Spherical Casimir energies and Dedekind sums

Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in Discussion altered. v3:typos corrected, 1 reference and comments added. v4:typos corrected. Ancillary results added in an appendi

Approximating Tverberg Points in Linear Time for Any Fixed Dimension

Let P be a d-dimensional n-point set. A Tverberg-partition of P is a partition of P into r sets P_1, ..., P_r such that the convex hulls conv(P_1), ..., conv(P_r) have non-empty intersection. A point in the intersection of the conv(P_i)'s is called a Tverberg point of depth r for P. A classic result by Tverberg implies that there always exists a Tverberg partition of size n/(d+1), but it is not known how to find such a partition in polynomial time. Therefore, approximate solutions are of interest. We describe a deterministic algorithm that finds a Tverberg partition of size n/4(d+1)^3 in time d^{O(log d)} n. This means that for every fixed dimension we can compute an approximate Tverberg point (and hence also an approximate centerpoint) in linear time. Our algorithm is obtained by combining a novel lifting approach with a recent result by Miller and Sheehy (2010).Comment: 14 pages, 2 figures. A preliminary version appeared in SoCG 2012. This version removes an incorrect example at the end of Section 3.

Facile method for trimethylsilylation of alcohols using hexamethyldisilazane and ammonium thiocyanate under neutral conditions

A highly efficient method for trimethylsilylation of primary, secondary, tertiary, allylic, and a variety of sugar-derived alcohols using hexamethyldisilazane in the presence of a catalytic amount of ammonium thiocyanate under neutral conditions is reported

Obesity: Pathogenesis and emerging targets for drug development

Obesity leads to premature death and impairs quality of life. In general, weight loss is responsible and reduced the risk of cardiovascular disease that is associated with obesity. One of the recognized and well establishment treatment option for weight loss i.e. pharmacotherapy where cardiovascular safety issues with some previous weight loss drugs raise concerns for newly approved pharmacotherapies. Previously, number of anti-obesity drugs that are already withdrawn from the market because of adverse side effects. In the present study, our group focused only on antiobesity drugs that are currently under investigation and also understand its pathogenesis.  Although lot of anti-obesity drugs are in the pipeline, the process for getting such type of drugs to be marketed has recently proven so difficult

Determinants on lens spaces and cyclotomic units

The Laplacian functional determinants for conformal scalars and coexact one-forms are evaluated in closed form on inhomogeneous lens spaces of certain orders, including all odd primes when the essential part of the expression is given, formally as a cyclotomic unitComment: 18 pages, 1 figur

Mental illness, poverty and stigma in India: a case-control study

OBJECTIVE: To assess the effect of experienced stigma on depth of multidimensional poverty of persons with severe mental illness (PSMI) in Delhi, India, controlling for gender, age and caste. DESIGN: Matching case (hospital)–control (population) study. SETTING: University Hospital (cases) and National Capital Region (controls), India. PARTICIPANTS: A case–control study was conducted from November 2011 to June 2012. 647 cases diagnosed with schizophrenia or affective disorders were recruited and 647 individuals of same age, sex and location of residence were matched as controls at a ratio of 1:2:1. Individuals who refused consent or provided incomplete interview were excluded. MAIN OUTCOME MEASURES: Higher risk of poverty due to stigma among PSMI. RESULTS: 38.5% of PSMI compared with 22.2% of controls were found poor on six dimensions or more. The difference in multidimensional poverty index was 69% between groups with employment and income of the main contributors. Multidimensional poverty was strongly associated with stigma (OR 2.60, 95% CI 1.27 to 5.31), scheduled castes/scheduled tribes/other backward castes (2.39, 1.39 to 4.08), mental illness (2.07, 1.25 to 3.41) and female gender (1.87, 1.36 to 2.58). A significant interaction between stigma, mental illness and gender or caste indicates female PSMI or PSMI from ‘lower castes’ were more likely to be poor due to stigma than male controls (p<0.001) or controls from other castes (p<0.001). CONCLUSIONS: Public stigma and multidimensional poverty linked to SMI are pervasive and intertwined. In particular for low caste and women, it is a strong predictor of poverty. Exclusion from employment linked to negative attitudes and lack of income are the highest contributors to multidimensional poverty, increasing the burden for the family. Mental health professionals need to be aware of and address these issues

An Intrusion Detection System Algorithm for Defending MANET against the DDoS Attacks.

Mobile ad hoc network (MANET) is rapidly deployable, self configuring network able to communicate with each other without the aid of any centralized system. There is no need for existing infrastructure base network. In MANET Wireless medium is radio frequencies and nodes are mobile, topology can be very dynamically. Nodes must be able to relay traffic since communicating nodes might be out of range. A MANET can be a standalone network or it can be connected to external networks like internet. Multihop operation of MANET requires a routing mechanism designed for mobile nodes are internet access mechanisms, self configuring networks requires an address allocation mechanism, mechanism to detect and act on, merging of existing networks and security mechanisms. As we know that there is no any centralized system so routing is done by node itself. Due to its mobility and self routing capability nature, there are many weaknesses in its security

Spherical Universe topology and the Casimir effect

The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies are expressed in terms of the polyhedral degrees and equivalent expressions given using the cyclic decomposition of the covering group. Scalar functional determinants are calculated and the spectral asymmetry function treated by the same approach with explicit forms on one-sided lens spaces.Comment: 33 pages, 1 figure. Typos corrected and one reference adde