Related papers: Dedieu-Shub Measures
We present a general Bayesian method for quantifying the statistical reliability of one-dimensional measures of scientific quality based on citation data. Two quality measures used in practice -- ``papers per year'' and ``Hirsch's $h$'' --…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
Several questions of scientometrics parameters organization are considered. Two new indices for scientific works citation analysis are proposed. They provide more detailed and reliable scientific significance assessment of individual…
The paper is an introduction to intuitionistic mathematics.
In this talk, some aspects of duality symmetries are presented.
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
Inertial motion analysis is having a growing interest during the last decades due to its advantages over classical optical systems. The technological solution based on inertial measurement units allows the measurement of movements in daily…
A simple technique of measurement of seeing in daytime and nighttime, based upon drift-scan observations, is presented, along with observational examples. This experience can be repeated easily in classroom contexts.
Measuring the mechanical properties of cells and tissues often involves indentation with a sphere, or compression between two plates. Previously, different theoretical approaches have been developed to retrieve material parameters (e.g.…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
This is an expository paper (in Spanish) about the metric approximation of groups.
A recent paper published in Am. J. Phys. describes an experiment designed to measure the one-way speed of light. Although the experiment is very interesting, in particular to be used in student laboratories, it is in fact determining the…
This article introduces the Multidimensional Research Assessment Matrix of scientific output. Its base notion holds that the choice of metrics to be applied in a research assessment process depends upon the unit of assessment, the research…
A novel definition of the stimulus-specific information is presented, which is particularly useful when the stimuli constitute a continuous and metric set, as for example, position in space. The approach allows one to build the spatial…
We propose the Star-Shaped deviation measures in the same vein as Star-Shaped risk measures and Star-Shaped acceptability indexes. We characterize Star-Shaped deviation measures through Star-Shaped acceptance sets and as the minimum of a…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
Given a distribution in the unite square and having iid sample from it the first question what a statistician might do to test the hypothesis that the sample is iid. For this purpose an extension of the Plancherel measure is introduced.…
A survey paper on some recent results on additive problems with prime powers.
These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.