Related papers: Complexity of Constructing Minimal Faithful Permut…

Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of $\mathbb Z^n$-graded modules. We consider them in the setting of local graded rings $R$, with grading over an abelian group, and give a…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…

In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on centroid clustering--one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportionally…

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher…

The discrimination between two unknown states can be performed by a universal programmable discriminator, where the copies of the two possible states are stored in two program systems respectively and the copies of data, which we want to…

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In…

Accurate predictions for the non-linear matter power spectrum are needed to confront theory with observations in current and near future weak lensing and galaxy clustering surveys. We propose a computationally cheap method to create an…

For fixed compact connected Lie groups H \subseteq G, we provide a polynomial time algorithm to compute the multiplicity of a given irreducible representation of H in the restriction of an irreducible representation of G. Our algorithm is…

We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…

Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…

The faithful dimension of a finite group $\mathrm G$ over $\mathbb C$, denoted by $m_\mathrm{faithful}(\mathrm G)$, is the smallest integer $n$ such that $\mathrm G$ can be embedded in $\mathrm{GL}_n(\mathbb C)$. Continuing our previous…

Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…

We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic…