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A method for computing the n'th decimal digit of pi in O(n^3 log(n)^3) time and with very little memory is presented here. The computation is based on the recently discovered Bailey-Borwein-Plouffe algorithm and the use of a new algorithm…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In…
Dynamic algorithms come in three main flavors: $\mathit{incremental}$ (insertions-only), $\mathit{decremental}$ (deletions-only), or $\mathit{fully}$ $\mathit{dynamic}$ (both insertions and deletions). Fully dynamic is the holy grail of…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
A classical problem in Distance Geometry, with multiple practical applications (in molecular structure determination, sensor network localization etc.) is to find the possible placements of the vertices of a graph with given edge lengths.…
Dates often contribute towards highly impactful medical decisions, but it is rarely clear how to extract this data. AI has only just begun to be used transcribe such documents, and common methods are either to trust that the output produced…
Given a hierarchical plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that its meets a deadline, or, alternately, that its {\em makespan} is less…
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing the minimum number of…
This paper describes a new method for reducing the error in a classifier. It uses an error correction update that includes the very simple rule of either adding or subtracting the error adjustment, based on whether the variable value is…
The algebraic degree of Boolean functions (or vectorial Boolean functions) is an important cryptographic parameter that should be computed by fast algorithms. They work in two main ways: (1) by computing the algebraic normal form and then…
We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…
The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of…
We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
Decimal-to-binary conversion is important to modern binary computers. The classical method to solve this problem is based on division operation. In this paper, we investigate a decimal-to-binary conversion method based on addition…
This paper describes recent advances in the combinatorial method for computing $\pi(x)$, the number of primes $\leq x$. In particular, the memory usage has been reduced by a factor of $\log x$, and modifications for shared- and…
In this paper we investigate the effect of the resummation of threshold logs on the rate for B -> X_s gamma. We calculate the differential rate dGamma/dE_gamma including the infinite set of terms of the form alpha_s^n log^{n+1}(1-x) and…
Conway's Fried Potato Problem seeks to determine the best way to cut a convex body in $n$ parts by $n-1$ hyperplane cuts (with the restriction that the $i$-th cut only divides in two one of the parts obtained so far), in a way as to…
Since the 21st century, artificial intelligence has been leading a new round of industrial revolution. Under the training framework, the optimization algorithm aims to stably converge high-dimensional optimization to local and even global…