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We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
A C# package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z_2 whose total number of solutions in Z_2 determines the output of the quantum computation…
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in…
We consider the post-training quantization problem, which discretizes the weights of pre-trained deep neural networks without re-training the model. We propose multipoint quantization, a quantization method that approximates a…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…
We present simplified formulae for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-to-use C++ library that allows computations in arbitrary…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Central to our derivation is the use of the high-order…
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…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
The state-of-the-art performance for several real-world problems is currently reached by convolutional neural networks (CNN). Such learning models exploit recent results in the field of deep learning, typically leading to highly performing,…
We examine the behavior of the number of $k$-term arithmetic progressions in a random subset of $\mathbb{Z}/n\mathbb{Z}$. We prove that if a set is chosen by including each element of $\mathbb{Z}/n\mathbb{Z}$ independently with constant…
We obtain polynomial decay rates for $C_{0}$-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded…
Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes.…
Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…
We make quantitative improvements to recently obtained results on the structure of the image of a large difference set under certain quadratic forms and other homogeneous polynomials. Previous proofs used deep results of Benoist-Quint on…