Kernel Approach Research Articles

A methodology for assessing multiple hazards applied to Sweden

Despite extensive efforts through various international initiatives to reduce global warming, it has been determined that human induced climate change is here, that the present scale of disruption of the climate is unprecedented and will continue. Increasing weather volatility can be expected, which will most likely increase exposure to weather related hazards, e.g. wildfires, flooding. The aim of this paper is to present an index-based multi-hazard risk assessment method to assess wildfires and flooding hazard for two municipalities within Sweden. The method is designed to be used by the Fire and Rescue Service (FRS) for planning purposes and can be modified to take the local FRS’s capabilities and local conditions into account, thereby improving hazard preparedness at a local level. The analysis presented indicates that, while the frequency of multi-hazard overlap from wildfires and flooding is greatest in more northern parts of Sweden, the method provides important information even when applied to areas with limited overlap. A variation of the hazard assessment using a box kernel sliding window was studied to investigate the sensitivity of the model for rapid variations of an individual hazard level. Given that resource needs will typically spread over several days for large scale natural hazards, the box kernel approach is valuable in helping to identify a span of days when resources associated with incident response might be needed. In the future, the model should be expanded to include additional single hazards, the application to additional municipalities and extension to FRS planning exercises for natural hazards.

Comparison of Reservoir Computing topologies using the Recurrent Kernel approach

Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its expressive power. However, many well-established RC paradigms, such as Leaky RC, Sparse RC, and Deep RC, are yet to be systematically analyzed in such a way. We define the Recurrent Kernel limit of all these RC topologies and conduct a convergence study for a wide range of activation functions and hyperparameters. Our findings provide new insights into various aspects of Reservoir Computing. First, we demonstrate that there is an optimal sparsity level which grows with the reservoir size. Furthermore, our analysis suggests that Deep RC should use reservoir layers of decreasing sizes. Finally, we perform a benchmark demonstrating the efficiency of Structured Reservoir Computing compared to vanilla and Sparse Reservoir Computing.

Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential

The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier–Stokes–Cahn–Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results.

Delayed kernels for longitudinal survival analysis and dynamic prediction.

Predicting patient survival probabilities based on observed covariates is an important assessment in clinical practice. These patient-specific covariates are often measured over multiple follow-up appointments. It is then of interest to predict survival based on the history of these longitudinal measurements, and to update predictions as more observations become available. The standard approaches to these so-called 'dynamic prediction' assessments are joint models and landmark analysis. Joint models involve high-dimensional parameterizations, and their computational complexity often prohibits including multiple longitudinal covariates. Landmark analysis is simpler, but discards a proportion of the available data at each 'landmark time'. In this work, we propose a 'delayed kernel' approach to dynamic prediction that sits somewhere in between the two standard methods in terms of complexity. By conditioning hazard rates directly on the covariate measurements over the observation time frame, we define a model that takes into account the full history of covariate measurements but is more practical and parsimonious than joint modelling. Time-dependent association kernels describe the impact of covariate changes at earlier times on the patient's hazard rate at later times. Under the constraints that our model (a) reduces to the standard Cox model for time-independent covariates, and (b) contains the instantaneous Cox model as a special case, we derive two natural kernel parameterizations. Upon application to three clinical data sets, we find that the predictive accuracy of the delayed kernel approach is comparable to that of the two existing standard methods.

Navigating interpretability and alpha control in GF-KCSD testing with measurement error: A Kernel approach

The Gradient-Free Kernel Conditional Stein Discrepancy (GF-KCSD), presented in our prior work, represents a significant advancement in goodness-of-fit testing for conditional distributions. This method offers a robust alternative to previous gradient-based techniques, specially when the gradient calculation is intractable or computationally expensive. In this study, we explore previously unexamined aspects of GF-KCSD, with a particular focus on critical values and test power—essential components for effective hypothesis testing. We also present novel investigation on the impact of measurement errors on the performance of GF-KCSD in comparison to established benchmarks, enhancing our understanding of its resilience to these errors. Through controlled experiments using synthetic data, we demonstrate GF-KCSD’s superior ability to control type-I error rates and maintain high statistical power, even in the presence of measurement inaccuracies. Our empirical evaluation extends to real-world datasets, including brain MRI data. The findings confirm that GF-KCSD performs comparably to KCSD in hypothesis testing effectiveness while requiring significantly less computational time. This demonstrates GF-KCSD’s capability as an efficient tool for analyzing complex data, enhancing its value for scenarios that demand rapid and robust statistical analysis.

Continuous mapping of forest canopy height using ICESat-2 data and a weighted kernel integration of multi-temporal multi-source remote sensing data aided by Google Earth Engine.

Forest Canopy Height (FCH) is a crucial parameter that offers valuable insights into forest structure. Spaceborne LiDAR missions provide accurate FCH measurements, but a significant challenge is their point-based measurements lacking spatial continuity. This study integrated ICESat-2's ATL08-derived FCH values with multi-temporal and multi-source remote sensing (RS) datasets to generate continuous FCH maps for northern forests in Iran. Sentinel-1/2, ALOS-2 PALSAR-2, and FABDEM datasets were prepared in Google Earth Engine (GEE) for FCH mapping, each possessing unique spatial and geometrical characteristics that differ from those of the ATL08 product. Given the importance of accurately representing the geometrical characteristics of the ATL08 segments in modeling FCH, a novel Weighted Kernel (WK) approach was proposed in this paper. The WK approach could better represent the RS datasets within the ATL08 ground segments compared to other commonly used resampling approaches. The correlation between all RS data features improved by approximately 6% compared to previously employed approaches, indicating that the RS data features derived after convolving the WK approach are more predictive of FCH values. Furthermore, the WK approach demonstrated superior performance among machine learning models, with random forests outperforming other models, achieving a coefficient of determination (R2) of 0.71, root mean square error (RMSE) of 4.92m, and mean absolute percentage error (MAPE) of 29.95%. Furthermore, in contrast to previous studies using only summer datasets, this study included spring and autumn data from Sentinel-1/2, resulting in a 6% increase in R2 and a 0.5-m decrease in RMSE. The proposed methodology filled the research gaps and improved the accuracy of FCH estimations.

Unstructured moving least squares material point methods: a stable kernel approach with continuous gradient reconstruction on general unstructured tessellations

Unstructured moving least squares material point methods: a stable kernel approach with continuous gradient reconstruction on general unstructured tessellations

Multitask methods for predicting molecular properties from heterogeneous data.

Data generation remains a bottleneck in training surrogate models to predict molecular properties. We demonstrate that multitask Gaussian process regression overcomes this limitation by leveraging both expensive and cheap data sources. In particular, we consider training sets constructed from coupled-cluster (CC) and density functional theory (DFT) data. We report that multitask surrogates can predict at CC-level accuracy with a reduction in data generation cost by over an order of magnitude. Of note, our approach allows the training set to include DFT data generated by a heterogeneous mix of exchange-correlation functionals without imposing any artificial hierarchy on functional accuracy. More generally, the multitask framework can accommodate a wider range of training set structures-including the full disparity between the different levels of fidelity-than existing kernel approaches based on Δ-learning although we show that the accuracy of the two approaches can be similar. Consequently, multitask regression can be a tool for reducing data generation costs even further by opportunistically exploiting existing data sources.

Novel definition of local baseline values for potentially toxic elements in Czech farmland using adaptive spatial weighting

Exploratory data analysis is commonly used in geoscientific research to identify various data populations within datasets. Frequently, the distribution-wise metrics for the statistical centre and spread are combined to define normal (background) ranges of topsoil contents of potentially toxic elements. When decreasing the geographical scale, the survey areas turn too heterogeneous for the statistical definition of a single background range. The traditional solution is the domain approach wherein various data populations (and their statistical parameters) can be attributed to contextual (geological, ecological) information. Nevertheless, summarising the entire data set from large areas as a single statistical entity would provide too much data reduction which would decrease sensitivity of detecting localised anthropogenic contamination and work wrong in areas of geogenic anomalies spatially larger than contamination. In this paper, we tested a novel numerical solution for deriving local distribution-wise baseline values via spatially limited sliding window combined with geographical weighting. Considering environmental variables (soil and topographical properties) at every analysed soil sample point, we extended the geographical kernel weighting approach which considers only spatial dimension (given by geographical coordinates). The advanced version combines two similarity modes to assign highest weights to the nearest points expected to share similar environmental contexts within the user-defined moving kernel. The method was implemented for data-mining in the Czech high-density monitoring data for agricultural soils which had to be firstly regressed to achieve analytical harmony between two distinct extraction methods employed in that monitoring, in particular cold diluted nitric acid and hot aqua regia. After the reliable harmonisation, local baseline values were delivered as the localised outer limits of variation using the proposed double-weighted kernel approach. We compared the estimated localised background ranges for 10 potentially toxic elements (As, Be, Cd, Co, Cr, Cu, Ni, Pb, V, and Zn) with those based on the conventional substrate-wise domain approach and single nationwide legislation thresholds. The comparison was also efficient in identifying an inappropriate aggregation of some geological units. Finally, the kernel approach delivered regional outer limits of variability sensitive to subtle regional variations of topsoil geochemistry.

Comparison of patch-based and synoptic connectivity algorithms with graph theory metrics. A case study in Reggio Calabria metropolitan area (South Italy)

ContextPredicting and mapping connectivity between habitats and populations is critical to addressing habitat loss and biodiversity issues. Several strategies in the literature exist to understand, restore, and preserve ecological connectivity. The main issue of the current research is to identify which connectivity modeling strategies are the most reliable for planning purposes. ObjectivesOur goals in this paper were to compare connectivity predictions using a wide variety of commonly used approaches to improve the understanding of the similarities and differences in the predictions of these methods. Specifically, we investigated the differences in connectivity predictions related to the connectivity algorithm, the number and distribution of source points, and the threshold distance at which connectivity is allowed between locations. First, we separately applied different strategies and methods commonly used in the literature to model connectivity in the same study area. Then, going through a series of hypotheses, we compared the different models to confirm or disprove the initial hypotheses. MethodsWe proposed 4 main hypotheses and 14 combinations of them, hypothesizing that what most influences the results of connectivity models are different dispersal distance thresholds; differences in connectivity algorithms, especially kernel, path, and graph theory-based approaches; differences in predictions produced by two different software tools, UNICOR and Graphab; use of source points derived from a synoptic or patch-based perspective. ResultsWe found that the dominant pattern of differences in the predictions of different connectivity analyses was related to the method of analysis, with clear differences between kernel, path, and graph-theory approaches and relatively little effect due to the density and distribution of source points or the distance threshold used to define dispersal capability. ConclusionsThis work provides one of the first comparisons of spatial predictions of different methods, frameworks, and parameterizations of connectivity models. Our results support environmental planning by clarifying what most influences predictions of movement patterns and how the predicted connectivity networks differ between different analytical frameworks.

HClave: An isolated execution environment design for hypervisor runtime security

Virtualization is the cornerstone of cloud computing, but the hypervisor, the crucial software component that enables virtualization, is known to suffer from various attacks. It is challenging to secure the hypervisor due to at least two reasons. On one hand, commercial hypervisors are usually integrated into a privileged Operating System (OS), which brings in a larger attack surface. On the other hand, multiple Virtual Machines (VM) share a single hypervisor, thus a malicious VM could leverage the hypervisor as a bridge to launch “cross-VM” attacks. In this work, we propose HClave, an isolated execution environment (IEE) design for hypervisor runtime. We decouple the virtualization layer into a tiny trusted computing base (TCB), a large non-secure OS, and multiple HClave IEEs through a bidirectional isolation approach. HClave extends the nested kernel approach to deprive the traditional OS from accessing the tiny TCB’s memory and creates an IEE for hypervisor runtime. We implemented HClave based on KVM and evaluated its effectiveness and efficiency through case studies. Experimental results show that HClave can significantly improve the security of the hypervisor with reasonable runtime overhead.

Comprehensive study of tri-hybrid nanofluid flow in a vertical channel with Cu, Al2O3, and TiO2 nanoparticles via fractional dynamics and non-local kernel approach

Nanofluids and hybrid nanofluids enhance the transfer of heat with low nanoparticle concentration. Tri-hybrid nanofluids combine different nanoparticles (NPs) to further increase the performance of base fluids. Tri-hybrid nanofluids have significant uses in several industries, including electronic cooling, heat transport, biomedical engineering as well as energy storage systems. This study investigates the thermal performance of tri-hybrid nanofluid in the existence of a magnetic field and porous saturated space along with copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) NPs dispersed in base fluid, i.e. water (H2O) flowing through a vertical channel by convection. The resultant partial differential equations based on Atangana–Baleanu time-fractional derivative (having non-singular and non-local kernel) are solved using the Laplace transform along with the appropriate physical conditions. The Stehfest as well as Tzou’s numerical approaches are then utilized to compute the Laplace inverse, to check the validity of obtained solutions and to get the graphical representations of, concentration, energy, and velocity fields. The results show that tri-hybrid nanofluids have advanced thermal as well as momentum characteristics compared to nanofluids and hybrid nanofluids.

Negative heat capacity in low-dimensional systems using non-local kernel approach

Negative heat capacity in low-dimensional systems using non-local kernel approach

Worldline path integrals for the graviton

We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coefficients related to the UV divergences of quantum gravity. These gauge invariant coefficients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the N=4 spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.

Series solution of time-fractional mhd viscoelastic model through non-local kernel approach

The study of ramped condition in the context of unsteady incompressible magnetohydrodynamic Casson fluid flow over a moving vertical plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. In this study, Casson fluid is considered unsteady under the influence of magnetic field. The fractional mathematical model is proposed by considering the effect of chemical reaction parameter of the flowing fluid. The governing equations are transformed into the dimensionless form and developed fractional models like Caputo-Fabrizio and Atangana-Baleanu Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for velocity, energy and momentum balances developed in terms of series. MATHCAD software is being used for numerical computations and the physical attributes of material and fractional parameters are discussed. To analyze their behavior clearly, two-dimensional graphical results are plotted for velocity profile and temperature as well. It has been concluded that the fluid’s velocity are reduced for larger values of the fractional parameter and Prandtl number and is maximum for small values of both parameters. Further, the velocity behavior becomes larger for isothermal condition as compared to ramped conditions.

Point Cloud Denoising and Feature Preservation: An Adaptive Kernel Approach Based on Local Density and Global Statistics.

Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud.

Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

This paper studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the above conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.

Measuring and Testing Multivariate Spatial Autocorrelation in a Weighted Setting: A Kernel Approach

AbstractWe propose and illustrate a general framework in which spatial autocorrelation is measured by the Frobenius product of two kernels, a feature kernel and a spatial kernel. The resulting autocorrelation index generalizes Moran's index in the weighted, multivariate setting, where regions, differing in importance, are characterized by multivariate features. Spatial kernels can traditionally be obtained from a matrix of spatial weights, or directly from geographical distances. In the former case, the Markov transition matrix defined by row‐normalized spatial weights must be made compatible with the regional weights, as well as reversible. Equivalently, space is specified by a symmetric exchange matrix containing the joint probabilities to select a pair of regions. Four original weight‐compatible constructions, based upon the binary adjacency matrix, are presented and analyzed. Weighted multidimensional scaling on kernels yields a low‐dimensional visualization of both the feature and the spatial configurations. The expected values of the first four moments of under the null hypothesis of absence of spatial autocorrelation can be exactly computed under a new approach, invariant orthogonal integration, thus permitting to test the significance of beyond the normal approximation, which only involves its expectation and expected variance. Various illustrations are provided, investigating the spatial autocorrelation of political and social features among French departments.

On Mitigating the Utility-Loss in Differentially Private Learning: A New Perspective by a Geometrically Inspired Kernel Approach

Privacy-utility tradeoff remains as one of the fundamental issues of differentially private machine learning. This paper introduces a geometrically inspired kernel-based approach to mitigate the accuracy-loss issue in classification. In this approach, a representation of the affine hull of given data points is learned in Reproducing Kernel Hilbert Spaces (RKHS). This leads to a novel distance measure that hides privacy-sensitive information about individual data points and improves the privacy-utility tradeoff via significantly reducing the risk of membership inference attacks. The effectiveness of the approach is demonstrated through experiments on MNIST dataset, Freiburg groceries dataset, and a real biomedical dataset. It is verified that the approach remains computationally practical. The application of the approach to federated learning is considered and it is observed that the accuracy-loss due to data being distributed is either marginal or not significantly high.

Operational Status Evaluation of Smart Electricity Meters Using Gaussian Process Regression With Optimized-ARD Kernel

Operational Status Evaluation (OSE) is essential for the health management of Smart Electricity Meters (SEM). This paper develops a machine learning-enabled OSE method for SEM. Specifically, the Gaussian Process Regression (GPR) is developed for modeling analysis, where an Optimized Automatic Relevance Determination (OARD) kernel is first used. Though the conventional ARD kernel structure can capture the potential mapping relationship between running time, temperature, humidity, and Measurement Error (ME), it cannot extract the influence degree of different stresses on the ME. To address this problem, an OARD kernel structure is proposed to identify the contribution of each part in ARD structure to the target data. Furthermore, the quartiles line instead of 95% confidence interval is exploited to enhance the performance of GPR for long-term prediction. Combining the two above improvements, a novel OSE model is established for the future-oriented long-term operation of the SEM. It is the first-known data-driven application that utilizes the GPR with OARD kernel to perform OSE for SEM. Actual SEM datasets collected from both dry and hot region are used for model validation and prediction. The results demonstrate that the proposed GPR model with OARD Matern52 kernel outperforms other conventional kernel approaches in the aspect of interpretability. More importantly, the operational status of the SEM in future can be assessed via the proposed OSE framework.