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The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…

Consider a rational point on an elliptic curve under an isogeny. Suppose that the action of Galois partitions the set of its pre-images into n orbits. It is shown that all such points above a certain height have their denominator divisible…

The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

One of the most fundamental tasks in data science is to assist a user with unknown preferences in finding high-utility tuples within a large database. To accurately elicit the unknown user preferences, a widely-adopted way is by asking the…

Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. The aim of this article is to give a result about the sum of euler's totient function from k equal 1 to n whene p divides n and p…

Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…

Flow matching models generate samples by numerically integrating a learned velocity field, with each integration step requiring a neural network evaluation. Fast generation therefore requires using a small fixed evaluation budget…

An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single…

We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…

In this paper we review the properties of families of numbers of the form $6n\pm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new…

This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T.…

We reframe scene flow as the task of estimating a continuous space-time ODE that describes motion for an entire observation sequence, represented with a neural prior. Our method, EulerFlow, optimizes this neural prior estimate against…

Four algorithms giving rise to graceful graphs from a known (non)graceful graph are described. Some necessary conditions for a graph to be highly graceful and critical are given. Finally some conjectures are made on graceful, critical and…

Let $\varphi$ be the Euler's function and fix an integer $k\ge 0$. We show that, for every initial value $x_1\ge 1$, the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi(x_n)+k$ for all $n\ge 1$ is eventually…

This paper introduces a code generator designed for node-level optimized, extreme-scalable, matrix-free finite element operators on hybrid tetrahedral grids. It optimizes the local evaluation of bilinear forms through various techniques…

A major computational bottleneck in modern High Energy Physics event generators arises from the integration of the matrix element, which requires repeated evaluations at different phase-space points to cover all possible initial- and…

For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…

Transpose convolution has shown prominence in many deep learning applications. However, transpose convolution layers are computationally intensive due to the increased feature map size due to adding zeros after each element in each row and…

Stream processing is mainstream (again): Widely-used stream libraries are now available for virtually all modern OO and functional languages, from Java to C# to Scala to OCaml to Haskell. Yet expressivity and performance are still lacking.…