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The triangulations of a regular convex polygon are enumerated according to the number of diagonals parallel to a fixed edge. The enumeration uses the Shapiro convolution identity, as well as an interpretation of this identity in terms of…
We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
Using cyclotomic classes of order twelve for certain finite fields, we construct an infinite family of almost difference sets and normally regular graphs applying the theory of cyclotomy. We show that in each of these fields neither the…
X-ray tomographic image reconstruction consists of determining an object function from its projections. In many applications such as non-destructive testing, we look for a fault region (air) in a homogeneous, known background (metal). The…
X-ray imaging is a fundamental tool of routine clinical diagnosis. Fluoroscopic imaging can further acquire X-ray images at video frame rates, thus enabling non-invasive in-vivo motion studies of joints, gastrointestinal tract, etc. For…
A famous problem in discrete geometry is to find all monohedral plane tilers, which is still open to the best of our knowledge. This paper concerns with one of its variants that to determine all convex polyhedra whose every cross-section…
Determining crystal structures from X-ray diffraction data is fundamental across diverse scientific fields, yet remains a significant challenge when data is limited to low resolution. While recent deep learning models have made…
We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…
In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on…
The numerical complex coupled-mode method used in a metal thin-film optic element is applied to a planar multilayer optical waveguide. All modes are required to satisfy Helmholtz Vectorial equation in an optical waveguide including bound…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…
Automatic tumor segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on convolutional neural networks (CNNs) have achieved the state-of-the-art performance, many…
Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
Accurate retinal vessel segmentation is a challenging problem in color fundus image analysis. An automatic retinal vessel segmentation system can effectively facilitate clinical diagnosis and ophthalmological research. Technically, this…
To separate the overlapped cells, a bottleneck detection approach is proposed in this paper. The cell image is segmented by slope difference distribution (SDD) threshold selection. For each segmented binary clump, its one-dimensional…
Accurate risk stratification of precancerous polyps during routine colonoscopy screening is a key strategy to reduce the incidence of colorectal cancer (CRC). However, assessment of low-grade dysplasia remains limited by subjective…