相关论文: Regular Variation and Raabe

A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…

One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…

In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…

We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the…

Directional inference for vector parameters based on higher order approximations in likelihood inference has recently been developed in the literature. Here we explore examples of directional inference where the calculations can be…

The assumption that we are typical observers plays a core role in attempts to make multiverse theories empirically testable. A widely shared worry about this assumption is that it suffers from systematic ambiguity concerning the reference…

The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition.…

Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary.…

In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions---it is not a scientific question. Good questions, when comparing theories, are operational---they deal with the…

When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…

One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Despite empirical researchers' best intention and effort to create…

The classical decision problem, as it is understood today, is the quest for a delineation between the decidable and the undecidable parts of first-order logic based on elegant syntactic criteria. In this paper, we treat the concept of…

The present work proposes an alternative approach to the problem of the emergence of classicality. Typical approaches developed in the literature derive the classical behaviour of a quantum system from conditions that concern the value of…

An experiment is described which proves, using single photons only, that the standard hidden variables assumptions (commonly used to derive Bell inequalities) are inconsistent with quantum mechanics. The analysis is very simple and…

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization…

The paper provides a new test of convergence and divergence of positive series. In particular, it extends the known test by Margaret Martin [%\emph{Bull. Amer. Math. Soc.} \textbf{47} (6), 452--457 (1941)]. \emph{Bull. Amer. Math. Soc.}…

We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…