Related papers: Fast Ramanujan-type Series for Logarithms. Part I
In an important paper, Zagier proved that certain half-integral weight modular forms are generating functions for traces of polynomials in the $j$-function. It turns out that Zagier's work makes it possible to algorithmically compute…
The main two algorithms for computing the numerical radius are the level-set method of Mengi and Overton and the cutting-plane method of Uhlig. Via new analyses, we explain why the cutting-plane approach is sometimes much faster or much…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears…
In this paper, we evaluate some series via the WZ method, and confirm several previous conjectures. For example, we prove the following two identities conjectured by the second author: $$\sum_{k=0}^{\infty} \frac{(28k^2 + 10k + 1)…
We prove some "divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ applying a Barnes-integrals strategy of the WZ-method.
The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a…
We introduce a new technique for evaluation of series with zeta coefficients and also for evaluation of certain integrals involving the logGamma function. This technique is based on Hankel integral representations of the Hurwitz zeta, the…
Listwise reranking is a key yet computationally expensive component in vision-centric retrieval and multimodal retrieval-augmented generation (M-RAG) over long documents. While recent VLM-based rerankers achieve strong accuracy, their…
We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. The method uses a finite set of function evaluations in the…
Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This…
Complex networks constitute the backbones of many complex systems such as social networks. Detecting the community structure in a complex network is both a challenging and a computationally expensive task. In this paper, we present the…
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them…
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our…
Using a modular equation of level $3$ and degree $23$ due to Chan and Liaw, we prove the fastest convergent rational Ramanujan-type series for $1/\pi$ of level $3$.
A classifier using byte n-grams as features is the only approach we have found fast enough to meet requirements in size (sub 2 MB), speed (multiple GB/s), and latency (sub 10 ms) for deployment in numerous malware detection scenarios.…
Since its invention HyperLogLog has become the standard algorithm for approximate distinct counting. Due to its space efficiency and suitability for distributed systems, it is widely used and also implemented in numerous databases. This…
The need to evaluate Logarithmic integrals is ubiquitous in essentially all quantitative areas including mathematical sciences, physical sciences. Some recent developments in Physics namely Feynman diagrams deals with the evaluation of…