Probabilistic Results Research Articles

Four Decades of Carrier Detection and Prenatal Diagnosis in Hemophilia A: Historical Overview, State of the Art and Future Directions.

Hemophilia A (HA), a rare recessive X-linked bleeding disorder, is caused by either deficiency or dysfunction of coagulation factor VIII (FVIII) resulting from deleterious mutations in the F8 gene encoding FVIII. Over the last 4 decades, the methods aimed at determining the HA carrier status in female relatives of HA patients have evolved from phenotypic studies based on coagulation tests providing merely probabilistic results, via genetic linkage studies based on polymorphic markers providing more accurate results, to next generation sequencing studies enabling highly precise identification of the causative F8 mutation. In parallel, the options for prenatal diagnosis of HA have progressed from examination of FVIII levels in fetal blood samples at weeks 20-22 of pregnancy to genetic analysis of fetal DNA extracted from chorionic villus tissue at weeks 11-14 of pregnancy. In some countries, in vitro fertilization (IVF) combined with preimplantation genetic diagnosis (PGD) has gradually become the procedure of choice for HA carriers who wish to prevent further transmission of HA without the need to undergo termination of pregnancies diagnosed with affected fetuses. In rare cases, genetic analysis of a HA carrier might be complicated by skewed X chromosome inactivation (XCI) of her non-hemophilic X chromosome, thus leading to the phenotypic manifestation of moderate to severe HA. Such skewed XCI may be associated with deleterious mutations in X-linked genes located on the non-hemophilic X chromosome, which should be considered in the process of genetic counseling and PGD planning for the symptomatic HA carrier. Therefore, whole exome sequencing, combined with X-chromosome targeted bioinformatic analysis, is highly recommended for symptomatic HA carriers diagnosed with skewed XCI in order to identify additional deleterious mutations potentially involved in XCI skewing. Identification of such mutations, which may profoundly impact the reproductive choices of HA carriers with skewed XCI, is extremely important.

Probabilistic wind power forecasting for newly-built wind farms based on multi-task Gaussian process method

The accurate training of a wind power forecasting (WPF) model for a newly built wind farm is difficult because of limited historical data. This study established a multitask learning architecture wherein the WPF in different wind farms represents an independent task. Subsequently, a novel short-term WPF model based on a multitask learning architecture was proposed. In this model, a multitask Gaussian process is used to capture the intertask conjunction, which contributed to the training of each task. The proposed methodological framework employs dependencies from other tasks wherein older wind farms contain substantial historical data to enhance the performance of tasks in which there is a newly built wind farm. Several numerical experiments were conducted using datasets from seven independent wind farms in Australia. The results show that the proposed scheme not only obtains improved point forecasting results but also produces better probabilistic forecasting results, thus demonstrating the superiority of the proposed method.

Travel Time Probability Prediction Based on Constrained LSTM Quantile Regression

Travel time reliability assessment has been widely used in recent years to evaluate the performance of transportation networks and measure the operation level of transportation systems. Weather, as one of the important factors influencing travel time reliability, affects the relationship between the supply and requirement of urban road networks. Considering the traffic characteristics under different traffic conditions, a study on the influence of weather on travel time reliability under different conditions is proposed to predict the probability of travelers completing their trips within the expected time under different weather conditions. Based on the urban road network data and cab trajectory data of Harbin city, this paper correlates the floating vehicle location with the road network information through a hidden Markov model to reduce the influence of vehicle trajectory errors on the calculation results of path travel time. To analyze the entire distribution of extreme travel time and its impact on the reliability of travel time under various traffic situations, it captures the tail features of the travel time distribution based on extreme value theory. Then, to increase the predictability of each quantile, it combines a deep-learning LSTM model and a quantile regression model to create a probabilistic travel time prediction model utilizing combined layers. The proposed model is compared with the linear quantile regression and neural network quantile regression models, and the model is evaluated in terms of point prediction results and probabilistic prediction results, respectively, to ensure the accuracy of predictions from the model. As a result, the prediction accuracy of the model in this paper is greatly improved, and the degree of violating quantile constraints is greatly reduced.

Moments of moments of primes in arithmetic progressions

AbstractWe establish unconditional ‐results for all weighted even moments of primes in arithmetic progressions. We also study the moments of these moments and establish lower bounds under the Generalized Riemann Hypothesis (GRH). Finally, under GRH and the Linear Independence Hypothesis (LI), we prove an asymptotic for all moments of the associated limiting distribution, which, in turn, indicates that our unconditional and GRH results are essentially best possible. Using our probabilistic results, we formulate a conjecture on the moments with a precise associated range of validity, which we believe is also best possible. This last conjecture implies a ‐analog of the Montgomery‐Soundararajan conjecture on the Gaussian distribution of primes in short intervals. The ideas in our proofs include a novel application of positivity in the explicit formula and the combinatorics of arrays of characters that are fixed by certain involutions.

Development of dynamic integrated consequence evaluation (DICE) for dynamic event tree approaches: Numerical validation for a loss of coolant accident

Although conventional probabilistic safety assessment (PSA) makes a sufficient contribution to evaluating the safety of nuclear facilities, it suffers some limitations in performing optimal assessments close to the actual behavior by reflecting time dependencies in accident management. However, integrated deterministic and probabilistic safety assessment (IDPSA) literally combines two methodologies to enable synchronized evaluation based on physical behavior, system availability of facilities, and operator's response. Dynamic integrated consequence evaluation (DICE) is one of the IDPSA tools developed for this purpose, which is the first achievement in South Korea and supported by a regulatory authority. Based on dynamic discrete event tree (DDET) methodology, DICE consists of a scheduler that supports the exchange of information between modules, including a physical module that computes thermal-hydraulic simulations, a diagnosis module that specifies branching points for safety systems, and a reliability module that provides system availability. This paper deals with numerical validation comparing the conventional deterministic and probabilistic results for a sample scenario with those of DICE, and discusses an application of DICE to support and extend the scope of conventional PSA through a case study. It is expected that DICE emphasizes the compliance with conventional PSA methodologies while providing magnified perception in investigating unforeseen scenarios.

Reliability analysis of pile-reinforced slopes in width-limited failure mode considering three-dimensional spatial variation of soil strength

Stabilization pile is a common measurement for landslide mitigation. In previous literatures, the deterministic safety factor Fs method has been well established for pile-reinforced slope stability analysis, for example by limit analysis. However, the Fs method by itself cannot reflect the inherent uncertainty and spatial variability of mechanical properties of soil. This paper presents a probabilistic analysis procedure for width-constrained pile-reinforced slope where the failure pattern and soil spatial variability are both accounted for under three-dimensional (3D) condition. A modified discretization kinematic analysis-based mechanism is employed as the deterministic model. The spatial variability of cohesion c and friction angle φ is modeled as lognormal random fields by using the Karhunen–Loève expansion. The sparse polynomial chaos expansion (SPCE) is used to construct the meta-model to reduce the computational cost in high dimensional stochastic problems. The failure probability, probability density function (PDF), and other useful reliability results can be provided by performing Monte Carlo simulations of the proposed SPCE meta-model. Finally, the influences of soil spatial variability, slope geometry, and pile parameters on the slope reliability are analyzed. The combination of the modified discretization mechanism and SPCE provides a useful tool for the probabilistic analysis of pile-reinforced earth slopes under 3D condition. The probabilistic simulation results are also helpful for reliability design of pile-reinforced slope in practice.

The Invisible Reality of Quantum Mechanics: The ‎‎‎Deterministic Perspective

The fundamental deterministic nature of quantum mechanics (QM) is mathematically demonstrated by the modeling of the ‎‎‎quantum (multiple) slit experiments; hence this paper is written from a deterministic perspective (DP) in quantum mechanics.‎ ‎Due to approximately 90 years of indeterminism and probabilistic statistical results, the theory consists of many ‎‎‎interpretations and is often regarded as counterintuitive. The latter is in the deterministic perspective not the case and is ‎‎‎illustrated with some examples. After a brief historic perspective, ‘invisible’ i.e. invisible entities of reality in mathematical ‎‎‎treatment, are introduced. These entities are handled by mathematics indirectly i.e. are described in a transformed domain ‎‎‎without variables violating the Heisenberg relation. In nature, i.e. on micro and macro levels, causality is fully ‘entangled’ with ‎‎‎energy, information - in the meaning of ordering or coding - as well as time. In contrast with the macro scale with many forms ‎‎‎and types of memory functions, without a memory property of quanta, causality is the bearer of information symmetry on ‎‎the ‎quantum scale. Further on in this DP paper: mathematical and philosophical consequences and influences in several ‎‎‎paragraphs, regarding subjects such as ‘free will’ and expected ‘threats to science’, the Bell inequalities, Alice and Bob & ‎‎‎entanglement, causality, information, retro-causality, spooky action, encryption and computing, teleportation, and in general ‎‎‎interpretations rooted in indeterminacy in QM as well as associated topics on independence, fine-tuning. The last paragraph ‎‎‎outlines the mathematical treatment of QM more extensively and may clarify references to the above-mentioned topics of ‎‎‎discussion in QM further.‎

Probabilistic Stability Design Charts for Shallow Passive Trapdoors in Spatially Variable Clays

Geotechnical engineers are faced with great uncertainty with regard to the stability design of soil structures such as retaining walls, foundations, and slope stability. Instead of using a deterministic approach by replacing the design parameter with a single mean number, Monte Carlo simulations could be used to provide better decisions by considering all possible outcomes under parametric uncertainty. This paper studies probabilistic failures of classical passive trapdoors in shallow depths with spatially random soils. The effects of soil strength variability are investigated for various spatial correlation lengths and trapdoor depths using the latest adaptive finite-element upper-bound limit analysis with second-order cone programming. In addition, probabilistic stability results are compared with those published in renowned literature, and a comprehensive probability of design failure (PF) charts is developed for a practical range of deterministic factors of safety. The extensive results reported in this paper would be of great interest to engineering practitioners because better decisions can be made in the design process and design confidence improved.

Human Emotion Detection Using Deep Learning

Abstract: Human emotions are the mental state of feelings and are spontaneous. There is no clear connection between emotions and facial expressions and there is significant variability making facial recognition a challenging research area. Emotion recognition becomes a popular topic of deep learning and provides more application fields in our daily life. The primary idea of our project is to process the input imagesof human facial emotion to train the pre-trained models on datasets. In recent years, Machine Learning (ML) and Neural Networks (NNs) have been used for emotion recognition. In this project, a Convolutional Neural Network (CNN) is used toextract features from images to detect emotions. The numerical result of the algorithm will show a probabilistic result of each labeled class.

Probabilistic Modeling and Uncertainty Quantification of Detailed Combustion Simulation for a Swirl Stabilized Spray Burner

To enable risk informed decisions in the simulation-based design and development of novel combustors, uncertainties in the simulation results must be considered. However, due to the high computational costs for their quantification, these uncertainties are commonly not taken into account. Therefore, this work aims at applying an efficient methodology for uncertainty quantification based on Polynomial Chaos Expansion to a semi-technical spray burner reflecting characteristics typically found in modern aeroengine combustors. This requires accurate treatment of the multicomponent liquid fuel, a combustion model relying on finite rate chemistry and a scale resolving hybrid turbulence model to account for highly unsteady flow features and combustion. To overcome the need for costly experimental data for the spray boundary conditions, an algebraic primary breakup model is utilized. The resulting reduction in a priori information is compensated through probabilistic modeling and uncertainty quantification. Due to their importance in the design process, temperature distribution in the gas phase as well as the flame position are considered as the primary quantities of interest. For these quantities of interest, moderate uncertainties are found in the probabilistic simulation results. Further, the predictive capability of the simulation model under uncertainties is quantitively assessed by defining accurary metrics for the gas phase temperature prediction. The study further reveals that the imposed input uncertainties affect quantities of interest in both the dispersed and the gas phase through phase coupling effects.

Robust Additive Value-Based Efficiency Analysis with a Hierarchical Structure of Inputs and Outputs

We introduce a novel methodological framework based on additive value-based efficiency analysis. It considers inputs and outputs organized in a hierarchical structure. Such an approach allows us to decompose the problem into manageable pieces and determine the analyzed units’ strengths and weaknesses. We provide robust outcomes by analyzing all feasible weight vectors at different hierarchy levels. The analysis concerns three complementary points of view: distances to the efficient unit, ranks, and pairwise preference relations. For each of them, we determine the exact extreme results and the distribution of probabilistic results. We apply the proposed method to a case study concerning the performance of healthcare systems in sixteen Polish voivodeships (provinces). We discuss the results based on the entire set of factors (the root of the hierarchy) and three subcategories. They concern health improvement of inhabitants, efficient financial management, and consumer satisfaction. Finally, we show the practical conclusions that can be derived from the hierarchical decomposition of the problem and robustness analysis.

Cost-Effectiveness of Cerebrolysin after Ischemic Stroke: Secondary Analysis of the CARS Study.

The cost-effectiveness of Cerebrolysin as an add-on therapy for moderate-severe acute ischemic stroke is a topic that remains understudied. This study aims to address this gap by performing a comprehensive cost-utility analysis using both deterministic and probabilistic methods from a payer perspective and within the Romanian inpatient care setting. Quality-adjusted life years (QALYs) were calculated using partial individual patient data from the 2016 Cerebrolysin and Recovery After Stroke (CARS) trial, utilizing three different health state valuation models. Cost data was extracted from actual acute care costs reported by Romanian public hospitals for reimbursement purposes for patients included in the CARS study. Incremental cost-effectiveness ratios were calculated for each treatment arm for the duration of the clinical trial. Deterministic analysis based on sample mean values indicates Cerebrolysin would be cost-effective at a threshold between roughly 18.8 and 29.9 thousand EUR, depending on valuation techniques. Probabilistic sensitivity analysis results indicate an 80% chance probability of cost-effectiveness of Cerebrolysin as an add-on therapy for acute ischemic stroke, considering a willingness-to-pay threshold of 50,000 EUR in a 90-day timeframe after stroke. Further economic evaluations of Cerebrolysin are needed to strengthen these findings, covering a timeframe of at least 12 months after the acute incident, which would account for treatment effects spanning beyond the first 90 days after ischemic stroke. These should be conducted to determine its cost-effectiveness under various care settings and patient pathways. Most importantly, modelling techniques are needed to answer important questions such as the estimates of population gain in QALYs after acute administration of Cerebrolysin and the potential offsetting of direct medical costs as a result of administering the intervention.

Cost‑Effectiveness of Lorlatinib in First-Line Treatment of Adult Patients with Anaplastic Lymphoma Kinase (ALK)‑Positive Non‑Small‑Cell Lung Cancer in Sweden.

We aimed to investigate the cost effectiveness of lorlatinib, a third-generation anaplastic lymphoma kinase (ALK) tyrosine kinase inhibitor (TKI), used first-line in Sweden to treat patients with ALK-positive (ALK+) non-small cell lung cancer (NSCLC). In January 2022, the European Medicines Agency (EMA) extended its approval of lorlatinib to include adult patients with ALK+ NSCLC not previously treated with an ALK inhibitor. Extended first-line approval was based on results from CROWN, a phase III randomized trial that enlisted 296 patients randomized 1:1 to receive lorlatinib or crizotinib. Our analysis compared lorlatinib against the first-generation ALK-TKI crizotinib, and second-generation ALK TKIs alectinib and brigatinib. A partitioned survival model with four health states [pre-progression, non-intracranial (non-central nervous system [CNS]) progression, CNS progression, and death] was constructed. The progressed disease state (which is typically modelled in cost-effectiveness analyses of oncology treatments) was explicitly separated into non-CNS and CNS progression as brain metastases, which are common in NSCLC, and can have a large impact on patient prognosis and health-related quality of life. Treatment effectiveness estimates in the lorlatinib and crizotinib arms of the model were derived from CROWN data, while indirect relative effectiveness estimates for alectinib and brigatinib were informed using network meta-analysis (NMA). Utility data were derived from the CROWN study in the base case, and cost-effectiveness results were compared when applying UK and Swedish value sets. Costs were obtained from Swedish national data. Deterministic and probabilistic sensitivity analyses were conducted to test model robustness. Fully incremental analysis identified crizotinib as the least costly and least effective treatment. Brigatinib was extendedly dominated by alectinib and, subsequently, alectinib was extendedly dominated by lorlatinib. Lorlatinib was associated with an incremental cost-effectiveness ratio (ICER) of Swedish Krona (SEK) 613,032 per quality-adjusted life-year (QALY) gained compared with crizotinib. Probabilistic results were generally consistent with deterministic results, and one-way sensitivity identified NMA HRs, alectinib and brigatinib treatment duration, and the CNS-progressed utility multiplier as key model drivers. The ICER of SEK613,032 for lorlatinib versus crizotinib falls below the typical willingness-to-pay threshold per QALY gained for high-severity diseases in Sweden (approximately SEK1,000,000). Furthermore, as brigatinib and alectinib were extendedly dominated in the incremental analysis, the results of our study indicate that lorlatinib may be considered a cost-effective treatment option for first-line patients with ALK+ NSCLC in Sweden when compared with crizotinib, alectinib, and brigatinib. Longer-term follow-up data for endpoints informing treatment effectiveness for all first-line treatments would help to reduce uncertainty in the findings.

Stochastic Navier–Stokes variational inequalities with unilateral boundary conditions: probabilistic weak solvability

UDC 519.21 We initiate the investigation of stochastic Navier–Stokes variational inequalities involving unilateral boundary conditions and nonlinear forcings driven by Wiener processes for which we establish the existence of a probabilistic weak (or martingale) solution. Our approach involves an intermediate penalized problem whose weak solution is obtained by means of Galerkin's method in combination with some analytic and probabilistic compactness results. The required probabilistic weak solution of the stochastic Navier–Stokes variational inequality is consecutively obtained through the limit transition in the penalized problem. The main result is new for stochastic Navier–Stokes variational inequalities. It is a stochastic counterpart of the work of Brezis on deterministic Navier–Stokes variational inequalities and generalizes several previous results on stochastic Navier-Stokes equations to stochastic Navier–Stokes variational inequalities with unilateral boundary conditions.

Step-wise segment partition based stationary subspace analysis and Gaussian mixture model for nonstationary process performance assessment

This article focuses on solving the problem of performance assessment for nonstationary processes without significant cointegrated correlations, which is a basic assumption of traditional methods. The time axis is replaced by indicator axis of working condition. Thus, the irregular non-stationarity along time axis could turns to be typical piecewise stationarity along indicator axis of working condition. The proposed method provides a general tool to deal with non-stationarities and relax the cointegrated restriction on variable correlations. Since a nonstationary process has specific working patterns under different conditions, the process can thus be divided into multiple segments along the axis of working condition. To characterize the properties of different performances within a segment meticulously, random sampling-based stationary subspace analysis (SSA) is conducted to separate the Gaussian and non-Gaussian subspaces. Since the operating performance is mainly distinguied by the non-Gaussian information, the non-Gaussian subspace obtained by SSA is further characterized by Gaussian mixture model (GMM). For online application, the segment model is selected by the indicator of working condition, and then the performance is assessed using Bayesian inference to provide a probabilistic result. The efficacy of the proposed method is validated by a coal mill from a real thermal power plant.

Explainable artificial intelligence in geoscience: A glimpse into the future of landslide susceptibility modeling

For decades, the distinction between statistical models and machine learning ones has been clear. The former are optimized to produce interpretable results, whereas the latter seeks to maximize the predictive performance of the task at hand. This is valid for any scientific field and for any method belonging to the two categories mentioned above. When attempting to predict natural hazards, this difference has lead researchers to make drastic decisions on which aspect to prioritize, a difficult choice to make. In fact, one would always seek the highest performance because at higher performances correspond better decisions for disaster risk reduction. However, scientists also wish to understand the results, as a way to rely on the tool they developed. Today, very recent development in deep learning have brought forward a new generation of interpretable artificial intelligence, where the prediction power typical of machine learning tools is equipped with a level of explanatory power typical of statistical approaches. In this work, we attempt to demonstrate the capabilities of this new generation of explainable artificial intelligence (XAI). To do so, we take the landslide susceptibility context as reference. Specifically, we build an XAI trained to model landslides occurred in response to the Gorkha earthquake (April 25, 2015), providing an educational overview of the model design and its querying opportunities. The results show high performance, with an AUC score of 0.89, while the interpretability can be extended to the probabilistic result assigned to single mapping units.

Simplex-Based Proximal Multicategory Support Vector Machine

The multicategory support vector machine (MSVM) has been widely used for multicategory classification. Despite its widespread popularity, regular MSVM cannot provide direct probabilistic results and suffers from excessive computational cost, as it is formulated on the hinge loss function and it solves a sum-to-zero constrained quadratic programming problem. In this study, we propose a general refinement of regular MSVM, termed as the simplex-based proximal MSVM (SPMSVM). Our SPMSVM uses a novel family of squared error loss functions in place of the hinge loss and it removes the explicit sum-to-zero constraint by the simplex structure. Consequently, the SPMSVM only requires solving an unconstrained linear system, leading to closed-form solutions. In addition, the SPMSVM can be cast into a weighted regression problem so that it is scalable for large-scale applications. Moreover, the SPMSVM naturally yields an estimate of the conditional category probability, which is more informative than regular MSVM. Theoretically, the SPMSVM is shown to include many existing MSVMs as its special cases, and its asymptotic and finite-sample statistical properties are well established. Simulations and real examples show that the proposed SPMSVM is a stable, scalable and competitive classifier.

Shannon information entropy, soliton clusters and Bose-Einstein condensation in log gravity

We give a probabilistic interpretation of the configurational partition function of the logarithmic sector of critical cosmological topologically massive gravity, in which the Hurwitz numbers considered in our previous works assume the role of probabilities in a distribution on cycles of permutations. In particular, it is shown that the permutations are distributed according to the Ewens sampling formula which plays a major role in the theory of partition structures and their applications to diffusive processes of fragmentation, and in random trees. This new probabilistic result together with the previously established evidence of solitons in the theory provide new insights on the instability originally observed in the theory. We argue that the unstable propagation of a seed soliton at single particle level induces the generation of fragments of defect soliton clusters with rooted tree configuration at multiparticle level, providing a disordered landscape. The Shannon information entropy of the probability distribution is then introduced as a measure of the evolution of the unstable soliton clusters generated. Finally, based on Feynman’s path integral formalism on permutation symmetry in the λ-transition of liquid helium, we argue that the existence of permutation cycles in the configurational log partition function indicates the presence of Bose-Einstein condensates in log gravity.

Quantification of the effects of different uncertainty sources on the seismic fragility functions of masonry-infilled RC frames

The presence of masonry infills is known to have a significant effect when assessing the seismic vulnerability of reinforced concrete (RC) structures, and including these elements in the numerical modelling has become imperative. In computationally-intense probabilistic analyses such as those integrated in performance-based earthquake engineering (PBEE) frameworks, the simulation of the masonry infills is often performed using the single strut approach/technique. Despite the advantages of this modelling approach, it can be related to several sources of uncertainty that can impact probabilistic performance results such as fragility functions. In this context, the proposed study examines the effect of the uncertainty associated to the parameters of the strut model representing the infills, and to the definition of global limit state thresholds reflecting the lateral deformation capacity of infilled structures. The study considers RC structures of different sizes and with different infill configurations, and the relative importance of both sources of uncertainty is analysed by comparing fragility functions defined for different limit states. The comparisons are first performed qualitatively followed by a statistical analysis based on the results of several two-sample tests. Results indicate that, depending on the infill modelling options and on the way limit state values are considered, the corresponding fragility functions can be significantly different. These results highlight the need for further research dedicated to the uncertainty quantification and propagation associated with limit state values for infilled structures and with empirical models that provide parameters for simulating the behaviour of infills under earthquake loading.

A cognition‐inspired trajectory prediction method for vehicles in interactive scenarios

AbstractTrajectory prediction of the ego vehicle is necessary for the cooperation driving of intelligent vehicles and drivers. Methods based on deep learning can fit complex functions, but they usually focus on vehicles' behavioral characteristics. However, vehicles' trajectories are closely related to the cognition results of drivers. Therefore, based on drivers' cognitive characteristics, a network model is designed to predict vehicle trajectories. Specifically, in the perception stage, featured grids are used that are in the driver's view to encode perceptual information; in the decision stage, convolution and graph attention operations are combined to model the driver's interaction with the surrounding traffic elements; in the motion stage, the elements are constrained in one hidden layer by vehicles' actual control inputs and design the corresponding method to obtain probabilistic results. With experiments in two typical scenarios, including intersection and roundabout, the proposed method can obtain reasonable prediction accuracy and generalizability. Meanwhile, abundant experiments are conducted and the results are compared, which reveal some common problems when predicting vehicle trajectories, particularly based on drivers' cognitive characteristics. These lessons learned from this study are summarized which may be useful for newcomers.