Related papers: Lower Bounds for Linear Operators
Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…
We prove new upper and lower bounds for the Online Orthogonal Vectors Problem ($\mathsf{OnlineOV}_{n,d}$). In this problem, a preprocessing algorithm receives $n$ vectors $x_1,\ldots,x_n\in\{0,1\}^d$ and constructs a data structure of size…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a…
We study *non-adaptive* Local Computation Algorithms (LCA). A reduction of Parnas and Ron (TCS'07) turns any distributed algorithm into a non-adaptive LCA. Plugging known distributed algorithms, this leads to non-adaptive LCAs for constant…
We prove a lower bound of $\Omega\left(n^{1.5}\right)$ for the number of product gates in non-commutative arithmetic circuits for an explicit $n$-variate degree-$n$ polynomial $f_{n}$ (over every field). We observe that this implies that…
Many constraints restricting the result of some computations over an integer sequence can be compactly represented by register automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising…
Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan--Pettie STOC'10; Long--Saranurak FOCS'22]…
In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and…
Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…
We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…
Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…
Many convex problems in machine learning and computer science share the same form: \begin{align*} \min_{x} \sum_{i} f_i( A_i x + b_i), \end{align*} where $f_i$ are convex functions on $\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \in…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…