Using linear algebra in decomposition of Farkas interpolants

The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas’ lemma. However, these interpolants do not always suit the verification task—in the worst case, they can even prevent the verification algorithm from converging. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants, obtained by identifying and separating independent components from the interpolant structure, using methods from linear algebra. We also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties. We experimentally show that the use of decomposed interpolants in model checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general.

     

Characterization and distribution of mechanically competent mineralized tissue in micropores of β-tricalcium phosphate bone substitutes

1. Download high-res image (357KB)
2. Download full-size image

     

An Advanced TALSPEAK Concept Using 2-Ethylhexylphosphonic Acid Mono-2-Ethylhexyl Ester as the Extractant

A method for separating the trivalent actinides and lanthanides is being developed using 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP]) as the extractant. The method is based on the preferential binding of the actinides in the aqueous phase by N-(2-hydroxyethyl)ethylenediamine-N,N’,N’-triacetic acid (HEDTA), which serves to keep the actinides in the aqueous phase while the lanthanides are extracted into an organic phase containing HEH[EHP]. The process is very robust, showing little dependence upon the pH or the HEH[EHP], HEDTA, and citrate concentrations over the ranges that might be expected in a nuclear fuel recycling plant. Single-stage runs with a 2-cm centrifugal contactor indicate that modifications to the process chemistry may be needed to increase the extraction rate for Sm, Eu, and Gd. The hydraulic properties of the system are favorable to application in centrifugal contactors.     

Modeling the Extraction Rate Coefficient for the Extraction of Yttrium by DEHPA Using Organic-Phase Recycle

ABSTRACT

Extraction of yttrium (Y) from sulfuric acid was studied using di(2-ethylhexyl) phosphate (DEHPA). A portion of the organic phase was recycled back into the mixer after extraction for the mixer to operate at a moderate organic-to-aqueous volumetric phase ratio while processing at a low organic-to-aqueous flow rate ratio. The effective performance of the mixer was evaluated when operating at different organic-phase flow fractions. To model the extraction rate coefficient, a 2-factor designed experiment was performed by conducting both equilibrium and mixer-settler tests. The organic-phase flow fraction was varied over four discrete levels while the extractant concentration was varied over three discrete levels. Increasing the organic-phase flow fraction yielded a continual increase in the extraction rate coefficient. In contrast, increasing the extractant concentration yielded an initial increase followed by a subsequent decrease in the extraction rate coefficient. The decline in the extraction rate coefficient was attributed to a decrease in the yttrium-extractant complex’s diffusion coefficient. High metal loading caused an elevated organic-phase viscosity and thus the low diffusion coefficient. An extraction rate coefficient model is proposed to describe the effects of extractant concentration, viscosity and organic-phase flow fraction. Mass transfer resistance was largely in the organic phase.     

A two‐step method for predicting time to flashover in room corner test fires using cone calorimeter data

A method to predict time to flashover in ISO 9705 room corner fire tests based on cone calorimeter data is proposed in this paper. The method involves classification of materials and estimation of time to flashover as two steps in sequence. In the first step, the investigated material is classified into discriminating material groups. In the second step, the time to flashover is calculated with a derived formula for the corresponding material group, which contains material density, time to ignition and heat release rate collected from small‐scale experiments. Compared with two existing models, the proposed method has improved the prediction precisions in both the time to flashover and classification of material categories for a wide range of materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Developments in Mannose-Based Treatments for Uropathogenic Escherichia coli-Induced Urinary Tract Infections

During their lifetime almost half of women will experience a symptomatic urinary tract infection (UTI) with a further half experiencing a relapse within six months. Currently UTIs are treated with antibiotics, but increasing antibiotic resistance rates highlight the need for new treatments. Uropathogenic Escherichia coli (UPEC) is responsible for the majority of symptomatic UTI cases and thus has become a key pathological target. Adhesion of type one pilus subunit FimH at the surface of UPEC strains to mannose-saturated oligosaccharides located on the urothelium is critical to pathogenesis. Since the identification of FimH as a therapeutic target in the late 1980s, a substantial body of research has been generated focusing on the development of FimH-targeting mannose-based anti-adhesion therapies. In this review we will discuss the design of different classes of these mannose-based compounds and their utility and potential as UPEC therapeutics.