相关论文: An error estimate for counting $S_3$-sextic number…
We obtain a power saving in the error term for a semigroup congruence lattice point count related to continued fractions. This is done by adapting arguments from recent work of Oh and Winter (2014) that give uniform bounds for certain…
The well-known result states that the square-free counting function up to $N$ is $N/\zeta(2)+O(N^{1/2})$. This corresponds to the identity polynomial $\text{Id}(x)$. It is expected that the error term in question is…
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We…
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
We prove matching upper and lower bounds for the average of the 6-torsion of class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine quartic threefold.
The COMPASS collaboration published precise data on production cross section of charged hadrons in lepton-hadron semi-inclusive deep inelastic scattering, showing almost an order of magnitude larger than next-to-leading order QCD…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of…
This paper introduces and develops a novel variable importance score function in the context of ensemble learning and demonstrates its appeal both theoretically and empirically. Our proposed score function is simple and more straightforward…
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
The positive effect of adding subword information to word embeddings has been demonstrated for predictive models. In this paper we investigate whether similar benefits can also be derived from incorporating subwords into counting models. We…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…
It is generally believed that knowing the light travel time up to the post-post-Minkowskian level (terms in $G^2$) is sufficient for modelling the most accurate experiments designed to test general relativity in a foreseeable future.…
When matter fields are included in chiral perturbation theory, the nonvanishing mass in the chiral limit introduces a new energy scale so that the loop diagrams including such matter field propagators spoil the usual power counting.…
In the paper we propose some new class of functions which is used to construct tail index estimators. Functions from this new class is non-monotone in general, but presents a product of two monotone functions: the power function and the…
We improve the unconditional explicit bounds for the error term in the prime counting function $\psi(x)$. In particular, we prove that, for all $x>2$, we have \[ \left| \psi(x)-x \right| < 9.22106 \, x \, (\log x)^{3/2}…
Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction…