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In this paper we prove that every pure-state $\Psi ^{(N)}$ of N (N$\geqslant 3)$ continuous variables corresponds to a pair of convex rigid covers (CRCs) structures in the continuous-dimensional Hilbert-Schmidt space. Next we strictly…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Fast and accurate prediction of optimal crystal structure, topology, and microstructures is important for accelerating the design and discovery of new materials. A challenge lies in the exorbitantly large structural and compositional space…
This paper deals with the highly challenging problem of reconstructing the shape of a refracting object from a single image of its resulting caustic. Due to the ubiquity of transparent refracting objects in everyday life, reconstruction of…
Coreset selection is powerful in reducing computational costs and accelerating data processing for deep learning algorithms. It strives to identify a small subset from large-scale data, so that training only on the subset practically…
Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the existing CG type methods are not robust to data corruption. To…
In the large-scale image retrieval task, the two most important requirements are the discriminability of image representations and the efficiency in computation and storage of representations. Regarding the former requirement, Convolutional…
Visual contrastive learning aims to learn representations by contrasting similar (positive) and dissimilar (negative) pairs of data samples. The design of these pairs significantly impacts representation quality, training efficiency, and…
An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms \[ \begin{cases} F = c_{1}x_1^3 + c_{2}x_2^3 + \cdots + c_{n}x_n^3 = 0, \\ G = d_{1}x_1^3 + d_{2}x_2^3 + \cdots + d_{n}x_n^3 =…
Convolutional neural networks (CNNs) have become commonplace in addressing major challenges in computer vision. Researchers are not only coming up with new CNN architectures but are also researching different techniques to improve the…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Multiple coverings of the farthest-off points ($(R,\mu)$-MCF codes) and the corresponding $(\rho,\mu)$-saturating sets in projective spaces $PG(N,q)$ are considered. We propose and develop some methods which allow us to obtain new small…
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing…
A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…
This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…
The canonical dimension is an invariant attached to admissible representations of p-adic reductive groups, which has only received significant attention in the case of mod-p representations. In the case of complex representations, the…
In this paper, we devote our interest to solving the real cubic truncated moment problem. We provide some results that allow to get a complete solution via a minimal representing measure. Some numerical examples are also presented to…
Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…
In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in…