Statistical modelling under epistemic data imprecision : some results on estimating multinomial distributions and logistic regression for coarse categorical data

Paper presented at 9th International Symposium on Imprecise Probability: Theories and Applications, Pescara, Italy, 2015. Abstract: The paper deals with parameter estimation for categorical data under epistemic data imprecision, where for a part of the data only coarse(ned) versions of the true values are observable. For different observation models formalizing the information available on the coarsening process, we derive the (typically set-valued) maximum likelihood estimators of the underlying distributions. We discuss the homogeneous case of independent and identically distributed variables as well as logistic regression under a categorical covariate. We start with the imprecise point estimator under an observation model describing the coarsening process without any further assumptions. Then we determine several sensitivity parameters that allow the refinement of the estimators in the presence of auxiliary information

Combining k-Induction with Continuously-Refined Invariants

Bounded model checking (BMC) is a well-known and successful technique for finding bugs in software. k-induction is an approach to extend BMC-based approaches from falsification to verification. Automatically generated auxiliary invariants can be used to strengthen the induction hypothesis. We improve this approach and further increase effectiveness and efficiency in the following way: we start with light-weight invariants and refine these invariants continuously during the analysis. We present and evaluate an implementation of our approach in the open-source verification-framework CPAchecker. Our experiments show that combining k-induction with continuously-refined invariants significantly increases effectiveness and efficiency, and outperforms all existing implementations of k-induction-based software verification in terms of successful verification results.Comment: 12 pages, 5 figures, 2 tables, 2 algorithm

A local grid refinement technique based upon Richardson extrapolation

A grid-embedding technique for the solution of two-dimensional incompressible flows governed by the Navier-Stokes equations is presented. A single coarse grid covers the whole domain, and local grid refinement B carried out in the regions of high gradients without changing the basic grid structure. A finite volume method with collocated primitive variables is employed, ensuring conservation at the interfaces of embedded grids, as well as global conservation. The method is applied to the simulation of a turbulent flow past a backward facing step, the flow over a square obstacle, and the flow in a sudden pipe expansion, and the predictions are compared with data published in the literature. They show that neither the convergence rate nor the stability of the method are affected by the presence of embedded grids. The grid-embedding technique yields significant savings in computing time to achieve the same accuracy obtained wing conventional grids. (C) 1997 by Elsevier Science Inc

pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual

pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features include a more efficient use of FEM, easier switching between different single parameter continuations, genuine multi-parameter continuation (e.g., fold continuation), more efficient implementation of nonlinear boundary conditions, cylinder and torus geometries (i.e., periodic boundary conditions), and a general interface for adding auxiliary equations like mass conservation or phase equations for continuation of traveling waves. The package (library, demos, manuals) can be downloaded at www.staff.uni-oldenburg.de/hannes.uecker/pde2pat

Steps in modular specifications for concurrent modules

© 2015 Published by Elsevier B.V.The specification of a concurrent program module is a difficult problem. The specifications must be strong enough to enable reasoning about the intended clients without reference to the underlying module implementation. We survey a range of verification techniques for specifying concurrent modules, in particular highlighting four key concepts: auxiliary state, interference abstraction, resource ownership and atomicity. We show how these concepts combine to provide powerful approaches to specifying concurrent modules

Numerical simulations with a first order BSSN formulation of Einstein's field equations

We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement and in particular binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of BSSN evolutions with very high accuracy numerical techniques, such as spectral collocation multi-domain or discontinuous Galerkin methods.Comment: To appear in Physical Review