Related papers: A new Algorithm for the Computation of logarithmic…
Weyl groups are ubiquitous, and efficient algorithms for them -- especially for the exceptional algebras -- are clearly desirable. In this paper we provide several of these, addressing practical concerns arising naturally for instance in…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
A range of applications for automatic machine learning need the generation process to be controllable. In this work, we propose a way to control the output via a sequence of simple actions, that are called semantic code classes. Finally, we…
We present LTLS, a technique for multiclass and multilabel prediction that can perform training and inference in logarithmic time and space. LTLS embeds large classification problems into simple structured prediction problems and relies on…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
We create a new online reduction of multiclass classification to binary classification for which training and prediction time scale logarithmically with the number of classes. Compared to previous approaches, we obtain substantially better…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
We study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The…
Let k be a number field. For an odd prime p and an integer i>1, the i-th \'etale wild kernel is contained in the second cohomology group of o'_k with coefficients in Zp(i), where o'_k is the ring of p-integers of k. Using Iwasawa theory, we…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
We develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over…
The interpretation of experimental measurements at the LHC requires accurate theoretical predictions for exclusive observables, and in particular the summation of soft and collinear radiation to all orders in perturbation theory. We report…
Let K/F be a cyclic extension of prime degree l over a number field F. If F has class number coprime to l, we study the structure of the l-Sylow subgroup of the class group of K. In particular, when F contains the l-th roots of unity, we…
We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic…
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials…
We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…