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We study the natural problem of Triplet Reconstruction (also Rooted Triplets Consistency or Triplet Clustering), originally motivated in computational biology and relational databases (Aho, Sagiv, Szymanski, and Ullman, 1981): given $n$…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
Quantum error mitigation schemes (QEM) have greatly enhanced the performance of quantum computers, mostly by reducing errors caused by interactions with the environment. Nevertheless, the presence of coherence errors, typically arising from…
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
Canonical relativized cylindric set algebras are used to sharpen the relative representation theorem for weakly associative relation algebras, that every complete atomic weakly associative relation algebra is isomorphic with the…
The well--known Freiman--Ruzsa Theorem provides a structural description of a set $A$ of integers with $|2A|\le c|A|$ as a subset of a $d$--dimensional arithmetic progression $P$ with $|P|\le c'|A|$, where $d$ and $c'$ depend only on $c$.…
Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets - Gaussian-type orbitals, Slater-type orbitals, as well as…
Precise characterization of noisy quantum operations plays an important role for realizing further accurate operations. Quantum tomography is a popular class of characterization methods, and several advanced methods in the class use error…
The aim of Reverse Mathematics(RM for short)is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak…
Catalytic computing concerns space bounded computation which starts with memory full of data that have to be restored by the end of the computation. Lossy catalytic computing, defined by Gupta et al. (2024) and fully characterized by…
Stone's representation theorem asserts a duality between Boolean algebras on the one hand and Stone space, which are compact, Hausdorff, and totally disconnected, on the other. This duality implies a natural isomorphism between the…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…
Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…
Robin Hirsch posed in 1996 the 'Really Big Complexity Problem': classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is…
Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be…
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 open-set recognition (OSR), a promising strategy is exploiting pseudo-unknown data outside given $K$ known classes as an additional $K$+$1$-th class to explicitly model potential open space. However, treating unknown classes without…
We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
In this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral K\"ahler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to…