Probabilistic Scaling Research Articles

Translation and validation of the Visual Function and Corneal Health Status (V-FUCHS) questionnaire into Spanish language

PurposeTo translate and validate the V-FUCHS questionnaire into Spanish in a population of patients with Fuchs endothelial dystrophy (DEF). MethodsThe V-FUCHS consists of 15 short, easily understandable questions that assess visual aspects of quality of life in patients with DEF, which can be gathered into a group of seven that assess the "Visual Difficulty" factor and another group of eight that assess the “Glare Factor”. For the translation and cultural adaptation, the standardized norms for this process were followed, among other phases, a translation, a back-translation and an application in patients with DEF. ResultsIn the first phase, consensus was reached on the Spanish translation of the V-FUCHS. Subsequently, 25 patients were included to carry out the pre-test phase with the aim of assessing the applicability and feasibility of the test. The score obtained a minimum value of -0.88 and a maximum value of +2.44, according to the Rasch probabilistic scale. The mean value obtained from the Visual Difficulty factor was 0.61 (±0.71), while the mean for the Glare Factor was 0.41 (±0.51). ConclusionThe validation of the V-FUCHS questionnaire, after its translation and adaptation into Spanish, proved to be a useful tool for assessing the visual quality of patients with DEF. Patients with a more advanced stage of the disease presented a greater severity in the test result. Likewise, the Glare Factor (Glare) correlates better with the pachymetric increase than with the visual acuity of the patient.

Traducción y validación del cuestionario Visual Function and Corneal Health Status (V-FUCHS) al idioma castellano

PurposeTo translate and validate the V-FUCHS questionnaire into Spanish in a population of patients with Fuchs endothelial dystrophy (DEF). MethodsThe V-FUCHS consists of 15 short, easily understandable questions that assess visual aspects of quality of life in patients with DEF, which can be gathered into a group of seven that assess the “Visual Difficulty” factor and another group of eight that assess the “Glare Factor”. For the translation and cultural adaptation, the standardized norms for this process were followed, among other phases, a translation, a back-translation and an application in patients with DEF. ResultsIn the first phase, consensus was reached on the Spanish translation of the V-FUCHS. Subsequently, 25 patients were included to carry out the pre-test phase with the aim of assessing the applicability and feasibility of the test. The score obtained a minimum value of −0.88 and a maximum value of +2.44, according to the Rasch probabilistic scale. The mean value obtained from the Visual Difficulty factor was 0.61 (±0.71), while the mean for the Glare factor was 0.41 (±0.51). ConclusionThe validation of the V-FUCHS questionnaire, after its translation and adaptation into Spanish, proved to be a useful tool for assessing the visual quality of patients with DEF. Patients with a more advanced stage of the disease presented a greater severity in the test result. Likewise, the Glare factor (Glare) correlates better with the pachymetric increase than with the visual acuity of the patient.

Fitting with matrix exponential mixtures generated by discrete probabilistic scaling

Matrix exponential (ME) distributions generalize phase-type distributions; however, their use in queueing theory is hampered by the difficulty of checking their feasibility. We propose a novel ME fitting algorithm that produces a valid distribution by construction. The ME distribution used during the fitting is a product of independent random variables that are easy to control in isolation. Consequently, the calculation of the CDF and the Mellin transform factorizes, making it possible to use these measures for the fitting without significant restriction on the distribution order. Trace-driven queueing simulations indicate that the resulting distributions yield highly accurate results.

Predicting the Risk of Mortality in Children using a Fuzzy-Probabilistic Hybrid Model.

Introduction The mortality risk in children admitted to Pediatric Intensive Care Units (PICU) is usually estimated by means of validated scales, which only include objective data among their items. Human perceptions may also add relevant information to prognosticate the risk of death, and the tool to use this subjective data is fuzzy logic. The objective of our study was to develop a mathematical model to predict mortality risk based on the subjective perception of PICU staff and to evaluate its accuracy compared to validated scales. Methods A prospective observational study in two PICUs (one in Spain and another in Latvia) was performed. Children were consecutively included regardless of the cause of admission along a two-year period. A fuzzy set program was developed for the PICU staff to record the subjective assessment of the patients' mortality risk expressed through a short range and a long range, both between 0% and 100%. Pediatric Index of Mortality 2 (PIM2) and Therapeutic Intervention Scoring System 28 (TISS28) were also prospectively calculated for each patient. Subjective and objective predictions were compared using the logistic regression analysis. To assess the prognostication ability of the models a stratified B-random K-fold cross-validation was performed. Results Five hundred ninety-nine patients were included, 308 in Spain (293 survivors, 15 nonsurvivors) and 291 in Latvia (282 survivors, 9 nonsurvivors). The best logistic classification model for subjective information was the one based on MID (midpoint of the short range), whereas objective information was the one based on PIM2. Mortality estimation performance was 86.3% for PIM2, 92.6% for MID, and the combination of MID and PIM2 reached 96.4%. Conclusions Subjective assessment was as useful as validated scales to estimate the risk of mortality. A hybrid model including fuzzy information and probabilistic scales (PIM2) seems to increase the accuracy of prognosticating mortality in PICU.

A correspondence between the multifractal model of turbulence and the Navier-Stokes equations.

The multifractal model of turbulence (MFM) and the three-dimensional Navier-Stokes equations are blended together by applying the probabilistic scaling arguments of the former to a hierarchy of weak solutions of the latter. This process imposes a lower bound on both the multifractal spectrum [Formula: see text], which appears naturally in the Large Deviation formulation of the MFM, and on [Formula: see text] the standard scaling parameter. These bounds respectively take the form: (i) [Formula: see text], which is consistent with Kolmogorov's four-fifths law ; and (ii) [Formula: see text]. The latter is significant as it prevents solutions from approaching the Navier-Stokes singular set of Caffarelli, Kohn and Nirenberg. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Chance-constrained sets approximation: A probabilistic scaling approach

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then scales these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problems in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.

Prediction Error Quantification Through Probabilistic Scaling

In this letter, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.

Random tensors, propagation of randomness, and nonlinear dispersive equations

We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global strong solutions for the nonlinear Schrödinger equations in dimension two, arXiv:1910.08492), to study the propagation of randomness under nonlinear dispersive equations. By applying this theory we establish almost-sure local well-posedness for semilinear Schrödinger equations in the full subcritical range relative to the probabilistic scaling (Theorem 1.1). The solution we construct has an explicit expansion in terms of multilinear Gaussians with adapted random tensor coefficients. As a byproduct we also obtain new results concerning regular data and long-time solutions, in particular Theorem 1.6, which provides long-time control for random homogeneous data, demonstrating the highly nontrivial fact that the first energy cascade happens at a much later time than in the deterministic setting. In the random setting, the probabilistic scaling is the natural scaling for dispersive equations, and is different from the natural scaling for parabolic equations. Our theory of random tensors can be viewed as the dispersive counterpart of the existing parabolic theories (regularity structures, para-controlled calculus and renormalization group techniques).

Ensemble forecasting system for the management of the Senegal River discharge: application upstream the Manantali dam

Providing useful inflow forecasts of the Manantali dam is critical for zonal consumption and agricultural water supply, power production, flood and drought control and management (Shin et al., Meteorol Appl 27:e1827, 2019). Probabilistic approaches through ensemble forecasting systems are often used to provide more rational and useful hydrological information. This paper aims at implementing an ensemble forecasting system at the Senegal River upper the Manantali dam. Rainfall ensemble is obtained through harmonic analysis and an ARIMA stochastic process. Cyclical errors that are within rainfall cyclical behavior from the stochastic modeling are settled and processed using multivariate statistic tools to dress a rainfall ensemble forecast. The rainfall ensemble is used as input to run the HBV-light to product streamflow ensemble forecasts. A number of 61 forecasted rainfall time series are then used to run already calibrated hydrological model to produce hydrological ensemble forecasts called raw ensemble. In addition, the affine kernel dressing method is applied to the raw ensemble to obtain another ensemble. Both ensembles are evaluated using on the one hand deterministic verifications such the linear correlation, the mean error, the mean absolute error and the root-mean-squared error, and on the other hand, probabilistic scores (Brier score, rank probability score and continuous rank probability score) and diagrams (attribute diagram and relative operating characteristics curve). Results are satisfactory as at deterministic than probabilistic scale, particularly considering reliability, resolution and skill of the systems. For both ensembles, correlation between the averages of the members and corresponding observations is about 0.871. In addition, the dressing method globally improved the performances of ensemble forecasting system. Thus, both schemes system can help decision maker of the Manantali dam in water resources management.

CBIR aided classification using extreme learning machine with probabilistic scaling in MRI brain image

AbstractAn enormous number of magnetic resonance imaging (MRI) brain images were produced in hospitals and several MRI centers. To exploit the diagnosis in MRI brain image, “content-based image retrieval (CBIR)” system is accessed in the MRI brain image database. In this paper, a content-based MRI brain image retrieval system is presented, which is helpful in the medical field to seek a diagnosis in an MRI brain image that is similar to the example given. This paper consists of preprocessing, feature extraction, feature selection, similarity measure, and classification. In the preprocessing phase, the Wiener filter is used to remove the unwanted pixels from an MRI brain image. In the second phase, the features related to MRI brain image are extracted using characteristics of shape, margin, and density of the MRI. In the third stage, the features of MRI brain image were reduced using principal component analysis. CBIR classification is used in this method to gain effectual results. In the first stage, retrieval images are obtained using similarity measures using the similarity between the query image features and the derived trained image features. Finally, the classification stage is an extreme learning machine with probabilistic scaling used to classify the obtained retrieval output image and the query image. The result demonstrates that the proposed CBIR approach is robust and effectual compared with other latest work.

Men's Beliefs About the Likelihood of Serodiscordance in Couples with an HIV-Positive Partner: Survey Evidence from Rural Uganda.

Few studies in sub-Saharan Africa have assessed men's knowledge about the likelihood of serodiscordance in couples with an HIV-positive partner and how this is affected by antiretroviral therapy (ART). Using a Likert scale and probabilistic scale, we elicited beliefs of 2532 rural Ugandan men about the likelihood of seroconcordance in married couples with an HIV-positive female partner who is either taking ART or not taking ART. Logistic regression analyses explored associations between beliefs and various health behaviors. Probabilistic scale responses were consistent with Likert scale responses. Seroconcordance was believed to be likely in the scenarios without ART and with ART, with mean seroconcordance likelihood of 8.1 and 6.6, respectively, on a scale of 0-10. The majority of participants (57%) believed the likelihood of seroconcordance was lower in the scenario with ART. The results suggest a need for enhanced education among men about serodiscordance in stable relationships and about the preventive effects of ART.

Scaling limits for super-replication with transient price impact

We prove a scaling limit theorem for the super-replication cost of options in a Cox–Ross–Rubinstein binomial model with transient price impact. The correct scaling turns out to keep the market depth parameter constant while resilience over fixed periods of time grows in inverse proportion with the duration between trading times. For vanilla options, the scaling limit is found to coincide with the one obtained by PDE-methods in (Math. Finance 22 (2012) 250–276) for models with purely temporary price impact. These models are a special case of our framework and so our probabilistic scaling limit argument allows one to expand the scope of the scaling limit result to path-dependent options.

English

This study presents an ensemble stream flow simulation with probability of occurrence accounting for errors of the GR4J turned to the Senegal River upper the Manantali dam. Through this approach, probability is associated to simulation at each time, with step and reliability of issues depending on probability scores. Results including the reliability of the results permit decision-makers to judge the reliability of their simulations. Past errors pattern of the model is used to perturb the model for issuing ensemble scenarios rather than classical single deterministic. Basic and reverse Box-Cox transformation is carried out to allow treatment of the errors through weighted multivariate Gaussian distribution. Statistic errors are then used to perturb the hydrological model to obtain ensemble issues (RAW-Ens). Furthermore, a post-processing method (affine kernel dressing) is performed to produce a dressed ensemble (AKD-Ens). Ensembles are evaluated at deterministic and probabilistic scale. Diagrams (attribute and ROC) are also used for this purpose. Evaluating methods reveal through scores that the system is reliable and that dressing method (AKD) improves quality of the raw ensemble drawn from the perturbed model. Key words: Senegal River, Bafing, Manantali dam, Ensemble simulation, Kernel dressing.

Unifying Particle‐Based and Continuum Models of Hillslope Evolution With a Probabilistic Scaling Technique

Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters that can be calibrated using available topographical data. This contrasts the use of particle‐based models, which may be more difficult to calibrate but are simpler and easier to implement and have the potential to provide insight into the statistics of grain motion. The realms of individual particles and the continuum, while disparate in geomorphological modeling, can be connected using scaling techniques commonly employed in probability theory. Here we motivate the choice of a particle‐based model of hillslope evolution, whose stationary distributions we characterize. We then provide a heuristic scaling argument, which identifies a candidate for their continuum limit. By simulating instances of the particle model, we obtain equilibrium hillslope profiles and probe their response to perturbations. These results provide a proof of concept in the unification of microscopic and macroscopic descriptions of hillslope evolution through probabilistic techniques and simplify the study of hillslope response to external influences.

빅 데이터의 자율 속성 감축을 위한 확장된 정보 엔트로피 기반 상관척도

고객 유형 분석에 쓰이는 다양한 데이터 분석 방법은 고객들을 위한 맞춤형 콘텐츠를 기획하고, 보다 편리한 서비스를 제공하기 위하여 고객들의 유형과 특성을 정확히 파악하는 것이 매우 중요하다. 본 논문에서는 정보의 손실을 줄이기 위한 일환으로 정보 엔트로피를 확장하여 속성의 불확실성을 이용한 k-modes 군집분석 알고리즘을 제안한다. 따라서 속성에 대한 유사도의 측정은 두 가지의 측면에서 고려되어진다. 하나는 각 분할의 중심에 대한 각 속성간의 불확실성을 측정하는 것이고, 다른 하나는 각 속성이 가지는 불확실성에 대한 확률적 분포에 대한 불확실성을 측정하는 것이다. 특히 속성내의 불확실성은 속성의 엔트로피를 확률적 정보로 변환하여 불확실성을 측정하기 때문에 최종적인 불확실성은 비확률적인 척도와 확률적인 척도에서 고려되어 진다. 여러 실험과 척도를 통하여 제안한 알고리즘의 정확도가 최적의 초기치를 기반으로 군집분석을 수행한 결과에 준수함을 보인다. Various data analysis methods used for customer type analysis are very important for game companies to understand their type and characteristics in an attempt to plan customized content for our customers and to provide more convenient services. In this paper, we propose a k-mode cluster analysis algorithm that uses information uncertainty by extending information entropy to reduce information loss. Therefore, the measurement of the similarity of attributes is considered in two aspects. One is to measure the uncertainty between each attribute on the center of each partition and the other is to measure the uncertainty about the probability distribution of the uncertainty of each property. In particular, the uncertainty in attributes is taken into account in the non-probabilistic and probabilistic scales because the entropy of the attribute is transformed into probabilistic information to measure the uncertainty. The accuracy of the algorithm is observable to the result of cluster analysis based on the optimal initial value through extensive performance analysis and various indexes.

Influence of Flow Velocity on Tsunami Loss Estimation

Inundation depth is commonly used as an intensity measure in tsunami fragility analysis. However, inundation depth cannot be taken as the sole representation of tsunami impact on structures, especially when structural damage is caused by hydrodynamic and debris impact forces that are mainly determined by flow velocity. To reflect the influence of flow velocity in addition to inundation depth in tsunami risk assessment, a tsunami loss estimation method that adopts both inundation depth and flow velocity (i.e., bivariate intensity measures) in evaluating tsunami damage is developed. To consider a wide range of possible tsunami inundation scenarios, Monte Carlo-based tsunami simulations are performed using stochastic earthquake slip distributions derived from a spectral synthesis method and probabilistic scaling relationships of earthquake source parameters. By focusing on Sendai (plain coast) and Onagawa (ria coast) in the Miyagi Prefecture of Japan in a case study, the stochastic tsunami loss is evaluated by total economic loss and its spatial distribution at different scales. The results indicate that tsunami loss prediction is highly sensitive to modelling resolution and inclusion of flow velocity for buildings located less than 1 km from the sea for Sendai and Onagawa of Miyagi Prefecture.

Ranges of the validity of power scaling laws in the description of scale effects of the strength of extended elements of machines and structures

The ranges of the validity of power laws to describe the scale effect of the strength of machine parts and structural elements are evaluated based on the probabilistic-statistical approach to analyzing the scale effect. For small structures, it is necessary to refute the basic assumption of Weibull’s theory on the statistical independence of the values of local strength at various points of structures and transition to using the mathematical model of random field of local strength, which makes it possible to take into account the correlation of strength properties of material in closely spaced points of structure. The derived results underlay the creation of the combined probabilistic scaling law of strength.

Quantile universal threshold

Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to zero, estimators such as lasso, elastic net and subset selection perform variable selection. One crucial step challenges all these estimators: the amount of thresholding governed by a threshold parameter $\lambda $. If too large, important features are missing; if too small, incorrect features are included. Within a unified framework, we propose a selection of $\lambda $ at the detection edge. To that aim, we introduce the concept of a zero-thresholding function and a null-thresholding statistic, that we explicitly derive for a large class of estimators. The new approach has the great advantage of transforming the selection of $\lambda $ from an unknown scale to a probabilistic scale. Numerical results show the effectiveness of our approach in terms of model selection and prediction.

Material and Geometric Heterogeneity Consideration for Cracking Risk Prediction of Young Age Behavior of Experimental Massive Reinforced Concrete Structure

This article presents the application of a thermo-hydro-chemo-mechanical (THCM) model to a real complex structure of reactor confinement (mock-up VERCORS from EDF) by taking into account the specificities of the construction (construction consequences), the distributed reinforcements and the material heterogeneity of massive structure. The experimental campaigns were conducted during and after the construction of VERCORS. The early-age behavior of concrete is first modelled based on a multiphasic hydration model to ensure the thermal evolution. Then a 3D mechanical model is used to predict the consequences of hydration, temperature and water variations on mechanical behavior. An alternative approach to consider the structural effect of distributed reinforcement without explicit meshing of reinforcements is implemented and is able to reproduce the influence of reinforcement on the crack patterns. Moreover, the “Weakest link localization” method is also adapted to deal with a probabilistic scale effect due to the material heterogeneity of massive structure. It permits to assess directly the most likely tensile strength which can treat the first crack in softening part of the loaded volume of structures.

ST-HASSET for volcanic hazard assessment: A Python tool for evaluating the evolution of unrest indicators

Short-term hazard assessment is an important part of the volcanic management cycle, above all at the onset of an episode of volcanic agitation (unrest). For this reason, one of the main tasks of modern volcanology is to use monitoring data to identify and analyse precursory signals and so determine where and when an eruption might occur. This work follows from Sobradelo and Martí [Short-term volcanic hazard assessment through Bayesian inference: retrospective application to the Pinatubo 1991 volcanic crisis. Journal of Volcanology and Geothermal Research 290, 111, 2015] who defined the principle for a new methodology for conducting short-term hazard assessment in unrest volcanoes. Using the same case study, the eruption on Pinatubo (15 June 1991), this work introduces a new free Python tool, ST-HASSET, for implementing Sobradelo and Martí (2015) methodology in the time evolution of unrest indicators in the volcanic short-term hazard assessment. Moreover, this tool is designed for complementing long-term hazard assessment with continuous monitoring data when the volcano goes into unrest. It is based on Bayesian inference and transforms different pre-eruptive monitoring parameters into a common probabilistic scale for comparison among unrest episodes from the same volcano or from similar ones. This allows identifying common pre-eruptive behaviours and patterns. ST-HASSET is especially designed to assist experts and decision makers as a crisis unfolds, and allows detecting sudden changes in the activity of a volcano. Therefore, it makes an important contribution to the analysis and interpretation of relevant data for understanding the evolution of volcanic unrest.