Conditional Value-at-Risk for Reachability and Mean Payoff in Markov Decision Processes

We present the conditional value-at-risk (CVaR) in the context of Markov chains and Markov decision processes with reachability and mean-payoff objectives. CVaR quantifies risk by means of the expectation of the worst p-quantile. As such it can be used to design risk-averse systems. We consider not only CVaR constraints, but also introduce their conjunction with expectation constraints and quantile constraints (value-at-risk, VaR). We derive lower and upper bounds on the computational complexity of the respective decision problems and characterize the structure of the strategies in terms of memory and randomization

Patching up the monopole potential

It is well known that a vector potential cannot be defined over the whole surface of a sphere around a magnetic monopole. A recent claim to the contrary is shown to have problems. It is explained however that a potential of the proposed type works if two patches are used instead of one. A general derivation of the Dirac quantization condition attempted with a single patch is corrected by introducing two patches. Further, the case of more than two patches using the original Wu-Yang type of potential is discussed in brief.Comment: 6 page

Universal criterion for black hole stability

It is shown that a non-rotating macroscopic black hole with very large horizon area can remain in stable thermal equilibrium with Hawking radiation provided {\it its mass, as a function of horizon area, exceeds its microcanonical entropy, i.e., its entropy when isolated, without thermal radiation or accretion, and having a constant horizon area} (in appropriate units). The analysis does not use properties of specific classical spacetimes, but depends only on the plausible assumption that the mass is a function of the horizon area for large areas.Comment: 6 pages Latex, no figures; an equation adde

Mass and charge fluctuations and black hole entropy

The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of non-rotating charged {\it macroscopic} black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to {\it fixed area} quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.Comment: 8 pages revtex, no figure

Universal canonical black hole entropy

Non-rotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a {\it universal} finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power law relation with the quantum area spectrum found in Non-perturbative Canonical Quantum General Relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterising this power law relation, where the canonical entropy (free energy) is seen to turn complex.Comment: Revtex, 5 pages, no figures. Typos corrected and a footnote and some references adde

A computer model for preliminary design and economics of container ships

This thesis is concerned with the development of a computer algorithm for determining the principal dimensions of a container ship at the preliminary design stage. The algorithm was devised to aid a Naval Architect to design the most economical ship, given the ship owner's requirements. The emphasis has been on developing an algorithm which acts as an aid in the design process. There are basically four models of the computer aided ship design which can be used in stages. The first model or algorithm is based on a deterministic approach with parametric variation of principal dimensions to locate the optimum design with minimum required freight rate. The second model incorporates optimisation techniques to arrive at the optimum ship. Though the optimisation technique is very powerful in the search of an optimum both in computer time and computing cost, the parametric method is preferred where a designer has little faith in the optimisation process or as an aid to check the answer arrived at in the optimisation process. The third model of the computer aided design can be used once the optimum has been found. A new approach to carry out sensitivity analysis is introduced. This approach overcomes the deficiencies of the past approach, in the sense that sensitivity analysis is carried out for achievable variation in variables rather than an arbitrary variation. The third model of computer aided design may be used once the designer has identified the variables, the variation of which, influences the required freight rate most. The use of the third model of the ship design may be adequate in identifying the total risk of the project. Together with sensitivity analysis, the designer can evaluate the total risk involved in an investment since the third model also incorporates a simple approach to risk analysis. However three estimates are required in the third model compared to single estimates of variables in the first and the second model. The fourth model incorporates the risk analysis by Monte Carlo method of simulation. In this model the designer can assess the xvii total risk of the project by generating the risk profile of the Required Freight Rate. The designer must either subjectively or objectively input the probability distribution of each of the influencing variables before using the fourth model. The four computer aided design models form a complete suite of computer programs, which can either be used in a deterministic mode, (first and second model), or in a probabilistic mode, (third and fourth model). Compared to previous ship design algorithms developed solely to deal with deterministic phase, this thesis incorporates ideas on how to incorporate uncertainty and assess risk in capital investment in a shipping venture. The designer can either use these computer models in stages, from deterministic phase to probabilistic phase or the models can be used on their own

Performance of wheat cultivars at varying fertility levels under system of wheat intensification and conventional method of wheat production system

A field experiment was conducted during rabi season of 2009-10 at Ranchi, Jharkhand to evaluate the performance of wheat cultivars at varying fertility levels under system of wheat intensification and conventional method of cultivation. The morpho-physiological analysis of growth and yield in wheat revealed that system of wheatintensification manifested higher total tillers m-2, leaf area index, dry matter accumulation, crop growth rate, number of spikes m-2, grains per spike and 1000-grain weight resulting in higher grain and straw yield over conventional method of cultivation. The net return and benefit: cost ratio as well as the nutrient uptake of nitrogen, phosphorus and potash was also recorded significantly higher under system of wheat intensification. Higher fertility level of 120 kg N ha-1, 60 kg P2O5 ha-1 and 40 kg K2O ha-1 also significantly improved the plant height, total tillers m-2, leaf area index, dry matter accumulation, crop growth rate, number of spikes m-2, grains per spike, 1000-grain weight, grain yield, straw yield, net return, benefit: cost ratio and nutrient uptake of nitrogen, phosphorus and potash. Among the wheat cultivars, K 9107 manifested significant improvement in growth attributes at all the growth stages resulting in significantly higher yield attributes, grain yield, straw yield, net return, benefit: cost ratio and nutrient uptake of nitrogen, phosphorus and potash than Birsa Gehu 3, HUW 468 and K 0307. Thus it can be concluded that the wheat variety K 9107 fertilized with 120 kg N ha-1, 60 kg P2O5 ha-1 and 40 kg K2O ha-1 under System of Wheat Intensification may able to boost up the wheat productivity under irrigated ecosystem of Chhotanagpur plateau region, India

Universal canonical entropy for gravitating systems

The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is argued to be determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by Non-perturbative Canonical Quantum General Relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonicai entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has univeral logarithmic corrections to the area law (from quantum spacetime fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.Comment: 6 pages revtex, one eps figure; based on talk delivered at the International Conference on Gravitation and Cosmology held at Kochi, India during 5-9 January, 200