Counting Statistics Research Articles

An extended class of multivariate counting processes and its main properties

Abstract In this paper, a new multivariate counting process model (called Multivariate Poisson Generalized Gamma Process) is developed and its main properties are studied. Some basic stochastic properties of the number of events in the new multivariate counting process are initially derived. It is shown that this new multivariate counting process model includes the multivariate generalized Pólya process as a special case. The dependence structure of the multivariate counting process model is discussed. Some results on multivariate stochastic comparisons are also obtained.

Tomography of a Spatially Resolved Single-Atom Detector in the Presence of Shot-to-Shot Number Fluctuations

The tomography of single-particle-resolved detectors is of primary importance for characterizing particle correlations, with applications in quantum metrology, quantum simulation, and quantum computing. However, it is a nontrivial task in practice due to the uncertainties on the statistics of the state impinging on the detector and to the unavoidable presence of noise that affects the measurement but does not originate from the detector. In this work, we address this problem for a three-dimensional single-atom-resolved detector where shot-to-shot atom-number fluctuations are a central issue in performing a quantum detector tomography. We overcome this difficulty by exploiting the parallel measurement of the counting statistics in subvolumes of the detector, from which we evaluate the effect of shot-to-shot fluctuations and perform a local tomography of the detector. In addition, we illustrate the validity of our method from applying it to Gaussian quantum states with different number statistics. Finally, we show that the response of microchannel plate detectors is well described by using a binomial distribution with the detection efficiency as a single parameter. Published by the American Physical Society 2024

A simplified approach to counting statistics with an imperfect pileup rejector

A simplified theoretical model is developed to predict counting statistics for a stationary Poisson process passing through a spectrometer with pulse-pileup rejection. The model is applicable to digital counters used for spectrometry as well as set-ups utilising analogue electronics for pulse shaping and pileup rejection. In comparison with an existing model for a perfect pileup rejector, the new model addresses the common imperfection of having a finite time resolution of the fast channel, allowing quasi-coincident signals to pass through the pile-up rejector. From the Laplace transform of a simplified interval-density distribution, approximate expressions are derived for the throughput factor and the variance of the number of counted events. The results are compared with computer simulations of a cascade of extending dead time and subsequent pileup rejection. In addition, a rigorous throughput factor is derived from probabilistic reasoning, as well as an effective throughput factor for singular and coincident events.

Entomopathogenic nematode detection and counting model developed based on A-star algorithm

Entomopathogenic nematodes are soil-dwelling living organisms widely employed in the biological control of agricultural insect pests, serving as a significant alternative to pesticides. In laboratory procedures, the counting process remains the most common, labor-intensive, time-consuming, and approximate aspect of studies related to entomopathogenic nematodes. In this context, a novel method has been proposed for the detection and quantification of Steinernema feltiae isolate using computer vision on microscope images. The proposed method involves two primary algorithmic steps: framing and isolation. Compared to YOLO-V5m, YOLO-V7m, and YOLO-V8m, the A-star-based developed network demonstrates significantly improved detection accuracy compared to other networks. The novel method is particularly effective in facilitating the detection of overlapping nematodes. The developed algorithm excludes processes that increase space and time complexity, such as the weight document, which contains the learned parameters of the deep learning model, model integration, and prediction time, resulting in more efficient operation. The results indicate the feasibility of the proposed method for detecting and counting entomopathogenic nematodes.

Sieve estimation of the accelerated mean model based on panel count data

Panel count data are gathered when subjects are examined at discrete times during a study, and only the number of recurrent events occurring before each examination time is recorded. We consider a semiparametric accelerated mean model for panel count data in which the effect of the covariates is to transform the time scale of the baseline mean function. Semiparametric inference for the model is inherently challenging because the finite-dimensional regression parameters appear in the argument of the (infinite-dimensional) functional parameter, i.e., the baseline mean function, leading to the phenomenon of bundled parameters. We propose sieve pseudolikelihood and likelihood methods to construct the random criterion function for estimating the model parameters. An inexact block coordinate ascent algorithm is used to obtain these estimators. We establish the consistency and rate of convergence of the proposed estimators, as well as the asymptotic normality of the estimators of the regression parameters. Novel consistent estimators of the asymptotic covariances of the estimated regression parameters are derived by leveraging the counting process associated with the examination times. Comprehensive simulation studies demonstrate that the optimization algorithm is much less sensitive to the initial values than the Newton–Raphson method. The proposed estimators perform well for practical sample sizes, and are more efficient than existing methods. An example based on real data shows that due to this efficiency gain, the proposed method is better able to detect the significance of practically meaningful covariates than an existing method.

Nonequilibrium steady state full counting statistics in the noncrossing approximation.

Quantum transport is often characterized not just by mean observables like the particle or energy current but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regimes. While most experiments are concerned with steady state properties, most accurate theoretical methods rely on computationally expensive propagation from a tractable initial state. Here, we propose a simple approach for computing the FCS through a junction directly at the steady state, utilizing the propagator noncrossing approximation. Compared to time propagation, our method offers reduced computational cost at the same level of approximation, but the idea can also be used within other approximations or as a basis for numerically exact techniques. We demonstrate the method's capabilities by investigating the impact of lead dimensionality on electronic transport in the nonequilibrium Anderson impurity model at the onset of Kondo physics. Our results reveal a distinct signature of one dimensional leads in the noise and Fano factor not present for other dimensionalities, showing the potential of FCS measurements as a probe of the environment surrounding a quantum dot.

Monitoring of Broccoli Flower Head Development in Fields Using Drone Imagery and Deep Learning Methods

For different broccoli materials, it used to be necessary to manually plant in a large area for the investigation of flower ball information, and this method is susceptible to subjective influence, which is not only time-consuming and laborious but may also cause some damage to the broccoli in the process of investigation. Therefore, the rapid and nondestructive monitoring of flower heads is key to acquiring high-throughput phenotypic information on broccoli crops. In this study, we used an unmanned aerial vehicle (UAV) to acquire hundreds of images of field-grown broccoli to evaluate their flower head development rate and sizes during growth. First, YOLOv5 and YOLOv8 were used to complete the position detection and counting statistics at the seedling and heading stages. Then, UNet, PSPNet, DeepLabv3+, and SC-DeepLabv3+ were used to segment the flower heads in the images. The improved SC-DeepLabv3+ model excelled in segmenting flower heads, showing Precision, reconciled mean F1-score, mean intersection over union, and mean pixel accuracy values of 93.66%, 95.24%, 91.47%, and 97.24%, respectively, which were 0.57, 1.12, 1.16, and 1.70 percentage points higher than the respective values achieved with the DeepLabv3+ model. Flower head sizes were predicted on the basis of the pixel value of individual flower heads and ground sampling distance, yielding predictions with an R2 value of 0.67 and root-mean-squared error of 1.81 cm. Therefore, the development rate and sizes of broccoli flower heads during growth were successively estimated and calculated. Compared with the existing technology, it greatly improves work efficiency and can help to obtain timely information on crop growth in the field. Our methodology provides a convenient, fast, and reliable way for investigating field traits in broccoli breeding.

Accurate measurements of delayed neutron data for reactor applications: methodology and application to 235U(nth,f)

Large inconsistencies still exist in nuclear data libraries regarding the kinetic parameters of delayed neutron (DN) precursors. As an example, there is a 17% gap between ENDF-B/VIII.0 and JEFF-3.3 on the average lifetime T1/2 of DN precursors from thermal fission of 235U. This parameter is of major importance for reactivity predictions of nuclear reactors in nominal or accidental configurations. In this context, CEA is actively participating to the ALDEN project (Average number and Lifetime of DElayed Neutrons) which aims at providing the nuclear data community with new data sets of DN from thermal and fast neutron induced fission of various actinides. A dedicated experimental setup was designed and optimized for that purpose and is presented in this paper. It consists of a “long counter” detector containing 16 proportional counters filled with 3He, embedded in a high density polyethylene matrix. The detector surrounds a fissile target prepared in the form of a miniature fission chamber, containing a few hundreds of micro-grams of fissile material. This set-up is connected to fast and efficient neutron shutters that can produce step-irradiations of variable durations. The equations driving the DN counting following step-irradiations of the fissile target are established and discussed in the perspective of DN yield or group parameter measurement. A comprehensive analysis of the different steps of data reduction is detailed: dead time characterization, Region of Interest (ROI) determination, absolute and relative efficiency calibration, fission rate estimation, irradiation time and background determination, DN decay curve production and physical parameter fitting. Following a prototype experiment performed in 2018 at the PF1b cold neutron beam line of Institute Laue Langevin (ILL, Grenoble, France), we discuss here the analysis of two campaigns occurring in 2019 and 2021 in which significant improvements were achieved in terms of background minimization, counting statistics and fission rate determination. The achievements of this work are the measurement of the delayed neutron emission per fission for the thermal neutron induced fission of 235U, estimated at (1.625 ± 0.010) % and the group parameters leading to an estimated lifetime of T1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{1/2}$$\\end{document} = (8.87 ± 0.10) s. Those results are consistent with the values recommended by the IAEA/CRP work and they come with reduced uncertainties compared with previously published results.

Comparisons of some new and existing EWMA schemes for binomial count processes with applications to monitoring hospital No-Shows

ABSTRACT Applications of several exponentially weighted moving average (EWMA) schemes for monitoring binomial count data have been widely used in the manufacturing and healthcare industries. However, practitioners may be confused about selecting the appropriate scheme for their needs. In this paper, we compare the performance of some existing EWMA schemes and a new EWMA scheme utilizing the weighted likelihood ratio test (WLRT), referred to as the EWLRT scheme. Firstly, some properties of the EWLRT scheme for binomial proportion are outlined. Next, a method for choosing the optimal smoothing parameter based on the relative mean index (RMI) is described, and various competing schemes are compared at the optimal level, which was not done in most previous studies. Additionally, current comparisons consider the zero-state (ZS) run-length performance and the conditional expected delay (CED) for a delayed shift. The results based on the Monte Carlo method indicate that the EWLRT scheme’s efficacy is somewhat more encouraging than that of its competitors in detecting small to moderate changes in terms of CED. Finally, a real example of monitoring hospital No-Shows, a necessary healthcare management process, describes the implementation.

Assessing the Precision and Accuracy of Foraminifera Elemental Analysis at Low Ratios

AbstractThe minor and trace element compositions of biogenic carbonates such as foraminifera are important tools in paleoceanography research. However, most studies have focused primarily on samples with element to calcium (El/Ca) ratios higher than the El/Ca range often found in benthic foraminifera. Here, we systematically assess the precision and accuracy of foraminifera elemental analysis across a wide range of El/Ca especially at relatively low ratios, using a method on a Thermo Scientific iCAP Qc quadrupole Inductively Coupled Plasma Mass Spectrometer (ICP‐MS). We focus on two benthic foraminifera species, Hoeglundina elegans and Cibicidoides pachyderma, and prepared a suite of solution standards based on their typical El/Ca ranges to correct for signal drift and matrix effects during ICP‐MS analysis and to determine analytical precision. We observe comparable precisions with published studies at high El/Ca, and higher relative standard deviations for each element at lower El/Ca, as expected from counting statistics. The overall long‐term analytical precision (2σ) of the H. elegans‐like consistency standard solutions was 6.5%, 4.6%, 5.0%, for Li/Ca, Mg/Ca, Mg/Li, and 6.4%, 10.0%, 4.2% for B/Ca, Cd/Ca, Sr/Ca. The precision for H. elegans‐like Mg/Li is equivalent to a temperature uncertainty of 0.5–1.1°C. Measurement precisions were also assessed based on three international standards (one solution and two powder standards) and replicate measurements of H. elegans and C. pachyderma samples. We provide file templates and program scripts that can be used to design calibration and consistency standards, prepare run sequences, and convert the raw ICP‐MS data into molar ratios.

Terror Death of Election Officials: What Are the Effects of Stress and Hypoxia?: A Literature Review

Background: This essay examines the most recent news, namely the passing of a voting committee member (PPS) in the general election (Pemilu), which included candidates for president, vice president, and legislature (Caleg). PPS saw 35 fatalities and 3.909 illnesses. Given that the counting and recapitulation process is still in progress, the likelihood of deaths and illnesses will only rise. Objective: The aim of this research is to find the relationship between hypoxia and stress in PPS officers who died due to physical exhaustion during election activities in Indonesia Methods: Articles containing information on hypoxia, comorbidity, stress, physical exhaustion, and its connection to death were included as inclusion criteria. There was a total of 25 papers that met the inclusion criteria after the literature analysis procedure was completed. Result: Along with the comorbid status, physical exhaustion, and stress play a significant part (comorbidities). This connection arises from the fact that physical exhaustion and stress induce hypoxia, which in turn affects immunity. The drop in blood oxygen levels, or hypoxia, disrupts and dysregulates the innate and adaptive immune systems. The chance of dying can rise when hypoxia and ongoing stress are present. Writing this paper proposes more investigation into the role that hypoxia and stress play as death risk factors. Conclusion: Hypoxia results from stress. what makes HIF the primary transcription factor active. When PPS officers activate their HIF in order to fulfill their mandate and fulfill their obligations under Law Number 7 of 2017 concerning General Elections, there is an elevated risk of death and morbidity.

KiDS-1000 and DES-Y1 combined: cosmology from peak count statistics

ABSTRACT We analyse the fourth data release of the Kilo Degree Survey (KiDS-1000) and extract cosmological parameter constraints based on the cosmic shear peak count statistics. Peaks are identified in aperture mass maps in which the filter is maximally sensitive to angular scales in the range 2–4 arcmin, probing deep into the non-linear regime of structure formation. We interpret our results with a simulation-based inference pipeline, sampling over a broad wCDM prior volume and marginalizing over uncertainties on shape calibration, photometric redshift distribution, intrinsic alignment, and baryonic feedback. Our measurements constrain the structure growth parameter and the amplitude of the non-linear intrinsic alignment model to $\Sigma _8 \equiv \sigma _8\left[\Omega _{\rm m}/0.3\right]^{0.60}=0.765^{+0.030}_{-0.030}$ and $A_{\rm IA}= 0.71^{+0.42}_{-0.42}$, respectively, in agreement with previous KiDS-1000 results based on two-point shear statistics. These results are robust against modelling of the non-linear physics, different scale cuts, and selections of tomographic bins. The posterior is also consistent with that from the Dark Energy Survey Year-1 peak count analysis presented in Harnois-Déraps et al., and hence we jointly analyse both surveys with a common pipeline. We obtain $\Sigma _8^{\rm joint} \equiv \sigma _8\left[\Omega _{\rm m}/0.3\right]^{0.57}=0.759^{+0.020}_{-0.017}$, in agreement with the PlanckwCDM results. The shear-CMB tension on this parameter increases to $3.1\sigma$ when forcing $w=-1.0$, and to $4.1\sigma$ if comparing instead with $S_{8,\Lambda {\rm CDM}}^{\rm joint} = 0.736^{+0.016}_{-0.018}$, one of the tightest constraints to date on this quantity. Residual biases in the photometric redshifts of the DES-Y1 data and in the modelling of small scales physics could lower this tension, however it is robust against other systematics. Limits in the accuracy of our emulator prevent us from constraining $\Omega _{\rm m}$.

Asymptotics for Finite-Time Ruin Probabilities of a Dependent Bidimensional Risk Model with Stochastic Return and Subexponential Claims

The paper considers a bidimensional continuous-time risk model with subexponential claims and Brownian perturbations, in which the price processes of the investment portfolio of the two lines of business are two geometric Lévy processes and the two lines of business share a common claim-number process, which is a renewal counting process. The paper mainly considers the claims of each line of business having a dependence structure. When the claims have subexponential distributions, the asymptotics of the finite-time ruin probabilities ψand(x1,x2;T) and ψsim(x1,x2;T) have been obtained. When the distributions of claims belong to the intersection of long-tailed and dominatedly varying-tailed distribution classes, the asymptotics of the finite-time ruin probability ψor(x1,x2;T) is given.

Quantile regression based on the counting process approach under dependent truncated data

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres.

Universal Defects Statistics with Strong Long-Range Interactions.

Quasi-static transformations, or slow quenches, of many-body quantum systems across quantum critical points generate topological defects. The Kibble-Zurek mechanism regulates the appearance of defects in a local quantum system through a classical combinatorial process. However, long-range interactions disrupt the conventional Kibble-Zurek scaling and lead to a density of defects that is independent of the rate of the transformation. In this Letter, we analytically determine the complete full counting statistics of defects generated by slow annealing a strong long-range system across its quantum critical point. We demonstrate that the mechanism of defect generation in long-range systems is a purely quantum process with no classical equivalent. Furthermore, universality is not only observed in the defect density but also in all the moments of the distribution. Our findings can be tested on various experimental platforms, including Rydberg gases and trapped ions.

Infinite-Horizon Probability of Ruin for a Variable-Memory Counting Process (Hawkes Process)

The reserve R(t) of an insurance company denotes the accumulated capital up to time ttt throughout its operational span. While this reserve can be modeled using stochastic processes, the endeavor remains notably intricate. The mathematical complexity presents a considerable obstacle for researchers within this domain. Prior research has predominantly focused on reserve models constructed from Markovian processes. In this manuscript, our attention shifts to risk models derived from non-Markovian processes, particularly those with claim arrivals governed by Hawkes processes. Before delving into the core subject matter, we provide an extensive review of the literature on counting processes with variable memory. This includes a thorough exploration of Hawkes processes, Gerber-Shiu functions, integro-differential equations, and Laplace transforms. These elements are crucial for computing the probability of ruin over an infinite time horizon, especially in scenarios where interdependence exists between inter-claim times. Additionally, we present the requisite mathematical tools essential for comprehending the contents of this article, specifically tailored for individuals with a foundational understanding of actuarial science. Furthermore, we have successfully determined the probability of ruin, marking a significant milestone in our investigation.

The efficacy of Diamond™ nucleic acid dye-stained cell counting techniques for forensic application

Touch DNA is one of the most common types of biological material collected during criminal investigations. Diamond™ Nucleic Acid Dye (DD) has been shown to aid in touch sample visualisation and target sampling. It has also been used as a method of shedder categorisation that is cheaper and quicker than DNA methods. However, the DD method routinely involves manual cell counting, which can result in intra and inter-person variability similar to other manual techniques used in forensic science, for example, fingerprint identification. Additionally, DD based shedder categorisation involves counting cells in a portion of the touch deposit to extrapolate an individual’s shedder status, and the sampling effect of such estimations is currently unknown.The present study tested different data analysis aspects of the DD method, including counting variability within and between people, shedder classification differences based on different counting methods (entire thumbprint, sub-section of a print with most cells, sub-section of a print deemed most representative of the entire thumbprint, and random sections), the use of ImageJ software to semi-automate counting and the use and extension of the DD method for investigating DNA Transfer, Persistence, Prevalence and Recovery (DNA-TPPR).The results of this study show that there are meaningful differences observed during counting processes both between and within people. These differences tended to increase as the factor of time, or the duration of counting, rather than the complexity of cell deposits being assessed. Investment in cell counting software that eliminates personal factors, such as boredom fatigue, can remedy most of these issues, however, will require optimisation, such as fibre recognition. Shedder testing was shown to be affected by the choice of sampling and categorisation methods, and suggested that using an entire finger or larger section size can provide increased precision. Finally, inverted worn gloves stained with DD may provide an acceptable alternative for hands in DNA-TPPR investigations, providing an interesting alternative for future research.

Identifying the contribution of communication and trust in aviation maintenance occurrences: A content analysis methodology

As communication and trust are both linked with safety, this paper aims to investigate their contribution to aviation maintenance incidents and accidents. For this purpose, the content analysis method is used to investigate whether trust and communication factors were present in aviation maintenance occurrences. Content analysis is used as a qualitative and quantitative tool. For the data analysis, apart from direct investigation for keywords throughout the material for analysis (aviation accident/incident reports with maintenance involvement), a survey tool was also employed. The items of this survey tool (Communication and Trust Question Set) were used to filter the reports’ text to indirectly identify the two factors under examination (communication and trust). As a qualitative tool, the content analysis yielded results via mapping and narrative techniques. As a quantitative tool, results were obtained and reported with the help of descriptive statistics (counts, frequencies). The results indicated that elements of trust and communication are indirectly detectable in aviation maintenance occurrences. Both ineffective communication and lack of trust were identified as a key accident/incident causal condition. Interpersonal trust is recommended to be included in the implementation requirements of any communication system. The limitations associated with the difference in the structure and consistency of the examined material are also discussed.

Digital Transformation Framework in Consumer Goods Wholesale Industry SMEs : Case Study in Wholesale SMEs of Babelan Districk

Small and Medium Industry (SMEs) is one type of business that has experienced a fairly developed growth valuation. Consumer goods wholesale SMEs have experienced rapid growth in the sales sector, specifically in the Babelan sub-district the consumer goods wholesale industry still uses a manual control system in running its business. The sales process with the Conventional System is carried out starting from stock control, sales activity control, sales process, cashier and revenue generation is still done manually. The manual control process causes a slow counting process, and a long process of re- ordering goods and losing assets. The solution needed at this time is the creation of a framework for Digital Transformation Steps in the sales process to facilitate the control of wholesale consumer goods business processes. The digital transformation framework is expected to modernize the sales process starting from the cashier system, revenue control system, sales activity control process and make it easier for wholesalers to order goods. This applied research is expected to be able to provide suggestions for wholesale consumer goods businesses in running their business in a more efficient and practical direction and can be a recommendation to be able to carry out a digitally transformed sales process.

Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime

We present a broad study of charge and heat transport in a mesoscopic system where one or several quantum Hall edge channels are strongly coupled to a floating Ohmic contact (OC). It is well-known that charge-current fluctuations emanating from the OC along the edge channels are highly susceptible to the OC charge capacitance in the heat Coulomb blockade regime (an impeded ability of the OC to equilibrate edge channels). Here, we demonstrate how potential and temperature fluctuations due to finite OC charge and heat capacities impact the heat-current fluctuations emitted from the OC. First, by assuming an infinite OC heat capacity, we show that the output heat-current noise is strongly dependent on the OC charge capacitance, following from a close relation between one-dimensional charge and heat currents. When also the OC heat capacity is finite, an interplay of potential and temperature fluctuations influences the heat transport. Concretely, we find that the effect of the charge capacitance on heat transport manifests in terms of a strongly increased energy relaxation time in the heat Coulomb blockade regime. Furthermore, we find expressions for a broad set of output observables, such as charge and heat auto- and cross correlations, as functions of input and OC fluctuations, depending on the relation between charge and energy relaxation times compared to the frequency of fluctuations and inverse (local) temperatures as well as on the number of edge channels attached to the OC. Finally, we show that a finite OC heat capacity transforms the full counting statistics of the output charge from Gaussian to non-Gaussian. Our findings provide opportunities to experimentally probe and harness the quantum nature of heat transport in strongly coupled electron circuits. Published by the American Physical Society 2024