501,204 research outputs found

    Upward-closed hereditary families in the dominance order

    Get PDF
    The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Hammer et al. and Merris, the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class F\mathcal{F} of graphs to be dominance monotone if whenever no realization of ee contains an element F\mathcal{F} as an induced subgraph, and dd majorizes ee, then no realization of dd induces an element of F\mathcal{F}. We present conditions necessary for a set of graphs to be dominance monotone, and we identify the dominance monotone sets of order at most 3.Comment: 15 pages, 6 figure

    Optimal split of orders across liquidity pools: a stochastic algorithm approach

    Get PDF
    Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues

    Optimal split of orders across liquidity pools: a stochastic algorithm approach

    Get PDF
    Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.Asset allocation, Stochastic Lagrangian algorithm, reinforcement principle, monotone dynamic system

    Split supersymmetry and the role of a light fermion in a supergravity-based scenario

    Full text link
    We investigate split supersymmetry (SUSY) within a supergravity framework, where local SUSY is broken by the F-term of a hidden sector chiral superfield X. With reasonably general assumptions, we show that the fermionic component of X will always have mass within a Tev. Though its coupling to the observable sector superfields is highly suppressed in Tev scale SUSY, we show that it can be enhanced by many orders in split SUSY, leading to its likely participation in accelerator phenomenology.We conclude with a specific example of such a scenario in a string based supergravity model.Comment: 12 Pages, Latex, Title changed, version thoroughly revise

    Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid

    Full text link
    Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid Q, which we call `Q-order'. This requires a theory of semicategories enriched in the quantaloid Q, that admit a suitable Cauchy completion. There is a quantaloid Idl(Q) of Q-orders and ideal relations, and a locally ordered category Ord(Q) of Q-orders and monotone maps; actually, Ord(Q)=Map(Idl(Q)). In particular is Ord(Omega), with Omega a locale, the category of ordered objects in the topos of sheaves on Omega. In general Q-orders can equivalently be described as Cauchy complete categories enriched in the split-idempotent completion of Q. Applied to a locale Omega this generalizes and unifies previous treatments of (ordered) sheaves on Omega in terms of Omega-enriched structures.Comment: 21 page
    • …
    corecore