Numerical computation of response time distributions using stochastic reward nets

We consider the numerical computation of response time distributions for closed product form queueing networks using thetagged customer approach. We map this problem on to the computation of the time to absorption distribution of a finite-state continuous time Markov chain. The construction and solution of these Markov chains is carried out using a variation of stochastic Petri nets called stochastic reward nets (SRNs). We examine the effects of changing the service discipline and the service time distribution at a queueing center on the response time distribution. A multiserver queueing network example is also presented. While the tagged customer approach for computing the response time distribution is not new, this paper presents a new approach for computing the response time distributions using SRNs.This research was sponsored in part by the National Science Foundation under Grant CCR-9108114 and by the Naval Surface Warfare Center under contract N60921-92-C-0161.     

On conformally related pp-waves

Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are pp-waves. Brinkmann’s result has been generalized to include the conformally invariant source terms. It has been shown that [4] if g _ik and _ik (=w ⁻² g _ik ; w: a scalar function), are distinct metrics having the same Einstein tensor, G _ik = _ik , then both represent (generalized) pp-waves and w _i is a null covariantly constant vector of g _ik . Thus pp-waves are the only candidates which yield conformally related nontrivial solutions of G _ik =T _ik = _ik , with T _ik being conformally invariant source. In this paper the functional form of the conformal factor for the conformally related pp-waves/generalized pp-waves has been obtained. It has been shown that the most general pp-wave, conformally related to ds ²=−2du[dv−mdy=Hdu]+P ⁻²[dy ²+dz ²], turns out to be (au+b)⁻² ds ², where a,b are constants. Only in the special case when m=0, H=1, and P=P(y, z), the conformal factor is (au+b)⁻² or (a(u+v)+b)⁻².     

Correlation and volatility in an Indian stock market: A random matrix approach

We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index.     

Two new fluorescent heterocyclic perimidines: first syntheses, crystal structure, and spectral characterization

An efficient one-pot synthesis of two new heterocyclic perimidines 4-(2,3-dihydro-1H-perimidin-2-yl)-2-methoxyphenol and 2-(quinoxalin-2-yl)-2,3-dihydro-1H-perimidine in good yields is presented. This methodology provides a simple, straightforward synthetic route to these interesting classes of heterocycles. Crystal structure, solvatochromism, and antibacterial activity of these organic compounds are discussed.     

N-methyl Benzimidazole Tethered Cholic Acid Amphiphiles Can Eradicate S. aureus-Mediated Biofilms and Wound Infections

Infections associated with Gram-positive bacteria like S. aureus pose a major threat as these bacteria can develop resistance and thereby limit the applications of antibiotics. Therefore, there is a need for new antibacterials to mitigate these infections. Bacterial membranes present an attractive therapeutic target as these membranes are anionic in nature and have a low chance of developing modifications in their physicochemical features. Antimicrobial peptides (AMPs) can disrupt the microbial membranes via electrostatic interactions, but the poor stability of AMPs halts their clinical translation. Here, we present the synthesis of eight N-methyl benzimidazole substituted cholic acid amphiphiles as antibacterial agents. We screened these novel heterocyclic cholic acid amphiphiles against different pathogens. Among the series, CABI-6 outperformed the other amphiphiles in terms of bactericidal activity against S. aureus. The membrane disruptive property of CABI-6 using a fluorescence-based assay has also been investigated, and it was inferred that CABI-6 can enhance the production of reactive oxygen species. We further demonstrated that CABI-6 can clear the pre-formed biofilms and can mitigate wound infection in murine models.     

Mulberry Leaves (Morus Rubra)-Derived Blue-Emissive Carbon Dots Fed to Silkworms to Produce Augmented Silk Applicable for the Ratiometric Detection of Dopamine

Silk fibers (SF) reeled from silkworms are constituted by natural proteins, and their characteristic structural features render them applicable as materials for textiles and packaging. Modification of SF with functional materials can facilitate their applications in additional areas. In this work, the preparation of functional SF embedded with carbon dots (CD) is reported through the direct feeding of a CD-modified diet to silkworms. Fluorescent and mechanically robust SF are obtained from silkworms (Bombyx mori) that are fed on CDs synthesized from the Morus rubra variant of mulberry leaves (MB-CDs). MB-CDs are introduced to silkworms from the third instar by spraying them on the silkworm feed, the mulberry leaves. MB-CDs are synthesized hydrothermally without adding surface passivating agents and are observed to have a quantum yield of 22%. With sizes of ≈4 nm, MB-CDs exhibited blue fluorescence, and they can be used as efficient fluorophores to detect Dopamine (DA) up to the limit of 4.39 nM. The nanostructures and physical characteristics of SF weren't altered when the SF are infused with MB-CDs. Also, a novel DA sensing application based on fluorescence with the MB-CD incorporated SF is demonstrated.