Explicit Rate Research Articles

Time-dependent electromagnetic scattering from dispersive materials

Abstract This paper studies time-dependent electromagnetic scattering from obstacles that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and passive homogeneous material, determines the wave–material interaction in the scatterer. The resulting problem is nonlocal in time inside the scatterer and is posed on an unbounded domain. Well-posedness of the scattering problem is shown using a formulation that is fully given on the surface of the scatterer via a time-dependent boundary integral equation. Discretizing this equation by convolution quadrature in time and boundary elements in space yields a provably stable and convergent method that is fully parallel in time and space. Under regularity assumptions on the exact solution we derive error bounds with explicit convergence rates in time and space. Numerical experiments illustrate the theoretical results and show the effectiveness of the method.

Social conformity updates the neural representation of facial attractiveness

People readily change their behavior to comply with others. However, to which extent they will internalize the social influence remains elusive. In this preregistered electroencephalogram (EEG) study, we investigated how learning from one’s in-group or out-group members about facial attractiveness would change explicit attractiveness ratings and spontaneous neural representations of facial attractiveness. Specifically, we quantified the neural representational similarities of learned faces with prototypical attractive faces during a face perception task without overt social influence and intentional evaluation. We found that participants changed their explicit attractiveness ratings to both in-group and out-group influences. Moreover, social conformity updated spontaneous neural representation of facial attractiveness, an effect particularly evident when participants learned from their in-group members and among those who perceived tighter social norms. These findings offer insights into how group affiliations and individual differences in perceived social norms modulate the internalization of social influence.

Convergence rates and central limit theorem for 3-D stochastic fractional Boussinesq equations with transport noise

This work investigates the 3-D stochastic modified fractional Boussinesq equations driven by transport noise on the torus. The existence of weak solutions is initially established through Galerkin approximation and compactness techniques. Subsequently, we demonstrate that the weak solutions of stochastic modified fractional Boussinesq equations converge to the unique solution of a deterministic Boussinesq model with fractional dissipation, subject to an appropriate noise scaling, along with providing the quantitative estimates with explicit convergent rates. Finally, the central limit theorem with an explicit convergence rate is established based on the aforementioned scaling limit. It is noteworthy that the scaling limit result of stochastic modified fractional Boussinesq equations to deterministic Boussinesq models with additional fractional dissipation implies that the transport noise regularizes the modified fractional Boussinesq equations, thus leading to “approximate weak uniqueness”.

Did interest rate guidance in emerging markets work?

Central banks in emerging market economies experimented with explicit interest rate guidance during 2020-2021. We explore the effectiveness of this policy. Despite some heterogeneity, interest rate guidance generally provided additional monetary stimulus, as reflected in lower medium-term yields and lower term spreads. The magnitude of the reduction in 10-year yields ranged between five and twenty basis points. In the immediate aftermath of the guidance, we do not observe a systematic negative market reaction – such as de-anchoring of inflation expectations, currency depreciation pressures, or increased sovereign credit risk – that would be associated with a loss of central bank credibility or with concerns about fiscal dominance.

Optimizing crop seeding rates on organic grain farms using on farm precision experimentation

Organic agriculture is often regarded as less damaging to the environment than conventional agriculture, though at the expense of lower yields. Field-specific precision agriculture may benefit organic production practices given the inherent need of organic farmers to understand spatiotemporal variation on large-scale fields. Here the primary research question is whether on-farm precision experimentation (OFPE) can be used as an adaptive management methodology to efficiently maximize farmer net returns using variable cover crop and cash crop seeding rates. Inputs of cash crop seed and previous-year green manure cover crop seed were experimentally varied on five different farms across the Northern Great Plains from 2019 to 2022. Experiments provided data to model the crop yield response, and subsequently net return, in response to input (seeding) rates plus a suite of other spatially explicit data from satellite sources. New, field-specific spatially explicit optimum input rates were generated to maximize net return including temporal variation in economic variables. Inputs were spatially optimized and using simulations it was found that the optimization strategies consistently out-performed other strategies by reducing inputs and increasing yields, particularly for non-tillering crops. By adopting site specific management, the average increase in net return for all fields was $50 ha−1. These results showed that precision agriculture technologies and remote sensing can be utilized to provide organic farmers powerful adaptive management tools with a focus on within-field spatial variability in response to primary input drivers of economic return. Continued OFPE for seeding rate optimization will allow quantification of temporal variability and subsequent probabilistic recommendations.

Stabilizing effect of the magnetic field and decay estimates for the 3D MHD equations with only one direction dissipation

This paper focuses on the stability and decay estimates of the 3D MHD equations with only one direction dissipation near a background magnetic field. The global stability and decay estimates of the 3D Navier-Stokes equations with only one direction dissipation remain an outstanding open problem. However, when coupled with the magnetic field in the MHD system involved here, the velocity field is shown to stabilize and decay in time. This result reveals that the magnetic field stabilizes and damps the electrically conducting fluids. By utilizing time-weighted methods and the method of bootstrapping argument, we establish that any perturbation near a magnetic field is globally stable in H3(R3). Furthermore, explicit decay rates in H2(R3) are obtained.

Annual variation in attribute importance to upland game hunter satisfaction in Nebraska

AbstractTo sustain recreational hunting participation, we need to identify what makes a hunting experience satisfying. Merely identifying which factors are important to hunter satisfaction may be insufficient, however, as factor importance could vary across consecutive hunting seasons. Using online surveys, completed by individuals who hunted upland game in Nebraska, USA, from 2018 to 2022, we applied importance grid analysis (IGA) and penalty–reward contrast analysis (PRCA) to examine how activity‐specific factors influenced satisfaction across 5 consecutive hunting seasons. Results suggested consistent differences between the explicit (perceived importance) and implicit (performance) importance of factors for each hunting season. Factors related to seeing birds and harvest held greater implicit importance than expected based on explicit importance ratings (τ > 0.55, P < 0.05), whereas factors relating to access and other hunters held relatively lower implicit importance (τ < 0.31, P < 0.05). The PRCA method consistently identified seeing game birds as a minimum requirement to upland game hunting (penalty β < −0.26, P < 0.01). However, factors relating to harvest, access, and other hunters emerged as important only within certain seasons. Using IGA and PRCA provided valuable insights about the importance of hunters seeing game birds, and how aspects of different hunting seasons may improve satisfaction for hunters.

Superlinear Krylov convergence under streamline diffusion FEM for convection‐dominated elliptic operators

AbstractThis paper studies the superlinear convergence of Krylov iterations under the streamline‐diffusion preconditioning operator for convection‐dominated elliptic problems. First, convergence results are given involving the diffusion parameter . Then the limiting case is studied on the operator level, and the convergence results are extended to this situation under some conditions, in spite of the lack of compactness of the perturbation operators. An explicit rate is also given.

A novel fuzzy neural collaborative filtering for recommender systems

In collaborative filtering recommendations, part of studies mainly focus on quantitatively learning user preferences based on explicit rating information. However, due to the uncertainty and complexity of decision-making scenarios, user preferences usually express ambiguity and diversity. Therefore, to fully capture user preferences from both qualitative and quantitative perspectives and improve the accuracy and reliability of recommendations, we propose a novel fuzzy neural collaborative filtering for recommender systems. Firstly, we qualitatively divide user preferences into fine-grained categories based on picture fuzzy set and transform the rating matrix into four preference degree matrices. Then, we employ Bernoulli matrix factorization to independently learn preference features of each submatrix to obtain picture fuzzy numbers. To enhance the adaptability of picture fuzzy set in recommender systems, we design an improved scoring function based on picture fuzzy number to effectively distinguish differences in user preference levels. In addition, we use a simple deep neural framework to quantitatively extract global preferences of users and fuse it with fine-grained preferences of users to thoroughly predict user preferences. Experiments on four benchmark datasets show that the proposed model outperforms other comparison methods in terms of recommendation accuracy. Compared with the closest competitor method, our model has the highest improvements of 5.08% and 4.04% in the metrics HR@10 and NDCG@10, respectively.

Interplay between depth and width for interpolation in neural ODEs

Neural ordinary differential equations have emerged as a natural tool for supervised learning from a control perspective, yet a complete understanding of the role played by their architecture remains elusive. In this work, we examine the interplay between the width p and the number of transitions between layers L (corresponding to a depth of L+1). Specifically, we construct explicit controls interpolating either a finite dataset D, comprising N pairs of points in Rd, or two probability measures within a Wasserstein error margin ɛ>0. Our findings reveal a balancing trade-off between p and L, with L scaling as 1+O(N/p) for data interpolation, and as 1+Op−1+(1+p)−1ɛ−d for measures.In the high-dimensional and wide setting where d,p>N, our result can be refined to achieve L=0. This naturally raises the problem of data interpolation in the autonomous regime, characterized by L=0. We adopt two alternative approaches: either controlling in a probabilistic sense, or by relaxing the target condition. In the first case, when p=N we develop an inductive control strategy based on a separability assumption whose probability increases with d. In the second one, we establish an explicit error decay rate with respect to p which results from applying a universal approximation theorem to a custom-built Lipschitz vector field interpolating D.

Generalized Fejér monotone sequences and their finitary content

We provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of generalized Fejér monotonicity where (1) the metric can be replaced by a much more general type of function measuring distances (including, in particular, certain Bregman distances), (2) full Fejér monotonicity is relaxed to a partial variant and (3) the distance functions are allowed to vary along the iteration. For such sequences, the paper provides explicit and effective rates of metastability and even rates of convergence, the latter under a regularity assumption that generalizes the notion of metric regularity introduced by Kohlenbach, López-Acedo and Nicolae, itself an abstract generalization of many regularity notions from the literature. In the second part of the paper, we apply the abstract quantitative results established in the first part to two algorithms: one algorithm for approximating zeros of maximally monotone and maximally ρ-comonotone operators in Hilbert spaces (in the sense of Combettes and Pennanen as well as Bauschke, Moursi and Wang) that incorporates inertia terms every other term and another algorithm for approximating zeros of monotone operators in Banach spaces (in the sense of Browder) that is only Fejér monotone w.r.t. a certain Bregman distance.

Federated dual averaging learning algorithm with delayed gradients for composite optimization

Federated learning offers a promising paradigm for training machine learning models in distributed edge networks. This paper focuses on a critical aspect of federated learning, specifically examining the influence of communication delays between the server and edge devices. We study the problem of federated composite optimization (FCO) in the scenario where communication delays are introduced due to client-sides. To tackle this issue, we propose a federated dual averaging learning algorithm that incorporates delayed gradients. We conduct a thorough convergence analysis of our algorithm taking into account the impact of the delayed gradient information. Our analysis demonstrates that under the assumption of bounded expected random delays, the algorithm exhibits the asymptotic convergence towards the optimal value. Furthermore, we present explicit convergence rates of the proposed algorithm for fixed and random delays. Our results show that the impact of delays on FCO problems with smooth loss functions gradually becomes negligible. Finally, to demonstrate the efficacy of the proposed algorithm, we conduct numerical simulations on the FEMNIST dataset utilizing ℓ1-regularized logistic regression. These experimental results confirm our findings that the algorithm converges effectively even in the presence of delays.

The use of conceptual ecological models to identify critical data and uncertainties to support numerical modeling: The northern Gulf of Mexico eastern oyster Crassostrea virginica example

AbstractObjectiveIncreasing reliance on numerical simulation models to help inform management and restoration choices benefits from careful consideration of critical early steps in model development. Along the northern coast of the Gulf of Mexico, the eastern oyster Crassostrea virginica fulfills important ecological and economic roles. Using the eastern oyster as an example, we draw on several recent frameworks outlining best practices for model development and application for restoration, conservation, and management.MethodsWe identify priority model questions, outline a conceptual ecological model (CEM) to guide numerical model development, and use this framework to identify uncertainties and research needs.ResultThe CEM uses a nested design, identifying explicit vital rates, processes, attributes, and outcomes for the species (oysters), population, and metapopulation (i.e., network of populations) levels in response to drivers of species, population, and metapopulation changes and changing environmental factors. Most management actions related to oyster restoration and harvest affect population attributes directly, but many coastal management actions and changes (i.e., climate change and coastal and water resource engineering) impact environmental factors that alter vital rates and attributes of oysters, populations, and metapopulations.ConclusionInvestment in studies targeting individual oyster‐ and population‐level multi‐stressor responses (filtration, respiration, growth, and reproduction) and improving hydrodynamic and environmental models targeting drivers that influence metapopulation vital rates and attributes (i.e., connectivity and substrate persistence) would contribute to reducing uncertainties. Development of numerical models covering the entire oyster life cycle and connectivity of populations using hydrodynamic models of current and predicted conditions to provide key abiotic and biotic factors influencing larval movement, recruitment, and on‐reef oyster vital rates would assist in balancing the goals of conservation, restoration, and fisheries management of this foundational estuarine species.

Personalized Recommendation Systems Powered By Large Language Models: Integrating Semantic Understanding and User Preferences

This study proposes a novel personalized recommendation system leveraging Large Language Models (LLMs) to integrate semantic understanding with user preferences [1]. The system addresses critical challenges in traditional recommendation approaches by harnessing LLMs' advanced natural language processing capabilities. We introduce a framework combining a fine-tuned Roberta semantic analysis model with a multi-modal user preference extraction mechanism.The LLM component undergoes domain adaptation using Masked Language Modeling on a corpus of 112,000 user reviews from the MyAnimeList dataset, followed by task-specific fine-tuning using contrastive learning. User preferences are modeled through a weighted combination of explicit ratings, review sentiment, and implicit feedback, incorporating temporal dynamics through a time-decay function. Experimental results demonstrate significant improvements over state-of-the-art baselines, including Matrix Factorization, Neural Collaborative Filtering, BERT4Rec, and LightGCN. Our LLM-powered system achieves an 8.6%increase in NDCG@10 and a 10.5% improvement in Mean Reciprocal Rank compared to the best-performing baseline. Ablation studies reveal the synergistic effect of integrating LLM-based semantic understanding with user preference modeling. Case studies highlight the system's ability to recommend long-tail items and provide cross-genre suggestions, showcasing its capacity for nuanced content understanding. Scalability analysis indicates that while the LLM-based approach has higher initial computational costs, its performance scales comparably to other deep learning models for larger datasets. This research contributes to the field by demonstrating the effectiveness of LLMs in enhancing recommendation accuracy and diversity. Future work will explore advanced LLM architectures, multi-modal data integration, and techniques to improve computational efficiency and interpretability of recommendations.

Maximizing tree carbon in croplands and grazing lands while sustaining yields

BackgroundIntegrating trees into agricultural landscapes can provide climate mitigation and improves soil fertility, biodiversity habitat, water quality, water flow, and human health, but these benefits must be achieved without reducing agriculture yields. Prior estimates of carbon dioxide (CO2) removal potential from increasing tree cover in agriculture assumed a moderate level of woody biomass can be integrated without reducing agricultural production. Instead, we used a Delphi expert elicitation to estimate maximum tree covers for 53 regional cropping and grazing system categories while safeguarding agricultural yields. Comparing these values to baselines and applying spatially explicit tree carbon accumulation rates, we develop global maps of the additional CO2 removal potential of Tree Cover in Agriculture. We present here the first global spatially explicit datasets calibrated to regional grazing and croplands, estimating opportunities to increase tree cover without reducing yields, therefore avoiding a major cost barrier to restoration: the opportunity cost of CO2 removal at the expense of agriculture yields.ResultsThe global estimated maximum technical CO2 removal potential is split between croplands (1.86 PgCO2 yr− 1) and grazing lands (1.45 PgCO2 yr− 1), with large variances. Tropical/subtropical biomes account for 54% of cropland (2.82 MgCO2 ha− 1 yr− 1, SD = 0.45) and 73% of grazing land potential (1.54 MgCO2 ha− 1 yr− 1, SD = 0.47). Potentials seem to be driven by two characteristics: the opportunity for increase in tree cover and bioclimatic factors affecting CO2 removal rates.ConclusionsWe find that increasing tree cover in 2.6 billion hectares of agricultural landscapes may remove up to 3.3 billion tons of CO2 per year – more than the global annual emissions from cars. These Natural Climate Solutions could achieve the Bonn Challenge and add 793 million trees to agricultural landscapes. This is significant for global climate mitigation efforts because it represents a large, relatively inexpensive, additional CO2 removal opportunity that works within agricultural landscapes and has low economic and social barriers to rapid global scaling. There is an urgent need for policy and incentive systems to encourage the adoption of these practices.

Liberals and Conservatives Rely on Very Similar Sets of Foundations When Comparing Moral Violations

Applications of moral foundations theory in political science have revealed differences in the degree to which liberals and conservatives explicitly endorse five core moral foundations of care, fairness, authority, loyalty, and sanctity. We argue that differences between liberals and conservatives in their explicit ratings of abstract and generalized moral principles do not imply that citizens with different political orientations have fundamentally different moral intuitions. We introduce a new approach for measuring the importance of the five moral foundations by asking U.K. and U.S. survey respondents to compare pairs of vignettes describing violations relevant to each foundation. We analyze responses to these comparisons using a hierarchical Bradley–Terry model which allows us to evaluate the relative importance of each foundation to individuals with different political perspectives. Our results suggest that, despite prominent claims to the contrary, voters on the left and the right of politics share broadly similar moral intuitions.

CLT for NESS of a reaction-diffusion model

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d \\le 3$$\\end{document} we show a central limit theorem for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.

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.