general framework
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2022 ◽  
Vol 73 ◽  
pp. 67-73
Author(s):  
Yiying Sun ◽  
Wenping Li ◽  
Zhuo Wang ◽  
Jiafu Shi ◽  
Zhongyi Jiang

Bernoulli ◽  
2022 ◽  
Vol 28 (1) ◽  
Author(s):  
Ricardo Carrizo Vergara ◽  
Denis Allard ◽  
Nicolas Desassis

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 125
Author(s):  
Damián G. Hernández ◽  
Inés Samengo

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.


Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 24
Author(s):  
Oles Dobosevych ◽  
Rostyslav Hryniv

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.


2022 ◽  
Vol 14 (2) ◽  
pp. 664
Author(s):  
Jianhong Luo ◽  
Shifen Qiu ◽  
Xuwei Pan ◽  
Ke Yang ◽  
Yuanqingqing Tian

With the improvements in per capita disposable income, and an increase in work-related pressure, demand for leisure consumption such as foot bath spas is constantly increasing. Analysis of leisure consumption sentiment is of great importance for the leisure service industry—to meet customer needs, improve service quality and improve customer relationship management. However, traditional sentiment analysis approaches only aimed to ascertain the overall sentiment of the customer, which is less effective for analyzing customer satisfaction on account of customer size, different customer locations, and different leisure holidays. Sentiment analysis via online reviews can assist different businesses, including foot bath spa services, to better inform the development of customer segmentation strategies and ensure optimal customer relationship management. Hence, the objective of this paper is to explore foot bath spa leisure consumption sentiment towards different holidays and different cities by applying data mining via online reviews, so as to help optimize customer segmentation. A novel general framework and related sentiment analysis methods were proposed and then conducted through a collection of datasets from customers’ textual reviews of foot bath spa merchants in three cities in China on the Meituan social media platform. Findings confirm that the proposed general framework and methods can be used to gain insights into the swing characteristics of sentiment towards different holidays and different cities, to better develop customer segmentation according to the city-holiday emoticon face patterns obtained through sentiment tendency analysis from online social media review data. The study results can help to develop better customer and marketing strategies, thereby creating sustainable competitive advantages, and can be extended to other fields to support sustainable development.


Author(s):  
Frederic Weber ◽  
Rico Zacher

AbstractWe establish a reduction principle to derive Li–Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting. Our approach is not based on curvature-dimension inequalities but on heat kernel representations of the solutions and consists in reducing the problem to the heat kernel. As an important application we solve a long-standing open problem by obtaining a Li–Yau inequality for positive solutions u to the fractional (in space) heat equation of the form $$(-\Delta )^{\beta /2}(\log u)\le C/t$$ ( - Δ ) β / 2 ( log u ) ≤ C / t , where $$\beta \in (0,2)$$ β ∈ ( 0 , 2 ) . We also show that this Li–Yau inequality allows to derive a Harnack inequality. We further illustrate our general result with an example in the discrete setting by proving a sharp Li–Yau inequality for diffusion on a complete graph.


Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 620
Author(s):  
Armin Tavakoli ◽  
Emmanuel Zambrini Cruzeiro ◽  
Erik Woodhead ◽  
Stefano Pironio

We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.


2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
André Marques ◽  
Fátima Silva Leite

<p style='text-indent:20px;'>This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [<xref ref-type="bibr" rid="b26">26</xref>] for submanifolds of an Euclidean space. We also prove some important properties of these rolling maps. After presenting the general framework, we analyse the particular rolling of hyperquadrics embedded in pseudo-Euclidean spaces. The central topic is the rolling of a pseudo-hyperbolic space over the affine space associated with its tangent space at a point. We derive the kinematic equations, as well as the corresponding explicit solutions for two specific cases, and prove the existence of a rolling map along any curve in that rolling space. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. Finally, for the central theme, we write the kinematic equations as a control system evolving on a certain Lie group and prove its controllability. The choice of the controls corresponds to the choice of a rolling curve.</p>


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