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Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a…

We propose a novel method for the construction of orthogonal arrays. The algorithm makes use of the Kronecker Product operator in association with unit column vectors to generate new orthogonal arrays from existing orthogonal arrays. The…

Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…

We introduce a novel approach to perform first-order optimization with orthogonal and unitary constraints. This approach is based on a parametrization stemming from Lie group theory through the exponential map. The parametrization…

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

With a computer-aided approach based on the connection with equitable partitions, we establish the uniqueness of the orthogonal array OA$(1536,13,2,7)$, constructed in [D.G.Fon-Der-Flaass. Perfect $2$-Colorings of a Hypercube, Sib. Math. J.…

We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any…

We characterize mixed-level orthogonal arrays in terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer-Friedman (BF) bound for pure-level orthogonal arrays and show that arrays attaining it are…

Randomized algorithms and data structures are often analyzed under the assumption of access to a perfect source of randomness. The most fundamental metric used to measure how "random" a hash function or a random number generator is, is its…

This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…

In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three…

Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…

The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…

The Erd\H{o}s-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general $n$-vertex graph if one imposes…

In 1996, Jackson and Martin proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp…

Recently the breakthrough method of hypergraph containers, developed independently by Balogh, Morris, and Samotij as well as Saxton and Thomason, has been used to study sparse random analogs of a variety of classical problems from…

In this article we determine five previously unknown covering array numbers (CANs). We do so using properties of so called balanced covering arrays together with a computational result for these. The balance properties allow us to…

Constrained orthogonal polynomials have been recently introduced in the study of the Hohenberg-Kohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we…

We give new explicit constructions of several fundamental objects in linear-algebraic pseudorandomness and combinatorics, including lossless rank extractors, weak subspace designs, and strong $s$-blocking sets over finite fields. Our focus…

Generalized $t$-designs, which form a common generalization of objects such as $t$-designs, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation of $t$-designs, \emph{Discrete Math.}\ {\bf 309}…