Decomposable Penalty Method for Generalized Game Problems with Joint Constraints

We consider an extension of a noncooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We suggest to combine a penalty method together with shares allocation of right-hand sides, which replaces the initial problem with a sequence of the usual Nash equilibrium problems together with an upper level variational inequality as a master problem. We show convergence of solutions of these auxiliary penalized problems to a solution of the initial game problem under weak coercivity conditions.Comment: 13 page

A little about models

We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate the effect of uncertainty on the known consumer demand model. We conclude that not every uncertainty can be represented by a random variable, and that these concepts are not equivalent. We discuss also the role of different information concepts in mathematical models. We give additional illustrative examples of models of quite complex systems.Comment: 15 page

Boris Lomov`s Systems Approach in the Context of the Science Culture of the Late Soviet Period

The focus of the article is the research program of B. F. Lomov, viewed through the prism of Russian scientific culture, while taking into account the nuances of the late Soviet period. Scientific culture is analyzed in accordance with a model that singles out practices as a typical and stable way of doing things, and patterns as cognitive elements that integrate culture into a concise whole. Viewed via this model, any innovation appears to involve introduction of new practices into the culture. That means the risk of the introduced practices colliding with existing patterns. There are three main patterns of the Russian scientific culture that operated in the Soviet period, which are described as formulas analogous with the themes of S. Moskovichi: (a) science is a state matter, (b) basic science creates groundwork for the technologies of the future, (c) science is a selfless service. The practices promoted within Lomov's program were largely associated with American engineering psychology as practiced by A. Chapanis, and, as such, collided with the organization of the Soviet scientific establishment, built around the patterns mentioned. As a consequence of this contention, the article examines the tension that arose in Soviet psychology in the 1970s and 1980s between the supporters of the activity theory of A. N. Leontiev on one side and B. F. Lomov’s systems approach on the other. It draws parallels between this collision and the collision of the practices promoted by Lomov with the patterns of the science culture of the late Soviet period. Both external and internal perspectives are employed: the article examines the theoretical contradictions between the activity theory and the systems approach, and at the same time investigates the context of the theoretical argument: the transfer of the leadership in the psychological science from the Academy of the Pedagogical Sciences to the Academy of Sciences of the USSR, the mosaic outlay of the newly established Institute of Psychology, the influence of new approaches to the organization of research

A Short Counterexample Property for Safety and Liveness Verification of Fault-tolerant Distributed Algorithms

Distributed algorithms have many mission-critical applications ranging from embedded systems and replicated databases to cloud computing. Due to asynchronous communication, process faults, or network failures, these algorithms are difficult to design and verify. Many algorithms achieve fault tolerance by using threshold guards that, for instance, ensure that a process waits until it has received an acknowledgment from a majority of its peers. Consequently, domain-specific languages for fault-tolerant distributed systems offer language support for threshold guards. We introduce an automated method for model checking of safety and liveness of threshold-guarded distributed algorithms in systems where the number of processes and the fraction of faulty processes are parameters. Our method is based on a short counterexample property: if a distributed algorithm violates a temporal specification (in a fragment of LTL), then there is a counterexample whose length is bounded and independent of the parameters. We prove this property by (i) characterizing executions depending on the structure of the temporal formula, and (ii) using commutativity of transitions to accelerate and shorten executions. We extended the ByMC toolset (Byzantine Model Checker) with our technique, and verified liveness and safety of 10 prominent fault-tolerant distributed algorithms, most of which were out of reach for existing techniques.Comment: 16 pages, 11 pages appendi

Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many figure

Photon storage in Lambda-type optically dense atomic media. II. Free-space model

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the Lambda system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov et al., Phys. Rev. A 76, 033804 (2007)].Comment: 26 pages, 8 figures. V2: significant changes in presentation, new references, higher resolution of figure

Photon storage in Lambda-type optically dense atomic media. I. Cavity model

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to C/(1+C) independent of the retrieval technique, where C is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of C/(1+C), any smooth input mode satisfying T C gamma >> 1 and a certain class of resonant input modes satisfying T C gamma ~ 1, where T is the duration of the input mode and 2 gamma is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage.Comment: 16 pages, 2 figures. V2: significant changes in presentation, new references, higher resolution of figure