513,536 research outputs found
Upward-closed hereditary families in the dominance order
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
of graphs to be dominance monotone if whenever no realization of
contains an element as an induced subgraph, and majorizes
, then no realization of induces an element of . 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
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
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
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
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
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