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Phase-change materials (PCMs) such as Ge-Sb-Te alloys are widely used in non-volatile memory applications due to their rapid and reversible switching between amorphous and crystalline states. However, their functional properties are…

The fundamental non-Hermitian nature of the forms of coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present letter shows how this can be used to advantage. Specifically, the…

Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the…

Recognizing apparel attributes has recently drawn great interest in the computer vision community. Methods based on various deep neural networks have been proposed for image classification, which could be applied to apparel attributes…

We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…

In recent years, a large number of genomic and epigenomic studies have been focusing on the integrative analysis of multiple experimental datasets measured over a large number of observational units. The objectives of such studies include…

We apply the coupled cluster method (CCM) to the Hamiltonian version of the latticised O(4) non-linear sigma model. The method, which was initially developed for the accurate description of quantum many-body systems, gives rise to two…

AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered…

Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely-used coupled cluster singles and doubles plus perturbative triples…

Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…

Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…

The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced,…

The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including…

In this work, a cut high-dimensional model representation (cut-HDMR) expansion based on multiple anchors is constructed via the clustering method. Specifically, a set of random input realizations is drawn from the parameter space and…

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to…

We describe further details of the Stochastic Coupled Cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in Full Configuration Interaction Quantum Monte Carlo. We describe an initiator…

Clustering is grouping of data by the proximity of some properties. We report on the possibility of increasing the efficiency of clustering of points in a plane using artificial quantum neural networks after the replacement of the two-level…

In this paper we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate…

We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…

Unsupervised learning, and more specifically clustering, suffers from the need for expertise in the field to be of use. Researchers must make careful and informed decisions on which algorithm to use with which set of hyperparameters for a…