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The growing demand for real-time data processing in applications such as neural networks and embedded control systems has spurred the search for faster, more efficient alternatives to traditional electronic systems. In response, we…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
Expanding the frontiers of information processing technologies and, in particular, computing with ever increasing speed and capacity has long been recognized an important societal challenge, calling for the development of the next…
Strong light-matter interactions facilitate not only emerging applications in quantum and non-linear optics but also modifications of materials properties. In particular the latter possibility has spurred the development of advanced…
In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint…
In this thesis, we propose to tackle this important issue by designing and realizing a novel nano-optical device based on the use of a photonic crystal (PC) structure to generate an efficient coupling between the external source and a NA.…
In the study of nuclear cross sections, the computational demands of data assimilation methods can become prohibitive when dealing with large data sets. We have developed a novel variant of the data thinning algorithm, inspired by the…
The need for solving optimization problems is prevalent in a wide range of physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Emerging artificial intelligence applications across the domains of computer vision, natural language processing, graph processing, and sequence prediction increasingly rely on deep neural networks (DNNs). These DNNs require significant…
The rational design of photonic nanostructures consists in anticipating their optical response from simple models or as variations of reference systems. This strategy is limited when different objectives are simultaneously targeted.…
Recently, there has been growing interest in unconventional computing as an approach for solving NP-hard problems, by developing dedicated hardware to find solutions more efficiently than conventional CPUs. In many of these approaches,…
Optical computing with integrated photonics brings a pivotal paradigm shift to data-intensive computing technologies. However, the scaling of on-chip photonic architectures using spatially distributed schemes faces the challenge imposed by…