In this paper, we study the asymptotic behavior of the maximum queue length in a fluid queue driven by a self-similar Gaussian process with non-stationary increments. We derive almost sure and in-probability convergence of the normalized maximum queue length, described by a function [Formula: see text], where [Formula: see text] is the Hurst parameter. We obtain sharp tail bounds for the distribution of the queue length, using Malliavin calculus, which explicitly depend on [Formula: see text] and the drift parameter [Formula: see text]. Our results generalize classical results on fractional Brownian motion (fBm) to broader classes such as sub-fractional Brownian motion (sub-fBm) and bi-fractional Brownian motion (bi-fBm). The key techniques introduced in this framework include Gaussian supremum localization, path-penalty large deviations, and metric entropy. Systems that exhibit long-range dependence and self-similarity are developed based on these results.

Volume-Weighted Golden Ratio Estimator (vGRE) for Drawdown and Tail-Risk Control for Wealth Portfolios

Abstract The lek hotspot hypothesis predicts that leks will form in areas where males are more likely to encounter females, providing wildlife managers with a framework supporting the use of leks as the focus for prairie and shrubland grouse conservation and monitoring. The lek hotspot hypothesis also implies that the number of males attending leks (lek size) will be higher in areas where there are more females. We used sharp‐tailed grouse ( Tympanuchus phasianellus ) to evaluate whether lek locations and lek size were more influenced by habitat requirements during different seasons or by landscape features that minimized risks to males attending leks or increased the probability of detection of leks by nearby females. First, we evaluated which landscape features influenced habitat selection and mortality risk during different seasons: nesting (April–June), brood‐rearing (June–August), early nonbreeding (September–November), and late nonbreeding (December–March) seasons in south‐central Wyoming ( n = 213 VHF‐marked females; 2017–2020). We found that habitat selection and mortality risk varied by season. Subsequently, we modeled lek locations and lek size relative to seasonal habitat requirements (selection and mortality risk) and landscape features to identify key variables explaining lek site selection and lek size. We found that lek site selection was related to landscape features that promoted the detection of leks by females and to seasonal habitat. Specifically, leks were located in areas surrounded by more herbaceous vegetation and litter, less rugged terrain, and more nesting habitat. We found that lek size was related to seasonal habitat, with larger leks surrounded by more brood‐rearing habitat. Our findings suggest that leks were located in areas that increased the probability of detection by females and in areas more likely to be frequented by females, consistent with the lek hotspot hypothesis. Our research supports continuing to use lek locations as focal points for habitat management for lekking grouse.

With the increasing global focus on sustainable development, circulating fluidized bed (CFB) boilers, as highly efficient and low-pollution combustion equipment, play an important role in energy production and environmental protection. However, the combustion efficiency and emission control of CFB boilers still face challenges, and there is an urgent need for multi-objective optimization through advanced technologies to support the goal of sustainable development. This study proposes an intelligent framework integrating Bidirectional Temporal Convolutional Network (BiTCN) and Hybrid Dung Beetle Optimizer (HDBO) for multi-objective optimization of combustion efficiency and NOx/SO2 emissions in CFB boilers. The BiTCN model captures bidirectional temporal dependencies between dynamic parameters (e.g., air-coal ratio, bed temperature) and target variables through operational data analysis. Three key improvements are implemented in DBO: (1) Chaotic initialization via sequential pattern mining (SPM) enhances population diversity and spatial coverage; (2) The osprey optimization algorithm (OOA) hunting mechanism replaces the original rolling update strategy, improving global exploration; (3) t-Distribution perturbation is applied to foraging beetles in later iterations, leveraging its “sharp peak and thick tail” characteristics to dynamically balance exploitation and exploration. Experimental results demonstrate 0.5–1% combustion efficiency improvement and 15.1%/30% reductions in NOx/SO2 emissions for a typical CFB boiler.

A sharp Gaussian tail bound for sums of uniforms

Identifying species and subspecies is the foundation for focusing conservation efforts and studying evolutionary ecology. Subspecies delineation has occurred using multiple data types, including ecological, morphological, and genetic data. There are currently seven recognized Sharp-tailed Grouse (Tympanuchus phasianellus, Linnaeus, 1758) subspecies, with two of these subspecies occurring in Wyoming: Columbian Sharp-tailed Grouse (T. p. columbianus) and plains Sharp-tailed Grouse (T. p. jamesi). There is a third population of Sharp-tailed Grouse in south-central Wyoming with an unknown subspecific identification. Historically, this population has been classified as Columbian Sharp-tailed Grouse; however, previous genetic evidence questioned this classification. To better understand the subspecific status of this south-central Wyoming population, our study used habitat characteristics, morphological characteristics, and genetic data (microsatellite loci and single nucleotide variants) collected from known Columbian Sharp-tailed Grouse, known plains Sharp-tailed Grouse, and the south-central Wyoming population of Sharp-tailed Grouse. We modeled differences among the populations using discriminant analysis of principal components and Random Forests classification models. Across all four datasets and both modeling techniques, we found that each population (Columbian Sharp-tailed Grouse, plains Sharp-tailed Grouse, and south-central Wyoming population of Sharp-tailed Grouse) generally represented its own cluster. Our results suggest that the population of Sharp-tailed Grouse in south-central Wyoming is different from both Columbian and plains Sharp-tailed Grouse. We recommend further evaluation of the subspecies of Sharp-tailed Grouse using more targeted phylogenomic studies to identify if Sharp-tailed Grouse in south-central Wyoming represent a separate subspecies or are a distinct population of another subspecies. Our results potentially change our understanding of Columbian Sharp-tailed Grouse distribution and management and highlight the importance of using a more comprehensive approach to identifying subspecies.

Abstract The ultrahigh resolution inelastic X-ray scattering (IXS) beamline at NSLS-II is designed and built to achieve sub-meV resolution at a moderate energy of 9.13 keV for IXS experiments with high momentum resolution and high spectral contrast. The key instrument is a novel spectrometer featuring a new type of analyzer optics, which combines post-sample collimation with angular dispersive crystal optics. As the first user instrument of its kind, the spectrometer has demonstrated unique research capabilities in exploring low momentum transfer (Q), THz dynamics in soft material systems characterized by mesoscopic heterogeneity and complexity, such as liquid crystals and bio-membranes. Ongoing efforts to improve performance since the start of user operations have resulted in a state-of-the-art energy resolution in routine operations of less than 1.4 meV, with sharp Gaussian-like tails, making it a premier IXS spectrometer for studying the dynamics of soft materials, while also delivering competitive performance for investigating phonon dynamics in hard condensed matter systems, including a broad range of quantum materials.

Autonomous aerial vehicles (AAVs) are desirable platforms for time-efficient and cost-effective task execution. 3-D path planning problems for AAVs can be treated as constrained multiobjective optimization problems. However, due to the complexity of real-world problems, the Pareto front frequently exhibits irregularity. For path planning problems characterized by sharp peaks and low tails on the Pareto front, this article proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D) with an adaptive areal weight adjustment (AAWA) strategy to make a tradeoff between the total flight path length and the terrain threat. AAWA is designed to improve the diversity and uniformity of the solutions. More specifically, AAWA first removes a crowded individual and its weight vector from the current population and then adds a sparse individual from the external elite population to the current population. To enable the newly added individual to evolve toward the sparser area of the population in the objective space, its weight vector is constructed by the objective function value of its neighbors. The experimental results in three types of synthetic scenarios and one realistic scenario demonstrate that MOEA/D-AAWA achieves uniformly distributed and diverse path solutions on sharp peaks and low tails, and provides a desired and collision-free compromise path.

Abstract As the demand for wind energy development increases across much of the Great Plains region, there is a need to understand how this type of energy generation may impact wildlife. Due to their extensive range across areas with high wind resources, plains sharp‐tailed grouse (Tympanuchus phasianellus jamesiTympanuchus phasianellus jamesi) represent a valuable species to evaluate how selection and survival are associated with existing wind energy infrastructure. We used spatial and demographic data collected from radio‐marked female sharp‐tailed grouse to evaluate resource selection (nest, brood‐rearing, and breeding season) and survival (nest and female) near existing wind energy infrastructure during the April to August breeding season over a 3‐year period from 2020 to 2022 in northeastern South Dakota, USA. We monitored 119 GPS‐marked females captured at eight leks over the study period. We did not find evidence that females selected nest sites in relation to wind energy infrastructure but found that females with broods and females during the breeding season (April–August) avoided areas near high densities of wind turbines within 1.0 and 5.0 km of their home range, respectively. We found consistent selection for lower lengths of transmission lines across all life stages at the home range scale. We did not detect an effect of wind energy infrastructure on nest or female survival. Based on the results of our study, limiting the siting (the process of selecting the optimal location for a project and the associated features) of wind turbines within 5.0 km of sharp‐tailed grouse breeding habitat may represent an important siting tool to minimize avoidance of otherwise suitable habitats.

New energy industry is an emerging industry in China with natural environmental protection attributes. However, new energy stock prices have fluctuated frequently in recent years, destabilising the market and affecting investment. Therefore, the article selects the daily closing prices of CSI New Energy Index from 1 August 2019 to 1 July 2024, and establishes a GARCH (1, 1) model through Eviews 13.0 to study the volatility of new energy stock prices in China. The results show that the new energy stock price return series has volatility aggregation and exhibits the characteristics of sharp peaks and thick tails.

The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to that regular part. Recently, several novel approaches have been proposed to transform the singular pencil into a regular pencil by relatively simple randomized modifications. In this work, we analyze three such methods by Hochstenbach, Mehl, and Plestenjak that modify, project, or augment the pencil using random matrices. All three methods rely on the normal rank and do not alter the finite eigenvalues of the original pencil. We show that the eigenvalue condition numbers of the transformed pencils are unlikely to be much larger than the δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}-weak eigenvalue condition numbers, introduced by Lotz and Noferini, of the original pencil. This not only indicates favorable numerical stability but also reconfirms that these condition numbers are a reliable criterion for detecting simple finite eigenvalues. We also provide evidence that, from a numerical stability perspective, the use of complex instead of real random matrices is preferable even for real singular matrix pencils and real eigenvalues. As a side result, we provide sharp left tail bounds for a product of two independent random variables distributed with the generalized beta distribution of the first kind or Kumaraswamy distribution.

Wind resources have characteristics of stochastic volatility, resulting in wind power forecast errors greatly. The short and medium-term wind power forecast error distribution of the actual wind farm operating system is analyzed, and a sharp peak and thick tail, with heavy tail and skewness characteristics, are presented. A skew-slash t distribution (SST distribution) is proposed to describe the error distribution of short-term wind power prediction, and the parameter estimation is carried out by probability density curve fitting. The fitting results of the wind power forecast error historical data of the Wind power plant based on SST distribution, t distribution, and t Location-slash distribution (TLS distribution) are obtained, and the fitting goodness and prediction accuracy are compared. The results show that the SST distribution can more effectively estimate the wind power prediction interval.

The changes in the annual distribution of mountain runoff during the period of 1965–2018 in Hexi Corridor, Northwest China

Since the listing of Shanghai crude oil futures in March 2018 its market performance has gradually attracted attention. The closing price data of the futures for the period from March 26, 2018 to April 17, 2023 are selected as observations, and a GARCH model is fitted to the futures log return series to analyze the development of Shanghai crude oil futures and its future trend. The study finds that extreme events such as the New Crown epidemic and the Russia-Ukraine conflict had led to high volatility of Shanghai crude oil futures, but the volatility gradually stabilized in the context of the double cycle at home and abroad. The study compares the effectiveness of the GARCH(1,1)-T model and the GARCH(1,1)-GED model in fitting the logarithmic returns of the Shanghai crude oil futures market. the GARCH(1,1)-T model is able to better capture the asymmetry of the market volatility and the phenomenon of sharp peaks and thick tails after taking into account the distributional characteristics of the residuals. In the paper, the closing price of Shanghai crude oil futures in the next 10 days is predicted according to the GARCH(1,1)-T model, and the short-term prediction effect is better.

HgTe nanocrystals (NCs) possess advantages including tunable infrared absorption spectra, solution processability, and low fabrication costs, offering new avenues for the advancement of next-generation infrared detectors. In spite of great synthetic advances, it remains essential to achieve customized synthesis of HgTe NCs in terms of industrial applications. Herein, by taking advantage of a high critical nucleation concentration of HgTe NCs, a continuous-dropwise (CD) synthetic approach that features the addition of the anion precursors in a feasible drop-by-drop fashion is demonstrated. The slow reaction dynamics enable size-customized synthesis of HgTe NCs with sharp band tails and wide absorption range fully covering the short- and mid-infrared regions. More importantly, the intrinsic advantages of CD process ensure high-uniformity and scale-up synthesis from batch to batch without compromising the excitonic features. The resultant HgTe nanocrystal photodetectors show a high room-temperature detectivity of 8.1 × 1011 Jones at 1.7µm cutoff absorption edge. This CD approach verifies a robust method for controlled synthesis of HgTe NCs and might have important implications for scale-up synthesis of other nanocrystal materials.

The interaction of two parallel unequal bubbles in a viscoelastic fluid is investigated numerically using OpenFoam, the volume of fluid method (VOF) combined with a surface tension model to trace the gas-liquid interface, and the Giesekus model to characterise the rheological properties of the fluid. The numerical results are in good agreement with experimental results from the literature. The effects of bubble diameter, initial spacing between bubbles and rheological properties of the fluid on the rise, and separation and convergence of the two bubbles are investigated. The flow field properties and viscoelastic stress distribution around the bubbles are explored. As the bubble spacing increases, the maximum and terminal velocities of the two bubbles increase, and the relative positions of the bubbles change when they come into contact. As the relaxation time λ increases, the contact time of the bubbles decreases, and the small bubbles tend to have an inverted teardrop shape and the large bubbles have less deformation and no sharp tail. The relaxation time directly affects the accumulation of viscoelastic stress, leading to changes in the velocity of the bubbles at contact, and their maximum and terminal velocities increase. Bubbles in highly elastic fluids are more prone to negative wake phenomena.

Abstract In‐person lek count surveys are commonly used for estimating population size and trends for prairie grouse. However, the emergence of noninvasive camera trap survey methods holds promise for more cost‐effective and precise estimates of lekking species. To evaluate the efficacy of using camera traps, we deployed a remote camera study at lekking grounds over 3 years in conjunction with in‐person surveys. Our objectives were to 1) develop an effective remote camera survey for greater prairie‐chickens (GRPC; Tympanuchus cupido ) and sharp‐tailed grouse (STGR; T. phasianellus ), 2) compare metrics of male detection, maximum male counts, and male abundance estimates derived from in‐person versus remote camera surveys, 3) assess lek activity over the survey season to inform survey timing, and 4) evaluate costs for each survey type. We found that in‐person surveys resulted in maximum male GRPC and STGR counts. The estimated number of male GRPC and STGR on leks were comparable between in‐person surveys and camera monitoring when accounting for detection probability with N‐mixture models. Camera traps constantly monitored leks over the season which provided daily and seasonal activity patterns of prairie grouse. Total cost of GRPC remote camera surveys was higher than in‐person surveys, but hourly cost was less ($0.77 vs. $160 per hour). Remote camera survey costs for GRPC were high because of time classifying photos which could be reduced by decreasing the amount of time remote cameras were operated or using automated classification software to remove blank photos. We believe the use of remote cameras could supplement in‐person surveys for future lek monitoring and aid future survey efforts by identifying yearly differences in activity and presence at leks inconsistently visited by birds.

In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions a / N a/N , where N N is fixed and a a runs through the set of mod N N residue classes which are coprime with N N . Our methods cover statistics such as the sum of partial quotients, the maximal partial quotient, the empirical distribution of partial quotients, Dedekind sums, and much more. We prove a sharp concentration inequality for the sum of partial quotients, and sharp tail estimates for the maximal partial quotient and for Dedekind sums, all matching the tail behavior in the limit laws which are known under an extra averaging over the set of possible denominators N N . We show that the distribution of partial quotients of reduced fractions with fixed denominator gives a very good fit to the Gauß–Kuzmin distribution. As corollaries we establish the existence of reduced fractions with a small sum of partial quotients resp. a small maximal partial quotient.

Abstract Translocation is a management tool used to restore or augment wildlife populations, but outcomes of translocations are often poorly documented and can have varying levels of success for improving wildlife population declines. The lesser prairie‐chicken ( Tympanuchus pallidicinctus ) is a prairie grouse endemic to the southern Great Plains. In response to declining abundance and distribution, in 2023 lesser prairie‐chickens were listed as threatened or endangered under the Endangered Species Act in different states. Translocation is a potential management response to population declines when there is an availability of unoccupied habitats, but translocation efficacy has not been evaluated for lesser prairie‐chickens. We translocated 411 lesser prairie‐chickens seasonally from 2016‐2019 and monitored the translocated lesser prairie‐chicken population from 2017–2022. To assess translocation as a management tool for lesser prairie‐chickens, we estimated survival for 2017–2020 and conducted lek surveys during 2017–2022. Over a fifth (22.8%, n = 94) of translocated birds either died or went missing within the first 2 weeks following release. Survival rates of translocated birds during the breeding (0.44 ± 0.02 [SE]) and nonbreeding (0.55 ± 0.03 [SE]) seasons were relatively low compared to nontranslocated lesser prairie‐chickens in other studies (0.63–0.93 for breeding season; 0.43–0.87 for non‐breeding season). Twenty‐seven percent of translocated birds survived to the breeding season after release (i.e., >1 year). Translocated lesser prairie‐chickens initiated 28 lekking sites over the study period. We estimated 77% of males available >2 weeks post release participated in lekking activity. The number of leks and male high counts on leks in the study area increased after translocation, peaking one year post‐translocation (an overall increase of 250% and 340%, respectively). However, both the number of leks and male high counts decreased (48% and 39%, respectively) within 3 years after translocation cessation. Establishment of leks and increasing lek attendance directly following translocation initially suggested that translocation could be a viable management tool. However, survival rates after translocation and declining lek counts following translocation indicates that the increased population abundance and occupied range from this translocation effort may be unsustainable. Our results highlight the necessity of monitoring to determine outcomes of a large lesser prairie‐chicken translocation. Other management strategies, such as targeted grassland restoration and management in areas of greatest lesser prairie‐chicken density, could be more beneficial for conservation of lesser prairie‐chicken populations.

Phylogenomics of the extinct Heath Hen provides support for sex-biased introgression among extant prairie grouse