Anomalous Self-Organization in Active Piles.

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

Kernel Function-Based Ambiguity Function and Its Application on DOA Estimation in Impulsive Noise.

To solve the problem that the traditional ambiguity function cannot well reflect the time-frequency distribution characteristics of linear frequency modulated (LFM) signals due to the presence of impulsive noise, two robust ambiguity functions: correntropy-based ambiguity function (CRAF) and fractional lower order correntropy-based ambiguity function (FLOCRAF) are defined based on the feature that correntropy kernel function can effectively suppress impulsive noise. Then these two robust ambiguity functions are used to estimate the direction of arrival (DOA) of narrowband LFM signal under an impulsive noise environment. Instead of the covariance matrix used in the ESPRIT algorithm by the spatial CRAF matrix and FLOCRAF matrix, the CRAF-ESPRIT and FLOCRAF-ESPRIT algorithms are proposed. Computer simulation results show that compared with the algorithms only using ambiguity function and the algorithms only using the correntropy kernel function-based correlation, the proposed algorithms using ambiguity function based on correntropy kernel function have good performance in terms of probability of resolution and estimation accuracy under various circumstances. Especially, the performance of the FLOCRAF-ESPRIT algorithm is better than the CRAF-ESPRIT algorithm in the environment of low generalized signal-to-noise ratio and strong impulsive noise.

A new robust Bayesian small area estimation via α -stable model for estimating the proportion of athletic students in California.

In the last few years, diabetes mellitus and obesity revealed to be one of the fastest-growing chronic diseases in youth in the United States. The number of new diabetes cases is dramatically increasing, and, for the moment, effective therapy does not exist. Experts believe that one of the causes of this increase is the decline in exercise behavior. The California Education Code requires local educational agencies (LEAs) to administer the FITNESSGRAM, the Physical Fitness Test (PFT), to Californian students of public schools. This test evaluates six fitness areas, and experts defined that a passing result on all six areas of the test represents a fitness level that offers some protection against the diseases associated with physical inactivity. We consider 2015-2016 data provided by the California Department of Education (CDE): for each Californian county ( m=57 ), we aim at estimating the county-level proportion of students with a score equal to six. To account for the heterogeneity of the phenomenon and the presence of outlying counties, we extend the standard area-level model by specifying the random effects as a symmetric α -stable (S α S) distribution that can accommodate different types of outlying observations. The model can accurately estimate the county-level proportion of students with a score equal to six. Results highlight some interesting relationships with social and economic situations in each county. The performance of the proposed model is also investigated through an extensive simulation study.

Parameter Estimation Based on Sigmoid Transform in Wideband Bistatic MIMO Radar System under Impulsive Noise Environment.

Since second-order statistics-based methods rely heavily on Gaussianity assumption and fractional lower-order statistics-based methods depend on a priori knowledge of non-Gaussian noise, there remains a void in wideband bistatic multiple-input/multiple-output (MIMO) radar systems under impulsive noise. In this paper, a novel method based on Sigmoid transform was used to estimate target parameters, which do not need a priori knowledge of the noise in an impulsive noise environment. Firstly, a novel wideband ambiguity function, termed Sigmoid wideband ambiguity function (Sigmoid-WBAF), is proposed to estimate the Doppler stretch and time delay by searching the peak of the Sigmoid-WBAF. A novel Sigmoid correlation function is proposed. Furthermore, a new MUSIC algorithm based on the Sigmoid correlation function (Sigmoid-MUSIC) is proposed to estimate the direction-of-departure (DOD) and direction-of-arrival (DOA). Then, the boundness of the Sigmoid-WBAF to the symmetric alpha stable () noise, the feasibility analysis of the Sigmoid-WBAF, and complexity analysis of the Sigmoid-WBAF and Sigmoid-MUSIC are presented to evaluate the performance of the proposed method. In addition, the Cramér⁻Rao bound for parameter estimation was derived and computed in closed form, which shows that better performance was achieved. Simulation results and theoretical analyses are presented to verify the effectiveness of the proposed method.

Waning and boosting: on the dynamics of immune status.

The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller's fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.

A Novel Parameter Estimation Method Based on a Tuneable Sigmoid in Alpha-Stable Distribution Noise Environments.

In this paper, a novel method, that employs a fractional Fourier transform and a tuneable Sigmoid transform, is proposed, in order to estimate the Doppler stretch and time delay of wideband echoes for a linear frequency modulation (LFM) pulse radar in an alpha-stable distribution noise environment. Two novel functions, a tuneable Sigmoid fractional correlation function (TS-FC) and a tuneable Sigmoid fractional power spectrum density (TS-FPSD), are presented in this paper. The novel algorithm based on the TS-FPSD is then proposed to estimate the Doppler stretch and the time delay. Then, the derivation of unbiasedness and consistency is presented. Furthermore, the boundness of the TS-FPSD to the symmetric alpha stable ( S α S ) noise, the parameter selection of the TS-FPSD, and the feasibility analysis of the TS-FPSD, are presented to evaluate the performance of the proposed method. In addition, the Cramér⁻Rao bound for parameter estimation is derived and computed in closed form, which shows that better performance has been achieved. Simulation results and theoretical analysis are presented, to demonstrate the applicability of the forgoing method. It is shown that the proposed method can not only effectively suppress impulsive noise interference, but it also does not need a priori knowledge of the noise with higher estimation accuracy in alpha-stable distribution noise environments.

Non-Gaussian Resistance Fluctuations in Gold-Nanoparticle-Based Gas Sensors: An Appraisal of Different Evaluation Techniques.

Volatile organic compounds, such as formaldehyde, can be used as biomarkers in human exhaled breath in order to non-invasively detect various diseases, and the same compounds are of much interest also in the context of environmental monitoring and protection. Here, we report on a recently-developed gas sensor, based on surface-functionalized gold nanoparticles, which is able to generate voltage noise with a distinctly non-Gaussian component upon exposure to formaldehyde with concentrations on the ppm level, whereas this component is absent, or at least much weaker, when the sensor is exposed to ethanol or to pure air. We survey four different statistical methods to elucidate a non-Gaussian component and assess their pros and cons with regard to efficient gas detection. Specifically, the non-Gaussian component was clearly exposed in analysis using level-crossing parameters, which require nothing but a modest computational effort and simple electronic circuitry, and analogous results could be reached through the bispectrum function, albeit with more intense computation. Useful information could be obtained also via the Lévy-stable distribution and, possibly, the second spectrum.

Annealed fractional Lévy-Ito diffusion models for protein generation.

Protein generation has numerous applications in designing therapeutic antibodies and creating new drugs. Still, it is a demanding task due to the inherent complexities of protein structures and the limitations of current generative models. Proteins possess intricate geometry, and sampling their conformational space is challenging due to its high dimensionality. This paper introduces novel Markovian and non-Markovian generative diffusion models based on fractional stochastic differential equations and the Lévy distribution, allowing for a more effective exploration of the conformational space. The approach is applied to a dataset of 40,000 proteins and evaluated in terms of Fréchet distance, fidelity, and diversity, outperforming the state-of-the-art by 25.4%, 35.8%, and 11.8%, respectively.

An Impact study of highway design on casualty and non-casualty traffic accidents.

Background Road Safety has become a worldwide concern due to the alarming repercussions road accidents may bear. This study examined the relationship between different geometric design elements and the accident rates on Rashid Bin Saeed Street, Arabian Gulf Street, and Sultan Bin Zayed Street in Abu Dhabi, United Arab Emirates. Methods The geometric design was collected from the satellite images of google earth in compliance with the standard geometric design manual of Abu Dhabi roads. The recorded geometric data consisted of the number of lanes, lane widths, median length, and width. The traffic volume data was provided by the Integrated Transport Center of Abu Dhabi, which was then converted into Annual Average Daily Traffic (AADT) for analytical purposes. For the studied roads, AADT ranges ranged between 26,509 and 121,890 vehicles per day. The crash data related to the period of 2012-2019 was collected from the online open-access data provided by the United Arab Emirates Ministry of Interior. The data provided had considered variables related to driver gender, age and speed, travel direction, and time of the day amongst other factors. A comprehensive statistical analysis was conducted to study the impact of geometric design elements on road safety through a stable distribution. Stable distributions are generally characterized by four parameters and expressed as X∼S(α,ß,σ,µ). The statistical model included several graphical representations such as accident frequency at two levels of severity, casualty and non-casualty accidents for different road segments, traffic volumes, day of the week, age of the injured person, and the geometric design parameters on the three roads. Variance-based methods of sensitivity analysis are also used that are a class of probabilistic approaches that quantify the input and output uncertainties as probability distributions and decompose the output variance into parts attributable to input variables and combinations of variables. The sensitivity of the output to an input variable is therefore measured by the amount of variance in the output caused by that input. Findings The results showed that the accident profiles differ with varying segments on each road, revealing some segments to be of higher accident rates than others. Also, a higher accident frequency was shown with young adult drivers, and a high majority of accidents had occurred on weekends. Regarding the road's geometric design, which is the focus of this study, a sensitivity analysis was made to determine the most influential geometric design element on accident frequency. Interpretation The number of lanes had the highest sensitivity index followed by the median width, and then came the lane width. Thus, modifying the number of lanes on a highway is anticipated to have the highest impact on accident frequency and road safety than any other geometric parameter.

Predicting suitable distribution areas of Juniperus przewalskii in Qinghai Province under climate change scenarios.

Juniperus przewalskii is important for water and soil conservation. It is one of the native tree species suitable for afforestation and greening in high-cold and arid areas of Qinghai Province. Predicting the potential geographic distribution of J. przewalskii in Qinghai Province under the climate change scenario will provide theoretical guidance for its management, introduction, and cultivation. In this study, the current potential distribution of J. przewalskii was simulated firstly based on 88 effective distributional records from field investigation and data collection via Maxent model and ArcGIS spatial analysis. We analyzed dominant factors affecting the potential distribution of J. przewa-lskii by Jackknife test and correlation coefficient. The distribution of J. przewalskii under three climate change scenarios (SSP126, SSP245, SSP585) with the climate model data of the sixth phase of the Coupled Model Intercomparison Projects (CMIP6) were predicted for 2061-2080. The results showed that the area under the receiver operating characteristic curve (AUC) of the Maxent model was greater than 0.92, suggesting a good predictive performance. Under current climatic condition, the suitable distribution area of J. przewalskii was mainly located in the eastern part of Qinghai Province, with the suitable area accounted for 11.2% of the total. The dominant factors affecting the distribution of J. przewalskii were altitude, annual precipitation, the minimum temperature of coldest month, and slope, with a cumulative contribution rate of 85.9%. The suitable areas of J. przewalskii altered under the three future climate scenarios. The suitable areas would shrink under the SSP245 scenario and expand under the SSP126 and SSP585 scenarios. The sui-table area of J. przewalskii would have the most obvious expansion under the SSP126 climate situation, with the expanding areas being mainly located in Zeku County, the north-central part of Henan Mongolian Autonomous County, and the southeast of Qilian County. Under three climatic scenarios, the suitable area of J. przewalskii would gradually migrate to high altitudes, but without clear altitudinal and longitudinal shifts.

Bridged parametric survival models: General paradigm and speed improvements.

BACKGROUND AND OBJECTIVE: With the recent surge in availability of large biomedical databases mostly derived from electronic health records, the need for the development of scalable marginal survival models with faster implementation cannot be more timely. The presence of clustering renders computational complexity, especially when the number of clusters is high. Marginalizing conditional survival models can violate the proportional hazards assumption for some frailty distributions, disrupting the connection to a conditional model. While theoretical connections between proportional hazard and accelerated failure time models exist, a computational framework to produce both for either marginal or conditional perspectives is lacking. Our objective is to provide fast, scalable bridged-survival models contained in a unified framework from which the effects and standard errors for the conditional hazard ratio, the marginal hazard ratio, the conditional acceleration factor, and the marginal acceleration factor can be estimated, and related to one another in a transparent fashion. Methods We formulate a Weibull parametric frailty likelihood for clustered survival times that can directly estimate the four estimands. Under a nonlinear mixed model specification with positive stable frailties powered by Gaussian quadrature, we put forth a novel closed form of the integrated likelihood that lowered the computational threshold for fitting these models. The method is illustrated on a real dataset generated from electronic health records examining tooth-loss. RESULTS: Our novel closed form of the integrated likelihood significantly lowered the computational threshold for fitting these models by a factor of 12 (36 compared to 3 min) for the R package parfm, and a factor of 2400 for Gaussian Quadrature (4.6 days compared to 3 min) in SAS. Moreover, each of these estimands are connected by simple relationships of the parameters and the proportional hazards assumption is preserved for the marginal model. Our framework provides a flow of analysis enabling the fit of any/all of the 4 perspective-parameterization combinations. Conclusions We see the potential usefulness of our framework of bridged parametric survival models fitted with the Static-Stirling closed form likelihood. Bridged-survival models provide insights on subject-specific and population-level survival effects when their relation is transparent. SAS and R codes, along with implementation details on a pseudo data are provided.

Mixed Distribution Models Based on Single-Cell RNA Sequencing Data.

Progress in single-cell RNA sequencing (scRNA-seq) has yielded a lot of valuable data. Analysis of these data can provide a new perspective for studying the intratumoral heterogeneity and identifying gene markers. In this paper, the scRNA-seq data of colorectal cancer (CRC) are analyzed, and it is found that the shape of the gene expression difference (GED) data shows certain distribution regularity. To study the distribution regularity, mixed stable-normal distribution (MSND) model and mixed stable-exponential distribution (MSED) model are constructed to fit the GED data. And the estimated parameters of MSND and MSED are used to describe some characteristics of their distribution. Through the comparison of root mean square error and the chi-squared goodness of fit test, it is found that the fitting effect of MSED and MSND are both better than that of stable distribution and Cauchy distribution. Considering the given quantile thresholds, MSND and MSED can be used to identify tumor-related genes. The results of functional analysis indicate that the selected genes are highly correlated with CRC. In addition, the parameters of MSND and MSED exhibit a certain trend with the development of CRC. To explore the association, Gene-set enrichment analysis (GSEA) is performed. The results of GSEA reveal that the trend can well characterize the intratumoral heterogeneity of CRC. In addition, the application of MSED model on hepatocellular carcinoma shows that our model can analyze other cancers. Overall, MSND model and MSED model can well fit the GED data in different disease stages, the parameters of the two models can characterize the heterogeneity of CRC tumor cells, and the two models can be used to identify genes highly correlated with tumors.

Ship Detection in SAR Image Based on the Alpha-stable Distribution.

This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alphastable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian distribution often fails to describe background sea clutter. In this study, we replace the Gaussian distribution with the Alpha-stable distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-stable distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-stable distribution over the CFAR algorithm based on the Gaussian distribution.

Predicting the influence of future climate change on the suitable distribution areas of Elaeagnus angustifolia.

Climate change significantly affects geographic distribution of plants worldwide. Understanding the influence of climate change on the suitable areas of afforestation tree species in China and taking timely countermeasures are crucial for improving the effectiveness of afforestation. Elaeagnus angustifolia is a good species for ecological restoration of degraded lands and control of desertification. Using MaxEnt and GIS, we predicted the changes of climatically suitable areas of this species under future climate scenarios, based on 182 records from herbaria and published literatures, and 13 climatic factors from BIOCLIM, Holdridge life zone and Kira index. The results showed that the four climate scenarios in 2070s had different effects on the climatically suitable areas of this species. The suitable areas would shrink in the lowest greenhouse gas emission (RCP 2.6) scenario. The shrinking areas were mainly located in the edge of the currently suitable areas in the northwest. The suitable areas would expand in the lower (RCP 4.5), the higher (RCP 6.0) and the highest (RCP 8.5) greenhouse gas emission scenarios. The expanding areas were mainly located in the northwestern arid regions of warm temperate zone, and northeastern sub-humid regions of middle temperate zone. There were obvious expansions in the northern arid and semi-arid regions of middle temperate zone, and southern humid regions of north-subtropical zone under RCP 8.5 scenario. The geographical centroids of future suitable ranges would move with a speed of 6-19 km·(10 a)-1. The altitudinal centroids were predicted to move to lower regions with a speed of 3-20 m·(10 a)-1. The stably suitable areas accounted for 83%-98% of the current distribution ranges of this species, which were generally stable under future climate change scenarios.

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI.

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI.

Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process.

One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size N is large and mutation rates are low, but not necessarily small compared to 1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy α-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in shortened form [11].

A characterization of Chover-type law of iterated logarithm.

ABSTRACT: Let 0 < α ≤ 2 and - ∞ <ß <∞. Let {X n ;n ≥ 1} be a sequence of independent copies of a real-valued random variable X and set S n = X 1+⋯+X n , n ≥ 1. We say X satisfies the (α,ß)-Chover-type law of the iterated logarithm (and write X∈C T L I L(α,ß)) if [Formula: see text] almost surely. This paper is devoted to a characterization of X ∈C T L I L(α,ß). We obtain sets of necessary and sufficient conditions for X∈C T L I L(α,ß) for the five cases: α = 2 and 0 < ß <∞, α = 2 and ß = 0, 1<α<2 and -∞<ß<∞, α = 1 and -∞ <ß <∞, and 0 < α <1 and -∞ <ß <∞. As for the case where α = 2 and -∞ <ß <0, it is shown that X∉C T L I L(2,ß) for any real-valued random variable X. As a special case of our results, a simple and precise characterization of the classical Chover law of the iterated logarithm (i.e., X∈C T L I L(α,1/α)) is given; that is, X∈C T L I L(α,1/α) if and only if [Formula: see text] where [Formula: see text] whenever 1< α ≤ 2. MATHEMATICS SUBJECT CLASSIFICATION 2000: Primary: 60F15; Secondary: 60G50.

Asymptotic behaviour of random walks with correlated temporal structure.

We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions. We derive the corresponding diffusion limit and prove its subdiffusive character. Analysing the set of corresponding coupled Langevin equations, we verify the speed of relaxation, Einstein relations, equilibrium distributions, ageing and ergodicity breaking.

A HIERARCHICAL MAX-STABLE SPATIAL MODEL FOR EXTREME PRECIPITATION.

Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a max-stable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model.

Limiting behavior of delayed sums under a non-identically distribution setup

We present an accurate description the limiting behavior of delayed sums under a non-identically distribution setup, and deduce Chover-type laws of the iterated logarithm for them. These complement and extend the results of Vasudeva and Divanji (Theory of Probability and its Applications, 37 (1992), 534-542).

Apresentamos uma descrição precisa do comportamento limite de somas retardadas, e deduzimos leis do tipo Chover de logaritmo iterado para as mesmas. Isso completa e estende os resultados de Vasudeva e Divanji (Theory of Probability and its Aplications, 37 (1992), 534-542).