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This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a…
We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…
Stability and protection of the electrical power systems are always of primary concern. Stability can be affected mostly by increase in the load demand. Power grids are overloaded in peak hours so more power generation units are required to…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…
In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…
Team assembly is a problem that demands trade-offs between multiple fairness criteria and computational optimization. We focus on four criteria: (i) fair distribution of workloads within the team, (ii) fair distribution of skills and…
When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…
We present an active-set method for minimizing an objective that is the sum of a convex quadratic and $\ell_1$ regularization term. Unlike two-phase methods that combine a first-order active set identification step and a subspace phase…
Groups of people or even robots often face problems they need to solve together. Examples include collectively searching for resources, choosing when and where to invest time and effort, and many more. Although a hierarchical ordering of…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
We study the parameterized complexity of a robust generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem; we are given a graph G with edges labeled with group elements, and the goal is to…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
Overpopulation in animal shelters contributes to increased disease spread and higher expenses on animal healthcare, leading to fewer adoptions and more shelter deaths. Additionally, one of the greatest challenges that shelters face is the…
The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the…
In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items and returns the first defective item in the specified order or returns null if there are no defectives. We refer…