Reconstruction of SU(1,1) States

We show how group symmetries can be used to reconstruct quantum states. In our scheme for SU(1,1) states, the input field passes through a non-degenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode. The density matrix in the Fock basis is retrieved from the measured data by least squares method after singular value decomposition of the design matrix. Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered.Comment: 8 pages, 5 figures, submitted to PR

Standard Chartered Bank: Women on Corporate Boards in India 2010

This first Standard Chartered Bank: Women on Corporate Boards in India 2010 report looks at the representation of women on the boards of India's leading companies on the Bombay Stock Exchange (BSE-100) . It ranks the companies in terms of the gender diversity of their boards, with those with the highest percentage of women on their boards appearing at the top. The report also examines the general topic of gender diversity on the boards of the BSE-100 by presenting the findings of interviews with 18 female directors of BSE-100 companies

A notion of graph likelihood and an infinite monkey theorem

We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.Comment: 6 pages, 1 EPS figur

Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.

The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers

Is there over-fishing in Indian waters?

In view of the vast expanse of the sea it was believed that the resources of the sea are almost inexhaustible and ,ve can put in more and more fishing effort to get higher and higher yield. Sufficient evidence has, however, been accumulated to show that this belief is not true. With the advent of steam trawling,\ud several nations began intensive fIshing in the North Sea towards the end of the nineteenth century and this resulted in rapid decline in the abundance of most of the species

A note on the production trend of marine shrimps in India

The paper reviews the production statistics of marine shrimps in the different maritime states of India from 1950 to 1962. It is pointed out that for a correct appraisal of the status of any fishery, it is necessary to have data on effort E and catch per unit effort in addition to the conventional data on catch C. A relationship between U and E has been developed and the status of the fishery of Metapenaeus dobsoni has been discussed in this connection with reference to the data on catch and effort obtained from trawler operations off Cochin

Fish Population Studies

Generally, we hear such questions as "what is the magnitude of our oil sardine or mackerel resources?" "Can we get more catch from these resources?" It is, therefore, proper that we carefully examine what is meant by a fishery resource e. g., oil sardine or mackerel resource. A fishery resource is just like any other natural resource (e. g., mineral resource, hydro-electric resource etc.) which is exploited by man. But at the same time, it differs considerably to character from other types like mineral resources. The coal resource in a region is limited in magnitude, even though sometimes we do not know the magnitude. From this fixed resource we can exploit at any desired rate. The resource will be completely exhausted after a period of time depending on the rate of exploitation. In this sense a mineral resource can be described as a non-renewable natural resource which is liable to get exhausted after some period of time. It is also a static resource because we always know how much of the resource remains, once we know how much has been removed. A fishery resource is very much different in character. It is a self-regulating renewable natural resource. Consider a fish population occupying a certain area of the sea. Now when a certain portion of the population is removed, the remaining portion in the habitat gets better food, more area to move about, and this results in faster growth rate, lesser mortality rates and also the spawns get better chance of survival- The result is that the resource resuscitates itself quickly. Apart from fishing, the population is also affected by many other fishery-independent environmental factors such as available food supply, change in salinity, temperature of the water, change in ocean-currents etc. Thus the fishery resource is a dynamic resource, ever changing due to impact of fishing and other fishery-independent factors

The Indian mackerel; V Population

Pradhan (1956) examining the mackerel landings at Karwar from 1948-49 to 1952-53 concluded that the sex composition of the commercial catches during the fishing season was roughly as 45% male and 55% female. Similar qualitative statements regarding sex distribution of commercial landings at various specific centres are available in the annual reports of the Central Marine Fisheries Research Institute. In 1965-66, the sex ratio studies at Cannanore indicated that the proportion of males was slightly higher than females (53.18:46.32) in the adult population. The predominance of males was also seen in Juveniles (modal size 135 mm). In the medium sized fish (modal size 205 mm) which contributed to the bulk of the catch, the sex-ratio was in the reverse order (40.7M;59.3F). In the same year, at Cochin females dominated the catches except for April and September (Central Marine Fisheries Research Institute Annual Report 1966). In 1966-67 season, the sex ratio during the fishing season was found to vary though in some centres was almost equal (Cenrtal Marine Fisheries Research Institute Annual Report 1967). In the first half of 1967-68 season, the sex-ratio of a sample analysed at Karwar showed that females were more numerous. At Mangalore, males were more numerous in the aggregate. Sexes were almost equally represented at Cochin and Cannanore. At Vizhinjam males were predominant in March. In the second half of the year, at Cannanore the females increased to more than twice that of males (Central Marine Fisheries Research Institute, Annual Report 1968). The above excerpts will show that there is no uniformity in the sex distribution in the commercial catches either among various centres or between various fishing seasons. In the absence of

Functions of a Fishery Data Centre

In the modern world. no government or b usiness house can funct ion properly without recourse to a wide variety of statistical informa,ion at its disposal. The statistical data constitute the quantitative information based on which development plans or expansion programmes are drawn up