Related papers: Three Euler's Sieves and a Fast Prime Generator (F…
Priority Sesh is a library for session-typed communication in Linear Haskell which offers strong compile-time correctness guarantees. Priority Sesh offers two deadlock-free APIs for session-typed communication. The first guarantees deadlock…
Modern GPUs are designed for regular problems and suffer from load imbalance when processing irregular data. Prior to our work, a domain expert selects the best kernel to map fine-grained irregular parallelism to a GPU. We instead propose…
The Eulerian fluid simulation is an important HPC application. The neural network has been applied to accelerate it. The current methods that accelerate the fluid simulation with neural networks lack flexibility and generalization. In this…
Sieves are constructed for twin primes in class I, which are of the form 2m+/-D, D>=3 odd. They are characterized by their twin-D-I rank m. They have no parity problem. Non-rank numbers are identified and counted using odd primes p>=5.…
It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…
Can we model Non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The Non-Euclidean property have posed a long term challenge in graph modeling. Despite recent graph neural networks and…
Let $X$ be a linear diffusion taking values in $(\ell,r)$ and consider the standard Euler scheme to compute an approximation to $\mathbb{E}[g(X_T)\mathbf{1}_{[T<\zeta]}]$ for a given function $g$ and a deterministic $T$, where…
High-performance deep learning depends on efficient tensor programs. In recent years, automatic tensor program optimization, also known as tensor compilation, has emerged as the primary approach to generating efficient tensor programs.…
A programmable optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should find a nonlinear phenomenon that overcomes weaknesses present in many…
We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first…
Euler diagrams are an intuitive and popular method to visualize set-based data. In a Euler diagram, each set is represented as a closed curve, and set intersections are shown by curve overlaps. However, Euler diagrams are not visually…
We study distributed graph algorithms that adopt an iterative vertex-centric framework for graph processing, popularized by the Google's Pregel system. Since then, there are several attempts to implement many graph algorithms in a…
We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations.…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
We present an efficient algorithm to compute the Euler factor of a genus 2 curve C/Q at an odd prime p that is of bad reduction for C but of good reduction for the Jacobian of C (a prime of ``almost good'' reduction). Our approach is based…
An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal…
Odd numbers can be indexed by the map k(n)=(n-3)/2, n belonging to 2N+3. We first propose a basic primality test using this index function that was first introduced in article (8). Input size of operations is reduced which improves…
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…
The endogenous grid method (EGM) accelerates dynamic programming by inverting the Euler equation, but it appears incompatible with Epstein-Zin preferences where the value function enters the Euler equation. This paper shows that a power…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…