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In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the…
In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
The Data Clustering (DC) problem is of central importance for the area of Machine Learning (ML), given its usefulness to represent data structural similarities from input spaces. Differently from Supervised Machine Learning (SML), which…
A $2-(v,k,\lambda)$ directed design (or simply a $2-(v,k,\lambda)DD$) is super-simple if its underlying $2-(v,k,2\lambda)BIBD$ is super-simple, that is, any two blocks of the $BIBD$ intersect in at most two points. A $2-(v,k,\lambda)DD$ is…
Color and structure are the two pillars that combine to give an image its meaning. Interested in critical structures for neural network recognition, we isolate the influence of colors by limiting the color space to just a few bits, and find…
We consider nearly-perfect cuboids (NPC), where the only irrational is one of the face diagonals. Obtained are three rational parametrizations for NPC with one parameter.
The most essential concept in concurrent multiscale methods involving atomistic-continuum coupling is how to define the relation between atomistic and continuum regions. A well-known coupling method that has been frequently employed in…
The single image super-resolution task is one of the most examined inverse problems in the past decade. In the recent years, Deep Neural Networks (DNNs) have shown superior performance over alternative methods when the acquisition process…
In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…
An increasing number of applications in computer vision, specially, in medical imaging and remote sensing, become challenging when the goal is to classify very large images with tiny informative objects. Specifically, these classification…
Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning. We present two contributions to the state of the art in CSC. First, we…
We examine the structure of compact metal nanoparticles (NPs) forming polyhedral sections of face centered (fcc) and body centered (bcc) cubic lattices, which are confined by facets characterized by highly dense {100}, {110}, and {111}…
Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings,…
In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We…
Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…
A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…
Lightweight image super-resolution (SR) methods aim at increasing the resolution and restoring the details of an image using a lightweight neural network. However, current lightweight SR methods still suffer from inferior performance and…