相关论文: An error estimate for counting $S_3$-sextic number…
Here, we give upper and lower bounds on the count of positive integers $n\le x$ dividing the $n$th term of a nondegenerate linearly recurrent sequence with simple roots.
In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error…
Machine learning plays an increasingly significant role in many aspects of our lives (including medicine, transportation, security, justice and other domains), making the potential consequences of false predictions increasingly devastating.…
This report first provides a brief overview of a number of supervised learning algorithms for regression tasks. Among those are neural networks, regression trees, and the recently introduced Nexting. Nexting has been presented in the…
The skip-thought model has been proven to be effective at learning sentence representations and capturing sentence semantics. In this paper, we propose a suite of techniques to trim and improve it. First, we validate a hypothesis that,…
We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new light on…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
The $p$-th power of the logarithm of the Catalan generating function is computed using the Stirling cycle numbers. Instead of Stirling numbers, one may write this generating function in terms of higher order harmonic numbers.
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
We explore power spectrum estimation in the context of a Gaussian approximation to the likelihood function. Using the Saskatoon data, we estimate the power averaged through a set of ten filters designed to make the errors on the power…
In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type $10^{500}$ for the sizes of solutions). Here we apply this algorithm to calculating…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
We discuss the power counting for effective field theories with narrow resonances near a two-body threshold. Close to threshold, the effective field theory is perturbative and only one combination of coupling constants is fine-tuned. In the…
We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in the unit disk.
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
We provide approximations to the prime counting function by various discretized versions of the logarithmic integral function, expressed solely in terms of the harmonic numbers. We demonstrate with explicit error bounds that these…
In a previous paper, some deviations were found in the O(p^6) low-energy constants that contribute to the pi pi-scattering lengths. This work completes the study of all the relevant couplings (r_1, ... r_6, r_S2). We also perform a…
The earlier work of the author on Frequency estimation in three-phase power systems ( that is included as the reference number 1) is expanded to the distributed setting in order present a framework for the implementation of such a frequency…
Can any element in a sufficiently large finite field be represented as a sum of two $d$th powers in the field? In this article, we recount some of the history of this problem, touching on cyclotomy, Fermat's last theorem, and diagonal…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…