We describe a technique that employs the stochastic Latent Topic Models framework to allow quantification of melanin and hemoglobin content in dermoscopy images. Such information bears useful implications for analysis of skin hyperpigmentation, and for classification of skin diseases. The proposed method outperforms existing approaches while allowing for more stringent and probabilistic modelin...

Uncertainty quantification is the state-of-the-art framework dealing with uncertainties arising in all kind of real-life problems. One of the framework’s functions is to propagate uncertainties from the stochastic input factors to the output quantities of interest, hence the name uncertainty propagation. To this end, polynomial chaos expansions (PCE) have been effectively used in a wide variety...

Technical applications are often modeled by systems of differential algebraic equations. The systems may include parameters that involve some uncertainties. We arrange a stochastic model for uncertainty quantification in the case of linear systems of differential algebraic equations. The generalized polynomial chaos yields a larger linear system of differential algebraic equations, whose soluti...

The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised analysis of such systems, we extend the reasoning power of arithmetic satisfiability-modulo-theory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) quantification over discrete variables within the mixed Boolean-arithmetic constraint system. This provides ...

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance) laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or boundary conditions. We focus on forward UQ or uncertainty propagation and review deterministic methods such as stochastic Galerkin and stochastic collocation finite volume methods for approximating random (fie...

A tradeoff is a situation that involves losing one quality or aspect of something in return for gaining another quality or aspect. Speaking about the tradeoff between performance and security indicates that both, performance and security, can be measured, and that to increase one, we have to pay in terms of the other. While established metrics for performance of systems exist this is not quite ...

Considering the valuation of forest stands based on revenue from wood sales, concession policy (such as carbon subsidies) and associated costs, the paper focuses on the stochastic control model to study the forest asset dynamic management. The key contribution is to find the optimal dynamic strategy about harvesting quantity in the continual and multiple periods in conditions of stochastic comm...

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos technique represents the density matrix as an expansion in orthogonal polynomials over the principle components of the stochastic process and yields a sparsely...

A novel methodology that combines recent advances in computational statistics and reduced-order modeling is presented to explore the application of Bayesian statistical inference to a stochastic inverse problem in radiative heat transfer. The underlying objective of this work is to reveal the potential of using statistical approaches, mainly Bayesian computational statistics and spatial statist...

The complexity, nonlinearity and nonstationarity of the cardiovascular system typically defy comprehensive and deterministic mathematical modeling, except from a statistical perspective. Living systems are governed by numerous, continuously changing, interacting variables in the presence of noise. Cardiovascular signals can be shown to be discontinuous alternations between deterministic traject...