TASS: The Toolkit for Accurate Scientific Software

The Toolkit for Accurate Scientific Software (TASS) is a suite of integrated tools for the formal verification of programs used in computational science, including numerically-intensive message-passing-based parallel programs. While TASS can verify a number of standard safety properties (such as absence of deadlocks and out-of-bound array indexing), its most powerful feature is the ability to establish that two programs are functionally equivalent. These properties are verified by performing an explicit state enumeration of a model of the program(s). In this model, symbolic expressions are used to represent the inputs and the values of variables. TASS uses novel techniques to simplify the symbolic representation of the state and to reduce the number of states explored and saved. The TASS front-end supports a large subset of C, including (multi-dimensional) arrays, structs, dynamically allocated data, pointers and pointer arithmetic, functions and recursion, and other commonly used language constructs. A number of experiments on small but realistic numerical programs show that TASS can scale to reasonably large configurations and process counts. TASS is open source software distributed under the GNU Public License. The Java source code, examples, experimental results, and reference materials are all available at .     

Improving the 1H indirect dimension resolution of 2D CRAMPS NMR spectra: a simulation and experimental investigation

An experimental and simulation investigation regarding the effect of various CRAMPS parameters (delays interleaved with the decoupling shape, z-rotation symmetry and offset frequency) on the DUMBO decoupling performance is presented using two model compounds, glycine and tyrosine·HCl. Although the conclusions of this work may be extended to the other homonuclear-decoupling schemes, this work focuses essentially on the effect of adding interleaved delays to DUMBO decoupling during the indirect dimension using different 2D pulse-scheme architectures. While the simulations revealed an increasing loss of the spectral resolution with longer delays (from 0 to 6 μs), the experimental 2D (1)H DUMBO NMR correlation spectra revealed that the inclusion of delays, during the indirect dimension, improves the (1)H resolution whether the z-rotation symmetry was used or not. The best experimental spectra are obtained when z-rotation symmetry and windows are combined.     

A Piecewise Line-Search Technique for Maintaining the Positive Definitenes of the Matrices in the SQP Method

A technique for maintaining the positive definiteness of the matrices in the quasi-Newton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a so-called piecewise line-search technique, while their positive definiteness in a complementary subspace is obtained by setting the augmentation parameter. In our experiment, the combination of these two ideas leads to a new algorithm that turns out to be more robust and often improves the results obtained with other approaches.     

FEVS: A Functional Equivalence Verification Suite for High-Performance Scientific Computing

Scientific computing poses many challenges to formal verification, including the facts that typical programs: (1) are numerically-intensive, (2) are highly-optimized (often by hand), and (3) often employ parallelism in complex ways. Another challenge is specifying correctness. One approach is to provide a very simple, sequential version of an algorithm together with the optimized (possibly parallel) version. The goal is to show the two versions are functionally equivalent, or provide useful feedback when they are not. We present a new verification suite consisting of pairs of programs of this form. The suite can be used to evaluate and compare tools that verify functional equivalence. The programs are all in C and the parallel versions use the Message Passing Interface. They are simpler than codes used in practice, but are representative of real coding patterns (e.g., manager-worker parallelism, loop tiling) and present realistic challenges to current verification tools. The suite includes solvers for the 1-d and 2-d diffusion equations, Jacobi iteration schemes, Gaussian elimination, and N-body simulation.     

Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models

Nonlinear Dynamics - The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling...     

Some Dido-type Inequalities

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Some Dido-type Inequalities

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Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

Evolution of material voids for highly anisotropic surface energy

In this paper we consider the evolution by surface diffusion of material voids in a linearly elastic solid, focusing on the evolution of voids with large surface energy anisotropy. It is well known that models for the time evolution of similar material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface. Here the ill-posedness is removed through a regularization which incorporates higher order terms in the surface energy. Spectrally accurate numerical simulations are performed to calculate the steady-state solution branches and time-dependent evolution of voids, with a particular emphasis on inferring trends in the zero regularization (c→0) limit. For steady voids with large anisotropy we find that apparent corners form as c→0. In the presence of elastic stresses σ the limiting corner angles are most often found to differ from angles found on the (σ=0) Wulff shape. For large elastic stresses we find that steady solutions no longer exist; instead the void steadily lengthens via a filamenting instability referred to as tip streaming.