scholarly journals Thermodynamic formalism for Haar systems in noncommutative integration: transverse functions and entropy of transverse measures

2020 ◽  
pp. 1-29
Author(s):  
ARTUR O. LOPES ◽  
JAIRO K. MENGUE
Keyword(s):  
Equivalence Relation ◽  
General Class ◽  
A Priori ◽  
Transfer Operator ◽  
Thermodynamic Formalism ◽  
Modular Functions ◽  
Noncommutative Integration

We consider here a certain class of groupoids obtained via an equivalence relation (the so-called subgroupoids of pair groupoids). We generalize to Haar systems in these groupoids some results related to entropy and pressure which are well known in thermodynamic formalism. We introduce a transfer operator, where the equivalence relation (which defines the groupoid) plays the role of the dynamics and the corresponding transverse function plays the role of the a priori probability. We also introduce the concept of invariant transverse probability and of entropy for an invariant transverse probability, as well as of pressure for transverse functions. Moreover, we explore the relation between quasi-invariant probabilities and transverse measures. Some of the general results presented here are not for continuous modular functions but for the more general class of measurable modular functions.

scholarly journals Entropy and variational principle for one-dimensional lattice systems with a generala prioriprobability: positive and zero temperature

2014 ◽  
Vol 35 (6) ◽  
pp. 1925-1961 ◽  
Author(s):  
A. O. LOPES ◽  
J. K. MENGUE ◽  
J. MOHR ◽  
R. R. SOUZA
Keyword(s):  
Infinite Product ◽  
A Priori ◽  
Transfer Operator ◽  
Thermodynamic Formalism ◽  
General Setting ◽  
Lattice Systems ◽  
Ruelle Operator ◽  
Finite Set ◽  
Zero Entropy ◽  
Infinite Set

We generalize several results of the classical theory of thermodynamic formalism by considering a compact metric space$M$as the state space. We analyze the shift acting on$M^{\mathbb{N}}$and consider a generala prioriprobability for defining the transfer (Ruelle) operator. We study potentials$A$which can depend on the infinite set of coordinates in$M^{\mathbb{N}}$. We define entropy and by its very nature it is always a non-positive number. The concepts of entropy and transfer operator are linked. If$M$is not a finite set there exist Gibbs states with arbitrary negative value of entropy. Invariant probabilities with support in a fixed point will have entropy equal to minus infinity. In the case$M=S^{1}$, and thea priorimeasure is Lebesgue$dx$, the infinite product of$dx$on$(S^{1})^{\mathbb{N}}$will have zero entropy. We analyze the Pressure problem for a Hölder potential$A$and its relation with eigenfunctions and eigenprobabilities of the Ruelle operator. Among other things we analyze the case where temperature goes to zero and we show some selection results. Our general setting can be adapted in order to analyze the thermodynamic formalism for the Bernoulli space with countable infinite symbols. Moreover, the so-called$XY$model also fits under our setting. In this last case$M$is the unitary circle$S^{1}$. We explore the differentiable structure of$(S^{1})^{\mathbb{N}}$by considering a certain class of smooth potentials and we show some properties of the corresponding main eigenfunctions.

Thermodynamic formalism for a modified shift map

2014 ◽  
Vol 14 (02) ◽  
pp. 1350020 ◽  
Author(s):  
Stephen Muir ◽  
Mariusz Urbański
Keyword(s):  
A Priori ◽  
Transfer Operator ◽  
Thermodynamic Formalism ◽  
Lattice Gases ◽  
Hölder Continuous ◽  
Full Generality ◽  
Counting Measure ◽  
Shift Map ◽  
Continuous Potential ◽  
Shift Action

We introduce a transfer operator and use it to prove some theorems of a classical flavor from thermodynamic formalism (including existence and uniqueness of appropriately defined Gibbs states and equilibrium states for potential functions satisfying Dini's condition and stochastic laws for Hölder continuous potential and observable functions) in a novel setting: the "alphabet" E is a compact metric space equipped with an a priori probability measure ν and an endomorphism T. The "modified shift map" S is defined on the product space Eℕ by the rule (x1x2x3…) ↦ (T(x2)x3…). The greatest novelty is found in the variational principle, where a term must be added to the entropy to reflect the transformation of the first coordinate by T after shifting. Our motivation is that this system, in its full generality, cannot be treated by the existing methods of either rigorous statistical mechanics of lattice gases (where only the true shift action is used) or dynamical systems theory (where the a priori measure is always implicitly taken to be the counting measure).

Collection of Ego-Centered Network Data with Computer-Assisted Interviews

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Joachim Gerich ◽  
Roland Lehner
Keyword(s):  
Survey Methods ◽  
A Priori ◽  
Dynamic Structure ◽  
Computer Assisted ◽  
Network Data ◽  
Great Effort ◽  
Self Administration ◽  
Face To Face ◽  
Full Network

Although ego-centered network data provide information that is limited in various ways as compared with full network data, an ego-centered design can be used without the need for a priori and researcher-defined network borders. Moreover, ego-centered network data can be obtained with traditional survey methods. However, due to the dynamic structure of the questionnaires involved, a great effort is required on the part of either respondents (with self-administration) or interviewers (with face-to-face interviews). As an alternative, we will show the advantages of using CASI (computer-assisted self-administered interview) methods for the collection of ego-centered network data as applied in a study on the role of social networks in substance use among college students.

Disrupted Salience and Cingulo-Opercular Network Connectivity During Impaired Rapid Instructed Task Learning in Schizophrenia

2021 ◽  
pp. 216770262095934
Author(s):  
Julia M. Sheffield ◽  
Holger Mohr ◽  
Hannes Ruge ◽  
Deanna M. Barch
Keyword(s):  
A Priori ◽  
Network Connectivity ◽  
Task Learning ◽  
Human Ability ◽  
Functional Brain Networks ◽  
Task Goals ◽  
Multivariate Pattern ◽  
And Control ◽  
Goal Directed Behavior

Rapid instructed task learning (RITL) is the uniquely human ability to transform task information into goal-directed behavior without relying on trial-and-error learning. RITL is a core cognitive process supported by functional brain networks. In patients with schizophrenia, RITL ability is impaired, but the role of functional network connectivity in these RITL deficits is unknown. We investigated task-based connectivity of eight a priori network pairs in participants with schizophrenia ( n = 29) and control participants ( n = 31) during the performance of an RITL task. Multivariate pattern analysis was used to determine which network connectivity patterns predicted diagnostic group. Of all network pairs, only the connectivity between the cingulo-opercular network (CON) and salience network (SAN) during learning classified patients and control participants with significant accuracy (80%). CON-SAN connectivity during learning was significantly associated with task performance in participants with schizophrenia. These findings suggest that impaired interactions between identification of salient stimuli and maintenance of task goals contributes to RITL deficits in participants with schizophrenia.

scholarly journals The Role of Global Appearance of Omnidirectional Images in Relative Distance and Orientation Retrieval

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3327
Author(s):  
Vicente Román ◽  
Luis Payá ◽  
Adrián Peidró ◽  
Mónica Ballesta ◽  
Oscar Reinoso
Keyword(s):  
Mobile Robotics ◽  
A Priori ◽  
Computational Cost ◽  
Relevant Information ◽  
Local Features ◽  
New Family ◽  
Lighting Conditions ◽  
Omnidirectional Images ◽  
Great Development

Over the last few years, mobile robotics has experienced a great development thanks to the wide variety of problems that can be solved with this technology. An autonomous mobile robot must be able to operate in a priori unknown environments, planning its trajectory and navigating to the required target points. With this aim, it is crucial solving the mapping and localization problems with accuracy and acceptable computational cost. The use of omnidirectional vision systems has emerged as a robust choice thanks to the big quantity of information they can extract from the environment. The images must be processed to obtain relevant information that permits solving robustly the mapping and localization problems. The classical frameworks to address this problem are based on the extraction, description and tracking of local features or landmarks. However, more recently, a new family of methods has emerged as a robust alternative in mobile robotics. It consists of describing each image as a whole, what leads to conceptually simpler algorithms. While methods based on local features have been extensively studied and compared in the literature, those based on global appearance still merit a deep study to uncover their performance. In this work, a comparative evaluation of six global-appearance description techniques in localization tasks is carried out, both in terms of accuracy and computational cost. Some sets of images captured in a real environment are used with this aim, including some typical phenomena such as changes in lighting conditions, visual aliasing, partial occlusions and noise.

scholarly journals Visualization approaches to support healthy aging: A systematic review

2016 ◽  
Vol 23 (3) ◽  
pp. 600 ◽  
Author(s):  
Uba Backonja ◽  
Nai-Ching Chi ◽  
Yong Choi ◽  
Amanda K Hall ◽  
Thai Le ◽  
...  
Keyword(s):  
Older Adults ◽  
Health Behaviors ◽  
Healthy Aging ◽  
A Priori ◽  
Aging In Place ◽  
Future Research ◽  
Health Technologies ◽  
Data Visualizations ◽  
Informatics Tools

Background: Health technologies have the potential to support the growing number of older adults who are aging in place. Many tools include visualizations (data visualizations, visualizations of physical representations). However, the role of visualizations in supporting aging in place remains largely unexplored.Objective: To synthesize and identify gaps in the literature evaluating visualizations (data visualizations and visualizations of physical representations), for informatics tools to support healthy aging.Methods: We conducted a search in CINAHL, Embase, Engineering Village, PsycINFO, PubMed, and Web of Science using a priori defined terms for publications in English describing community-based studies evaluating visualizations used by adults aged ≥65 years.Results: Six out of the identified 251 publications were eligible. Most studies were user studies and varied methodological quality. Three visualizations of virtual representations supported performing at-home exercises. Participants found visual representations either (a) helpful, motivational, and supported their understanding of their health behaviors or (b) not an improvement over alternatives. Three data visualizations supported understanding of one’s health. Participants were able to interpret data visualizations that used precise data and encodings that were more concrete better than those that did not provide precision or were abstract. Participants found data visualizations helpful in understanding their overall health and granular data.Conclusions: Studies we identified used visualizations to promote engagement in exercises or understandings of one’s health. Future research could overcome methodological limitations of studies we identified to develop visualizations that older adults could use with ease and accuracy to support their health behaviors and decision-making.

scholarly journals Family quarrels in seeds and rapid adaptive evolution in Arabidopsis

2019 ◽  
Vol 116 (19) ◽  
pp. 9463-9468 ◽  
Author(s):  
Katherine S. Geist ◽  
Joan E. Strassmann ◽  
David C. Queller
Keyword(s):  
Adaptive Evolution ◽  
Kin Selection ◽  
Conflicts Of Interest ◽  
A Priori ◽  
Flowering Plant ◽  
Rapid Adaptation ◽  
Arms Races ◽  
Evolutionary Conflict ◽  
Alternative Hypotheses

Evolutionary conflict can drive rapid adaptive evolution, sometimes called an arms race, because each party needs to respond continually to the adaptations of the other. Evidence for such arms races can sometimes be seen in morphology, in behavior, or in the genes underlying sexual interactions of host−pathogen interactions, but is rarely predicted a priori. Kin selection theory predicts that conflicts of interest should usually be reduced but not eliminated among genetic relatives, but there is little evidence as to whether conflict within families can drive rapid adaptation. Here we test multiple predictions about how conflict over the amount of resources an offspring receives from its parent would drive rapid molecular evolution in seed tissues of the flowering plant Arabidopsis. As predicted, there is more adaptive evolution in genes expressed in Arabidopsis seeds than in other specialized organs, more in endosperms and maternal tissues than in embryos, and more in the specific subtissues involved in nutrient transfer. In the absence of credible alternative hypotheses, these results suggest that kin selection and conflict are important in plants, that the conflict includes not just the mother and offspring but also the triploid endosperm, and that, despite the conflict-reducing role of kinship, family members can engage in slow but steady tortoise-like arms races.

The Role of Dimensional Distinctiveness in Children's and Adults' Artifact Categorization

2005 ◽  
Vol 16 (2) ◽  
pp. 137-144 ◽  
Author(s):  
Rubi Hammer ◽  
Gil Diesendruck
Keyword(s):  
Preschool Children ◽  
Contextual Factors ◽  
A Priori ◽  
Functional Similarity ◽  
Second Stage ◽  
Functional Dimension

There are conflicting results as to whether preschool children categorize artifacts on the basis of physical or functional similarity. The present study investigated the effect of the relative distinctiveness of these dimensions in children's categorization. In a physical-distinctive condition, preschool children and adults were initially asked to categorize computer-animated artifacts whose physical appearances were more distinctive than their functions. In a function-distinctive condition, the functional dimension of objects was more distinctive than their physical appearances. Both conditions included a second stage of categorization in which both dimensions were equally distinctive. Participants in a control condition performed only this stage of categorization. Adults in all conditions and stages consistently categorized by functional similarity. In contrast, children's categorization was affected by the relative distinctiveness of the dimensions. Children may not have a priori specific beliefs about how to categorize novel artifacts, and thus may be more susceptible to contextual factors.

Multiple boundary blow-up solutions for nonlinear elliptic equations

2003 ◽  
Vol 133 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Amandine Aftalion ◽  
Manuel del Pino ◽  
René Letelier
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Positive Parameter ◽  
Number Of Solutions ◽  
Bounded Smooth Domain ◽  
Nonlinear Elliptic ◽  
Bounded Smooth

We consider the problem Δu = λf(u) in Ω, u(x) tends to +∞ as x approaches ∂Ω. Here, Ω is a bounded smooth domain in RN, N ≥ 1 and λ is a positive parameter. In this paper, we are interested in analysing the role of the sign changes of the function f in the number of solutions of this problem. As a consequence of our main result, we find that if Ω is star-shaped and f behaves like f(u) = u(u−a)(u−1) with ½ < a < 1, then there is a solution bigger than 1 for all λ and there exists λ0 > 0 such that, for λ < λ0, there is no positive solution that crosses 1 and, for λ > λ0, at least two solutions that cross 1. The proof is based on a priori estimates, the construction of barriers and topological-degree arguments.

scholarly journals Statistical Primer for Athletic Trainers: Understanding the Role of Statistical Power in Comparative Athletic Training Research

2018 ◽  
Vol 53 (7) ◽  
pp. 716-719
Author(s):  
Monica R. Lininger ◽  
Bryan L. Riemann
Keyword(s):  
Sample Size ◽  
Athletic Training ◽  
Treatment Effect ◽  
Statistical Power ◽  
Athletic Trainers ◽  
A Priori ◽  
Significant Treatment ◽  
Training Research ◽  
Α Level

Objective: To describe the concept of statistical power as related to comparative interventions and how various factors, including sample size, affect statistical power.Background: Having a sufficiently sized sample for a study is necessary for an investigation to demonstrate that an effective treatment is statistically superior. Many researchers fail to conduct and report a priori sample-size estimates, which then makes it difficult to interpret nonsignificant results and causes the clinician to question the planning of the research design.Description: Statistical power is the probability of statistically detecting a treatment effect when one truly exists. The α level, a measure of differences between groups, the variability of the data, and the sample size all affect statistical power.Recommendations: Authors should conduct and provide the results of a priori sample-size estimations in the literature. This will assist clinicians in determining whether the lack of a statistically significant treatment effect is due to an underpowered study or to a treatment's actually having no effect.

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