Related papers: A note on the notion "statistical symmetry"
The purpose of this note is to clarify the logical relationship between joint measurability and contextuality for quantum observables in view of recent developments [1-4].
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…
Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…
The main purpose of this short article is to give a brief overview of the development of the very interesting weak measurement protocol. I add some comments relating to the reality of weak values, and also comment on the allowed values of…
Nearly a decade ago, the science community was introduced to the $h$-index, a proposed statistical measure of the collective impact of the publications of any individual researcher. It is of course undeniable that any method of reducing a…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
During the last two decades, in statistical process monitoring plentiful new methods appeared with synthetic-type control charts being a prominent constituent. These charts became popular designs for several reasons. The two most important…
This article explores the critical role of statistical analysis in precision medicine. It discusses how personalized healthcare is enhanced by statistical methods that interpret complex, multidimensional datasets, focusing on predictive…
We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…
When a physicist says that a theory is fine-tuned, they mean that it must make a suspiciously precise assumption in order to explain a certain observation. This is evidence that the theory is deficient or incomplete. One particular case of…
In this short note I review and discuss fundamental options for physical and logical data layouts as well as the impact of the choices on data processing. I should say in advance that these notes offer no new insights, that is, everything…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons…