Successive Pursuit with a Bounded Detection Domain

We study a coplanar model of the successive pursuit of two evaders with unlimited turn rates of the players and a bounded detection domain of a pursuer. Involved in catching the first evader, the pursuer may lose sight of the other. In this case, it must search later for the lost evader in the plane. We describe two guaranteed pursuit strategies obtained as solutions of differential games. Both strategies include a two-stage strategy to shorten to a specified quantity the distance to the nearer evader, and a two-stage strategy to search and capture the other.The strategies are distinguished by their search plans. First, coalition is pursued as a whole. Then, to minimize an uncertainty index, the pursuer approaches the first evader using the strategy of successive pursuit with the unmoved second evader at its last observed position. Subsequently, the pursuer moves directly to that position of the second evader, or according to the more complex plan, alternates between traversing a straight line and arcs of logarithmic spirals. After detection, the remaining evader is captured with the use of a simple pursuit strategy.The barriers fit the strategies. We call them approximate, since they bound the states where the pursuer succeeds with the guaranteed (but not optimal as in the case of ordinary barriers) strategies. These barriers are surfaces of constant values of a special game of degree. The more complex search plan secures a wider winning area.Geometrical interpretations and some numerical results for a set of parameters of the game are provided.     

A dynamical characterization of evolutionarily stable states

Evolutionary stability, the central solution concept in evolutionary game theory, is closely related to local asymptotic stability in a certain nonlinear dynamical system operating on the state space, the so-called "replicator dynamics". However, a purely dynamical characterization of evolutionary stability is not available in an elementary manner. This characterization can be achieved by investigating so-called "derived games" which consist of mixed strategies corresponding to successful states in the original game. Using well-known facts, several characterization results are obtained within this context. These also may shed light on the extremality properties of evolutionary stability.     

Recent Strategies and Applications for l-Asparaginase Confinement

l-asparaginase (ASNase, EC 3.5.1.1) is an aminohydrolase enzyme with important uses in the therapeutic/pharmaceutical and food industries. Its main applications are as an anticancer drug, mostly for acute lymphoblastic leukaemia (ALL) treatment, and in acrylamide reduction when starch-rich foods are cooked at temperatures above 100 °C. Its use as a biosensor for asparagine in both industries has also been reported. However, there are certain challenges associated with ASNase applications. Depending on the ASNase source, the major challenges of its pharmaceutical application are the hypersensitivity reactions that it causes in ALL patients and its short half-life and fast plasma clearance in the blood system by native proteases. In addition, ASNase is generally unstable and it is a thermolabile enzyme, which also hinders its application in the food sector. These drawbacks have been overcome by the ASNase confinement in different (nano)materials through distinct techniques, such as physical adsorption, covalent attachment and entrapment. Overall, this review describes the most recent strategies reported for ASNase confinement in numerous (nano)materials, highlighting its improved properties, especially specificity, half-life enhancement and thermal and operational stability improvement, allowing its reuse, increased proteolysis resistance and immunogenicity elimination. The most recent applications of confined ASNase in nanomaterials are reviewed for the first time, simultaneously providing prospects in the described fields of application.     

Ordered field property for stochastic games when the player who controls transitions changes from state to state

In this paper, we consider a zero-sum stochastic game with finitely many states restricted by the assumption that the probability transitions from a given state are functions of the actions of only one of the players. However, the player who thus controls the transitions in the given state will not be the same in every state. Further, we assume that all payoffs and all transition probabilities specifying the law of motion are rational numbers. We then show that the values of both a -discounted game, for rational , and of a Cesaro-average game are in the field of rational numbers. In addition, both games possess optimal stationary strategies which have only rational components. Our results and their proofs form an extension of the results and techniques which were recently developed by Parthasarathy and Raghavan (Ref. 1).The author wishes to thank Professor T. E. S. Raghavan for introducing him to this problem and for discussing stochastic games with him on many occasions. This research was supported in part by AFOSR Grant No. 78–3495B.     

Maximum survival capability of an aircraft in a severe windshear

This paper is concerned with guidance strategies and piloting techniques which ensure near-optimum performance and maximum survival capability in a severe windshear. The take-off problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is assumed.First, six particular guidance schemes are considered, namely: constant alpha guidance; maximum alpha guidance; constant velocity guidance; constant absolute path inclination guidance; constant rate of climb guidance; and constant pitch guidance. Among these, it is concluded that the best one is the constant pitch guidance.Next, in an effort to improve over the constant pitch guidance, three additional trajectories are considered: the optimal trajectory, which minimizes the maximum deviation of the absolute path inclination from a reference value, while employing global information on the wind flow field; the gamma guidance trajectory, which is based on the absolute path inclination and which approximates the behavior of the optimal trajectory, while employing local information on the windshear and the downdraft; and the simplified gamma guidance trajectory, which is the limiting case of the gamma guidance trajectory in a severe windshear and which does not require precise information on the windshear and the downdraft.The essence of the simplified gamma guidance trajectory is that it yields a quick transition to horizontal flight. Comparative numerical experiments show that the survival capability of the simplified gamma guidance trajectory is superior to that of the constant pitch trajectory and is close to that of the optimal trajectory.Next, with reference to the simplified gamma guidance trajectory, the effect of the feedback gain coefficient is studied. It is shown that larger values of the gain coefficient improve the survival capability in a severe windshear; however, excessive values of the gain coefficient are undesirable, because they result in larger altitude oscillations and lower average altitude.Finally, with reference to the simplified gamma guidance trajectory, the effect of time delays is studied, more specifically, the time delay ₁ in reacting to windshear onset and the time delay ₂ in reacting to windshear termination. While time delay ₂ has little effect on survival capability, time delay ₁ appears to be critical in the following sense: smaller values of ₁ correspond to better survival capability in a severe windshear, while larger values of ₁ are associated with a worsening of the survival capability in a severe windshear.This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516, and by Boeing Commercial Airplane Company.     

Stochastic scheduling problems II-set strategies-

The paper introduces the finite class of set strategies for stochastic scheduling problems. It is shown that the knownstable classes of strategies such as ES and MES strategies are of this type, as arelist-scheduling strategies such as LEPT and SEPT and other, more complicatedpriority-type strategies. Roughly speaking, set strategies are characterized by the fact that the decision as to which jobs should be started at timet depends only on the knowledge of the two sets of jobs finished up to timet and being processed at timet. Contrary to list scheduling strategies, set strategies may involve deliberate idleness of machines, i.e. may not be greedy and can therefore not generally be induced by priority rules. It is demonstrated that set strategies have useful properties. They are e.g. ⁿ -almost everywhere continuous and therefore show satisfactorystability behaviour w.r.t. weak convergence of the joint distribution of job durations. Furthermore, the optimum w.r.t.all strategies is already attained on this class if job durations are independent and exponentially distributed and the performance measure fulfills a certainshift condition. This shift property is a quite natural concept and generalizes aspects of the notion ofadditivity in semi-Markov decision theory and stochastic dynamic optimization. Its complete analytical characterization is a major object of this paper. Typical additive cost criteria such as makespan and flowtime are of course covered, which yields simultaneously a first step towards generalization of optimality of LEPT and SEPT rules, as known for special cases. In fact, in view of the obtained optimality result, the question of when deliberate idleness of machines can be avoided, gains considerable interest, as it characterizes stochastic environments in whichpriority strategies are optimal. This provides a major link with current research on the analysis of networks of queues in the context of computer systems.The work of the first two authors was supported by the Minister für Wissenschaft und Forschung des Landes Nordrhein-Westfalen, while the work of the last author was supported by DAAD.     

Incentive equilibrium in an overlapping-generations environmental game

We consider two overlapping generations that want to coordinate their strategies of working, consuming and controlling pollution. Since the cooperative solution is not an equilibrium, and hence is not a self-enforcing contract, a mechanism is required to sustain it. We show how incentive strategies, and the resulting incentive equilibrium, could provide such a mechanism. We also derive the conditions that ensure the credibility of these strategies.     

Optimal Policies to Obtain the Most Join Results

Consider two finite or infinite populations, each member of which carries a positive integer valued label. Samples are drawn without replacement. A match is said to occur between two sampled members if they are from different populations and carry the same label. The object is to sample from the two sources in an order that maximizes the number of matches, uniformly across all steps. An optimal strategy is identified in the infinite case. In the finite case, while an optimal policy is shown to not always exist, we identify a policy which beats one that is commonly used. The work is motivated by a database problem in computer science. Many of the results are established through the probabilistic technique of coupling.     

Li-rich layered oxides: Structure,capacity and voltage fading mechanisms and solving strategies

Lithium rich layered oxides (LLOs) are attractive cathode materials for Li-ion batteries owing to their high capacity (>250 mA h g^–1) and suitable voltage (∼3.6 V). However, they suffer from serious voltage and capacity fading, which is focused in this review. First, an overview of crystal structure, band structure and electrochemical performances of LLOs is provided. After that, current understanding on oxygen loss, capacity fading and voltage fading is summarized. Finally, five strategies to mitigate capacity and voltage fading are reviewed. It is believed that these understandings can help solve the fading problems of LLOs.