematics 2021-04-19 Itay Kaplan , Nicholas Ramsey , Saharon Shelah

The main ideas behind nuclear supersymmetry are presented, starting from the basic concepts of symmetry and the methods of group theory in physics. We propose new, more stringent experimental tests that probe the supersymmetry…

Nuclear Theory · Physics 2017-11-02 A. Frank , J. Barea , R. Bijker

Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. Proofs based on ultrafilters tend to be shorter and more…

Dynamical Systems · Mathematics 2013-10-17 Jakub Konieczny

The present document aims at providing a short, didactical introduction to three standard versions of the Kalman filter, namely its variants identified as Basic, Extended, and Unscented. The application of these algorithms in three…

Systems and Control · Computer Science 2016-07-20 E. Matsinos

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…

High Energy Physics - Theory · Physics 2010-12-17 A. Morozov