Related papers: Powered numbers in short intervals II
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some…
This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
Let a polynomial $f \in \mathbb{Z}[X_1,\ldots,X_n]$ be given. The square sieve can provide an upper bound for the number of integral $\mathbf{x} \in [-B,B]^n$ such that $f(\mathbf{x})$ is a perfect square. Recently this has been generalized…
In multigroup data settings with small within-group sample sizes, standard $F$-tests of group-specific linear hypotheses can have low power, particularly if the within-group sample sizes are not large relative to the number of explanatory…
The divisibility of truncated binomial series by their exponent n is analyzed. Divisibility is shown to depends on the divisibility characteristics of the integers constituting the binomials. Series division by the highest possible powers…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data generating processes when high-dimensional nuisance models are estimated by post-model-selection or…
We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for…
This paper provides nonparametric identification results for random coefficient distributions in perturbed utility models. We cover discrete and continuous choice models. We establish identification using variation in mean quantities, and…
In the late eighties, Hildebrand and Tenenbaum proved an asymptotic formula for the number of positive integers below $x$, having exactly $\nu$ distinct prime divisors: $\pi_{\nu}(x) \sim x \delta_{\nu}(x)$. Here we consider the restricted…
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…
In this paper we present a method for producing asymptotic estimates for the number of integers in a given S having only ``small'' prime factors. The conditions that need to be verified are simpler than those required by other methods, and…
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…
In this paper we establish function field versions of two classical conjectures on prime numbers. The first says that the number of primes in intervals (x,x+x^epsilon] is about x^epsilon/log x and the second says that the number of primes…