Counting Statistics Research Articles

The structure of the spin^{ℎ} bordism spectrum

Spin h ^h manifolds are the quaternionic analogue to spin c \text {spin}^c manifolds. We compute the spin h \text {spin}^h bordism groups at the prime 2 2 by proving a structure theorem for the cohomology of the spin h \text {spin}^h bordism spectrum M S p i n h \mathrm {MSpin^h} as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of M S p i n h \mathrm {MSpin^h} as a wedge sum of familiar spectra. We also compute the decomposition of H ∗ ( M S p i n h ; Z / 2 Z ) H^*(\mathrm {MSpin^h};\mathbb {Z}/2\mathbb {Z}) explicitly in degrees up through 30 via a counting process.

Counting jumps: does the counting process count?

In this paper, we develop a ‘jump diffusion type’ financial model based on renewal processes for the discontinuous part of the risk driver, and study its ability to price options and accurately reproduce the corresponding implied volatility surfaces. In this model, the log-returns process displays finite mean and variance, and non-vanishing skewness and excess kurtosis over a long period. The proposed construction is parsimonious, and it allows for a simple and intuitive pricing formula for European vanilla options; furthermore, it offers an efficient Monte Carlo sample path generator for the pricing of exotic options. We illustrate the performance of the proposed framework using observed market data, and we study the features of the best fitting model specifications.

Deep generative denoising networks enhance quality and accuracy of gated cardiac PET data.

Cardiac positron emission tomography (PET) can visualize and quantify the molecular and physiological pathways of cardiac function. However, cardiac and respiratory motion can introduce blurring that reduces PET image quality and quantitative accuracy. Dual cardiac- and respiratory-gated PET reconstruction can mitigate motion artifacts but increases noise as only a subset of data are used for each time frame of the cardiac cycle. The objective of this study is to create a zero-shot image denoising framework using a conditional generative adversarial networks (cGANs) for improving image quality and quantitative accuracy in non-gated and dual-gated cardiac PET images. Our study included retrospective list-mode data from 40 patients who underwent an 18F-fluorodeoxyglucose (18F-FDG) cardiac PET study. We initially trained and evaluated a 3D cGAN-known as Pix2Pix-on simulated non-gated low-count PET data paired with corresponding full-count target data, and then deployed the model on an unseen test set acquired on the same PET/CT system including both non-gated and dual-gated PET data. Quantitative analysis demonstrated that the 3D Pix2Pix network architecture achieved significantly (p value<0.05) enhanced image quality and accuracy in both non-gated and gated cardiac PET images. At 5%, 10%, and 15% preserved count statistics, the model increased peak signal-to-noise ratio (PSNR) by 33.7%, 21.2%, and 15.5%, structural similarity index (SSIM) by 7.1%, 3.3%, and 2.2%, and reduced mean absolute error (MAE) by 61.4%, 54.3%, and 49.7%, respectively. When tested on dual-gated PET data, the model consistently reduced noise, irrespective of cardiac/respiratory motion phases, while maintaining image resolution and accuracy. Significant improvements were observed across all gates, including a 34.7% increase in PSNR, a 7.8% improvement in SSIM, and a 60.3% reduction in MAE. The findings of this study indicate that dual-gated cardiac PET images, which often have post-reconstruction artifacts potentially affecting diagnostic performance, can be effectively improved using a generative pre-trained denoising network.

Introducing Grid WAR: rethinking WAR for starting pitchers

Abstract The baseball statistic “Wins Above Replacement” (WAR) has emerged as one of the most popular evaluation metrics. But it is not readily observed and tabulated; WAR is an estimate of a parameter in a vaguely defined model with all its attendant assumptions. Industry-standard models of WAR for starting pitchers from FanGraphs and Baseball Reference all assume that season-long averages are sufficient statistics for a pitcher’s performance. This provides an invalid mathematical foundation for many reasons, especially because WAR should not be linear with respect to any counting statistic. To repair this defect, as well as many others, we devise a new measure, Grid WAR, which accurately estimates a starting pitcher’s WAR on a per-game basis. The convexity of Grid WAR diminishes the impact of “blow-up” games and up-weights exceptional games, raising the valuation of pitchers like Sandy Koufax, Whitey Ford, and Catfish Hunter who exhibit fundamental game-by-game variance. Although Grid WAR is designed to accurately measure historical performance, it has predictive value insofar as a pitcher’s Grid WAR is better than Fangraphs’ FIP WAR at predicting future performance. Finally, at https://gridwar.xyz we host a Shiny app which displays the Grid WAR results of each MLB game since 1952, including career, season, and game level results, which updates automatically every morning.

3D visualization in turbid water using optimal photon counting and a GAT-based peplography method

Peplography is a three-dimensional (3D) approach for the visualization of targets in environments characterized by heavy scattering. It detects ballistic photons and subsequently generates a 3D image using integral imaging, where the expected number of ballistic photons is set arbitrarily. However, it affects the robustness of the method and accuracy in the analysis of results. Therefore, we propose a method to determine the optimal number of ballistic photons based on the maximum entropy of the photon counting image. Because accuracy in visualizing 3D targets may be compromised due to extraneous photons and fluctuations in photon intensity, we also address this challenge by integrating the generalized Anscombe transformation (GAT) with the conventional peplography technique. The noise caused by an image sensor during image acquisition can be modeled as a Poisson–Gaussian noise, and the photon counting process can be modeled as a Poisson process. Addressing such noise indirectly involves applying the GAT to the reconstructed image to stabilize its variance, denoising the stabilized data with a Gaussian denoising algorithm (i.e., non-local means filtering), and subsequently applying an exact unbiased inverse GAT to the denoised data. Experimental validation is conducted through experiments, with comparisons to conventional peplography, wavelet peplography, and a few standard dehazing and machine learning methods. Various image quality metrics such as correlation, structural similarity, the peak signal-to-noise ratio, and the natural image quality evaluator are used to demonstrate the superiority of the proposed method over conventional ones.

Influence patterns of shear-thickening gel on overload transmission: a numerical simulation study

To address signal aliasing challenges encountered by smart munition fuzes during penetration and layer counting processes, this study employs shear-thickening gel (STG) as a cushioning protective material for accelerometers. Based on the SHPB test platform, the test is designed and the finite element numerical simulation is carried out. The thickness of the shear-thickening gel specimen is treated as a research variable, enabling a systematic analysis of its mechanical filtering effect on overload acceleration. Furthermore, a spring-damping physical model for the cushioning structure is established, facilitating a theoretical exploration of the filtering mechanism on the acceleration signal. Research findings indicate that within a certain frequency bandwidth, STG materials can effectively filter out high-frequency signals received by the accelerometer. Additionally, augmenting the thickness of STG materials has a positive impact on achieving superior filtering performance within the high-frequency range.

Estimation of Oil Palm Tree Quantity Using Oil Palm Ecognition and SAGA GIS Based on UAV Imagery (Case Study: Dumai, Riau)

Abstract Oil palm is a plantation commodity in Indonesia that drives the growth of the national economy. The growth of oil palm is rapidly expanding every year, thus requiring efficient land monitoring strategies. Tree counting is one technique used to monitor current conditions in vast plantation areas. Utilizing UAV technology in agricultural mapping is the best option as a tool for capturing high-resolution aerial photos. The objective of this research is to automatically count the number of oil palm trees by comparing two methods and algorithms. GEOBIA (Geography-Based Image Analysis) and Deep Learning classification are methods used for automatic object counting. In this study, high-resolution aerial photo data was utilized, making object detection much more feasible. The research applied the Template Matching and Watershed Segmentation algorithm models in a sample area of 32.5 hectares divided into two blocks: Unknown-2 and E-1. It can be concluded that both methods, with their respective algorithm models, are sufficiently relevant for use in the automatic counting process of oil palm trees. This is evidenced by the accuracy test error values, which are not more than 15%, indicating that the counted oil palm tree results can be used for further data analysis.

Deep learning based linear energy transfer calculation for proton therapy

Objective. This study aims to address the limitations of traditional methods for calculating linear energy transfer (LET), a critical component in assessing relative biological effectiveness (RBE). Currently, Monte Carlo (MC) simulation, the gold-standard for accuracy, is resource-intensive and slow for dose optimization, while the speedier analytical approximation has compromised accuracy. Our objective was to prototype a deep-learning-based model for calculating dose-averaged LET (LETd) using patient anatomy and dose-to-water (DW) data, facilitating real-time biological dose evaluation and LET optimization within proton treatment planning systems. Approach. 275 4-field prostate proton Stereotactic Body Radiotherapy plans were analyzed, rendering a total of 1100 fields. Those were randomly split into 880, 110, and 110 fields for training, validation, and testing. A 3D Cascaded UNet model, along with data processing and inference pipelines, was developed to generate patient-specific LETd distributions from CT images and DW. The accuracy of the LETd of the test dataset was evaluated against MC-generated ground truth through voxel-based mean absolute error (MAE) and gamma analysis. Main results. The proposed model accurately inferred LETd distributions for each proton field in the test dataset. A single-field LETd calculation took around 100 ms with trained models running on a NVidia A100 GPU. The selected model yielded an average MAE of 0.94 ± 0.14 MeV cm−1 and a gamma passing rate of 97.4% ± 1.3% when applied to the test dataset, with the largest discrepancy at the edge of fields where the dose gradient was the largest and counting statistics was the lowest. Significance. This study demonstrates that deep-learning-based models can efficiently calculate LETd with high accuracy as a fast-forward approach. The model shows great potential to be utilized for optimizing the RBE of proton treatment plans. Future efforts will focus on enhancing the model’s performance and evaluating its adaptability to different clinical scenarios.

Excited-State Half-Lives in ^{130}Cd and the Isospin Dependence of Effective Charges.

The known I^{π}=8_{1}^{+}, E_{x}=2129-keV isomer in the semimagic nucleus ^{130}Cd_{82} was populated in the projectile fission of a ^{238}U beam at the Radioactive Isotope Beam Factory at RIKEN. The high counting statistics of the accumulated data allowed us to determine the excitation energy, E_{x}=2001.2(7) keV, and half-life, T_{1/2}=57(3) ns, of the I^{π}=6_{1}^{+} state based on γγ coincidence information. Furthermore, the half-life of the 8_{1}^{+} state, T_{1/2}=224(4) ns, was remeasured with high precision. The new experimental information, combined with available data for ^{134}Sn and large-scale shell model calculations, allowed us to extract proton and neutron effective charges for ^{132}Sn, a doubly magic nucleus far-off stability. A comparison to analogous information for ^{100}Sn provides first reliable information regarding the isospin dependence of the isoscalar and isovector effective charges in heavy nuclei.

A reliability model for non-isothermal isotropic damages

This study introduces a novel lifetime distribution originating from the Neyman Type A distribution. We built a Neyman Type A counting process and developed a survival function. Some statistical properties of the new distribution were presented, such as the resulting humped hazard function and its convergence. An accelerated test model structure with Arrhenius law was specified, and the effects of different accelerating stresses were analyzed. The hazard function implied by the model is inversely proportional to the stress, which results in interesting features and provides an efficient approach to describe the lifespan phenomena of some engineering metals and bulbs under low temperatures. The estimation of parameters of the accelerated model by maximum likelihood, mean time to failure, and expected number of failures are discussed in the numerical experiments.

Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport.

Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.

Statistical Modeling of Right-Censored Spatial Data Using Gaussian Random Fields

Consider a fixed number of clustered areas identified by their geographical coordinates that are monitored for the occurrences of an event such as a pandemic, epidemic, or migration. Data collected on units at all areas include covariates and environmental factors. We apply a probit transformation to the time to event and embed an isotropic spatial correlation function into our models for better modeling as compared to existing methodologies that use frailty or copula. Composite likelihood technique is employed for the construction of a multivariate Gaussian random field that preserves the spatial correlation function. The data are analyzed using counting process and geostatistical formulation that led to a class of weighted pairwise semiparametric estimating functions. The estimators of model parameters are shown to be consistent and asymptotically normally distributed under infill-type asymptotic spatial statistics. Detailed small sample numerical studies that are in agreement with theoretical results are provided. The foregoing procedures are applied to the leukemia survival data in Northeast England. A comparison to existing methodologies provides improvement.

Monitoring insect numbers and biodiversity with a vertical-beam entomological radar.

Concerns about perceived widespread declines in insect numbers have led to recognition of a requirement for long-term monitoring of insect biodiversity. Here we examine whether an existing, radar-based, insect monitoring system developed for research on insect migration could be adapted to this role. The radar detects individual larger (greater than 10 mg) insects flying at heights of 150-2550 m and estimates their size and mass. It operates automatically and almost continuously through both day and night. Accumulation of data over a 'half-month' (approx. 15 days) averages out weather effects and broadens the source area of the wind-borne observation sample. Insect counts are scaled or interpolated to compensate for missed observations; adjustment for variation of detectability with range and insect size is also possible. Size distributions for individual days and nights exhibit distinct peaks, representing different insect types, and Simpson and Shannon-Wiener indices of biodiversity are calculated from these. Half-month count, biomass and index statistics exhibit variations associated with the annual cycle and year to year changes that can be attributed to drought and periods of high rainfall. While species-based biodiversity measures cannot be provided, the radar's capacity to estimate insect biomass over a wide area indicates utility for tracking insect population sizes. This article is part of the theme issue 'Towards a toolkit for global insect biodiversity monitoring'.

Online detection of the incidence via transfer learning

AbstractThe counting process has abundant applications in reality, and Poisson process monitoring actually has received extensive attention and research. However, conventional methods experience poor performance when shifts appears early and only small number of historical observations in Phase I can be used for estimation. To overcome it, we creatively propose a new online monitoring algorithm under the transfer learning framework, which utilizes the information from observations of additional data sources so that the target process can be described better. By making the utmost of the somewhat correlated data from other domains, which is measured by a bivariate Gamma distributed statistic presented by us, the explicit properties (e.g., posterior probability mass function, posterior expectation, and posterior variance) are also strictly proved. Furthermore, based on the above theoretical results, we design two computationally efficient control schemes in Phase II, that is a control chart based on the cumulative distribution function for large shifts and an exponentially weighted moving average control chart for small shifts. For a better understanding of the more practical applications and transferability matter, we provide some optimal values for parameter setting. Extensive numerical simulations and a case of skin cancer incidence in America verify the superiorities of our approach.

Method for stabilizing the detection efficiency of grazing angle incidence boron-lined neutron detectors

Boron-lined gaseous neutron detectors intrinsically suffer from the “self-absorption” effect and hence their neutron detection efficiencies might be nonconstant, when the threshold of them undergoes unexpected variation. To address this problem, we propose a maximum likelihood estimation-based threshold determining method, via which the pulse height spectra acquired under different high voltages could be rescaled to the same abscissa axis of deposited energies. Monte Carlo simulations were conducted to study the relationship between the precision of the threshold determination and the counting statistics, as well as the energy deposition spectrum, indicating that the grazing angle incidence neutron detector can achieve a fairly small relative standard variation for a spectrum with a modest total neutron counts. A prototype grazing angle incidence neutron detector has been constructed and tested under high voltages ranging from 500 V to 950 V. The experimental results show that, with the maximum likelihood estimation-based method, the threshold's relative standard deviations are less than 10% even with a total neutron counts as low as 100. As a result, the maximum relative variance of the counting plateau curve is 4.8% in the region of [500 V, 900 V] when the detector operates at a grazing angle of 1.8°. The results presented in this study indicate that combining the grazing angle incidence and the maximum likelihood estimation-based threshold determining method would be a promising way to achieve stable neutron detection efficiency for neutron detectors with the boron layer as the neutron convertor.

Analysis of Students' Combinatorial Thinking Model in Solving Combinatorics Problems

The purpose of this study was to analyze students’ combinatorial thinking in solving combinatorics problems. This study was organized into two related areas. The first focused on whether students applied combinatorial thinking in Lockwoods’ model, and the second emphasized on students’ ability in solving the given combinatorics problems. This research method used was a qualitative descriptive method. Participants of this study were students majoring mathematics education at Bung Hatta University who took combinatorics courses. Five combinatorics problems were given to the students and then analyzed. The result showed that based on Lockwoods’ model, the aspect of combinatorial thinking that was more widely applied in solving combinatorics problems was the counting process. However, most students who were able to solve problems quite well, and tended to solve problems with steps from formulating, followed by the process of counting to reach a set outcome. Whereas students who did the counting process stage without formulating problems into mathematics expressions, generally checked a set of outcomes by trial and errors. It can also be noted that in general, f/or any problem given, the percentage of students who faced difficulties when formulating problems into mathematical expressions or on the counting process was more that 50%, and the number of students who reached the correct set of outcomes was relatively low. Keywords: student, combinatorial thinking model, solving combinatorics problems

A dynamic count process

The current paper aims to complement the recent development of the observation-driven models of dynamic counts with a parametric-driven one for a general case, particularly discrete two parameters exponential family distributions. The current paper proposes a finite semiparametric exponential mixture of SETAR processes of the conditional mean of counts to capture the nonlinearity and complexity. Because of the intrinsic latency of the conditional mean, the general additive state-space representation of dynamic counts is firstly proposed then stationarity and geometric ergodicity are established under a mild set of conditions. We also propose to estimate the unknown parameters by using quasi maximum likelihood estimation and establishes the asymptotic properties of the quasi maximum likelihood estimators (QMLEs), particularly T-consistency and normality under the relatively mild set of conditions. Furthermore, the finite sample properties of the QMLEs are investigated via simulation exercises and an illustration of the proposed process is presented by applying the proposed method to the intraday transaction counts per minute of AstraZeneca stock.

Flexible Bayesian reliability demonstration testing

AbstractThe aim is to demonstrate the reliability of a population at consecutive points in time, where a sample at each current point must prove that at least 100% of the devices function until the next point with a probability of at least . To test the reliability of the population, we flexibilise standard lifetime models by allowing the unknown parameter(s) of the corresponding counting process to vary in time. At the same time, we assign a prior distribution that assumes the parameters to be constant within a certain interval. This flexibilisation has several advantages: it can be applied for all parametric lifetimes; its Markov property allows the efficient derivation of the number of defective devices, even for a large number of testing times; and the inference is less certain and hence more realistic and leads to less frequent acceptance of poor quality populations. On the other hand, the inference is stabilised by the informative prior. Based on the flexibilisation of the homogeneous Poisson process (HPP), we derive acceptance sampling plans to test the future reliability of a population. Applying the zero failure sampling plans on simulations of Weibull processes shows their good frequentist properties and their robustness. In the case of utility meters subject to German regulations (Mess‐ und Eichverordnung (MessEV). 2014: 2010–2073.), application of the derived sequential sampling plans when the conditions of these plans are met can lead to an extension of the verification validity period. These sampling plans protect the consumer better than those from an HPP and are still cost efficient.

Artificial intelligence for beach monitoring: An experimental study of beach attendance at El Rodadero, Colombia

Having accurate data on the number of beach users is vital for planning services and managing overcrowding at high-demand tourist destinations. Obtaining this data has traditionally been a time-consuming task. This study proposes a novel approach to automating the counting process based on computer vision and artificial intelligence. Three HIKVISION PTZ (“Point, Tilt, Zoom”) surveillance cameras were installed on the roofs of the strategic buildings of El Rodadero, Santa Marta, D.T.C.H. Colombia. This observation system provided more than 150 000 observations spanning more than a year (September 2022–October 2023). An algorithm based on the YOLOv5 architecture was trained using a dataset containing over 50 000 labels of people at the beach or in water backgrounds. Applied to surveillance camera images in El Rodadero, Santa Marta, D.T.C.H. Colombia., this algorithm had the ability to identify individuals with high spatiotemporal detail. Beach users were detected over water and on the beach with true positive rates of 81% and 89%, respectively. The counts of beach users made by the model were highly correlated with counts verified by humans with an R2 of 91%. When compared to these expected numbers, the model counted an average of 2–18% fewer people, with a lower error on the beach than on the water. Adjusting for that underestimation the average occupancy at El Rodadero was 125 132 m2 per person, but during peak times, such as long weekends, this number decreased to less than 3 m2 per person. This information is critical for authorities to make informed decisions and for visitors to choose less crowded beaches, avoiding overcrowding. To facilitate access to this information, an automated web system had been created that displayed updated results and allowed downloads for registered users.

Walnut Recognition Method for UAV Remote Sensing Images

During the process of walnut identification and counting using UAVs in hilly areas, the complex lighting conditions on the surface of walnuts somewhat affect the detection effectiveness of deep learning models. To address this issue, we proposed a lightweight walnut small object recognition method called w-YOLO. We reconstructed the feature extraction network and feature fusion network of the model to reduce the volume and complexity of the model. Additionally, to improve the recognition accuracy of walnut objects under complex lighting conditions, we adopted an attention mechanism detection layer and redesigned a set of detection heads more suitable for walnut small objects. A series of experiments showed that when identifying walnut objects in UAV remote sensing images, w-YOLO outperforms other mainstream object detection models, achieving a mean Average Precision (mAP0.5) of 97% and an F1-score of 92%, with parameters reduced by 52.3% compared to the YOLOv8s model. Effectively addressed the identification of walnut targets in Yunnan, China, under the influence of complex lighting conditions.