Local Regularity Research Articles

Farmers market food safety: A comprehensive review of training needs in the U.S.

Farmers markets offer an apparently easy way for small-scale or hobbyist food producers to sell fresh produce, meat, and poultry from their farms or dis­tribute value-added products, but they may be unaware of the foodborne illness risks associated with both fresh produce and derivative products, as well as of their local food safety requirements. Food guidance and rules vary from state to state and market to market, making it difficult for indi­viduals to navigate the various regulatory levels. Even if a local food producer is exempt from these rules due to their amount of sales, they will still benefit greatly from resources and educational tools that increase awareness and knowledge of food safety best practices. This review discusses current knowledge of and guidelines for food safety in farmers markets based on peer-reviewed and grey literature as well as published guidelines and recommendations. We examine facilities and supplies, regulatory measures, education and train­ing, and Good Farmers Market Practices as pre­ventive measures to enhance food safety in farmers markets, which are critical to local and regional food systems. Overall, we identified various barri­ers to implementing farmers market food safety standards and practices in this scoping review; removing these barriers will require the participa­tion of local regularity authorities, market managers, vendors, and consumers.

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method’s performance. Our algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

A super-resolution algorithm of Ghost Imaging using CNN with Grouped orthonormalization algorithm Constraint

Ghost imaging (GI) is capable of reconstructing images under low-light conditions by single-pixel measurements. However, improving image resolution often requires extensive single-pixel sampling, limiting practical applications. Here we propose a super-resolution algorithm of GI using Convolutional neural network with Grouped orthonormalization algorithm Constraint (GICGC), which aims to reconstruct images at super-resolution with strong local regularities and self-similarity. The proposed algorithm, a versatile approach, has been demonstrated to outperform several other widely used GI algorithms in terms of spatial resolution and sampling rate. Our findings are supported by rigorous benchmark tests and experimental validations in challenging environments, including multimode fibers. The imaging experimental results demonstrate that GICGC achieves superior performance in reconstructing image linewidth and contrast, effectively doubling resolution capability by approximately 2.1 times, indicating significant potential in biomedical imaging and other fields. We believe this study represents a novel breakthrough in universal super-resolution ghost imaging and paves the way for its practical applications.

Local regularity for the space-homogenous Landau equation with very soft potentials

Local regularity for the space-homogenous Landau equation with very soft potentials

Locally Adaptive Shrinkage Priors for Trends and Breaks in Count Time Series

Non-stationary count time series characterized by features such as abrupt changes and fluctuations about the trend arise in many scientific domains including biophysics, ecology, energy, epidemiology, and social science domains. Current approaches for integer-valued time series lack the flexibility to capture local transient features while more flexible models for continuous data types are inadequate for universal applications to integer-valued responses such as settings with small counts. We present a modeling framework, the negative binomial Bayesian trend filter (NB-BTF), that offers an adaptive model-based solution to capturing multiscale features with valid integer-valued inference for trend filtering. The framework is a hierarchical Bayesian model with a dynamic global-local shrinkage process. The flexibility of the global-local process allows for the necessary local regularization while the temporal dependence induces a locally smooth trend. In simulation, the NB-BTF outperforms a number of alternative trend filtering methods. Then, we demonstrate the method on weekly power outage frequency in Massachusetts townships. Power outage frequency is characterized by a persistent low level trend with occasional spikes. These illustrations show the estimation of a smooth, non-stationary trend with adequate uncertainty quantification.

Multi-Scale Classification and Contrastive Regularization: Weakly Supervised Large-Scale 3D Point Cloud Semantic Segmentation

With the proliferation of large-scale 3D point cloud datasets, the high cost of per-point annotation has spurred the development of weakly supervised semantic segmentation methods. Current popular research mainly focuses on single-scale classification, which fails to address the significant feature scale differences between background and objects in large scenes. Therefore, we propose MCCR (Multi-scale Classification and Contrastive Regularization), an end-to-end semantic segmentation framework for large-scale 3D scenes under weak supervision. MCCR first aggregates features and applies random downsampling to the input data. Then, it captures the local features of a random point based on multi-layer features and the input coordinates. These features are then fed into the network to obtain the initial and final prediction results, and MCCR iteratively trains the model using strategies such as contrastive learning. Notably, MCCR combines multi-scale classification with contrastive regularization to fully exploit multi-scale features and weakly labeled information. We investigate both point-level and local contrastive regularization to leverage point cloud augmentor and local semantic information and introduce a Decoupling Layer to guide the loss optimization in different spaces. Results on three popular large-scale datasets, S3DIS, SemanticKITTI and SensatUrban, demonstrate that our model achieves state-of-the-art (SOTA) performance on large-scale outdoor datasets with only 0.1% labeled points for supervision, while maintaining strong performance on indoor datasets.

Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the p-Laplacian

For a given constant λ>0 and a bounded Lipschitz domain D⊂Rn (n≥2), we establish that almost-minimizers of the functionalJ(v;D)=∫D∑i=1m|∇vi(x)|p+λχ{|v|>0}(x)dx,1<p<∞, where v=(v1,⋯,vm), and m∈N, exhibit optimal Lipschitz continuity in compact sets of D. Furthermore, assuming p≥2 and employing a distinctly different methodology, we tackle the issue of boundary Lipschitz regularity for v. This approach simultaneously yields an alternative proof for the optimal local Lipschitz regularity for the interior case.

The Rate of Convergence of Bregman Proximal Methods: Local Geometry Versus Regularity Versus Sharpness

The Rate of Convergence of Bregman Proximal Methods: Local Geometry Versus Regularity Versus Sharpness

Determining coefficients for a fractional p-Laplace equation from exterior measurements

We consider an inverse problem of determining the coefficients of a fractional p -Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficients. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set.

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

Generalized local Morrey regularity of elliptic systems

Generalized local Morrey regularity of elliptic systems

Application of locally regularized extremal shift to the problem of realization of a prescribed motion

Abstract A controlled system of differential equations under the action of an unknown disturbance is considered. The problem discussed in the paper consists in constructing algorithms for forming a control that provides the realization of a prescribed motion for any admissible disturbance. Namely these algorithms should provide the closeness in the metric of the space of differentiable functions of a phase trajectory of a given controlled system and some etalon trajectory of an analogous system functioning when any outer actions are absent. As the space of admissible disturbances, we take the space of measurable square integrable (with respect to the Euclidean norm) functions. The cases of inaccurate measurements of phase trajectories of both systems at all times and at discrete times are under study. Two computer oriented algorithms for solving the problem are designed. The algorithms are based on the (well-known in the theory of guaranteed control) method of extremal shift. In the process, its local (at each time of control correction) regularization is performed by the method of smoothing functional (the Tikhonov method). In addition, estimates for algorithm’s convergence rate are presented.

The relative multifractal analysis of a vector function in a metric space

ABSTRACT Scale invariance is a widely used concept for analysing real data from many different applications, and multifractal analysis has become the standard and powerful tool in signal processing. It characterizes the data by globally and geometrically describing the fluctuations of the local regularity. In this paper, we study the relative vectorial multifractal formalism based on vectorial multifractal Hewitt-Stromberg measures. We use a function defined on balls in a metric space and Banach valued, which is more general than measures. This leads to results on the simultaneous behaviour of possibly many local Hölder exponents. As an application, we study the relative multifractal formalism of branching random walk on the Galton-Watson tree.

Calibrated confidence learning for large-scale real-time crash and severity prediction

Real-time crash and severity prediction is a complex task, and there is no existing framework to predict crash likelihood and severity together. Creating such a framework poses numerous challenges, particularly not independent and identically distributed (non-IID) data, large model sizes with high computational costs, missing data, sensitivity vs. false alarm rate (FAR) trade-offs, and real-world deployment strategies. This study introduces a novel modeling technique to address these challenges and develops a deployable real-world framework. We used extensive real-time traffic and weather data to develop a crash likelihood prediction modeling prototype, leveraging our preliminary work of spatial ensemble modeling. Next, we equipped this spatial ensemble model with local model regularization to calibrate model confidence training. The investigated regularizations include weight decay, label smoothing and knowledge distillation. Furthermore, post-calibration on model outputs was conducted to improve severity rating identification. We tested the framework to predict crashes and severity in real-time, categorizing crashes into four levels. Results were compared with benchmark models, real-world deployment mechanisms were explained, traffic safety improvement potential and sustainability aspects of the study were discussed. Modeling results demonstrated excellent performance, and fatal, severe, minor and PDO crash severities were predicted with 91.7%, 83.3%, 85.6%, and 87.7% sensitivity, respectively, and with very low FAR. Similarly, the viability of our model to predict different severity levels for specific crash types, i.e., all-crash types, rear-end crashes, and sideswipe/angle crashes, were examined, and it showed excellent performance. Our modeling technique showed great potential for reducing model size, lowering computational costs, improving sensitivity, and, most importantly, reducing FAR. Finally, the deployment strategy for the proposed crash and severity prediction technique is discussed, and its potential to predict crashes with severity levels in real-time will make a substantial contribution to tailoring specific strategies to prevent crashes.

Dissecting Mismatch Negativity: Early and Late Subcomponents for Detecting Deviants in Local and Global Sequence Regularities.

Mismatch negativity (MMN) is commonly recognized as a neural signal of prediction error evoked by deviants from the expected patterns of sensory input. Studies show that MMN diminishes when sequence patterns become more predictable over a longer timescale. This implies that MMN is composed of multiple subcomponents, each responding to different levels of temporal regularities. To probe the hypothesized subcomponents in MMN, we record human electroencephalography during an auditory local-global oddball paradigm where the tone-to-tone transition probability (local regularity) and the overall sequence probability (global regularity) are manipulated to control temporal predictabilities at two hierarchical levels. We find that the size of MMN is correlated with both probabilities and the spatiotemporal structure of MMN can be decomposed into two distinct subcomponents. Both subcomponents appear as negative waveforms, with one peaking early in the central-frontal area and the other late in a more frontal area. With a quantitative predictive coding model, we map the early and late subcomponents to the prediction errors that are tied to local and global regularities, respectively. Our study highlights the hierarchical complexity of MMN and offers an experimental and analytical platform for developing a multitiered neural marker applicable in clinical settings.

Class-driven nonnegative matrix factorization with manifold regularization for data clustering

Nonnegative matrix factorization (NMF) is an effective technique to extract the underlying low-dimensional structure of data by utilizing its parts-based representation, which has been widely used in feature extraction and machine learning. However, NMF is an unsupervised learning algorithm without utilizing the discriminative prior information. In this paper, we put forward a new class-driven NMF with manifold regularization (MCDNMF) algorithm, which incorporates both the local manifold regularization and the label information of data into the NMF model. Specifically, MCDNMF not only encodes the local geometrical structure of data space by using the manifold regularization, but also takes the available label information by introducing the class-driven constraint. This class-driven constraint forces the new representations of data points to be more similar within the same class while different between other classes. Therefore, the discriminative abilities of clustering are greatly boosted. Experimental results on several datasets validate the effectiveness of proposed MCDNMF in comparison with the other state-of-the-art methods.

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Impulsive gravitational waves are theoretical models of short but violent bursts of gravitational radiation. They are commonly described by two distinct spacetime metrics, one of local Lipschitz regularity and the other one even distributional. These two metrics are thought to be ‘physically equivalent’ since they can be formally related by a ‘discontinuous coordinate transformation’. In this paper we provide a mathematical analysis of this issue for the entire class of nonexpanding impulsive gravitational waves propagating in a background spacetime of constant curvature. We devise a natural geometric regularisation procedure to show that the notorious change of variables arises as the distributional limit of a family of smooth coordinate transformations. In other words, we establish that both spacetimes arise as distributional limits of a smooth sandwich wave taken in different coordinate systems which are diffeomorphically related.

Manifold regularized deep canonical variate analysis with interpretable attribute guidance for three-phase flow process monitoring

Oil–gas–water three-phase flow has multiple flow states, exhibiting dynamic, nonlinear, and instantaneous behaviors. Monitoring and analysis of flow state are crucial for ensuring safe operation of industrial processes. However, the absence of a universal definition for three-phase flow states, owing to the complex flow characteristics and structures, leads to that labeling three-phase flow states by categories is impractical. For comprehensive monitoring and analysis, the flow states should be described from both global (e.g., the dominant phase) and local (e.g., the interphase structure) aspects. Given the aforementioned challenges, the work aims to address the accurate identification of typical three-phase flow states and to meticulously monitor and analyze the continuous evolutionary process of three-phase flow. To achieve it, the manifold regularized deep canonical variate analysis with attribute guidance (Ag-MRDCVA) is proposed, which not only introduces an innovative monitoring paradigm that designs state attributes for process description but also facilitates knowledge transfer from typical flow states to transition states. For enhancing the model’s feature embedding capabilities, an attribute guidance module is introduced to increase supervision information at both class and attribute levels. Then, convolutional neural network (CNN) backbones are developed with a dual objective of global serial correlation and local manifold regularization, which capture spatiotemporal information at both global and local scales, facilitating effective attribute encoding and characterization of flow states. Finally, the attribute evolution heat map and a monitoring metric (MM) collectively offer a compelling and comprehensive analysis of the three-phase flow process. Extensive experiments demonstrate that Ag-MRDCVA surpasses existing methods, showcasing its ability to minutely monitor the process while providing reasonable explanations.

Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event

In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and [Formula: see text]-boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios.

Federated Label-Noise Learning with Local Diversity Product Regularization

Training data in federated learning (FL) frameworks can have label noise, since they must be stored and annotated on clients' devices. If trained over such corrupted data, the models learn the wrong knowledge of label noise, which highly degrades their performance. Although several FL schemes are designed to combat label noise, they suffer performance degradation when the clients' devices only have limited local training samples. To this end, a new scheme called federated label-noise learning (FedLNL) is developed in this paper. The key problem of FedLNL is how to estimate a noise transition matrix (NTM) accurately in the case of limited local training samples. If a gradient-based update method is used to update the local NTM on each client's device, it can generate too large gradients for the local NTM, causing a high estimation error of the local NTM. To tackle this issue, an alternating update method for the local NTM and the local classifier is designed in FedLNL, where the local NTM is updated by a Bayesian inference-based update method. Such an alternating update method makes the loss function of existing NTM-based schemes not applicable to FedLNL. To enable federated optimization of FedLNL, a new regularizer on the parameters of the classifier called local diversity product regularizer is designed for the loss function of FedLNL. The results show that FedLNL improves the test accuracy of a trained model by up to 25.98%, compared with the state-of-the-art FL schemes that tackle label-noise issues.