On the hardness of approximating label-cover

The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724-733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29-40] to Label-Cover showing it NP-hard to approximate to within 2^{(logn)1−o(1)}. This improves upon the best previous hardness of approximation results known for this problem.We also consider the Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307-320]. We show some hardness results for certain levels in this hierarchy, and place Label-Cover between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of Label-Cover in it.     

In praise of alternative medicine: views of a healthcare consumer and college health employee

The blood flow property is one of the factors determining blood perfusion and oxygen supply. The viscosity of the blood is primarily related to the hematocrit, but also to the amount of fibrinogen and other macromolecules present in the blood. Patients with ischemic heart disease have shown a rapid and safe improvement in their hemorheological state when treated with heparin-induced extracorporeal low-density lipoprotein (LDL) precipitation (HELP). In this study we used two extracorporeal hemapheresis methods, plasmapheresis (PP) and immunoadsorption (IA), in 15 patients (eight patients treated with PP and seven patients with IA) with various diseases. Hemorheological variables and plasma fibrinogen were measured before and after the first and before the third treatment performed at 3 consecutive days. The aim of our study was to investigate the immediate effects of these two treatment modalities on the flow properties of blood. Immediately after the first PP and IA session statistically significant declines in plasma fibrinogen concentration, plasma viscosity, whole blood viscosity, and erythrocyte aggregation tendency were found. These changes persisted before the third treatment session. The erythrocyte fluidity and hematocrit remained unchanged. We conclude that extracorporeal hemapheresis therapy, with plasmapheresis or immunoadsorption, affects the blood rheology by decreasing the plasma viscosity and erythrocyte aggregation tendency. The decrease in plasma fibrinogen is probably the main factor underlying that, but other factors such as a decrease in immunoglobulins may also be of importance.     

The Prominin-1-Derived Peptide Improves Cardiac Function Following Ischemia

Myocardial infarction (MI) remains the leading cause of death in the western world. Despite advancements in interventional revascularization technologies, many patients are not candidates for them due to comorbidities or lack of local resources. Non-invasive approaches to accelerate revascularization within ischemic tissues through angiogenesis by providing Vascular Endothelial Growth Factor (VEGF) in protein or gene form has been effective in animal models but not in humans likely due to its short half-life and systemic toxicity. Here, we tested the hypothesis that PR1P, a small VEGF binding peptide that we developed, which stabilizes and upregulates endogenous VEGF, could be used to improve outcome from MI in rodents. To test this hypothesis, we induced MI in mice and rats via left coronary artery ligation and then treated animals with every other day intraperitoneal PR1P or scrambled peptide for 14 days. Hemodynamic monitoring and echocardiography in mice and echocardiography in rats at 14 days showed PR1P significantly improved multiple functional markers of heart function, including stroke volume and cardiac output. Furthermore, molecular biology and histological analyses of tissue samples showed that systemic PR1P targeted, stabilized and upregulated endogenous VEGF within ischemic myocardium. We conclude that PR1P is a potential non-invasive candidate therapeutic for MI.     

Using Modeling Tasks to Facilitate the Development of Percentages

This study analyzes the development of percentages knowledge by seventh graders given a sequence of activities starting with a realistic modeling task, in which students were expected to create a model that would facilitate the reinvention of percentages. In the first two activities, students constructed their own pricing model using fractions and then extended the model while experiencing reinvention and extension of their knowledge of percentages. In the last two activities, they coped with a realistic changing reference situation. A control group used a traditional instructional unit. A pretest and two posttests showed between-group differences.     

Harnessing “Click”‐Type Chemistry for the Preparation of Novel Electronic Materials

Sequence‐independent or “click”‐type chemistry is applied for the preparation of novel π‐conjugated oligomers. A variety of bi‐functional monomers for Wittig–Horner olefination are developed and applied in a sequential protection–deprotection process for the preparation of structurally similar π‐conjugated oligomers. Selected oligomers are incorporated as the organic semiconductors in light‐emitting diodes and a field‐effect transistor, demonstrating the potential of the approach.     

A bacteriophage reagent for Salmonella: molecular studies on Felix 01

Felix 01 (F01) is a bacteriophage originally isolated by Felix and Callow which lyses almost all Salmonella strains and has been widely used as a diagnostic test for this genus. Molecular information about this phage is entirely lacking. In the present study, the DNA of the phage was found to be a double-stranded linear molecule of about 80 kb. 11.5 kb has been sequenced and in this region A + T content is 60%. There are relatively few restriction endonuclease cleavage sites in the native genome and clones show this is due to their absence rather than modification. A restriction map of the genome has been constructed. The ends of the molecule cannot be ligated although they contain 5' phosphates. At least 60% of the genome must encode proteins. In the sequenced portion, many open reading frames exist and these are tightly packed together. These have been examined for homology to published proteins but only 1 to 17 shows similarity to known proteins. F01 is therefore the prototype of a new phage family. On the basis of restriction sites, codon usage and the distribution of nonsense codons in the unused reading frames, a strong case can be made for natural selection that reacts to mRNA structure and function.     

Multiconsistency and Robustness with Global Constraints

We propose a natural generalization of arc-consistency, which we call multiconsistency: a value v in the domain of a variable x is k-multiconsistent with respect to a constraint C if there are at least k solutions to C in which x is assigned the value v. We present algorithms that determine which variable-value pairs are k-multiconsistent with respect to several well known global constraints. In addition, we show that finding super solutions is sometimes strictly harder than finding arbitrary solutions for these constraints and suggest multiconsistency as an alternative way to search for robust solutions.Supported by the Danish Research Agency (grant # 272-05-0081).Basic Research in Computer Science, funded by the Danish National Research Foundation.     

On the Effective Deployment of Functional Formal Verification

We examine IBM's exploitation of formal verification using RuleBase—a formal verification tool developed by the IBM Haifa Research Laboratory. The goal of the paper is methodological. We identify an integrated methodology for the deployment of formal verification which involves three complementary modes: architectural verification, block-level verification, and design exploration.