Probability Ratio Research Articles

Enhancing yellow-green emission in Eu/Tb co-doped tellurite glasses controlled by Lu2O3

In this research, Lu2O3 was incorporated into Eu3+ and Tb3+ co-doped tellurite glasses to enhance structural stability and modify the yellow-green emission. A series of microstructural analyses, including Differential Scanning Calorimetry (DSC), Raman spectroscopy, and density measurements, confirmed that the addition of Lu2O3 causes the long-chain or cyclic Te-O-Te network structure to break, resulting in the formation of more [TeO3], which in turn leads to an increase in non-bridging oxygens (NBO) and lowers the phonon energy of the matrix material. Fluorescence spectral characterization revealed that both green and yellow luminescence intensities peaked when Lu2O3 concentration reached 15 %. Additionally, the Judd-Ofelt theory supports its superior laser performance. With the addition of Lu2O3,The radiative transition probability (Arad), lifetime (τrad), and branching ratio (β) of the excited states of Tb3+ and Eu3+ have all been enhanced.Under the regulation of 15% Lu2O3, The maximum absorption cross-section of at 544 nm is 1.88×10-20 cm2, and the maximum emission cross-section is 2.14×10-20 cm2. At 611 nm, the maximum absorption cross-section is 1.05×10-20 cm2, and the maximum emission cross-section is 1.44×10-20 cm2. The decay curve indicates a fluorescence lifetime enhancement from 0.6 ms to 1 ms with Lu2O3. These results underscore the potential of Lu2O3 modulated Eu3+/Tb3+ co-doped tellurium glass as an effective yellow-green laser gain medium.

Awareness Revision and Belief Extension

ABSTRACT What norm governs how an agent should change their beliefs when they encounter a completely new possibility? Orthodox Bayesianism has no answer, as it takes all learning to involve updating prior beliefs. A partial proposal is Reverse Bayesianism, which mandates the preservation of ratios of prior probabilities, but it faces counterexamples introduced by Mahtani (2021). I propose to separate awareness growth into two stages: awareness revision and belief extension. I argue that Mahtani’s cases highlight that we need to theorize awareness revision before we can define a proposal for belief extension, such as Reverse Bayesianism. I provide a formal model of awareness revision which makes explicit how propositions are distinguished within awareness states and identified across them. Reformulating Reverse Bayesianism to take input from my model allows it to navigate Mahtani-style cases. My model leaves open how agents choose to identify propositions across awareness states, and I propose that they ought to do so conservatively: preserving undisturbed prior reasoning about the structure of their awareness. I then spell out this proposal in a special case. This is a partial proposal, and I close with a discussion of how to elaborate on it and how to advance research into awareness revision.

Closed-form solutions for Bernoulli and compound Poisson branching processes in random environments*

Abstract For branching processes, the generating functions for the limit distributions of the so-called ratios of probabilities of rare events satisfy Schröder-type integral–functional equations. With the exception of a few special cases, the corresponding equations cannot be solved analytically. I found a large class of Poisson-type offspring distributions for which the Schröder-type functional equations can be solved analytically. Moreover, for the asymptotics of limit distributions, the power and constant factors can be written explicitly. As a bonus, Bernoulli branching processes in random environments are treated. The beauty of this example is that the explicit formula for the generating function is unknown. Nevertheless, the closed-form expressions for the power and constant factors in the asymptotic can be written with the help of some effective techniques. The asymptotic expansion also contains oscillatory terms absent in the Poisson case. It is shown that at power three in the Bernoulli binomial kernels, short-phase discrete oscillations turn into long-phase continuous ones.

Effect of Photon Vortex Generated in Extremely Strong Magnetic Fields on Stellar Nucleosynthesis

It is thought that photon vortices are predominantly produced in extremely strong magnetic fields in the Universe. Because the photon vortex may cause significant large angular momentum transfer in interactions with atomic nuclei, stellar nucleosynthesis in such astrophysical environments is affected. In the present study, we calculate the ratios of the photon absorption transition probabilities of photon vortices with Bessel wave to photons described by the plane wave. The result shows enhancement of excitation of states with large total angular momentum by optimization of the divergence angle of the incident photon vortex in momentum space. However, the average cross section for the photon vortex turns out to be identical with that for the plane wave. Therefore, even when Bessel photons are predominantly produced in astrophysical environments, the isotopic abundances of the synthesized elements are not changed.

A new omnibus SPRT chart for monitoring process mean and variability based on the average number of observations to signal

The recent development of the omnibus sequential probability ratio test (OSPRT) chart marks a significant contribution to the advancement of joint monitoring schemes. As the OSPRT chart is a variable-sample-size control chart, practitioners often wish to understand its inspection efficiency, i.e. the number of observations it samples before producing a signal. In this article, we propose two enhanced optimization designs for the OSPRT chart based on the average number of observations of signal (ANOS) and expected value of the ANOS (EANOS) metrics under deterministic and unknown shift sizes, respectively. The ANOS metric is central to our design as it perfectly combines both the average run length (ARL) and the average sample number. A comparative analysis reveals that the OSPRT chart outperforms four benchmarking control charts in terms of the ANOS and EANOS metrics. Finally, an implementation of the OSPRT chart is presented with a ball shear test dataset.

Early Address Detection: A Soft Vertical Handover Approach in Proxy Mobile IPv6

Study’s Excerpt Handover technique for Proxy Mobile IPv6 (PMIPv6) networks through a proactive IP address allocation approach is introduced. It significantly reduces handover-blocking probability and latency, thereby ensuring smoother transitions between WLAN and WiMAX domains. It is proved to be superior to velocity-aware handover methods. Full Abstract This study presents an enhanced handover technique for Proxy Mobile IPv6 (PMIPv6) networks aimed at improving mobility management in heterogeneous wireless environments. The proposed scheme introduces a proactive approach where the anchor Local Mobility Anchor (LMA) obtains IP addresses for the Mobile Node (MN) before it leaves the home network, facilitating faster handovers between Wireless Local Area Network (WLAN) and Worldwide Interoperability for Microwave Access (WiMAX) domains. The performance of the proposed scheme was evaluated through both mathematical analysis and network simulation, comparing it with a velocity-aware handover approach. Three key metrics were assessed: handover completion probability, handover latency, and packet loss ratio. Mathematical modeling demonstrated the scheme’s effectiveness in reducing handover-blocking probability and latency across various MN velocities. Simulation results, conducted using NS2.35, further established these findings, showing improvements in the number of successful handovers, reduced handover delay, and decreased packet loss compared to the velocity-aware approach. The study’s outcomes indicate that the proposed scheme offers a more efficient handover mechanism, particularly beneficial for maintaining service continuity in heterogeneous network environments.

Anomaly Detection in Time Series Data

This paper presents a novel unsupervised approach for anomaly detection in marine diesel engines using a Transformer Neural Network based autoencoder (TAE) and residual analysis with Sequential Probability Ratio Test (SPRT) and Sum of Squares of Normalized Residuals (SSNR). This approach adeptly captures temporal dependencies within normal time-series data without the necessity for labeled failure data. To assess the performance of the proposed methodology, a dataset containing faulty data is generated under the same operational profile as the normal training data. The model undergoes training using normal data, after which the faulty data is reconstructed utilizing the trained model. Subsequently, SPRT and SSNR are used to analyze the residuals from the observed and reconstructed faulty data. Significant deviations surpassing a predefined threshold are identified as anomalous behavior. Additionally, this study explores various architectures of Transformer neural networks and other types of neural networks to conduct a comprehensive comparative analysis of the performance of the proposed approach. Insights and recommendations derived from the performance analysis are also presented, offering valuable information for potential users to leverage. The experimental results demonstrate that the proposed approach can accurately and efficiently detect anomalies in marine diesel engines. Therefore, this approach can be considered as a promising solution for early anomaly detection, leading to timely maintenance and repair, and preventing costly downtime. Also, avoid accidents with probability severe consequences.

Design and Synthesis of a Novel Pyrazole-Based Molecule with Potential Anticancer and Antimicrobial effects: A Multifaceted in silico Approach

Although cancer remains the largest cause of morbidity and mortality globally, there is growing concern about the usage of cancer drugs due to their serious side effects. Therefore, a compound, 3,5-di(1H-indol-6-yl)-4,5-dihydro-1H-pyrazole-1-carboxamide, was synthesized using a mixture of (E)-1, 3-Di(1H-indol-3-yl) prop-2-en-1-one, semicarbazide hydrochloride, and sodium acetate. It was then examined for its anticancer and antimicrobial properties using molecular docking, molecular dynamic simulations and molecular mechanics, and generalised born surface area (MM/GBSA). The molecular docking was performed by targeting the cancer and antimicrobial associated proteins, namely protein tyrosine phosphatase L1 (1WCH), tankyrase-1 (5ETY), and phosphotransferase enzyme family protein (6SUI). Eventually, 3,5-di(1H-indol-6-yl)-4,5-dihydro-1H-pyrazole-1-carboxamide was found to be the most promising drug candidate for fighting both cancer and microbial infections. With docking scores of -9.730 Kcal/mol for 1WCH, -9.142 Kcal/mol for 5ETY, and -7.026 Kcal/mol for 6SUI, it showed strong interactions with all the target proteins. To investigate the binding stability of 3,5-di(1H-indol-6-yl)-4,5-dihydro-1H-pyrazole-1-carboxamide with the target molecules, molecular dynamics simulations were performed for 100 ns on the docked complexes. With an RMSD of less than 2.8Å, the synthesized compound was highly stable with all of the targets for 100 ns. Furthermore, the evaluation of the binding free energies (MM/GBSA) of these complexes revealed that the simulated environment had no significant influence on the binding energies, implying the synthesized molecule has strong binding affinities with the target proteins. Furthermore, in the toxicity assessment, the active probability ratio for 3,5-di(1H-indol-6-yl)-4,5-dihydro-1H-pyrazole-1-carboxamide was less than 0.60, indicating a low probability of organ toxicity and endpoint toxicity. Based on the results, the research concludes that the synthesized novel pyrazole-based compound could be a promising candidate for the development of new therapeutic drugs for the treatment of cancer and microbial infections.

SROR: A Secure and Reliable Opportunistic Routing for VANETs

In Vehicular Ad Hoc Networks (VANETs), high mobility of vehicles issues a huge challenge to the reliability and security of transmitting packets. Therefore, a Secure and Reliable Opportunistic Routing (SROR) is proposed in this paper. During construction of Candidate Forwarding Nodes (CFNs) set, the relative velocity, connectivity probability, and packet forwarding ratio are taken into consideration. The aim of SROR is to maximally improve the packet delivery ratio as well as reduce the end-to-end delay. The selection of a relay node from CFNs is formalized as a Markov Decision Process (MDP) optimization. The SROR algorithm extracts useful knowledge from historical behavior of nodes by interacting with the environment. This useful knowledge are utilized to select the relay node as well as to prevent the malicious nodes from forwarding packets. In addition, the influence of different learning rate and exploratory factor policy on rewards of agents are analyzed. The experimental results show that the performance of SROR outperforms the benchmarks in terms of the packet delivery ratio, end-to-end delay, and attack success ratio. As vehicle density ranges from 10 to 50 and percentage of malicious vehicles is fixed at 10%, the average of packet delivery ratio, end-to-end delay, and attack success ratio are 0.82, 0.26s, and 0.37, respectively, outperforming benchmark protocols.

Calibrating Observational Health Record Data Against a Randomized Trial

The conditions required for health record data sources to accurately assess treatment effectiveness remain unclear. Emulation of randomized clinical trials (RCTs) with health record data and subsequent calibration of the results can help elucidate this. To pilot an emulation of the KEYNOTE-189 RCT using a commercially available electronic health record (EHR) data source. This retrospective cohort study used an EHR database spanning from April 2007 to February 2023. Follow-up began on treatment initiation and proceeded until an outcome event, loss to follow-up, end of data, or end of study period (640 days). The population-based cohort was ascertained from EHRs provided by 52 health systems across the US. Eligibility criteria were defined as closely as possible to the benchmark RCT. Patients with non-small cell lung cancer initiating first-line treatment for metastatic disease were included. Patients with evidence of squamous non-small cell lung cancer, primary nonlung malignant neoplasms, or identified EGFR/ALK variations were excluded. Data were analyzed from June to October 2023. Initiation of first-line pembrolizumab and chemotherapy and chemotherapy alone. Chemotherapy in both groups was defined as a combination of pemetrexed and platinum-based (carboplatin or cisplatin) therapy. Outcomes of interest were 12-month survival probability and mortality hazard ratio (HR). A total of 1854 patients (mean [SD] age, 63.7 [9.6] years; 971 [52.4%] men) were eligible, including 589 patients who initiated pembrolizumab and chemotherapy and 1265 patients who initiated chemotherapy only. The cohort included 364 Black patients (19.6%) and 1445 White patients (77.9%). The 12-month survival probabilities were 0.60 (95% CI, 0.54-0.65) in the pembrolizumab group and 0.58 (95% CI, 0.55-0.62) in the chemotherapy-only group, compared with 0.69 (95% CI, 0.64-0.74) in the KEYNOTE-189 pembrolizumab group and 0.49 (95% CI, 0.42-0.56) in the KEYNOTE-189 chemotherapy-only group. The mortality HR was 0.95 (95% CI, 0.78-1.16), compared with 0.49 (95% CI, 0.38-0.64) in the KEYNOTE-189 RCT. In this cohort study piloting an RCT emulation, results were incongruous with the benchmark trial. Differences in patient treatment and data capture between the RCT and EHR populations, confounding by indication, treatment crossover, and accuracy of captured diagnoses may explain these findings. Future feasibility assessments will require data sources to have important oncology-specific measures curated.

Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States.

Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.

Sequential analysis of variance: Increasing efficiency of hypothesis testing.

Researchers commonly use analysis of variance (ANOVA) to statistically test results of factorial designs. Performing an a priori power analysis is crucial to ensure that the ANOVA is sufficiently powered, however, it often poses a challenge and can result in large sample sizes, especially if the expected effect size is small. Due to the high prevalence of small effect sizes in psychology, studies are frequently underpowered as it is often economically unfeasible to gather the necessary sample size for adequate Type-II error control. Here, we present a more efficient alternative to the fixed ANOVA, the so-called sequential ANOVA that we implemented in the R package "sprtt." The sequential ANOVA is based on the sequential probability ratio test (SPRT) that uses a likelihood ratio as a test statistic and controls for long-term error rates. SPRTs gather evidence for both the null and the alternative hypothesis and conclude this process when a sufficient amount of evidence has been gathered to accept one of the two hypotheses. Through simulations, we show that the sequential ANOVA is more efficient than the fixed ANOVA and reliably controls long-term error rates. Additionally, robustness analyses revealed that the sequential and fixed ANOVAs exhibit analogous properties when their underlying assumptions are violated. Taken together, our results demonstrate that the sequential ANOVA is an efficient alternative to fixed sample designs for hypothesis testing. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Beta Distribution Function for Cooperative Spectrum Sensing against Byzantine Attack in Cognitive Wireless Sensor Networks

In order to explore more spectrum resources to support sensors and their related applications, cognitive wireless sensor networks (CWSNs) have emerged to identify available channels being underutilized by the primary user (PU). To improve the detection accuracy of the PU signal, cooperative spectrum sensing (CSS) among sensor paradigms is proposed to make a global decision about the PU status for CWSNs. However, CSS is susceptible to Byzantine attacks from malicious sensor nodes due to its open nature, resulting in wastage of spectrum resources or causing harmful interference to PUs. To suppress the negative impact of Byzantine attacks, this paper proposes a beta distribution function (BDF) for CSS among multiple sensors, which includes a sequential process, beta reputation model, and weight evaluation. Based on the sequential probability ratio test (SPRT), we integrate the proposed beta reputation model into SPRT, while improving and reducing the positive and negative impacts of reliable and unreliable sensor nodes on the global decision, respectively. The numerical simulation results demonstrate that, compared to SPRT and weighted sequential probability ratio test (WSPRT), the proposed BDF has outstanding effects in terms of the error probability and average number of samples under various attack ratios and probabilities.

Coordination of the back flashover probability of HVAC and HVDC on a hybrid transmission tower

The demand for power transfer has increased throughout the green transition, especially as power generation is becoming increasingly decentralized. However, constructing new transmission lines and towers has met with public opposition. One option to increase transmission capacity while minimizing the erection of new towers is to use hybrid HVAC-HVDC multi-circuit towers. If not carefully designed, considerably more back flashovers could occur to the more vulnerable DC circuit. This paper investigates the effect of a change in insulator size on the ratio of back flashovers between AC and DC circuits on the same hybrid tower by using a PSCAD model with HVAC-HVDC hybrid towers. A back flashover ratio calculation method is developed and used in combination with an algorithm to provide a DC insulator length based on a predetermined back flashover ratio. The algorithm allows for faster design of the insulator sizes for a multi-circuit tower, coordinating the ratio of back flashover probabilities to either the HVAC or the HVDC circuit.

Improving the safety of radiotherapy treatment processes via incident-driven FMEA feedback loops.

Failure mode and effects analysis (FMEA) is a valuable tool for radiotherapy risk assessment, yet its outputs might be unreliable due to failures not being identified or due to a lack of accurate error rates. A novel incident reporting system (IRS) linked to an FMEA database was tested and evaluated. The study investigated whether the system was suitable for validating a previously performed analysis and whether it could provide accurate error rates to support the expert occurrence ratings of previously identified failure modes. Twenty-three pre-identified failure modes of our external beam radiotherapy process, covering the process steps from patient admission to treatment delivery, were proffered on dedicated FMEA feedback and incident reporting terminals generated by the IRS. The clinical setting involved a computed tomography scanner, dosimetry, and five linacs. Incoming reports were used as basis to identify additional failure modes or confirm initial ones. The Kruskal-Wallis H test was applied to compare the risk priorities of the retrospective and prospective failure modes. Wald's sequential probability ratio test was used to investigate the correctness of the experts' occurrence ratings by means of the number of incoming reports. Over a 15-month period, 304 reports were submitted. There were 0.005 (confidence interval [CI], 0.0014-0.0082) reported incidents per imaging study and 0.0006 (CI, 0.0003-0.0009) reported incidents per treatment fraction. Sixteen additional failure modes could be identified, and their risk priorities did not differ from those of the initial failure modes (p=0.954). One failure mode occurrence rating could be increased, whereas the other 22 occurrence ratings could not be disproved. Our approach is suitable for validating FMEAs and deducing additional failure modes on a continual basis. Accurate error rates can only be provided if a sufficient number of reports is available.

Implementing Component Degradations into a Modelica Model of an iPWR System to Develop Health Monitoring Techniques

The economic operation of small modular reactors will partly rely on managing and reducing inspection and maintenance activities while supporting new operational paradigms like load-following. Turbine control valves throttle the steam from the steam generator into the steam turbine while maintaining the pressure within the steam generator at a constant set point. Degradation of these components could impact the ability to manage electrical power production. Utilizing the Idaho National Laboratory Hybrid repository and the Oak Ridge National Laboratory TRANSFORM library developed for multiphysics simulations in Dymola/Modelica, an integral pressurized water reactor system was modeled based on the available specifications of the NuScale power module. The effects of various component degradation modes have been implemented into the model in order to simulate faulted plant data during both steady-state and load-following operations. The fault modes resemble different physical fault modes that may occur at an operating nuclear power plant; a leaking turbine control valve and a valve actuator failure due to loss of hydraulic pressure have been implemented. A neural network autoencoder is employed in conjunction with statistical analysis, namely, simple signal thresholding (SST) or sequential probability ratio testing (SPRT), to identify the presence of a fault. Fuzzy logic is additionally employed in a novel and promising manner to classify the state of the system based on the cumulative sum of the neural network residuals. SST and SPRT are both successfully validated using healthy data and proved capable of identifying both fault types; fuzzy logic identified the false positives and classified the faulted data correctly.

Food Environment After Implementation of a Healthy Checkout Policy

In March 2021, Berkeley, California, became the world's first jurisdiction to implement a healthy checkout policy, which sets nutrition standards for foods and beverages in store checkouts. This healthy checkout ordinance (HCO) has the potential to improve customers' dietary intake if stores comply by increasing the healthfulness of foods and beverages at checkouts. To compare the percentage of checkout products that were HCO compliant and that fell into healthy and unhealthy food and beverage categories before and 1 year after HCO implementation in Berkeley relative to comparison cities. In this cohort study in which Berkeley implemented an HCO and other cities did not, a difference-in-differences analysis was conducted of 76 258 product facings at checkouts of 23 stores in Berkeley and 75 stores in 3 comparison cities in California. Data were collected in February 2021 (approximately 1 month before implementation of the HCO) and 1 year later in February 2022 and analyzed from October 2023 to May 2024. The HCO, which permits only the following products at checkouts in large food stores: nonfood and nonbeverage products, unsweetened beverages, and foods with 5 g or less of added sugars per serving and 200 mg or less of sodium per serving in the following categories: sugar-free gum and mints, fruit, vegetables, nuts, seeds, legumes, yogurt or cheese, and whole grains. A product facing's (1) HCO compliance and (2) category, including healthy compliant categories and unhealthy noncompliant categories, determined using a validated photograph-based tool to assess product characteristics. Of the 76 258 product facings at store checkouts, the percentage that were HCO compliant increased from 53% (4438 of 8425) to 83% (5966 of 7220) in Berkeley, a 63% increase relative to comparison cities (probability ratio [PR], 1.63; 95% CI, 1.41-1.87). The percentage of food and beverage checkout facings that were HCO compliant increased in Berkeley from 29% (1652 of 5639) to 62% (2007 of 3261), a 125% increase relative to comparison cities (PR, 2.25; 95% CI, 1.80-2.82). The percentage of Berkeley food and beverage facings consisting of candy, sugar-sweetened beverages, and other sweets significantly decreased (candy: from 30% [1687 of 5639] to 6% [197 of 3261]; PR, 0.21; 95% CI, 0.10-0.42; sugar-sweetened beverages: from 11% [596 of 5639] to 5% [157 of 3261]; PR, 0.41; 95% CI, 0.23-0.75; other sweets: from 7% [413 of 5639] to 3% [101 of 3261]; PR, 0.37; 95% CI, 0.15-0.88), while the percentage consisting of unsweetened beverages (from 4% [226 of 5639] to 19% [604 of 3261]; PR, 4.76; 95% CI, 2.54-8.91) and healthy foods (from 6% [350 of 5639] to 20% [663 of 3261]; PR, 2.90; 95% CI, 1.79-4.72) significantly increased. This cohort study of the first healthy checkout policy found substantial improvements in the healthfulness of food environments at checkouts 1 year after implementation of the policy. These results suggest that healthy checkout policies have the potential to improve the healthfulness of store checkouts.

Development of a sequential sampling plan for classifying Thrips tabaci (Thysanoptera: Thripidae) populations in onion fields.

Onion thrips, Thrips tabaci Lindeman, is a global pest of onion crops, causing substantial economic damage by diminishing bulb yields and transmitting plant pathogens. Insecticides are used to manage T. tabaci infestations with control decisions traditionally based on action thresholds that require visually counting thrips on a fixed, predetermined number of onion plants per field. However, this approach for treatment decisions is inefficient when thrips populations are well above or below the action threshold. The aim of this research was to develop a sequential sampling plan that would provide a rapid and reliable classification of thrips populations in commercial onion fields above or below prespecified management thresholds. The study was conducted in a total of 24 commercial onion fields in New York in 2021 and 2022. Taylor's power law and Wald's Sequential Probability Ratio Test were used in concert to develop each sampling plan. Simulated and historical field data of thrips populations were used to further validate the efficacy of each sampling plan. Results demonstrated the sequential sampling plan required an average of 78% fewer samples to make a control decision compared with the traditional fixed-sampling approach. Treatment decisions were reached in 72% of cases after inspecting only 10 plants, while only 6% of the cases required examining more than 25 plants. Comparisons with fixed-sample sizes ranging from 23 to 68 plants revealed a 96% agreement in decision-making and a 78% reduction in sampling effort when using the sequential sampling plans.

A class of sequential multi-hypothesis tests

In this article, we deal with sequential testing of multiple hypotheses. In the general scheme of construction of optimal tests based on the backward induction, we propose a modification which provides a simplified (generally speaking, and suboptimal) version of the optimal test, for any particular criterion of optimization. We call this DBC version (the one with Dropped Backward Control) of the optimal test. In particular, for the case of two simple hypotheses, dropping backward control in the Bayesian test produces the classical sequential probability ratio test (SPRT). Similarly, dropping backward control in the modified Kiefer-Weiss solutions produces Lorden’s 2-SPRTs. In the case of more than two hypotheses, we obtain in this way new classes of sequential multi-hypothesis tests, and investigate their properties. The efficiency of the DBC-tests is evaluated with respect to the optimal Bayesian multi-hypothesis test and with respect to the matrix sequential probability ratio test (MSPRT) by Armitage. In a multihypothesis variant of the Kiefer-Weiss problem for binomial proportions the performance of the DBC-test is numerically compared with that of the exact solution. In a model of normal observations with a linear trend, the performance of the DBC-test is numerically compared with that of the MSPRT. Some other numerical examples are presented. In all the cases the proposed tests exhibit a very high efficiency with respect to the optimal tests (more than 99.3% when sampling from Bernoulli populations) and/or with respect to the MSPRT (even outperforming the latter in some scenarios).

Extremely high wall pressure events in shock wave and turbulent boundary layer interactions using DNS data

This study investigates high-amplitude Extreme Wall Pressure fluctuation Events (EWPEs) in Shock wave/Turbulent Boundary Layer Interactions (STBLIs) through the conditional sampling of direct numerical simulation databases. The aim is to evaluate the effect of STBLIs and their strength on the statistical properties and associated turbulent structures of EWPEs using the conditional-averaging and clustering method. The temporal statistical results show that the occurrence probability and contribution ratio of EWPEs decrease downstream of strong STBLI, but their duration and interval time increase. Regarding two-dimensional wall pressure structures, the large population of small-scale structures becomes more elongated, but strong interactions induce a greater number of large-scale structures. The pairing of wall pressure events with a higher occurrence probability is verified by the joint probability density functions. Conditional analysis reveals that, as the interaction strength increases, the ejection motion associated with positive events occurs farther downstream and the spanwise vortex core locating above negative events is lifted up along the wall-normal direction. Moreover, analysis associates the paired wall pressure events with the sweep, ejection, and swirl motions in STBLIs, where hairpin eddies play an important role in the formation of positive–negative paired wall pressure structures.