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    ABSTRACT: A new test is presented for the BIBO stability of delay systems of neutral type with a single delay, specified in terms of their transfer functions, enabling us to decide on some cases that were previously open. Next, a class of fractional systems is considered, and a method is given for determining the stability intervals for such systems.
    Systems & Control Letters 01/2014; 64:43–46.
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    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 07/2012; 370(1971):3273-6.
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    ABSTRACT: This paper introduces a general continuous-time mathematical framework for solution of dynamic mean-variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean-variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme's symmetry on trading behaviour and fund performance.
    04/2012;
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    ABSTRACT: The natural world's interconnectivity should inspire better models of the Universe, says Barry Cooper.
    Nature 02/2012; 482(7386):465.
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    ABSTRACT: Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations leads to corresponding hierarchies of such equations for which conservation laws and Lax pairs are constructed. Finally, using the continuous symmetry reduction approach, an integrable, multidimensionally consistent system of partial differential equations is derived in relation with the lattice modified Boussinesq system.
    Physics Letters A 12/2011; 376(35).
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    ABSTRACT: Since the foot-and-mouth disease outbreak of 2001 in the United Kingdom, there has been debate about the sharing, between government and industry, both the costs of livestock disease outbreaks and responsibility for the decisions that give rise to them. As part of a consultation into the formation of a new body to manage livestock diseases, government veterinarians and economists produced estimates of the average annual costs for a number of exotic infectious diseases. In this article, we demonstrate how the government experts were helped to quantify their uncertainties about the cost estimates using formal expert elicitation techniques. This has enabled the decisionmakers to have a greater appreciation of government experts' uncertainty in this policy area.
    Risk Analysis 10/2011; 32(5):881-93.
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    ABSTRACT: The cubic-quintic Swift-Hohenberg equation (SH35) provides a convenient order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use SH35 with an additional quadratic term to determine the qualitative effects of breaking the midplane reflection symmetry on the properties of spatially localized structures in these systems. Our results describe how the snakes-and-ladders organization of localized structures in SH35 deforms with increasing symmetry breaking and show that the deformation ultimately generates the snakes-and-ladders structure familiar from the quadratic-cubic Swift-Hohenberg equation. Moreover, in nonvariational systems, such as convection, odd-parity convectons necessarily drift when the reflection symmetry is broken, permitting collisions among moving localized structures. Collisions between both identical and nonidentical traveling states are described.
    Physical Review E 07/2011; 84(1 Pt 2):016204.
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    ABSTRACT: We consider a class of map, recently derived in the context of cluster mutation. In this paper, we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra of a special family of functions associated with these maps. A bi-Hamiltonian structure is derived and used to construct a sequence of Poisson-commuting functions and hence show complete integrability. Canonical coordinates are derived, with the map now being a canonical transformation with a sequence of commuting invariant functions. Compatibility of a pair of these functions gives rise to Liouville's equation and the map plays the role of a Bäcklund transformation.
    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 03/2011; 369(1939):1264-79.
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    ABSTRACT: We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R4. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces.
    Advances in Mathematics. 02/2011;
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    ABSTRACT: A relational first order structure is homogeneous if it is countable (possibly finite) and every isomorphism between finite substructures extends to an automorphism. This article is a survey of several aspects of homogeneity, with emphasis on countably infinite homogeneous structures. These arise as Fraissé limits of amalgamation classes of finite structures. The subject has connections to model theory, to permutation group theory, to combinatorics (for example through combinatorial enumeration, and through Ramsey theory), and to descriptive set theory. Recently there has been a focus on connections to topological dynamics, and to constraint satisfaction. The article discusses connections between these topics, with an emphasis on examples, and on special properties of an amalgamation class which yield important consequences for the automorphism group.
    Discrete Mathematics. 01/2011;
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