Non-singular circulant graphs and digraphs

We give necessary and sufficient conditions for a few classes of known circulant graphs and/or digraphs to be singular. The above graph classes are generalized to $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$, with certain restrictions. We also obtain a necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.Comment: 12 page

Representation of Cyclotomic Fields and Their Subfields

Let \K be a finite extension of a characteristic zero field \F. We say that the pair of $n\times n$ matrices $(A,B)$ over \F represents \K if \K \cong \F[A]/ where \F[A] denotes the smallest subalgebra of M_n(\F) containing $A$ and $$ is an ideal in \F[A] generated by $B$. In particular, $A$ is said to represent the field \K if there exists an irreducible polynomial q(x)\in \F[x] which divides the minimal polynomial of $A$ and \K \cong \F[A]/. In this paper, we identify the smallest circulant-matrix representation for any subfield of a cyclotomic field. Furthermore, if $p$ is any prime and \K is a subfield of the $p$-th cyclotomic field, then we obtain a zero-one circulant matrix $A$ of size $p\times p$ such that (A,\J) represents \K, where \J is the matrix with all entries 1. In case, the integer $n$ has at most two distinct prime factors, we find the smallest 0-1 companion-matrix that represents the $n$-th cyclotomic field. We also find bounds on the size of such companion matrices when $n$ has more than two prime factors.Comment: 17 page

Patent Pooling for Promoting Access to Antiretroviral Drugs (ARVs) – A Strategic Option for India

The current HIV/AIDS scenario in India is quite grim with an estimated 2.4 million people living with HIV/AIDS (PLHA) in 2008, just behind South Africa and Nigeria. The anti-retroviral drugs (ARVs) remain the main stay of global HIV/AIDS treatment. Over 30 ARVs (single and FDCs) available under six categories viz., NRTIs (nucleoside reverse transcriptase inhibitors), NNRTIs (non-nucleoside reverse transcriptase inhibitors), Protease inhibitors, the new Fusion inhibitors, Entry inhibitors-CCR5 co-receptor antagonists and HIV integrase strand transfer inhibitors. The major originator companies for these ARVs are: Abbott, Boehringer Ingelheim (BI), Bristol-Myers Squibb (BMS), Gilead, GlaxoSmithKline (GSK), Merck, Pfizer, Roche, and Tibotec. Beginning with zidovidine in 1987, all the drugs are available in the developed countries. In India, about 30 ARVs are available as generics manufactured by Aurobindo, Hyderabad, Andhra Pradesh; Cipla Limited, Goa; Emcure Pharmaceuticals, Pune, Maharashtra; Hetero Drugs, Hyderabad, Andhra Pradesh; Macleods Pharmaceuticals, Daman; Matrix Laboratories, Nashik, Maharashtra; Ranbaxy, Sirmour, Himachal Pradesh; and Strides Arcolab, Bangalore, Karnataka. The National AIDS Control Organization (NACO) set up in 1992 by the Govt. of India provides free ARVs to HIV positive patients in India since 2004. The drugs available in India include both single drugs and FDCs covering both first line and second line ARVs. Even while there are claims of stabilization of the disease load, there is still huge gap of those who require ARVs as only about 150,000 PLHA receive the ARVs from the Govt. and other sources. Access to ARVs therefore is still a cause of serious concern ever since India became fully Trade Related Aspects of Intellectual Property Rights (TRIPS)-complaint in 2005. Therefore, the Indian pharmaceutical companies cannot make generics for those for drugs introduced post-2005 due to product patent regime. Other concerns include heat stable, other better formulations and second line ARVs for adults and more drugs and formulations for paediatric groups, that are still to be widely available in India and other developing countries. To examine whether strong intellectual property (IP) protection systems are to be considered important barriers for the limited or lack of access to ARVs, we studied the patent profile of the ARVs of the originator companies within and outside India. We could record 93 patents in the United States Patent & Trademark Office (USPTO). The originator companies have been also aggressively filing and enforcing patents in India. There have been a few efforts by companies like Gilead and GSK to grant licenses to generic manufacturers in developing countries, ostensibly to promote access to ARVs through lower (two-tier) pricing. These steps are considered as too little and too late. There is an urgent need to look for alternative strategies to promote access to ARVs both linked to and independent of IPRs. Patent pooling as a viable strategy mooted by the UNITAID should be seriously explored to promote access to ARVs. India is ideally suited for trying out the patent pool strategy as most of the global requirement of affordable ARV drugs for HIV/AIDS treatment is sourced from Indian generic companies

Need for diversification of coastal aquaculture

There is large potential for coastal aquaculture in the vast stretches of shallow coastal waters, creeks, bays lagoons and mudflats along the northeast coast of India comprising Andhra Pradesh, Orissa and West Bengal. Considering the good prospects for ariculture along the Indian coasts, the Central Marine Research Institute has carried out research and developed techniques for the culture of several groups of cultivable organisms like prawns, finfishes, crabs, the molluscan shellfishes like oysters, mussels, clams, pearl oyster and cephalopods, holothurians and seaweeds

CO2 Emissions reduction strategies and economic development of India

This paper examines the consequences of alternative CO2 emission reduction strategies on economic development and, in particular, the implications for the poor by empirically implementing an economy-wide model for India over a 35-year time horizon. A multi-sectoral, inter-temporal model in the activity analysis framework is used for this purpose. The model with specific technological alternatives, endogenous income distribution, truly dynamic behaviour and covering the whole economy is an integrated top-down bottom-up model. The results show that CO2 emission reduction imposes costs in terms of lower GDP and higher poverty. Cumulative emission reduction targets are, however, preferable to annual reduction targets and that a dynamically optimum strategy can help reduce the burden of emission reductions. The scenarios involving compensation for the loss in welfare are not very encouraging as they require large capital inflows. Contrasted with these, scenarios involving tradable emission quota give India an incentive to be carbon efficient. It becomes a net seller for the first 25 years and because of reduction in carbon intensity it would demand less in later years when it becomes a net buyer. The results suggest that for India, and other developing countries, the window of opportunity to sell carbon quotas is the next two decades or so.