Explore the vast range of titles available.

Drought is projected to become more severe and widespread as global warming continues in the twenty-first century, but hydroclimatic changes and their drivers are not well examined in the latest projections from phase 6 of the Coupled Model Intercomparison Project (CMIP6). Here, precipitation (P), evapotranspiration (E), soil moisture (SM), and runoff (R) from 25 CMIP6 models, together with self-calibrated Palmer drought severity index with Penman—Monteith potential evapotranspiration (scPDSIpm), are analyzed to quantify hydroclimatic and drought changes in the twenty-first century and the underlying causes. Results confirm consistent drying in these hydroclimatic metrics across most of the Americas (including the Amazon), Europe and the Mediterranean region, southern Africa, and Australia, although the drying magnitude differs, with the drying being more severe and widespread in surface SM than in total SM. Global drought frequency based on surface SM and scPDSIpm increases by ~25%–100% (50%–200%) under the SSP2-4.5 (SSP5-8.5) scenario in the twenty-first century together with large increases in drought duration and areas, which result from a decrease in the mean and flattening of the probability distribution functions of SM and scPDSIpm, while the R-based drought changes are relatively small. Changes in both P and E contribute to the SM change, whereas scPDSIpm decreases result from ubiquitous PET increases and P decreases over subtropical areas. The R changes are determined primarily by P changes, while the PET change explains most of the E increase. Intermodel spreads in surface SM and R changes are large, leading to large uncertainties in the drought projections.

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

The 2022 heatwave in China featured record‐shattering high temperatures, raising questions about its origin and possible link to global warming. Here we show that the maximum temperature anomalies over Central China reached 13.1°C in the summer of 2022, which is ∼4.2σ above the 1981–2010 mean with a return period of tens of thousands of years. Our results suggested that the persistent high‐pressure anomaly and associated extreme heatwave likely resulted mainly from internal variability, although anthropogenic warming has increased the probability of such extreme heatwaves. We also estimate that the 2022‐like heatwave becomes six to seven times more likely under persistent high‐pressure conditions when compared to stochastic circulation states. Due to a shift toward warmer mean temperatures and a flattening of the probability distribution function, such rare extreme heatwaves are projected to become much more common at a global warming level of 4°C, occurring once about every 8.5 years. Plain Language Summary China experienced an extensive and long‐lasting heatwave in the summer of 2022, especially in the middle reaches of the Yangtze River. Using state‐of‐the‐art reanalysis and models, here we show that the 2022 heatwave is among the most severe events ever recorded in China with a return period of tens of thousands of years. The atmospheric circulation patterns associated with the 2022 heatwave are not caused by external forcing, but due to internal atmospheric variability characterized by extremely warm anomalies and positive high‐pressure anomalies around central China, which increase the chance of such events by more than six times. A shift of the temperature distribution toward higher mean values and enlarged variability under global warming would increase the chances of new record‐breaking temperatures in the future. Such rare heatwaves in the natural and present climate could become much more common in the middle reaches of the Yangtze River under anthropogenic warming, occurring at least once every eight years at a global warming level of 4°C. Thus, efforts to build social resilience to extreme heatwaves are therefore urgently needed. Key Points Atmospheric circulation patterns associated with the 2022 heatwave likely resulted from internal variability, enhanced by external forcing The 2022‐like heatwave becomes six to seven times more likely under persistent high‐pressure conditions compared to stochastic circulation states Such rare heatwaves in natural and present climate are projected to become more common by 2100, occurring at least once every eight years

This work is devoted to the study of rates of convergence of the empirical measures \\mu_{n} = \\frac {1}{n} \\sum_{k=1}^n \\delta_{X_k}, n \\geq 1, over a sample (X_{k})_{k \\geq 1} of independent identically distributed real-valued random variables towards the common distribution \\mu in Kantorovich transport distances W_p. The focus is on finite range bounds on the expected Kantorovich distances \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) or \\big [ \\mathbb{E}(W_{p}^p(\\mu_{n},\\mu )) \\big ]^1/p in terms of moments and analytic conditions on the measure \\mu and its distribution function. The study describes a variety of rates, from the standard one \\frac {1}{\\sqrt n} to slower rates, and both lower and upper-bounds on \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

Unlike the real line, the real space ℝ d , for d ≥ 2, is not canonically ordered. As a consequence, such fundamental univariate concepts as quantile and distribution functions and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has been an open problem for more than half a century, generating an abundant literature and motivating, among others, the development of statistical depth and copula-based methods. We show that, unlike the many definitions proposed in the literature, the measure transportation-based ranks and signs introduced in Chernozhukov, Galichon, Hallin and Henry (Ann. Statist. 45 (2017) 223–256) enjoy all the properties that make univariate ranks a successful tool for semiparametric inference. Related with those ranks, we propose a new center-outward definition of multivariate distribution and quantile functions, along with their empirical counterparts, for which we establish a Glivenko–Cantelli result. Our approach is based on McCann (Duke Math. J. 80 (1995) 309–323) and our results do not require any moment assumptions. The resulting ranks and signs are shown to be strictly distribution-free and essentially maximal ancillary in the sense of Basu (Sankhyā 21 (1959) 247–256) which, in semiparametric models involving noise with unspecified density, can be interpreted as a finite-sample form of semiparametric efficiency. Although constituting a sufficient summary of the sample, empirical center-outward distribution functions are defined at observed values only. A continuous extension to the entire d-dimensional space, yielding smooth empirical quantile contours and sign curves while preserving the essential monotonicity and Glivenko–Cantelli features of the concept, is provided. A numerical study of the resulting empirical quantile contours is conducted.

We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From these formulas, we deduce exact formulas for the cumulative distribution function of the product of two correlated zero-mean normal random variables.

In this paper, we explore the utility of resting-state EEG measures as potential biomarkers for the detection and assessment of cognitive decline in mild cognitive impairment (MCI) and Alzheimer’s disease (AD). Neurophysiological biomarkers of AD derived from EEG and FDG-PET, once characterized and validated, would expand the set of existing diagnostic molecular biomarkers of AD pathology with associated biomarkers of disease progression and neural dysfunction. Since symptoms of AD often begin to appear later in life, successful identification of EEG-based biomarkers must account for age-related neurophysiological changes that occur even in healthy individuals. To this end, we collected EEG data from individuals with AD (n = 26), MCI (n = 53), and cognitively normal healthy controls stratified by age into three groups: 18–40 (n = 129), 40–60 (n = 62) and 60–90 (= 55) years old. For each participant, we computed power spectral density at each channel and spectral coherence between pairs of channels. Compared to age matched controls, in the AD group, we found increases in both spectral power and coherence at the slower frequencies (Delta, Theta). A smaller but significant increase in power of slow frequencies was observed for the MCI group, localized to temporal areas. These effects on slow frequency spectral power opposed that of normal aging observed by a decrease in the power of slow frequencies in our control groups. The AD group showed a significant decrease in the spectral power and coherence in the Alpha band consistent with the same effect in normal aging. However, the MCI group did not show any significant change in the Alpha band. Overall, Theta to Alpha ratio (TAR) provided the largest and most significant differences between the AD group and controls. However, differences in the MCI group remained small and localized. We proposed a novel method to quantify these small differences between Theta and Alpha bands’ power using empirically derived distributions of spectral power across the time domain as opposed to averaging power across time. We defined Power Distribution Distance Measure (PDDM) as a distance measure between probability distribution functions (pdf) of Theta and Alpha power. Compared to average TAR, using PDDF enhanced the statistical significance, the effect size, and the spatial distribution of significant effects in the MCI group. We designed classifiers for differentiating individual MCI and AD participants from age-matched controls. The classification performance measured by the area under ROC curve after cross-validation were AUC = 0.85 and AUC = 0.6, for AD and MCI classifiers, respectively. Posterior probability of AD, TAR, and the proposed PDDM measure were all significantly correlated with MMSE score and neuropsychological tests in the AD group.

The local number varianceσ2(R)associated with a spherical sampling window of radiusRenables a classification of many-particle systems ind-dimensional Euclidean spaceRdaccording to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To more completely characterize density fluctuations, we carry out an extensive study of higher-order moments or cumulants, including the skewnessγ1(R), excess kurtosisγ2(R), and the corresponding probability distribution functionP[N(R)]of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. To carry out this comprehensive program, we derive new theoretical results that apply to general point processes, and we conduct high-precision numerical studies. Specifically, we derive explicit closed-form integral expressions forγ1(R)andγ2(R)that encode structural information up to three-body and four-body correlation functions, respectively. We also derive rigorous bounds onγ1(R),γ2(R), andP[N(R)]for general point processes and corresponding exact results for general packings of identical spheres. High-quality simulation data forγ1(R),γ2(R), andP[N(R)]are generated for each model. We also ascertain the proximity ofP[N(R)]to the normal distribution via a novel Gaussian “distance” metricl2(R). Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes in two or higher dimensions such thatγ1(R)∼l2(R)∼R−(d+1)/2andγ2(R)∼R−(d+1)for largeR. The convergence to a CLT is slower for standard nonhyperuniform models and slowest for the “antihyperuniform” model studied here. We prove that one-dimensional hyperuniform systems of class I or anyd-dimensional lattice cannot obey a CLT. Remarkably, we discover a type of universality in that, for all of our models that obey a CLT, the gamma distribution provides a good approximation toP[N(R)]across all dimensions for intermediate to large values ofR, enabling us to estimate the large-Rscalings ofγ1(R),γ2(R), andl2(R). For anyd-dimensional model that “decorrelates” or “correlates” withd, we elucidate whyP[N(R)]increasingly moves toward or away from Gaussian-like behavior, respectively. Our work sheds light on the fundamental importance of higher-order structural information to fully characterize density fluctuations in many-body systems across length scales and dimensions, and thus has broad implications for condensed matter physics, engineering, mathematics, and biology.

Traditional structural uncertainty analysis is mainly based on probability models and requires the establishment of accurate parametric probability distribution functions using large numbers of experimental samples. In many actual engineering problems, the probability distributions of some parameters can be established due to sufficient samples available, whereas for some parameters, due to the lack or poor quality of samples, only their variation intervals can be obtained, or their probability distribution types can be determined based on the existing data while some of the distribution parameters such as mean and standard deviation can only be given interval estimations. This thus will constitute an important type of probability-interval hybrid uncertain problem, in which the aleatory and epistemic uncertainties both exist. The probability-interval hybrid uncertainty analysis provides an important mean for reliability analysis and design of many complex structures, and has become one of the research focuses in the field of structural uncertainty analysis over the past decades. This paper reviews the four main research directions in this area, i.e., uncertainty modeling, uncertainty propagation analysis, structural reliability analysis, and reliability-based design optimization. It summarizes the main scientific problems, technical difficulties, and current research status of each direction. Based on the review, this paper also provides an outlook for future research in probability-interval hybrid uncertainty analysis.

Understanding how different physical processes can shape the probability distribution function (PDF) of surface temperature, in particular the tails of the distribution, is essential for the attribution and projection of future extreme temperature events. In this study, the contribution of soil moisture–atmosphere interactions to surface temperature PDFs is investigated. Soil moisture represents a key variable in the coupling of the land and atmosphere, since it controls the partitioning of available energy between sensible and latent heat flux at the surface. Consequently, soil moisture variability driven by the atmosphere may feed back onto the near-surface climate—in particular, temperature. In this study, two simulations of the current-generation Geophysical Fluid Dynamics Laboratory (GFDL) Earth System Model, with and without interactive soil moisture, are analyzed in order to assess how soil moisture dynamics impact the simulated climate. Comparison of these simulations shows that soil moisture dynamics enhance both temperature mean and variance over regional “hotspots” of land–atmosphere coupling. Moreover, higher-order distribution moments, such as skewness and kurtosis, are also significantly impacted, suggesting an asymmetric impact on the positive and negative extremes of the temperature PDF. Such changes are interpreted in the context of altered distributions of the surface turbulent and radiative fluxes. That the moments of the temperature distribution may respond differentially to soil moisture dynamics underscores the importance of analyzing moments beyond the mean and variance to characterize fully the interplay of soil moisture and near-surface temperature. In addition, it is shown that soil moisture dynamics impacts daily temperature variability at different time scales over different regions in the model.