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We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…

Numerical Analysis · Mathematics 2022-11-15 Ramona Anton , Nicolae Mihalache , François Vigneron

We study Nekrasov's deformed partition function of 5-dimensional supersymmetric Yang-Mills theory compactified on a circle. Mathematically it is the generating function of the characters of the coordinate rings of the moduli spaces of…

Algebraic Geometry · Mathematics 2007-05-23 Hiraku Nakajima , Kota Yoshioka

It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{\alpha t})$ time, given $t$ non-Clifford gates and a decomposition efficiency $\alpha$. The past years have seen a…

Quantum Physics · Physics 2024-12-24 Wira Azmoon Ahmad , Matthew Sutcliffe

We prove the neo-classical inequality with the optimal constant, which was conjectured by T. J. Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310]. For the proof, we introduce the fractional order Taylor's series with residual terms. Their…

Classical Analysis and ODEs · Mathematics 2010-06-08 Keisuke Hara , Masanori Hino

High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…

Quantum Physics · Physics 2026-01-21 Dong An , Konstantina Trivisa

Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…

Computational Complexity · Computer Science 2023-05-26 Leif Eriksson , Victor Lagerkvist

In exploratory factor analysis, rotation techniques are employed to derive interpretable factor loading matrices. Factor rotations deal with equality-constrained optimization problems aimed at determining a loading matrix based on measure…

Statistics Theory · Mathematics 2025-05-01 Ryoya Fukasaku , Michio Yamamoto , Yutaro Kabata , Yasuhiko Ikematsu , Kei Hirose

We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver…

Logic in Computer Science · Computer Science 2009-04-23 David Monniaux

New numerical algorithms based on rational functions are introduced that can solve certain Laplace and Helmholtz problems on two-dimensional domains with corners faster and more accurately than the standard methods of finite elements and…

Numerical Analysis · Mathematics 2022-10-12 Abinand Gopal , Lloyd N. Trefethen

While quantum computers have shown significant promise for electronic structure calculations, their potential to accelerate density functional theory (DFT) calculations remains unclear. In this work, we present a qubit-efficient encoding…

We describe an algorithm to numerically evaluate Riemann theta functions in any dimension in quasi-linear time in terms of the required precision, uniformly on reduced input. This algorithm is implemented in the FLINT number theory library…

Number Theory · Mathematics 2025-11-26 Noam D. Elkies , Jean Kieffer

When placed in parallel magnetic and electric fields, the electron trajectories of a classical hydrogen atom are chaotic. The classical escape rate of such a system can be computed with classical trajectory Monte Carlo techniques, but these…

Chaotic Dynamics · Physics 2025-03-21 Ethan T. Custodio , Sulimon Sattari , Kevin A. Mitchell

We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…

Machine Learning · Computer Science 2018-02-21 Vishesh Jain , Frederic Koehler , Elchanan Mossel

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…

Numerical Analysis · Mathematics 2007-05-23 James Demmel , Ioana Dumitriu , Olga Holtz , Robert Kleinberg

Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…

Optimization and Control · Mathematics 2019-12-05 Qingyin Ma , John Stachurski

This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…

Logic in Computer Science · Computer Science 2007-05-23 Andrew Gacek , Gopalan Nadathur

We show in this paper that third- and fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives.…

Fluid Dynamics · Physics 2008-08-14 Marc E. Brachet , Pablo D. Mininni , Duane L. Rosenberg , Annick Pouquet

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Data Structures and Algorithms · Computer Science 2026-04-29 Michał Szyfelbein

Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and quantum chaos. We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical…

Quantum Physics · Physics 2021-03-17 Sreeram PG , Naga Dileep Varikuti , Vaibhav Madhok

Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids…