This work investigates the approximate verification of probabilistic specifications expressed as any non-nested PCTL formula over Markov processes on general state spaces. The contribution puts forward new algorithms, based on higher-order function approximation, for the efficient computation of approximate solutions with explicit bounds on the error. Approximation error related to higher-order...

We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable singularities in the distribution of the fluid’s pressure. The origin of this difficulty is that, nea...

We show that classification rules used in ordinal regression are equivalent to a certain class of linear multi-class classifiers. This observation not only allows to design new learning algorithms for ordinal regression using existing methods for multi-class classification but it also allows to derive new models for ordinal regression. For example, one can convert learning of ordinal classifier...

Abstract: An important traffic engineering problem for OSPF networks is the determination of optimal link weight system for a given objective function such as the Fortz-Thorup (FT) piece-wise linear convex function. In this paper, we show that the optimal link weights are obtained from the slopes of the FT function when approached from the dual space. This also suggests that the slopes can be a...

This is a further development of [10] regarding multilevel preconditioning for symmetric interior penalty discontinuous Galerkin finite element approximations of second order elliptic problems. We assume that the mesh on the finest level is a results of a geometrically refined fixed coarse mesh. The preconditioner is a multilevel method that uses a sequence of finite element spaces of either co...

Modelling biochemical networks can be achieved by iteratively analyzing parts of the systems via top-down or bottom-up approaches. It is feasible to piece-wise model the biochemical networks from scratch by employing strategies able to assemble reusable components. In this paper, we investigate a set of strategies that can be employed in a bottom-up piece-wise modelling framework, to obtain syn...

In this paper, we propose a relaxation-based method with Fast Automatic Differentiation (FAD) for solving nonlinear problems. We called this method as R-FAD in this paper. By the proposed R-FAD the large circuits of neurons having complex nonlinear and Piece-Wise Linear (PWL) functions are modeled in terms of macro-models and can be analyzed by relaxation-based algorithm keeping the structure o...

Network C is a programming language designed for constructing simulation models of VLSI circuits and systems. The language, which is a superset of C, supports a range of modeling capabilities including appi ximate solution of KirchofF equations at the circuit level and discrete event functional simulation at the system level. When used to model a MOS circuit, the system first decomposes the cir...

The literature on solutions for claims problems mainly orbits three canonical rules: Proportional, the Constrained Equal Awards and Losses. Mixtures of these have been proposed to design alternative approaches solve problems. We consider piece-wise convex mixtures as two relevant tools. Piece-wise mixture guarantees that each agent obtains a minimal reimbursement, when it is available, while re...