Related papers: Class Number and Regulator Computation in Purely C…

We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use sieving techniques adapted from the number field sieve…

This note pursues the techniques of modified psi classes on the stack of stable maps (cf. [Graber-Kock-Pandharipande]) to give concise solutions to the characteristic number problem of rational curves in P^2 or P^1 x P^1 with a cusp or a…

In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…

Let $K$ be a totally real number field of degree $n$ over $\mathbb{Q}$, with discriminant and regulator $\Delta_K, R_K$ respectively. In this paper, using a similar method to van Woerden, we prove that the number of classes of perfect unary…

We study the geometry of Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves in binary classification problems. The key finding is that many of the most commonly used binary classification metrics are merely functions…

We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…

We determine the Galois group of the 2-class field tower for two particular families of imaginary quadratic number fields $k$ with $2$-class field tower of length $2$.

We use machine learning to study the moduli space of genus two curves, specifically focusing on detecting whether a genus two curve has $(n, n)$-split Jacobian. Based on such techniques, we observe that there are very few rational moduli…

Let $F$ be a totally real number field of class number one, and let $K$ be a CM-field with $F$ as its maximal real subfield. For each positive integer $N$, we construct a class group of certain binary quadratic forms over $F$ which is…

A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…

We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we…

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…

Shanks's infrastructure algorithm and Buchmann's algorithm for computing class groups and unit groups of rings of integers of algebraic number fields are most naturally viewed as computations inside Arakelov class groups. In this paper we…

A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both a reference governor for the bottom layer and as a feedback controller for the regulated…

We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards.…

We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex…

A toy model (suggested by Klauder) is analyzed from the perspective of First Class and Second Class Dirac constrained systems. The comparison is made by turning a First Class into a Second Class system with the introduction of suitable…

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…

Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…

For an algebraic number field K with 3-class group \(Cl_3(K)\) of type (3,3), the structure of the 3-class groups \(Cl_3(N_i)\) of the four unramified cyclic cubic extension fields \(N_i\), \(1\le i\le 4\), of K is calculated with the aid…