Related papers: Special metrics
We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
Seminal works \cite{CRT,DonohoUnsigned,DonohoPol} generated a massive interest in studying linear under-determined systems with sparse solutions. In this paper we give a short mathematical overview of what was accomplished in last 10 years…
An array of large observational programs using ground-based and space-borne telescopes is planned in the next decade. The forthcoming wide-field sky surveys are expected to deliver a sheer volume of data exceeding an exabyte. Processing the…
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…
The emerging topic of sequential recommender systems has attracted increasing attention in recent years.Different from the conventional recommender systems including collaborative filtering and content-based filtering, SRSs try to…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.
The design, fabrication, and predicted performance of a new type of magnetic scanning probe microscope based on the newly discovered phenomenon of extraordinary magnetoresistance (EMR) is described. It is shown that the new probe should…
The status of precision electroweak data, tests of the standard model, determination of its parameters, and constraints on new physics, are surveyed.
Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…
This is a write-up of a lecture at the level of a physics colloquium. There exists an idealized mathematical formulation of strong interactions which has no free parameters but is known to describe the real world quite accurately. Over the…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
Automated metrics for Machine Translation have made significant progress, with the goal of replacing expensive and time-consuming human evaluations. These metrics are typically assessed by their correlation with human judgments, which…
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
Looking ahead to the next decade and imagining the landscape of astronomy in 2020, it is clear that astronomical surveys, large and small, plus extensive follow-up projects, will be a great engine of progress in our profession. Surveys have…
This article briefly summarizes the increasingly precise observational estimates of the cosmological parameters. After three years on the stump, the Lambda-CDM model is still the leading candidate. Although the Universe is expanding, our…