Cumulative Distribution Function Research Articles

Morph-SSL: Self-Supervision With Longitudinal Morphing for Forecasting AMD Progression From OCT Volumes.

The lack of reliable biomarkers makes predicting the conversion from intermediate to neovascular age-related macular degeneration (iAMD, nAMD) a challenging task. We develop a Deep Learning (DL) model to predict the future risk of conversion of an eye from iAMD to nAMD from its current OCT scan. Although eye clinics generate vast amounts of longitudinal OCT scans to monitor AMD progression, only a small subset can be manually labeled for supervised DL. To address this issue, we propose Morph-SSL, a novel Self-supervised Learning (SSL) method for longitudinal data. It uses pairs of unlabelled OCT scans from different visits and involves morphing the scan from the previous visit to the next. The Decoder predicts the transformation for morphing and ensures a smooth feature manifold that can generate intermediate scans between visits through linear interpolation. Next, the Morph-SSL trained features are input to a Classifier which is trained in a supervised manner to model the cumulative probability distribution of the time to conversion with a sigmoidal function. Morph-SSL was trained on unlabelled scans of 399 eyes (3570 visits). The Classifier was evaluated with a five-fold cross-validation on 2418 scans from 343 eyes with clinical labels of the conversion date. The Morph-SSL features achieved an AUC of 0.779 in predicting the conversion to nAMD within the next 6 months, outperforming the same network when trained end-to-end from scratch or pre-trained with popular SSL methods. Automated prediction of the future risk of nAMD onset can enable timely treatment and individualized AMD management.

Intention-to-treat outcomes of patients with hepatocellular carcinoma receiving immunotherapy before liver transplant: the multicenter VITALITY study

The use of immune checkpoint inhibitors (ICI) in patients with advanced hepatocellular carcinoma (HCC) has become widespread with encouraging outcomes in the neoadjuvant setting. Safety and intention to treat (ITT) outcomes in the peri transplant setting are currently based on small and heterogenous single center reports. This first multiregional US study (2016-2023) included 117 consecutive HCC patients assessed for LT and treated preoperatively with ICIs. Intention to treat ITT and survival analyses were conducted with evaluation of post LT rejection rates. In total, 86 (73.5%) patients exceeded MC and 65 (75.6%) were successfully downstaged (DS) within a median of 5.6 months. 43 (36.7%) underwent transplantation, including 18 (15.4%) within MC and 23 (19.7%) initially beyond and DS. Overall, 94% of the cohort received concurrent ICIs and locoregional therapies. No grade 4-5 adverse events occurred on the waiting list. The 3-year cumulative probability of dropout was 28% for those within MC and 48% for those beyond. Independent predictors of dropout included: being beyond MC (p<0.001), AFP doubling from baseline (p=0.014) and radiographic responses (p<0.001). The 3-year ITT survival was 71.1% (73.5% within MC vs 69.7% beyond MC, p=0.329), with 3-year post LT survival rate of 85%. Post-LT rejection occurred in 7 patients, six received their last dose of ICI less than 3 months prior to LT, resulting in one graft loss. The first multicenter evaluation of HCC patients receiving ICI pre-LT demonstrates favorable survival and safety outcomes, justifying continued utilization and further evaluation of this strategy in clinical practice. High tumor burden, doubling of AFP levels, and radiographic response were identified as predictors of unfavorable oncologic outcomes. The first multicenter evaluation of pre-transplant immune-checkpoint-inhibitors in hepatocellular carcinoma to show promising intention-to-treat survival, safety and rejection rates. Immune-checkpoint-inhibitors, either alone or combined with LRT, demonstrate reliable efficacy. This preoperative strategy could be particularly beneficial for high-risk patients, including those requiring downstaging or with elevated AFP levels despite locoregional treatment. These findings fill current knowledge gaps and offer reassuring evidence for the feasibility of pre-transplant use of immune-checkpoint-inhibitors, pending results from ongoing trials.

On Epidemiological and Actuarial Analyses of Health Insurance Models for Communicable Diseases

This article examines an SIDRS disease model design for insurance contracts, in which the insured population is exposed to the risks of communicable diseases. For the epidemiological models, the population is structured into four demographic groups, namely: susceptibles (S), infected PHs undergoing treatment (I), infected PHs who are diseased (D), and infected PHs who recovered (R) from the disease, with part of the latter thereafter re-entering the group of susceptibles (S) and continuing with the insurer by paying premiums until he or she is infected again. The infective class is a union of the class of those undergoing treatment, deceased policy holders (PHs), and those who have recovered. The number of deceased PHs is counted as part of the insured population because the number PHs who die of the disease must be accounted for and are entitled to claims. The insurance policies are designed for the members of the susceptible group: the latter constantly face the risk of infection and death due to the disease. The probability of PHs remaining susceptible for the SIDRS disease model is formulated. The probability density function (PDF) and cumulative distribution function (CDFs) for the SIDRS disease model for an insurance policy are obtained. For the actuarial part, we used actuarial techniques and principles to determine the financial obligations of the parties and the insurance amounts for the insurer and PHs. The cumulative insurance reserve for an annuity and a lump sum plan are also considered. To ascertain the risk of insolvency, premium adjustment for the PHs is considered. Some numerical computations of the results arising from our model analyses are also considered in this article. This article has practical applications in health insurance schemes. It is also applicable in the determination of insurance premiums payable by PHs who did not have the disease and insurance claims receivable by those who are hospitalized or die of the disease. Our model can also be practically applicable in the determination of health insurance reserves for communicable diseases.

Shannonian Maximum Entropy Balking Threshold Mechanism (BTM) for a Stable M/G/1 Queue with Significant Applications of M/G/1 Queue Theory to Augmented Reality (AR)

An exposition is undertaken to analytically derive validate the Shannonian Maximum Entropy BTM for the underlying stable queue. Most importantly, the analytic derivation of the upper and lower bounds 0f the absolute difference between Shannonian Cumulative service time distribution functions (CDFs) with and without balking. Typical numerical experiments are provided. Additionally, some applications of M/G/1 queue theory to AR are given. Some challenging open problems are addressed combined with closing remarks and future research directions.

Late effects after allogeneic haematopoietic cell transplantation in children and adolescents with non-malignant disorders: a retrospective cohort study

Continued advances in haematopoietic cell transplantation (HCT) for children with non-malignant diseases (NMDs) have led to a growing population of survivors in whom late occurring toxic effects remain a challenge. We investigated the incidence of and risk factors for post-transplant toxicities in a contemporary cohort of children and adolescents undergoing HCT for NMDs. In this retrospective cohort study, we extracted data from the Center for International Blood and Marrow Transplantation Research (CIBMTR) database to analyse timing and incidence of effects and risk factors associated with late effects of HCT for treatment of NMDs at age 21 years or younger. Late effects of interest were avascular necrosis, cataracts, congestive heart failure, myocardial infarction, diabetes, gonadal dysfunction, growth hormone deficiency, hypothyroidism, renal failure requiring dialysis, and neurological events (stroke and seizure). Cumulative incidence of each late effect was calculated at 5 years and 7 years after HCT. Risk factors were evaluated in Cox proportional hazards regression analyses. Main exposures were primary NMD, age, sex, ethnicity and race, insurance, donor and graft type, myoablative conditioning, total-body irradiation exposure, graft-versus-host disease (GVHD), and transplant year. Primary outcomes were rates, cumulative incidence probability (95% CI), and risk-factors for organ-specific late effects. Between Jan 1, 2000, and Dec 31, 2017, 7785 patients aged 21 years or younger underwent HCT. 1995 patients were ineligible or did not consent to be included. 5790 patients from 171 centres were included in the analysis. 3505 (60·5%) of 5790 patients were male and 2285 (39·5%) were female. 2106 (36·4%) patients were White, 771 (13·3%) were Hispanic, and 773 (12·7%) were Black. 1790 (30·9%) patients were non-USA residents. Median age at HCT was 5·5 years (range 0·0-21·0). 1127 (19%) of 5790 patients had one late effect, and 381 (7%) had at least two. At 7 years post-HCT, the cumulative incidence probability was 1·9 (95% CI 1·5-2·3) for cataracts, 4·9 (4·3-5·6) for diabetes, 2·6 (2·1-3·1) for gonadal dysfunction, 3·2 (2·7-3·8) for hypothyroidism, 5·0 (4·4-5·7) for growth disturbance, 8·1 (7·4-8·9) for renal failure, 1·6 (1·3-2·0) for avascular necrosis, 0·6 (0·4-0·8) for congestive heart failure, 0·2 (0·1-0·3) for myocardial infarction, and 9·4 (8·6-10·2) for neurological effects. Age 10 years or older at HCT, unrelated donor source, total-body irradiation, and GVHD were identified as risk factors for long-term effects. The findings highlight the need for, and access to, multidisciplinary and lifelong follow-up for children undergoing HCT for NMDs. As more children undergo treatment with cellular therapies for non-malignant conditions, further analyses of post-transplant data could increasingly guide treatment decisions and subsequent long-term surveillance. National Cancer Institute, National Heart, Lung and Blood Institute, National Institute of Allergy and Infectious Diseases, Health Resources and Services Administration, and Office of Naval Research.

Analytically pricing volatility options and capped/floored volatility swaps with nonlinear payoffs in discrete observation case under the Merton jump-diffusion model driven by a nonhomogeneous Poisson process

In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized variance has historically impeded the development of a robust analytical valuation approach for such instruments. Through the application of the cumulative distribution function of the realized variance conditional on Poisson jumps, we have derived explicit expectations for the derivative payoffs articulated as functions of the extremum values of the square root of the realized variance. We delineate precise pricing structures for an array of instruments, encompassing variance and volatility swaps, variance and volatility options, and their respective capped and floored variations, alongside establishing put-call parity and relationships for capped and floored positions. Complementing the theoretical advancements, we substantiate the practical efficacy and precision of our solutions via Monte Carlo simulations, articulated through multiple numerical examples. Conclusively, our analysis extends to the quantification of jump impacts on the fair strike prices of volatility derivatives with nonlinear payoffs, facilitated by our analytic pricing expressions.

Minimizing distance between distribution functions: discrete counterparts to continuous random variables with applications in non-life insurance and stochastic reliability

In this work, we propose a novel family of procedures for deriving a discrete counterpart to a continuous probability distribution. They are based on a class of distances between cumulative distribution functions, including the Cramér, the Cramér-von Mises, and the Anderson-Darling distances as particular cases. The discrete counterpart is defined and derived as the random variable which minimizes its distance to the assigned continuous probability distribution among all the discrete random variables supported on the set of integers (or positive integers). Applications are provided with reference to the exponential and the normal distributions, among others; the discrete counterparts are derived, and their main properties are discussed, also in comparison with the one obtained through an existing discretization technique based on the preservation of the cumulative distribution function at integer values. Parameter estimation for these discrete analogs is discussed, along with an analysis of two real datasets, where they are compared in terms of goodness-of-fit with some popular discrete distributions. Furthermore, in order to highlight the effectiveness and the benefits derived from the proposed discretization procedures, we illustrate two practical applications in actuarial science and in reliability engineering. In the former case, the problem of determining the distribution of the total claims amount for a non-life insurance portfolio is considered, where the claim sizes can be modelled as iid random variables, and the number of claims is random as well. Actuaries use a recursive calculation method based on Panjer's formula, which requires an appropriate discretization of the individual claim distribution, and therefore the proposed procedures can be used. Since we consider two simple cases where the distribution of the total claims amount is analytically acquirable, the efficacy of the discretization procedures in the final approximation can be easily assessed and turns out to be satisfactory, especially when compared to the existing discretization. The latter case considers the determination of the reliability parameter for a complex stress-strength model. Here, the approximation by discretization is compared to Monte Carlo simulation and shown to be relevant: with a comparable if not smaller computational effort, discretization leads to similar results as simulation. Such discretizations can also naturally be applied to more complex problems such as scenario generation in stochastic programming. R code for this article is provided as supplementary material.

Analysis of impulse withstand voltage of ester-based nanofluids

Ester-based nanofluids constitute an effective ecological alternative to petroleum-derived dielectric fluids for electrical engineering industry. Pulse induced dielectric breakdown is a key cause of power device failure. In this paper, we deal with the lightning impulse breakdown voltage (LI BDV) in natural and synthetic ester-based (NE and SE) nanofluids with various concentrations of magnetite (Fe3O4) and fullerene (C60) nanoparticles. The nanofluids show a decrement in positive polarity LI+ BDV as compared with the base ester. Negative polarity LI- BDV in the nanofluids is similar to that of base oils. Weibull statistical distributions are applied to analyse the results at different cumulative probabilities of 1 %, 10 %, and 50 %. Natural ester with C60 nanoparticles shows higher positive LI+ BDV values at a low probability level, while the negative LI- BDV reaches higher values at higher probability levels. The decreased LI BDV in NE and SE due to the magnetite nanoparticles are attributed to the nanoparticle clustering and percolation. The tendency of C60 nanoparticles to enhance the LI BDV in NE but not in SE is interpreted in the view of the nanoparticle concentration and oil's viscosity effect on the streamer branching and propagation.

AN ALGEBRAIC APPROACH FOR NEUTROSOPHIC RANDOM VARIABLES BY THE REFINED AH-ISOMETRY

In this article, we are going to extend the definition of literal neutrosophic random variables to literal refined neutrosophic random variables and we will study its new properties. We derive and present various concepts including refined neutrosophic probability distribution function in the continuous case, refined neutrosophic cumulative distribution function of continuous refined neutrosophic random variables, refined neutrosophic expected value, refined neutrosophic variance, refined neutrosophic standard deviation, refined neutrosophic mean deviation, refined neutrosophic rth quartiles, refined neutrosophic moments generating function, and refined neutrosophic characteristic function. Additionally, the paper includes many solved examples and applications. This paper opens the road to generalizing many concepts in neutrosophic probability theory specially neutrosophic reliability theory, neutrosophic stochastic processes, and neutrosophic queuing theory.

A method to obtain the trapping energy and trapping range between hydrogen and defects at finite temperature

The binding energy between hydrogen (H) and defects in solid phase materials has been widely studied, which is of vital importance to understand the H retention effects and defect growth mechanisms. However, present studies of binding energy through density functional theory (DFT) or the molecular statics (MS) method were usually performed at 0 K, which could not take the influence of entropy into consideration. In this work, a thermodynamic method has been proposed to obtain the trapping energy between H and defects at finite temperatures. The method is based on the rate theory, which uses trapping energy (V) and trapping range (δ) to describe the trapping properties of defects. Ultimately, a parameterized H spatial cumulative distribution function at thermodynamic equilibrium state could be given. The trapping energy and trapping range parameters in the function can be determined by contrast with the results obtained from molecular dynamics or other methods. This method has been applied to calculate the trapping energies and trapping ranges of H to helium bubble and grain boundary, respectively. Further discussion has been made on the discrepancy between trapping energies obtained by this method and the conventional DFT/MS method.

Failure probability of F-100 Pratt &amp; Whitney-220E turbofan engine on F-16 fighting falcon aircraft

Engine failure is a condition where the engine operates outside normal conditions. One of the abnormal conditions that occurs can be caused by a fault that occurs in each engine module. Engine module is one of the components on an aircraft that functions for supports the aircraft to fly and controls all engine operations, wether on the ground and during flight. The problem can occur in each engine module at any time causing engine failure. Therefore, it is necessary to carry out further analysis to determine the cause of the failure that occurred, as well as to implement appropriate mitigation measures. The method used is the Fault Tree Analysis (FTA) method, which is a method for identifying risks that contribute to failure and determining failure probability. From the analysis using the qualitative fault tree analysis method 71 events were obtained with 35 basic events. Meanwhile, the quantitative analysis produces a cumulative probability failure of 0.747. The probability value has almost reached 1, therefore preventive maintenance has to be carried out to prevent functional failure.

Continuity risk evaluation of the Bayesian posterior integrity monitoring against multiple faults

Compared to the prior integrity monitoring of global navigation satellite system (GNSS), the posterior integrity monitoring incorporates the used GNSS measurements into the computation of integrity risk, thereby providing a more accurate representation of the reliability of position solution. However, the continuity risk evaluation in posterior integrity monitoring remains an unresolved issue. After formulating the posterior integrity risk of each event hypothesis as a parity function, we propose a method to evaluate the posterior continuity risk by computing the cumulative probability of false alarm within a sphere constructed in the parity space. This approach guarantees a conservative estimate of the probability of false alarm, thereby establishing an upper bound for posterior continuity risk. Experiment and analysis based on positioning cases involving GPS, Galileo, and BeiDou satellites suggest that the posterior integrity monitoring can achieve a lower probability of false alarm compared to prior integrity monitoring under certain integrity monitoring configurations. Furthermore, the evaluation accuracy of probability of false alarm inversely correlates with the severity of the differences in solution separation variances.

Modeling insurance loss data using novel approach of moment exponential model: Inference, actuarial measures and application

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.

Ergodic Rate Analysis of Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surface-Assisted Rate-Splitting Multiple Access Systems Based on Discrete Phase Shifts.

In this paper, we combine simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) with rate-splitting multiple access (RSMA) technology and investigate the ergodic rate performance of an STAR-assisted RSMA system. Considering the discrete phase shifts of the STAR-RIS in practice, the downlink performance of STAR-RIS-assisted RSMA with discrete phase shifts is compared to that with continuous phase shifts. Firstly, the cumulative distribution function of signal-to-interference-plus-noise ratio (SINR) of users is analyzed. Then, the total ergodic rate of the system and its approximate closed-form solution are, respectively, derived based on the cumulative distribution function of users. The simulation results validate the effectiveness of the theoretical analysis, showing good agreement between the derived theoretical ergodic rate and the corresponding simulations. Although the system performance with discrete phase shifts is inferior to that with continuous phase shifts due to quantization errors, the performance of the continuous phase shift system is well approximated when the quantization bit of the phase shift system reaches 3 in the simulations. Additionally, the impact of the number of STAR-RIS elements on the system's performance is analyzed.

Fuzzy system reliability analysis based on new aging indexes

The concept of aging plays an important role in reliability analysis. The aim of this paper is providing the novel method to definition aging indexes based on fuzzy random variables and using the concept of α-pessimistic in both parametric and non-parametric approaches. In parametric approach, the concepts of survival function, hazard rate function and mean residual function were extended for fuzzy random variables. After that, we obtain and analyse these indexes for fuzzy exponential and fuzzy two-parameter Weibull distributions as two frequently used lifetime distribution in reliability theory. Moreover, with the assumption that the distribution of fuzzy observations is unknown (non-parametric approach), first an estimate for the fuzzy distribution function is presented, and then an estimate for the aging indices of the system is investigated. To do this, the concept of fuzzy empirical distribution function is investigated as an estimator of cumulative distribution function. Moreover, some properties of investigated estimator have been established.

Failed Ahmed glaucoma valves: trabeculectomy versus repeat shunt surgery

IntroductionTo investigate the outcomes of trabeculectomy (TRAB) versus repeat Ahmed glaucoma valve (re-AGV) implantation in eyes with Ahmed glaucoma valve (AGV) failure.MethodsThis quasi-experimental study includes patients with failed AGV implants requiring additional surgical intervention between 2018 and 2022. Patients in the TRAB group underwent a fornix-based procedure with mitomycin C 0.01% injection (0.1 mL). Eyes in the re-AGV group underwent repeat shunt surgery. The choice of the procedure was based on conjunctival condition. The primary outcome measure was surgical success rate based on various intraocular pressure (IOP) targets and percentages of IOP reduction from baseline: IOP ≤ 21 mmHg and 20% reduction (conventional criteria), IOP ≤ 18 and > 20% reduction (criterion A), IOP ≤ 15 and > 25% reduction (criterion B), and IOP ≤ 12 and > 30% reduction (criterion C).ResultsForty-eight eyes of 48 patients were operated and reported herein, consisting of 22 eyes of 22 patients undergoing TRAB and 26 eyes of 26 subjects undergoing re-AGV. No significant difference was observed between the study groups in terms of initial diagnoses, baseline IOP or the number of prior surgeries. The cumulative probability of survival at one year was significantly higher in the trabeculectomy group using the three stricter success definitions. In both study groups, IOP was significantly reduced from baseline at all postoperative visits, and was significantly lower in the TRAB group at all time points beyond one month. At 12 months, 5% of TRAB versus 48% of re-AGV eyes required glaucoma medications (P < 0.001). The rate of complications was comparable between the study groups (P = 0.76) but there was a trend toward a greater need for repeat surgery in the re-AGV group (4 eyes versus nil, P = 0.07).ConclusionsTrabeculectomy can be considered a safe and effective surgical option in eyes with failed AGV leading to significantly lower IOP levels and more favorable success rates than re-AGV in selected patients.

Real-Time Indoor Visible Light Positioning (VLP) Using Long Short Term Memory Neural Network (LSTM-NN) with Principal Component Analysis (PCA).

New applications such as augmented reality/virtual reality (AR/VR), Internet-of-Things (IOT), autonomous mobile robot (AMR) services, etc., require high reliability and high accuracy real-time positioning and tracking of persons and devices in indoor areas. Among the different visible-light-positioning (VLP) schemes, such as proximity, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and received-signal-strength (RSS), the RSS scheme is relatively easy to implement. Among these VLP methods, the RSS method is simple and efficient. As the received optical power has an inverse relationship with the distance between the LED transmitter (Tx) and the photodiode (PD) receiver (Rx), position information can be estimated by studying the received optical power from different Txs. In this work, we propose and experimentally demonstrate a real-time VLP system utilizing long short-term memory neural network (LSTM-NN) with principal component analysis (PCA) to mitigate high positioning error, particularly at the positioning unit cell boundaries. Experimental results show that in a positioning unit cell of 100 × 100 × 250 cm3, the average positioning error is 5.912 cm when using LSTM-NN only. By utilizing the PCA, we can observe that the positioning accuracy can be significantly enhanced to 1.806 cm, particularly at the unit cell boundaries and cell corners, showing a positioning error reduction of 69.45%. In the cumulative distribution function (CDF) measurements, when using only the LSTM-NN model, the positioning error of 95% of the experimental data is >15 cm; while using the LSTM-NN with PCA model, the error is reduced to <5 cm. In addition, we also experimentally demonstrate that the proposed real-time VLP system can also be used to predict the direction and the trajectory of the moving Rx.

Associations of ambient air pollution with incidence and dynamic progression of atrial fibrillation

The influence of air pollution on dynamic changes in clinical state from healthy to atrial fibrillation (AF), further AF-related complications and ultimately, death are unclear. We aimed to investigate the relationships between air pollution and the occurrence and progression trajectories of AF. We retrieved 442,150 participants free of heart failure (HF), myocardial infarction (MI), stroke and dementia at baseline from UK Biobank. Exposures to air pollution for each transition stage were estimated at the geocoded residential address of each participant using the bilinear interpolation approach. The outcomes were incident AF, complications, and death. Multi-stage models were used to evaluate the associations between air pollution and dynamic progression of AF. Over a 12.6-year median follow-up, a total of 21,670 incident AF patients were identified, of whom, 4103 developed complications and 1331 died. PM2.5, PM10, NOx and NO2 were differentially positively associated, while O3 was negatively associated with risks of progression trajectories of AF. PM2.5 exposure was significantly associated with an increased risk of progression. The associations of PM2.5, PM10, NOx, and NO2 on incident AF were generally more pronounced compared to other transitions. The cumulative transition probabilities were generally higher in individuals with higher exposure levels of PM2.5, PM10, NOx, and NO2 and lower exposure to O3. Air pollution could potentially have a role in increasing the risk of both the occurrence and progression of AF, emphasizing the significance of air pollution interventions in both the primary prevention of AF and the management of AF-related outcomes.

Physical layer security in SWIPT-based cooperative vehicular relaying networks

The future of autonomous transportation systems depends on energy sustainability and secure information exchange from low-power vehicular sensors, hence the increased interest in vehicular sensor charging using simultaneous wireless information and power transfer (SWIPT). This study investigates the physical layer security of a SWIPT-based radio frequency energy harvesting cooperative vehicular relaying network subjected to cascade Nakagami-m and double Nakagami-m (DN) fading channels. In the considered system model, a stationary source communicates with a mobile destination through a power-splitting-based decode-and-forward relay in the presence of a mobile passive eavesdropper. Based on the Gamma-distributed first term of the Laguerre series, new statistical probability density function (PDF) and cumulative distribution function (CDF) expressions for the DN are derived to accurately model the complex cascaded fading scenario. The secrecy performance metrics analyzed are the secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZSC), and the intercept probability (IP). In addition, the asymptotic SOP (ASOP) is investigated in the high signal-to-noise ratio (SNR) to enhance the comprehension of the secrecy performance. Based on the derived ASOP, the secrecy diversity order (SDO) of the proposed system is determined and examined. Particularly, we present analytical closed-form expressions for the secrecy performance metrics and provide a detailed understanding of the impact of the system parameters under the cascade fading scenario. Then, a power splitting (PS) optimization problem is formulated to minimize the SOP. The results demonstrate a reduction in the SOP with the proposed PS scheme compared to the equal PS scheme. The obtained analytical findings are validated using Monte Carlo simulations.

Beyond Auto‐Models: Self‐Correlated Sui‐Model Respecifications

This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models.