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We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…
The notion of $\textbf{Gray}$-category, a semi-strict $3$-category in which the middle four interchange is weakened to an isomorphism, is central in the study of three-dimensional category theory. In this context it is common practice to…
We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant…
A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits non-analyticity such as divergence. Critical points can be first classified as…
We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement…
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…
ColorCheckers are reference standards that professional photographers and filmmakers use to ensure predictable results under every lighting condition. The objective of this work is to propose a new fast and robust method for automatic…
Earlier it was described to which extent the Alexander polynomial in several variables of an algebraic link in the Poincar\'e sphere determines the topology of the link. It was shown that, except some explicitly described cases, the…
Precise segmentation of the left ventricle (LV) within cardiac MRI images is a prerequisite for the quantitative measurement of heart function. However, this task is challenging due to the limited availability of labeled data and motion…
We report the first observation of the smectic C--smectic I (C--I) critical point by Xray diffraction studies on a binary system. This is in confirmity with the theoretical idea of Nelson and Halperin that coupling to the molecular tilt…
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal…
Boundaries are among the primary visual cues used by human and computer vision systems. One of the key problems in boundary detection is the label representation, which typically leads to class imbalance and, as a consequence, to thick…
Exceptional points(EPs), branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce, are ubiquitous in non-Hermitian systems. Many novel properties and applications have been proposed around the EPs. One of the…
The weighted essentially non-oscillatory {technique} using a stencil of $2r$ points (WENO-$2r$) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of $r+1$…
Infrared spectroscopy is key to elucidate molecular structures, monitor reactions and observe conformational changes, while providing information on both structural and dynamical properties. This makes the accurate prediction of infrared…
Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species…
We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…
We propose a Classification Via Clustering (CVC) algorithm which enables existing clustering methods to be efficiently employed in classification problems. In CVC, training and test data are co-clustered and class-cluster distributions are…
We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase…