Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Evolutionary games with two timescales

We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Visual ecology of Indian carpenter bees II: adaptations of eyes and ocelli to nocturnal and diurnal lifestyles

Most bees are diurnal, with behaviour that is largely visually mediated, but several groups have made evolutionary shifts to nocturnality, despite having apposition compound eyes unsuited to vision in dim light. We compared the anatomy and optics of the apposition eyes and the ocelli of the nocturnal carpenter bee, Xylocopa tranquebarica, with two sympatric species, the strictly diurnal X. leucothorax and the occasionally crepuscular X. tenuiscapa. The ocelli of the nocturnal X. tranquebarica are unusually large (diameter ca. 1 mm) and poorly focussed. Moreover, their apposition eyes show specific visual adaptations for vision in dim light, including large size, large facets and very wide rhabdoms, which together make these eyes 9 times more sensitive than those of X. tenuiscapa and 27 times more sensitive than those of X. leucothorax. These differences in optical sensitivity are surprisingly small considering that X. tranquebarica can fly on moonless nights when background luminance is as low as 10(-5) cd m(-2), implying that this bee must employ additional visual strategies to forage and find its way back to the nest. These strategies may include photoreceptors with longer integration times and higher contrast gains as well as higher neural summation mechanisms for increasing visual reliability in dim light.

A model for visual recognition of alphanumerics

In this paper we propose a hypothetical scheme for recognizing the alphanumerics. The scheme is based on the known physiological structure of the visual cortex and the concept of a short Lino extractor nouron (SLEN). We assumo four basic typca of such units for extracting vertical, horizontal, right and left inclined straight line segments. The patterns reconstructed from the scheme show perfect agreement with the test patterns. The model indicates that the recognition of letters T and H requires extraction of the largest number of features.

Visual Analysis of Biomolecular Surfaces

Surface models of biomolecules have become crucially important for the study and understanding of interaction between biomolecules and their environment. We argue for the need for a detailed understanding of biomolecular surfaces by describing several applications in computational and structural biology. We review methods used to model, represent, characterize, and visualize biomolecular surfaces focusing on the role that geometry and topology play in identifying features on the surface. These methods enable the development of efficient computational and visualization tools for studying the function of biomolecules.

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.

Bicriterion differential games with qualitative outcomes

Combat games are studied as bicriterion differential games with qualitative outcomes determined by threshold values on the criterion functions. Survival and capture strategies of the players are defined using the notion of security levels. Closest approach survival strategies (CASS) and minimum risk capture strategies (MRCS) are important strategies for the players identified as solutions to four optimization problems involving security levels. These are used, in combination with the preference orderings of the qualitative outcomes by the players, to delineate the win regions and the secured draw and mutual kill regions for the players. It is shown that the secured draw regions and the secured mutual kill regions for the two players are not necessarily the same. Simple illustrative examples are given.

Solution concepts in continuous-kernel multicriteria games

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.

Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

Determination of rational strategies for players in two-target games

This paper addresses some of the basic issues involved in the determination of rational strategies for players in two-target games. We show that unlike single-target games where the task of role assignment and selection of strategies is conceptually straightforward, in two-target games, many factors like the preference ordering of outcomes by players, the relative configuration of the target sets and secured outcome regions, the uncertainty about the parameters of the game, etc., also influence the rational selection of strategies by players. The importance of these issues is illustrated through appropriate examples.

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Fluorescence and visual sensing of nitroaromatic explosives using electron rich discrete fluorophores

Several pi-electron rich fluorescent aromatic compounds containing trimethylsilylethynyl functionality have been synthesized by employing Sonogashira coupling reaction and they were characterized fully by NMR (H-1, C-13)/IR spectroscopy. Incorporation of bulky trimethylsilylethynyl groups on the peripheral of the fluorophores prevents self-quenching of the initial intensity through pi-pi interaction and thereby maintains the spectroscopic stability in solution. These compounds showed fluorescence behavior in chloroform solution and were used as selective fluorescence sensors for the detection of electron deficient nitroaromatics. All these fluorophores showed the largest quenching response with high selectivity for nitroaromatics among the various electron deficient aromatic compounds tested. Quantitative analysis of the fluorescence titration profile of 9,10-bis(trimethylsilylethynyl) anthracene with picric acid provided evidence that this particular fluorophore detects picric acid even at ppb level. A sharp visual detection of 2,4,6-trinitrotoluene was observed upon subjecting 1,3,6,8-tetrakis (trimethylsilylethynyl) pyrene fluorophore to increasing quantities of 2,4,6-trinitrotoluene in chloroform. Furthermore, thin film of the fluorophores was made by spin coating of a solution of 1.0 x 10(-3) M in chloroform or dichloromethane on a quartz plate and was used for the detection of vapors of nitroaromatics at room temperature. The vapor-phase sensing experiments suggested that the sensing process is reproducible and quite selective for nitroaromatic compounds. Selective fluorescence quenching response including a sharp visual color change for nitroaromatics makes these fluorophores as promising fluorescence sensory materials for nitroaromatic compounds (NAC) with a detection limit of even ppb level as judged with picric acid.

A Gradient-Based Comparison Measure for Visual analysis of Multifield Data

We introduce a multifield comparison measure for scalar fields that helps in studying relations between them. The comparison measure is insensitive to noise in the scalar fields and to noise in their gradients. Further, it can be computed robustly and efficiently. Results from the visual analysis of various data sets from climate science and combustion applications demonstrate the effective use of the measure.