Random Field Research Articles

High Energy Storage Performance in BiFeO3-Based Lead-Free High-Entropy Ferroelectrics.

Dielectric capacitors are widely used in advanced electrical and electronic systems due to the rapid charge/discharge rates and high power density. High comprehensive energy storage properties are the ultimate ambition in the field of application achievements. Here, the high-entropy strategy is proposed to design and fabricate single-phase homogeneous (Bi0.5Ba0.1Sr0.1Ca0.2Na0.1)(Fe0.5Ti0.3Zr0.1Nb0.1)O3 ceramic, the hierarchical heterostructure including rhombohedral-tetragonal multiphase nanoclusters and locally disordered oxygen octahedral tilt can lead to the increased dielectric relaxation, diffused phase transition, diverse local polarization configurations, grain refinement, ultrasmall polar nanoregions, large random field, delayed polarization saturation and improved breakdown field. Accordingly, a giant Wrec ≈13.3 J cm-3 and a high η ≈78% at 66.4kV mm-1 can be simultaneously achieved in the lead-free high-entropy BiFeO3-based ceramic, showing an obvious advantage in overall energy-storage properties over BiFeO3-based lead-free ceramics. Moreover, an ultrafast discharge rate (t0.9 = 18ns) can be achieved at room temperature, concomitant with favorable temperature stability in the range of 20-160 °C, due to the enhanced diffuse phase transition and fast polarization response. This work provides a feasible pathway to design and generate dielectric materials exhibiting high comprehensive energy-storage performance.

JPSSL: SAR Terrain Classification Based on Jigsaw Puzzles and FC-CRF

Effective features play an important role in synthetic aperture radar (SAR) image interpretation. However, since SAR images contain a variety of terrain types, it is not easy to extract effective features of different terrains from SAR images. Deep learning methods require a large amount of labeled data, but the difficulty of SAR image annotation limits the performance of deep learning models. SAR images have inevitable geometric distortion and coherence speckle noise, which makes it difficult to extract effective features from SAR images. If effective semantic context features cannot be learned for SAR images, the extracted features struggle to distinguish different terrain categories. Some existing terrain classification methods are very limited and can only be applied to some specified SAR images. To solve these problems, a jigsaw puzzle self-supervised learning (JPSSL) framework is proposed. The framework comprises a jigsaw puzzle pretext task and a terrain classification downstream task. In the pretext task, the information in the SAR image is learned by completing the SAR image jigsaw puzzle to extract effective features. The terrain classification downstream task is trained using only a small number of labeled data. Finally, fully connected conditional random field processing is performed to eliminate noise points and obtain a high-quality terrain classification result. Experimental results on three large-scene high-resolution SAR images confirm the effectiveness and generalization of our method. Compared with the supervised methods, the features learned in JPSSL are highly discriminative, and the JPSSL achieves good classification accuracy when using only a small amount of labeled data.

Regularized Loss With Hyperparameter Estimation for Weakly Supervised Single Class Segmentation.

We propose a new image level weakly supervised segmentation approach for datasets with a single object class of interest. Our approach is based on a regularized loss function inspired by the classical Conditional Random Field (CRF) modeling. Our loss models properties of generic objects, and we use it to guide CNN towards segments that are more likely to correspond to the object, thus avoiding the need for pixel precise annotations. Training CNN with regularized loss is a difficult task for gradient descent. We develop an annealing algorithm which is crucial for a successful training. Furthermore, we develop an approach for hyperparameter setting for the most important components of our regularized loss. This is far from trivial, since there is no pixel precise ground truth for guidance. The advantage of our method is that we use a standard CNN architecture and an easy to interpret loss function, derived from classical CRF models. Furthermore, we apply the same loss function for any task/dataset. We first evaluate our approach for salient object segmentation and co-segmentation. These tasks naturally involve one object class of interest. Then we adapt our approach to image level weakly supervised multi-class semantic segmentation. We obtain state-of-the-art results.

An analytical approach to predict fatigue strength of corroded steel plates using random field-based corrosion surface modeling

This study introduces a probabilistic method to predict the fatigue strength of corroded steel members by incorporating uncertainties related to corrosion depth and surface morphology using random field modeling. The modeling successfully captured the probability density of the target corrosion depth, accurately representing corrosion geometric characteristics. Validation against fatigue testing on corroded rolled beams showcased the method’s accuracy across a range of stress levels. The application of the proposed method for time-variant fatigue strength predictions unveiled a rapid decline in both fatigue constant A and the constant amplitude fatigue threshold (CAFT) during the initial stages of corrosion. In marine and urban environments, fatigue strength fell rapidly within the first 3 years after corrosion initiation, whereas in rural environments, fatigue strength was anticipated to start to decline gradually after 5 years. These projections underscore the necessity of regular inspections to assess the condition of protective coatings. Moreover, the degradation curves generated by this method can serve as a foundational element in establishing an effective maintenance strategy for structures.

Caterpillar movement mediates spatially local interactions and determines the relationship between population density and contact.

While interactions in nature are inherently local, ecological models often assume homogeneity across space, allowing for generalization across systems and greater mathematical tractability. Density-dependent disease models are a prominent example of models that assume homogeneous interactions, leading to the prediction that disease transmission will scale linearly with population density. In this study, we examined how the scale of larval butterfly movement interacts with the resource landscape to influence the relationship between larval contact and population density in the Baltimore checkerspot (Euphydryas phaeton). Our study was inspired by the recent discovery of a viral pathogen that is transmitted horizontally among Baltimore checkerspot larvae. We used multi-year larvae location data across six Baltimore checkerspot populations in the eastern U.S. to test whether larval nests are spatially clustered. We then integrated these spatial data with larval movement data in different resource contexts to investigate whether heterogeneity in spatially local interactions alters the assumed linear relationship between larval nest density and contact. We used Correlated Random Walk (CRW) models and field observations of larval movement behavior to construct Probability Distribution Functions (PDFs) of larval dispersal, and calculated the overlap in these PDFs to estimate conspecific contact within each population. We found that all populations exhibited significant spatial clustering in their habitat use. Subsequent larval movement rates were influenced by encounters with host plants and larval age, and under many movement scenarios, the scale of predicted larval movement was not sufficient to allow for the "homogeneous mixing" assumed in density dependent disease models. Therefore, relationships between population density and larval contact were typically non-linear. We also found that observed use of available habitat patches led to significantly greater contact than would occur if habitat use were spatially random. These findings strongly suggest that incorporating larval movement and spatial variation in larval interactions is critical to modeling disease outcomes in E. phaeton. Epidemiological models that assume a linear relationship between population density and larval contact have the potential to underestimate transmission rates, especially in small populations that are already vulnerable to extinction.

Quantifying the relative importance of biotic and abiotic factors in landscape-based models of stream fish distributions

AbstractLotic fish species distributions are frequently predicted using remotely sensed habitat variables that characterize the adjacent landscape and serve as proxies for instream habitat. Recent advancements in statistical methodology, however, allow for leveraging fish assemblage data when predicting distributions. This is important because assemblage composition likely provides better information about instream habitat compared to landscape-derived metrics and therefore may improve predictions. To better understand the value of using multi-species fish data in species distribution modeling, we fit two conditional random fields (CRF) models to quantify the relative importance of fish assemblage co-occurrence, landscape-derived habitat variables, and interactions between these two predictor groups (i.e., effects of co-occurrence could be context-dependent) at over 1200 stream catchments in Pennsylvania, USA. We first compared predictive performance of CRF models against traditionally used single-species logistic regressions (generalized linear models; GLMs) and found that inclusion of fish assemblage data often improved predictive performance. The multi-species CRF models performed significantly better at predicting occurrence for 63% of species with an average percent increase in AUC of 25% compared to GLMs. Furthermore, the CRF identified species co-occurrences as more informative, and thus relatively more important, at predicting occurrence than the other effect types. The CRF also suggested that allowing these biotic effects to be context-dependent was important for predicting occurrence of many species. These findings illustrate the value of fish assemblage data for landscape-scale species distribution modeling and leveraging this information can improve predictions and inferences to help inform the management and conservation of freshwater fishes.

Analysis of Beijing Traffic Violations Based on the BERT-CRF Model

Traffic violations are a major cause of traffic accidents, yet current research falls short in comprehensively analysing these violations and the  named entity method fails to extract the name of traffic violation events from records, thereby lacking in providing guidance for managing urban traffic violations. By expanding the People’s Daily dataset from 71,456 words to 95,291 words, the BERT-CRF (Bidirectional Encoder Representations from Transformers-Conditional Random Field) model achieves an accuracy rate of 88.53%, a recall rate of 92.90% and an F1 score of 90.66%, successfully identifying event, time and location named entities within traffic violations. The data of traffic violations is then enhanced through forward geocoding and the Bayesian formula, and traffic violations are analysed from time, space, administrative region, gender and weather, to provide support for the dynamic allocation of law enforcement forces on traffic scenes and the precise management oftraffic violations.

Random dynamic response analysis of an asphalt concrete core wall dam on deep overburden with double random factors

The spatial variability of material parameters and the randomness of ground motion are factors that influence the seismic response of a dam. To obtain more reliable seismic response results, it is crucial to study the influence of various uncertain factors on the response to earthquakes. In this paper, the K-L series expansion method and LH sampling technique are combined to characterize the spatial correlation of material parameters using a Gaussian autocorrelation function. This allows for the simulation of random fields of material parameters. By improved the Clough-Penzien power spectrum model and incorporating the concept of a random function, it becomes possible to generate nonstationary random ground motion that accurately reflects the site conditions. Taking an asphalt concrete core dam on deep overburden as an example, a random dynamic response analysis was conducted, considering various random factors. Statistical analysis and distribution testing were conducted on the horizontal acceleration and vertical permanent deformation responses. The process of the evolution of the probability density of the horizontal acceleration at the top of the dam was determined using the generalized probability density evolution method. This method helps to reveal the influence of various random factors on the response of the dam body. The research results show that among the spatial variability of material parameters and the randomness of ground motions, the randomness of ground motions is the main influencing factor of the random response results of the dam body. The mean response of two random factors is significantly larger than that of a single random factor. When considering dual random factors simultaneously, the complexity of the random factors increases, resulting in statistical properties that differ from those of single random factors. Therefore, to obtain more reliable random seismic response results, it is necessary to consider both the spatial variability of material parameters and the randomness of ground motions.

Infinite disorder renormalization fixed point for the continuum random field Ising chain

Infinite disorder renormalization fixed point for the continuum random field Ising chain

Mean Field Analysis and Simulations of Zero Temperature Hysteresis in the Diluted 3-State Random Field Clock Model

Mean Field Analysis and Simulations of Zero Temperature Hysteresis in the Diluted 3-State Random Field Clock Model

Predicting ground vibrations from railway tunnels using an improved 2.5D FEM-PML model with soil spatial variability

PurposeThis study establishes a method for predicting ground vibrations caused by railway tunnels in unsaturated soils with spatial variability.Design/methodology/approachFirst, an improved 2.5D finite-element-method-perfect-matching-layer (FEM-PML) model is proposed. The Galerkin method is used to derive the finite element expression in the ub-pl-pg format for unsaturated soil. Unlike the ub-v-w format, which has nine degrees of freedom per node, the ub-pl-pg format has only five degrees of freedom per node; this significantly enhances the calculation efficiency. The stretching function of the PML is adopted to handle the unlimited boundary domain. Additionally, the 2.5D FEM-PML model couples the tunnel, vehicle and track structures. Next, the spatial variability of the soil parameters is simulated by random fields using the Monte Carlo method. By incorporating random fields of soil parameters into the 2.5D FEM-PML model, the effect of soil spatial variability on ground vibrations is demonstrated using a case study.FindingsThe spatial variability of the soil parameters primarily affected the vibration acceleration amplitude but had a minor effect on its spatial distribution and attenuation over time. In addition, ground vibration acceleration was more affected by the spatial variability of the soil bulk modulus of compressibility than by that of saturation.Originality/valueUsing the 2.5D FEM-PML model in the ub-pl-pg format of unsaturated soil enhances the computational efficiency. On this basis, with the random fields established by Monte Carlo simulation, the model can calculate the reliability of soil dynamics, which was rarely considered by previous models.

Performance assessment of corroded stiffened steel plates considering non-Gaussian spatial correlated corrosion random field

This paper investigates the effect of corrosion randomness on the compression performance of stiffened steel plates. An anisotropic non-Gaussian random filed model is proposed to characterize the corrosion depth of the corroded steel plate surface. The specimens of corroded steel plate were obtained utilizing the artificial climate environment method. Corrosion characteristics were measured through 3D-scanning and reverse modeling. Statistical methods are utilized to analyze corrosion depth, including probability distribution and correlation coefficient. Two models are proposed for steel plate placing flatly and inclinedly, respectively. It is found that for both models corrosion depth follows truncated GEV distribution, and the correlation coefficient follows a bidirectional exponential function. To investigate the effect of non-Gaussian and correlation characteristics on bearing capacity, the proposed model is used for generating anisotropic non-Gaussian corrosion random fields for stiffened steel plates. Generated samples were used for finite element analysis. It is found the ignorance of non-Gaussian or correlation of the corrosion depth field will underestimate the deterioration of bearing capacity of stiffened steel plates. Finally, a parametric study on the correlation coefficients of the corrosion field indicates that correlation length will affect the residual bearing capacity of corroded steel plate. The proposed random field for corrosion depth of steel plate could be used for potential application on the safety assessment of corroded steel structures.

Cross-modality mapping using image varifolds to align tissue-scale atlases to molecular-scale measures with application to 2D brain sections

This paper explicates a solution to building correspondences between molecular-scale transcriptomics and tissue-scale atlases. This problem arises in atlas construction and cross-specimen/technology alignment where specimens per emerging technology remain sparse and conventional image representations cannot efficiently model the high dimensions from subcellular detection of thousands of genes. We address these challenges by representing spatial transcriptomics data as generalized functions encoding position and high-dimensional feature (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling regions as homogeneous random fields with unknown transcriptomic feature distribution. We solve simultaneously for the minimizing geodesic diffeomorphism of coordinates through LDDMM and for these latent feature densities. We map tissue-scale mouse brain atlases to gene-based and cell-based transcriptomics data from MERFISH and BARseq technologies and to histopathology and cross-species atlases to illustrate integration of diverse molecular and cellular datasets into a single coordinate system as a means of comparison and further atlas construction.

Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.

Aberrant functional connectivity associated with drug response in patients with newly diagnosed epilepsy.

To analyze the local functional activity and connectivity features of the brain associated with drug response inpatients newly diagnosed with epilepsy (NDE) who are naïve to anti-seizure medication (ASM). Recruited patients, underwent functional magnetic resonance imaging at baseline, and were assigned to the well-controlled (WC, n = 28) or uncontrolled (UC, n = 11) groups based on their response to ASM. Healthy participants were included in the control group (HC, n = 29). The amplitudes of low-frequency fluctuation (ALFF) and fractional ALFF (fALFF) were used to measure local functional activity, and voxel-wise degree centrality (DC) and seed-based functional connectivity (FC) were used to evaluate the connecting intensity of the brain areas. Compared to the HC and WC groups, the UC group had higher ALFF values in the left posterior central gyrus (PoCG.L) and left inferior temporal gyrus (ITG.L) and higher DC in the bilateral PoCG (Gaussian random field correction, voxel-level P < 0.001, and cluster-level P < 0.05). Both PoCG and ITG.L in the UC group showed stronger FC with multiple brain regions, mainly located in the occipital and temporal lobes, compared to the HC or WC group, while the WC group showed decreased or similar FC compared to the HC group. Excessive enhancement of brain functional activity or connecting intensity in ASM-naïve patients with NDE may be associated with a higher risk of poor drug response.

Uncertainty Analysis of Post-Failure Behavior in Landslides Based on SPH Method and Generalized Geotechnical Random Field Theory

In slope stability analysis, the inherent heterogeneity and spatial variability of soil significantly influence the aftermath of landslides, including critical aspects like runout distance, influence distance, and volume. This research integrates Smoothed Particle Hydrodynamics (SPH) with random field theory to precisely model the large deformation events in slopes with anisotropic shear parameters, while leveraging Graphics Processing Unit (GPU) parallel computing to expedite the generation of random field samples and SPH simulations. This approach meticulously examines how spatial heterogeneity of soil affects slope instability, simulating soil parameters across varied geological settings. It considers the fluctuation scale of anisotropy, the cross-correlation of cohesion and the angle of internal friction, along with their coefficient of variation (CV), to elucidate their impact on landslide magnitude and severity. This study furnishes a robust tool for a holistic assessment of slope impacts and landslide volumes. Additionally, by delineating the computational efficiency disparities between GPUs and Central processing units (CPUs), it underscores the pronounced efficiency benefits of GPU computing. The insights garnered offer fresh perspectives and methodologies in slope stability analysis and disaster risk evaluation, contributing to the finer prediction and management of this prevalent and grave geological hazard.

Nonlinear dynamical response of sinusoidal impulsive actuated piezoelectric/porous sandwich nanoharvesters via GM-based meshfree collocation formulations

In this paper a new effective computational approach based upon a meshless collocation formulation of the Gurtin-Murdoch (GM) continuum elasticity is described. The newly developed computational model for the third-order shear flexible elastic plates is then employed to analyze the nonlinear dynamical response of piezoelectric/porous sandwich nanoharvesters subjected to a sinusoidal impulsive actuation. The material properties relevant to the porous passive core having uniform or two graded through thickness porosity dispersions are estimated using the approach of Gaussian random field. The weak form of model conception is discretized and solved numerically via employing an incorporation of the polynomial and radial basis functions having the capability to remove any feasible singularity as well as taking more precise approximation into account within the GM-based meshfree collocation formulations. It is deduced that by contemplating the surface stress tensor via the established GM-based model, the achieved voltage from the sinusoidal impulsive actuated sandwich nanoharvesters reduces, especially for those possessing lower thickness. Also, it is deduced that for the fully simply supported impulsive actuated sandwich nanoharvester, by changing the porosity decoration of distribution from the uniform decoration to FGO and FGX graded ones, the significance of the role of surface stress tensor in the achieved voltage reduces from 12.45% to 12.28%, and enhances from 12.45% to 12.64%, respectively. For the fully clamped impulsive actuated sandwich nanoharvester, by changing the porosity decoration of distribution from the uniform decoration to FGO and FGX graded ones, the significance of the role of surface stress tensor in the achieved voltage reduces from 15.01% to 14.68%, and enhances from 15.01% to 15.37%, respectively.

Probabilistic analysis of lateral behaviour of offshore wind turbine monopile considering uncertainties of geological model and loads

Due to the complex geological, meteorological and hydrological conditions, along with the limited availability of field measurements, multiple uncertainties are related to the performance analysis of the offshore wind turbine. The main sources of uncertainty are the geological model and the environmental loads. However, the geological model uncertainty and loads uncertainty were often characterized separately in previous studies. To this end, this article proposes a novel framework for the coupled characterization of the geological model and loads uncertainties. With this new framework, the geological model is generated using a conditional random field method, in which the stratigraphic and geo-properties uncertainties are characterized simultaneously. Next, environmental parameters are considered as random variables, and the cross correlation between different environmental parameters is captured with the Pearson correlation coefficient. Then, multiple realizations of the geological model and these of environmental parameters are sampled with Monte Carlo simulation. With these generated realizations as inputs, the monopile foundation performance could then be analyzed probabilistically considering uncertainties of the geological model and loads. To demonstrate the effectiveness of the new framework, a case study of an offshore site in Taiwan is conducted. Further, a comparative study is performed to quantitatively reveal the influence of different uncertainty sources on site characterization and monopile behaviour assessment, through which the superiority of the presented framework is demonstrated.

Pattern dynamics of density and velocity fields in segregation of fluid mixtures.

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.

Interpolation problems for random fields on Sierpinski’s carpet

The prediction of stochastic processes and the estimation of random fields of different natures is becoming an increasingly common field of research among scientists of various specialties. However, an analysis of papers across different estimating problems shows that a dynamic approach over an iterative and recursive interpolation of random fields on fractal is still an open area of investigation. There are many papers related to the interpolation problems of stationary sequences, estimation of random fields, even on the perforated planes, but all of this still provides a place for an investigation of a more complicated structure like a fractal, which might be more beneficial in appliances of certain industry fields. For example, there has been a development of mobile phone and WiFi fractal antennas based on a first few iterations of the Sierpinski carpet. In this paper, we introduce an estimation for random fields on the Sierpinski carpet, based on the usage of the known spectral density, and calculation of the spectral characteristic that allows an estimation of the optimal linear functional of the omitted points in the field. We give coverage of an idea of stationary sequence estimating that is necessary to provide a basic understanding of the approach of the interpolation of one or a set of omitted values. After that, the expansion to random fields allows us to deduce a dynamic approach on the iteration steps of the Sierpinski carpet. We describe the numerical results of the initial iteration steps and demonstrate a recurring pattern in both the matrix of Fourier series coefficients of the spectral density and the result of the optimal linear functional estimation. So that it provides a dependency between formulas of the different initial sizes of the field as well as a possible generalizing of the solution for N-steps in the Sierpinski carpet. We expect that further evaluation of the mean squared error of this estimation can be used to identify the possible iteration step when further estimation becomes irrelevant, hence allowing us to reduce the cost of calculations and make the process viable.