Littlewood polynomials with high order zeros

Let be the minimal length of a polynomial with coefficients divisible by . Byrnes noted that for each , and asked whether in fact . Boyd showed that for all , but . He further showed that , and that is one of the 5 numbers , or . Here we prove that . Similarly, let be the maximal power of dividing some polynomial of degree with coefficients. Boyd was able to find for . In this paper we determine for .

     

Rapid Antibiotic Susceptibility Determination for <Emphasis Type="Italic">Yersinia pestis</Emphasis> Using Flow Cytometry Spectral Intensity Ratio (SIR) Fluorescence Analysis

Rapid antimicrobial susceptibility tests (ASTs) are essential tool for proper treatment of patients infected by Yersinia pestis (Y. pestis), the causative agent of plague, or for post-exposure prophylaxis of a population exposed to a naturally acquired or deliberately prepared resistant variant. The standard AST of Y. pestis is based on bacterial growth and requires 24–48 h of incubation in addition to the time required for prior isolation of a bacterial culture from the clinical or environmental sample, which may take an additional 24–48 h. In this study, we present a new and rapid AST method based on a fluorescence determination of the minimum inhibitory concentration (MIC). Our method includes the incubation of bacteria with an antibiotic, followed by staining of the bacteria with oxonol dye (SynaptoGreen C4/FM1–43), which enables the rapid detection of an antibiotic’s effect on bacterial viability. We show that stained, non-viable bacteria exhibit a spectral redshift and an increase in fluorescence intensity compared to intact control bacteria. Based on these criteria, we developed a rapid flow cytometer measurement procedure and a unique spectral intensity ratio (SIR) analysis that enables determination of antibiotic susceptibility for Y. pestis within 6 h instead of the 24 to 48 h required for the standard AST. This new rapid determination of antibiotic susceptibility could be crucial for reducing mortality and preventing the spread of disease.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

Gravitation, the Quantum and Bohr's Correspondence Principle

The black hole combines in some sense both thehydrogen atom and the black-bodyradiation problems of quantum gravity. Thisanalogy suggests that black-hole quantization may be thekey to a quantum theory of gravity. During the last twenty-fiveyears evidence has been mounting that black-hole surfacearea is indeed quantized, with uniformally spaced areaeigenvalues. There is, however, no general agreement on the spacing of the levels. In thisessay we use Bohr's correspondence principle to providethis missing link. We conclude that the fundamental areaunit is 4h ln 3. This is the unique spacing consistent both with the area-entropythermodynamic relation for black holes, withBoltzmann-Einstein formula in statistical physics andwith Bohr's correspondence principle.     

Time-dependent random walks and the theory of complex adaptive systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are time dependent. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk, the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.     

Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.     

Computational modeling and in-vitro/in-silico correlation of phospholipid-based prodrugs for targeted drug delivery in inflammatory bowel disease

Targeting drugs to the inflamed intestinal tissue(s) represents a major advancement in the treatment of inflammatory bowel disease (IBD). In this work we present a powerful in-silico modeling approach to guide the molecular design of novel prodrugs targeting the enzyme PLA₂, which is overexpressed in the inflamed tissues of IBD patients. The prodrug consists of the drug moiety bound to the sn-2 position of phospholipid (PL) through a carbonic linker, aiming to allow PLA₂ to release the free drug. The linker length dictates the affinity of the PL-drug conjugate to PLA₂, and the optimal linker will enable maximal PLA₂-mediated activation. Thermodynamic integration and Weighted Histogram Analysis Method (WHAM)/Umbrella Sampling method were used to compute the changes in PLA₂ transition state binding free energy of the prodrug molecule (??G^tr) associated with decreasing/increasing linker length. The simulations revealed that 6-carbons linker is the optimal one, whereas shorter or longer linkers resulted in decreased PLA₂-mediated activation. These in-silico results were shown to be in excellent correlation with experimental in-vitro data. Overall, this modern computational approach enables optimization of the molecular design of novel prodrugs, which may allow targeting the free drug specifically to the diseased intestinal tissue of IBD patients.     

Updates on synthesis and biological activities of 1,3,4-oxadiazole: A review

The new era of heterocyclic moieties which are developed in the decades plays a very important role in the treatment of various diseases. Among them are 1,3,4-oxadiazoles, a heterocyclic five-membered ring which plays an vital role in the development of newer medicinal compounds for treating various biological activities, such as proliferation of cells, tuberculosis, allergy, viral diseases, etc. The present review will summarize the various synthetic approaches which will be correlated with the biological activities so that the information in future may be used by many researches to give a path breaking lead in the field of medicinal chemistry.     

Lipschitz representations of subsets of the cube

We show that for any class of uniformly bounded functions with a reasonable combinatorial dimension, the vast majority of small subsets of the -dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of , unless the Lipschitz constant is very large. We apply this result to the case when consists of linear functionals of norm at most one on a Hilbert space.