SDDs are Exponentially More Succinct than OBDDs

Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are essentially as tractable as ordered binary decision diagrams (OBDDs), but tend to be more succinct in practice. This makes SDDs a prominent representation language, with many applications in artificial intelligence and knowledge compilation. We prove that SDDs are more succinct than OBDDs also in theory, by constructing a family of boolean functions where each member has polynomial SDD size but exponential OBDD size. This exponential separation improves a quasipolynomial separation recently established by Razgon (2013), and settles an open problem in knowledge compilation

Resource management for software defined data centers for heterogeneous infrastructures

Software Defined Data Center (SDDC) provides more resource management flexibility since everything is defined as a software, including the network as Software Defined Network (SDN).Typically, cloud providers overlook the network, which is configured in static way. SDN can help to meet applications goals with dynamic network configuration and provide best-efforts for QoS. Additionally, SDDC might benefit by instead of be composed by heavy Virtual Machines, use light-weight OS Containers. Despite the advantages of SDDC and OS Containers, it brings more complexity for resource provisioning. The goal of this project is to optimize the management of container based workloads deployed on Software defined Data Centers enabled with heterogeneous network fabrics through the use of network-aware placement algorithms that are driven by performance models

Tsirelson's problem and Kirchberg's conjecture

Tsirelson's problem asks whether the set of nonlocal quantum correlations with a tensor product structure for the Hilbert space coincides with the one where only commutativity between observables located at different sites is assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products of C*-algebras would imply a positive answer to this question for all bipartite scenarios. This remains true also if one considers not only spatial correlations, but also spatiotemporal correlations, where each party is allowed to apply their measurements in temporal succession; we provide an example of a state together with observables such that ordinary spatial correlations are local, while the spatiotemporal correlations reveal nonlocality. Moreover, we find an extended version of Tsirelson's problem which, for each nontrivial Bell scenario, is equivalent to the QWEP conjecture. This extended version can be conveniently formulated in terms of steering the system of a third party. Finally, a comprehensive mathematical appendix offers background material on complete positivity, tensor products of C*-algebras, group C*-algebras, and some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy

The density condition in projective tensor products

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Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Density conditions in Fréchet and (DF)-spaces

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Digital Neutron-Gamma Discrimination Performance of Stilbene in Comparison with Plastic Scintillators

No abstract available