18,076 research outputs found
Implementation in mixed Nash equilibrium
A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskinâs definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskinâs monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium
Infinitesimal local operations and differential conditions for entanglement monotones
Much of the theory of entanglement concerns the transformations that are
possible to a state under local operations with classical communication (LOCC);
however, this set of operations is complicated and difficult to describe
mathematically. An idea which has proven very useful is that of the {\it
entanglement monotone}: a function of the state which is invariant under local
unitary transformations and always decreases (or increases) on average after
any local operation. In this paper we look on LOCC as the set of operations
generated by {\it infinitesimal local operations}, operations which can be
performed locally and which leave the state little changed. We show that a
necessary and sufficient condition for a function of the state to be an
entanglement monotone under local operations that do not involve information
loss is that the function be a monotone under infinitesimal local operations.
We then derive necessary and sufficient differential conditions for a function
of the state to be an entanglement monotone. We first derive two conditions for
local operations without information loss, and then show that they can be
extended to more general operations by adding the requirement of {\it
convexity}. We then demonstrate that a number of known entanglement monotones
satisfy these differential criteria. Finally, as an application, we use the
differential conditions to construct a new polynomial entanglement monotone for
three-qubit pure states. It is our hope that this approach will avoid some of
the difficulties in the theory of multipartite and mixed-state entanglement.Comment: 21 pages, RevTeX format, no figures, three minor corrections,
including a factor of two in the differential conditions, the tracelessness
of the matrix in the convexity condition, and the proof that the local purity
is a monotone under local measurements. The conclusions of the paper are
unaffecte
Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?
We discuss the monotonicity under local operations and classical
communication (LOCC) of systematically constructed quantities aiming at
quantification of entanglement properties of multipartite quantum systems. The
so-called generalized multipartite concurrences can qualify as legitimate
entanglement measures if they are monotonous under LOCC. In the paper we give a
necessary and sufficient criterion for their monotonicity.Comment: 7 pages, 1 figure, minor changes - clarity of proofs improve
Entanglement monotones
In the context of quantifying entanglement we study those functions of a
multipartite state which do not increase under the set of local
transformations. A mathematical characterization of these monotone magnitudes
is presented. They are then related to optimal strategies of conversion of
shared states. More detailed results are presented for pure states of bipartite
systems. It is show that more than one measure are required simultaneously in
order to quantify completely the non-local resources contained in a bipartite
pure state, while examining how this fact does not hold in the so-called
asymptotic limit. Finally, monotonicity under local transformations is proposed
as the only natural requirement for measures of entanglement.Comment: Revtex, 13 pages, no figures. Previous title: "On the
characterization of entanglement". Major changes in notation and structure.
Some new results, comments and references have been adde
Formal Synthesis of Control Strategies for Positive Monotone Systems
We design controllers from formal specifications for positive discrete-time
monotone systems that are subject to bounded disturbances. Such systems are
widely used to model the dynamics of transportation and biological networks.
The specifications are described using signal temporal logic (STL), which can
express a broad range of temporal properties. We formulate the problem as a
mixed-integer linear program (MILP) and show that under the assumptions made in
this paper, which are not restrictive for traffic applications, the existence
of open-loop control policies is sufficient and almost necessary to ensure the
satisfaction of STL formulas. We establish a relation between satisfaction of
STL formulas in infinite time and set-invariance theories and provide an
efficient method to compute robust control invariant sets in high dimensions.
We also develop a robust model predictive framework to plan controls optimally
while ensuring the satisfaction of the specification. Illustrative examples and
a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16
pages, double colum
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