Explicit Rate Research Articles

A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed balance are revisited in terms of the supersymmetric quantum Hamiltonian H that can be obtained from the Markov generator via a similarity transformation. We first focus on the large deviations at level 2 for the empirical density p^(C) of the configurations C seen during a trajectory over the large time window [0,T] , and rewrite the explicit Donsker–Varadhan rate function as the matrix element I[2][p^(.)]=⟨p^|H|p^⟩ involving the square-root ket |p^⟩ . (The analog formula is also discussed for reversible diffusion processes as a comparison.) We then consider the explicit rate functions at higher levels, in particular for the joint probability of the empirical density p^(C) and the empirical local activities a^(C,C′) characterizing the density of jumps between two configurations (C,C′) . Finally, the explicit rate function for the joint probability of the empirical density p^(C) and of the empirical total activity A^ that represents the total density of jumps of a long trajectory is written in terms of the two matrix elements ⟨p^|H|p^⟩ and ⟨p^|Hoff|p^⟩ , where Hoff represents the off-diagonal part of the supersymmetric Hamiltonian H. This general framework is then applied to pure or random spin chains with single-spin-flip or two-spin-flip transition rates, where the supersymmetric Hamiltonian H corresponds to quantum spin chains with local interactions involving Pauli matrices of two or three neighboring sites. It is then useful to introduce the quantum density matrix ρ^=|p^⟩⟨p^| associated with the empirical density p^(.) in order to rewrite the various rate functions in terms of reduced density matrices involving only two or three neighboring sites.

Stability for the magnetic Bénard system with partial dissipation

We prove the stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in T2. Neglecting the effect of the temperature, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.

Stability and optimal decay for the 3D anisotropic magnetohydrodynamic equations

AbstractThis paper investigates the stability problem and large time behavior of solutions to the three‐dimensional magnetohydrodynamic equations with horizontal velocity dissipation and magnetic diffusion only in the direction. By applying the structure of the system, time‐weighted methods, and the method of bootstrapping argument, we prove that any perturbation near the background magnetic field (1, 0, 0) is globally stable in the Sobolev space . Furthermore, explicit decay rates in are obtained. Motivated by the stability of the three‐dimensional Navier–Stokes equations with horizontal dissipation, this paper aims to understand the stability of perturbations near a magnetic background field and reveal the mechanism of how the magnetic field generates enhanced dissipation and helps stabilize the fluid.

The primacy of experience in language processing: Semantic priming is driven primarily by experiential similarity

The organization of semantic memory, including memory for word meanings, has long been a central question in cognitive science. Although there is general agreement that word meaning representations must make contact with sensory-motor and affective experiences in a non-arbitrary fashion, the nature of this relationship remains controversial. One prominent view proposes that word meanings are represented directly in terms of their experiential content (i.e., sensory-motor and affective representations). Opponents of this view argue that the representation of word meanings reflects primarily taxonomic structure, that is, their relationships to natural categories. In addition, the recent success of language models based on word co-occurrence (i.e., distributional) information in emulating human linguistic behavior has led to proposals that this kind of information may play an important role in the representation of lexical concepts. We used a semantic priming paradigm designed for representational similarity analysis (RSA) to quantitatively assess how well each of these theories explains the representational similarity pattern for a large set of words. Crucially, we used partial correlation RSA to account for intercorrelations between model predictions, which allowed us to assess, for the first time, the unique effect of each model. Semantic priming was driven primarily by experiential similarity between prime and target, with no evidence of an independent effect of distributional or taxonomic similarity. Furthermore, only the experiential models accounted for unique variance in priming after partialling out explicit similarity ratings. These results support experiential accounts of semantic representation and indicate that, despite their good performance at some linguistic tasks, the distributional models evaluated here do not encode the same kind of information used by the human semantic system.

Decoding the language of first impressions: Comparing models of first impressions of faces derived from free-text descriptions and trait ratings.

First impressions formed from facial appearance predict important social outcomes. Existing models of these impressions indicate they are underpinned by dimensions of Valence and Dominance, and are typically derived by applying data reduction methods to explicit ratings of faces for a range of traits. However, this approach is potentially problematic because the trait ratings may not fully capture the dimensions on which people spontaneously assess faces. Here, we used natural language processing to extract 'topics' directly from participants' free-text descriptions (i.e., their first impressions) of 2222 face images. Two topics emerged, reflecting first impressions related to positive emotional valence and warmth (Topic 1) and negative emotional valence and potential threat (Topic 2). Next, we investigated how these topics were related to Valence and Dominance components derived from explicit trait ratings. Collectively, these components explained only ~44% of the variance in the topics extracted from free-text descriptions and suggested that first impressions are underpinned by correlated valence dimensions that subsume the content of existing trait-rating-based models. Natural language offers a promising new avenue for understanding social cognition, and future work can examine the predictive utility of natural language and traditional data-driven models for impressions in varying social contexts.

General Decay Rates of the Solution Energy in a Viscoelastic Wave Equation With Boundary Feedback and a Nonlinear Source

In a bounded domain, we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary and certain initial data. We establish an explicit and general decay rate result, using some properties of the convex functions. Our new results substantially improve several earlier related results in the literature. Keywords: General decay, nonlinear source, viscoelastic, wave equation, relaxation function.

Can mindfulness-based training impact explicit and implicit attitudes and sustainable nutrition behavior? A focus on vegetarianism

ObjectivesThe aim of this study was to investigate the impact of a mindfulness intervention (IG) compared to an inactive control group (CG) on explicit and implicit attitudes toward vegetarian and meat-based foods, nutrition behavior measures, trait mindfulness and wellbeing. MethodsIn the IG (N = 66), we implemented a mindfulness-based intervention consisting of eight weekly group sessions online, along with an additional half-day session held on campus. The CG (N = 71) received no intervention or training. We employed a pre-/post-intervention design involving questionnaires (trait mindfulness, wellbeing, sustainable nutrition behavior scale), an online supermarket scenario, as well as an explicit rating task and an implicit association task using pictures of vegetarian and meat-based foods. Additionally, a voluntary follow-up testing was conducted two months after the final group session. ResultsNo intervention effects were observed on explicit and implicit attitudes, wellbeing, or nutrition behavior measures. However, there was an increase in trait mindfulness within the IG. Exploratory cross-sectional findings indicated that trait mindfulness facets such as “Acting with Awareness” and “Outer Awareness”, along with explicit attitudes, were significant predictors of self-reported sustainable consumption behavior. Additionally, sex and explicit attitudes were identified as significant predictors of vegetarian consumption behavior in the online supermarket task. ConclusionOur findings could not substantiate previous claims regarding the potential causal effects of mindfulness practice on sustainable consumption behavior, specifically in the realm of sustainable and vegetarian nutrition, as well as subjective wellbeing. Future studies may benefit from implementing longer-term mindfulness-based interventions and considering other potential decisive factors, such as connectedness to nature and others. Integrating training elements focusing on these specific variables into the intervention could be valuable.

A novel similarity measure SF-IPF for CBKNN with implicit feedback data

PurposeThe increasing popularity of music streaming services also increases the need to customize the services for each user to attract and retain customers. Most of the music streaming services will not have explicit ratings for songs; they will have only implicit feedback data, i.e user listening history. For efficient music recommendation, the preferences of the users have to be infered, which is a challenging task.Design/methodology/approachPreferences of the users can be identified from the users' listening history. In this paper, a hybrid music recommendation system is proposed that infers features from user's implicit feedback and uses the hybrid of content-based and collaborative filtering method to recommend songs. A Content Boosted K-Nearest Neighbours (CBKNN) filtering technique was proposed, which used the users' listening history, popularity of songs, song features, and songs of similar interested users for recommending songs. The song features are taken as content features. Song Frequency–Inverse Popularity Frequency (SF-IPF) metric is proposed to find the similarity among the neighbours in collaborative filtering. Million Song Dataset and Echo Nest Taste Profile Subset are used as data sets.FindingsThe proposed CBKNN technique with SF-IPF similarity measure to identify similar interest neighbours performs better than other machine learning techniques like linear regression, decision trees, random forest, support vector machines, XGboost and Adaboost. The performance of proposed SF-IPF was tested with other similarity metrics like Pearson and Cosine similarity measures, in which SF-IPF results in better performance.Originality/valueThis method was devised to infer the user preferences from the implicit feedback data and it is converted as rating preferences. The importance of adding content features with collaborative information is analysed in hybrid filtering. A new similarity metric SF-IPF is formulated to identify the similarity between the users in collaborative filtering.

Strongly Kreiss bounded operators in UMD Banach spaces

In this paper we give growth estimates for ‖Tn‖\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert T^n\\Vert $$\\end{document} for n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\rightarrow \\infty $$\\end{document} in the case T is a strongly Kreiss bounded operator on a UMD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{UMD}\\,}}$$\\end{document} Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-spaces, but also intermediate UMD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{UMD}\\,}}$$\\end{document} spaces such as non-commutative Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-spaces and variable Lebesgue spaces.

Touch me or touch me not: Emotion regulation by affective touch in human adults.

In mammals, including humans, affective touch (AT) supports the establishment and maintenance of social connections and mitigates the effects of social conflict and ostracism. AT is used to describe slowly moving, low-forced mechanical stimulation that is frequently perceived as pleasant. In humans, AT has been addressed particularly for its role in promoting bonding and emotional regulation during early development; however, more recent studies have suggested that AT also preserves physical and emotional well-being in adulthood. Here, we investigated whether AT can buffer adults' experience of negative emotions as reflected in their behavioral and physiological responses to emotionally arousing stimuli. Participants were stimulated on their forearms using AT or tapping (T) while they viewed a series of emotionally arousing and neutral images, and we measured their skin conductance response and their explicit rating of the images' unpleasantness. We found that AT, but not T, reduced the arousal and perceived unpleasantness of the emotional stimuli but not the neutral ones, revealing the soothing role of AT in emotional contexts. The second aim of the study was to explore the possibility that AT might benefit some individuals more than others, according to their individual differences. To this aim, we assessed individuals' empathy and sensory processing sensitivity, as well as their perception of AT itself. Results revealed that while empathy did not predict changes in emotional processing irrespective of tactile stimulation, individuals with higher sensitivity reported AT as less pleasant. We discuss the possible factors mediating the observed interindividual variability in AT perception. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results

Abstract In this study, we consider a viscoelastic Shear beam model with no rotary inertia. Specifically, we study ρ 1 φ t t − κ ( φ x + ψ ) x + ( g ∗ φ x x ) ( t ) = 0 , − b ψ x x + κ ( φ x + ψ ) = 0 , \begin{array}{rcl}{\rho }_{1}{\varphi }_{tt}-\kappa {\left({\varphi }_{x}+\psi )}_{x}+\left(g\ast {\varphi }_{xx})\left(t)& =& 0,\\ -b{\psi }_{xx}+\kappa \left({\varphi }_{x}+\psi )& =& 0,\end{array} where the convolution memory function g g belongs to a class of L 1 ( 0 , ∞ ) {L}^{1}\left(0,\infty ) functions that satisfies g ′ ( t ) ≤ − ξ ( t ) ϒ ( g ( t ) ) , ∀ t ≥ 0 , g^{\prime} \left(t)\le -\xi \left(t)\Upsilon \left(g\left(t)),\hspace{1.0em}\forall t\ge 0, where ξ \xi is a positive nonincreasing differentiable function and ϒ \Upsilon is an increasing and convex function near the origin. Using just this general assumptions on the behavior of g g at infinity, we provide optimal and explicit general energy decay rates from which we recover the exponential and polynomial rates when ϒ ( s ) = s p \Upsilon \left(s)={s}^{p} and p p covers the full admissible range [ 1 , 2 ) \left[1,2) . Given this degree of generality, our results improve some of earlier related results in the literature.

New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type

In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related results in the literature.

On the convergence of gradient descent for robust functional linear regression

Functional data analysis offers a set of statistical methods concerned with extracting insights from intrinsically infinite-dimensional data and has attracted considerable amount of attentions in the past few decades. In this paper, we study robust functional linear regression model with a scalar response and a functional predictor in the framework of reproducing kernel Hilbert spaces. A gradient descent algorithm with early stopping is introduced to solve the corresponding empirical risk minimization problem associated with robust loss functions. By appropriately selecting the early stopping rule and the scaling parameter of the robust losses, the convergence of the proposed algorithm is established when the response variable is bounded or satisfies a moment condition. Explicit learning rates with respect to both estimation and prediction error are provided in terms of regularity of the regression function and eigenvalue decay rate of the integral operator induced by the reproducing kernel and covariance function.

Enhancing Educational Design Capabilities through Interactive Mobile and Adaptive Learning Platforms: An Empirical Study

With the continuous advancement of educational technology, interactive mobile and adaptive learning platforms are playing an increasingly important role in the field of education. This is particularly evident in the development of educational design skills among education students, as these platforms showcase their unique value. Educational design capability is a crucial skill for education students, directly related to the quality of designing and implementing future teaching activities. Traditional methods of education often fail to fully consider individual student differences, resulting in inadequate cultivation of personalized capabilities. This study aims to explore and achieve precise cultivation of educational design capabilities in education students through interactive, mobile, and adaptive learning platforms. This paper first reviews the current application of interactive mobile and adaptive learning platforms to cultivate educational design capabilities. It highlights deficiencies in existing research methods related to personalized matching and recommendation system design. To address these deficiencies, this study proposes a new set of adaptive matching methods. These methods include capability characteristic recognition based on competitive advantage thinking, the construction of individual strength models, as well as matching calculation, and decision- making scheme optimization using the projection decision method and the Hungarian method. Additionally, the study designs a learning project recommendation algorithm based on explicit ratings to enhance the accuracy and personalization of learning project recommendations. The application of these methods not only enhances the educational design capabilities of education students but also provides new theoretical support and practical guidance for the development of interactive, mobile, and adaptive learning platforms.

Coexistence and locally exponential stability of multiple equilibrium points for fractional-order impulsive control Cohen–Grossberg neural networks

Different from the existing multiple Mittag-Leffler stability or multiple asymptotic stability, the multiple exponential stability, which has explicit and faster convergence rate, is investigated in this paper for fractional-order impulsive control Cohen–Grossberg neural networks. First, by using the definition of Dirac delta function, the fractional-order control Cohen–Grossberg neural networks are translated into fractional-order impulsive neural networks, in which pulse effect relies on the fractional order of the addressed system. Then, based on maximum norm, 1−norm and general q−norm (q=2n), a series of novel criteria are obtained respectively to ensure that such n−neuron neural networks can have ∏i=1n(2Li+1) total equilibrium points and ∏i=1n(Li+1) locally exponentially stable equilibrium points, by utilizing the known fixed point theorem, the method of average impulsive interval, the theory of fractional-order differential equations, and the method of Lyapunov function. This paper’s investigation reveals the effects of impulsive function, impulsive interval, and fractional order on the dynamic behaviors. Finally, theoretical results are shown to be effective by four illustrative examples.

On the rate of convergence of Yosida approximation for the nonlocal Cahn–Hilliard equation

Abstract It is well-known that one can construct solutions to the nonlocal Cahn–Hilliard equation with singular potentials via Yosida approximation with parameter $\lambda \to 0$. The usual method is based on compactness arguments and does not provide any rate of convergence. Here, we fill the gap and we obtain an explicit convergence rate $\sqrt{\lambda }$. The proof is based on the theory of maximal monotone operators and an observation that the nonlocal operator is of Hilbert–Schmidt type. Our estimate can provide convergence result for the Galerkin methods where the parameter $\lambda $ could be linked to the discretization parameters, yielding appropriate error estimates.

Enhancing Urban Climate‐Energy Modeling in the Community Earth System Model (CESM) Through Explicit Representation of Urban Air‐Conditioning Adoption

AbstractImproved representation of urban processes in Earth System Models (ESMs) is a pressing need for climate modeling and climate‐driven urban energy studies. Despite recent improvements to its fully coupled Building Energy Model (BEM), the current Community Land Model Urban (CLMU) in the Community Earth System Model (CESM) lacks the infrastructure to model air‐conditioning (AC) adoption explicitly. This undermines CESM's fidelity in modeling urban climate and energy use, and limits its use in climate and energy risk assessments. Here, we establish a new parameterization scheme in CESM that represents AC adoption explicitly through an AC adoption rate parameter in the BEM of CLMU, and build a present‐day, global, survey‐based, and spatially explicit AC adoption rate data set at country and sub‐country level that is integrated within CESM. The new data set can be leveraged for other ESMs or global‐scale models and analyses. The explicit AC adoption scheme and the AC adoption rate data set significantly improve the accuracy of anthropogenic heat modeling due to AC in CESM. The new parameterization scheme makes it possible to evaluate the effects of changing AC adoption on global urban energy and climate using CESM. These developments enhance CESM in its use for climate impact assessments under future climate and socioeconomic development scenarios, and represent continued efforts in better representing urban processes and coupled human‐urban‐Earth dynamics in ESMs.

Exponential stability of fractional‐order uncertain systems with asynchronous switching and impulses

AbstractDifferent from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality , by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results.

Canopy Heterogeneity and Environmental Variability Drive Annual Budgets of Net Ecosystem Carbon Exchange in a Tidal Marsh

AbstractTidal salt marshes are important ecosystems in the global carbon cycle. Understanding their net carbon exchange with the atmosphere is required to accurately estimate their net ecosystem carbon budget (NECB). In this study, we present the interannual net ecosystem exchange (NEE) of CO2 derived from eddy covariance (EC) for a Spartina alterniflora salt marsh. We found interannual NEE could vary up to 3‐fold and range from −58.5 ± 11.3 to −222.9 ± 12.4 g C m−2 year−1 in 2016 and 2020, respectively. Further, we found that atmospheric CO2 fluxes were spatially dependent and varied across short distances. High biomass regions along tidal creek and estuary edges had up to 2‐fold higher annual NEE than lower biomass marsh interiors. In addition to the spatial variation of NEE, regions of the marsh represented by distinct canopy zonation responded to environmental drivers differently. Low elevation edges (with taller canopies) had a higher correlation with river discharge (R2 = 0.61), the main freshwater input into the system, while marsh interiors (with short canopies) were better correlated with in situ precipitation (R2 = 0.53). Lastly, we extrapolated interannual NEE to the wider marsh system, demonstrating the potential underestimation of annual NEE when not considering spatially explicit rates of NEE. Our work provides a basis for further research to understand the temporal and spatial dynamics of productivity in coastal wetlands, ecosystems which are at the forefront of experiencing climate change induced variability in precipitation, temperature, and sea level rise that have the potential to alter ecosystem productivity.

Higher-order multi-scale computational approach and its convergence for nonlocal gradient elasticity problems of composite materials

A novel higher-order multi-scale computational approach for efficient nonlocal gradient elasticity simulation of composite materials is proposed in this paper. Based on the use of decoupling technique, raw fourth-order nonlocal gradient equations with periodically oscillatory coefficients are decoupled as the new second-order multi-scale equations for reducing the continuity requirements when implementing multi-scale simulation. Next, a novel macro-micro coupled multi-scale computational model with higher-order corrected terms is rigorously devised for high-resolution multi-scale and nonlocal analysis of composite materials via multi-scale asymptotic analysis. Then, the local error analysis of higher-order multi-scale solutions in the point-wise sense illustrates that establishing higher-order asymptotic corrected terms plays a vital role in investigating the micromechanical mechanisms. Moreover, a rigorous global error estimation with an explicit rate of higher-order multi-scale solutions is first derived in the energy norm sense. In addition, an efficient multi-scale numerical algorithm is presented to effectively simulate nonlocal gradient elasticity problems of composite materials based on finite element method (FEM). And we also derive the convergence estimation of the proposed numerical algorithm. Finally, numerical experiments are conducted to gauge the efficiency and accuracy of the proposed higher-order multi-scale method. This paper offers a unified higher-order two-scale computational framework for enabling nonlocal gradient elasticity behavior simulation of composite materials.