892 research outputs found
Existence of the D0-D4 Bound State: a detailed Proof
We consider the supersymmetric quantum mechanical system which is obtained by
dimensionally reducing d=6, N=1 supersymmetric gauge theory with gauge group
U(1) and a single charged hypermultiplet. Using the deformation method and
ideas introduced by Porrati and Rozenberg, we present a detailed proof of the
existence of a normalizable ground state for this system
Recommendation Subgraphs for Web Discovery
Recommendations are central to the utility of many websites including
YouTube, Quora as well as popular e-commerce stores. Such sites typically
contain a set of recommendations on every product page that enables visitors to
easily navigate the website. Choosing an appropriate set of recommendations at
each page is one of the key features of backend engines that have been deployed
at several e-commerce sites.
Specifically at BloomReach, an engine consisting of several independent
components analyzes and optimizes its clients' websites. This paper focuses on
the structure optimizer component which improves the website navigation
experience that enables the discovery of novel content.
We begin by formalizing the concept of recommendations used for discovery. We
formulate this as a natural graph optimization problem which in its simplest
case, reduces to a bipartite matching problem. In practice, solving these
matching problems requires superlinear time and is not scalable. Also,
implementing simple algorithms is critical in practice because they are
significantly easier to maintain in production. This motivated us to analyze
three methods for solving the problem in increasing order of sophistication: a
sampling algorithm, a greedy algorithm and a more involved partitioning based
algorithm.
We first theoretically analyze the performance of these three methods on
random graph models characterizing when each method will yield a solution of
sufficient quality and the parameter ranges when more sophistication is needed.
We complement this by providing an empirical analysis of these algorithms on
simulated and real-world production data. Our results confirm that it is not
always necessary to implement complicated algorithms in the real-world and that
very good practical results can be obtained by using heuristics that are backed
by the confidence of concrete theoretical guarantees
On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
We give a new proof of uniqueness of solutions to the Gross-Pitaevskii
hierarchy, first established by Erdos, Schlein and Yau, in a different space,
based on space-time estimates
The Geometric Phase and Gravitational Precession of D-Branes
We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in
the background of D4-branes, the first excited states undergo a holonomy
described by a non-Abelian Berry connection. At weak coupling this is an SU(2)
connection over R^5, known as the Yang monopole. At strong coupling, the
holonomy is recast as the classical gravitational precession of a spinning
particle. The Berry connection is the spin connection of the near-horizon limit
of the D4-branes, which is a continuous deformation of the Yang and anti-Yang
monopole.Comment: 23 pages; v3: typos correcte
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Scaling of load in communications networks
We show that the load at each node in a preferential attachment network
scales as a power of the degree of the node. For a network whose degree
distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with
eta = gamma - 1, implying that the probability distribution for the load is
p(l) ~ 1/l^2 independent of gamma. The results are obtained through scaling
arguments supported by finite size scaling studies. They contradict earlier
claims, but are in agreement with the exact solution for the special case of
tree graphs. Results are also presented for real communications networks at the
IP layer, using the latest available data. Our analysis of the data shows
relatively poor power-law degree distributions as compared to the scaling of
the load versus degree. This emphasizes the importance of the load in network
analysis.Comment: 4 pages, 5 figure
A class of phylogenetic networks reconstructable from ancestral profiles
Rooted phylogenetic networks provide an explicit representation of the
evolutionary history of a set of sampled species. In contrast to
phylogenetic trees which show only speciation events, networks can also
accommodate reticulate processes (for example, hybrid evolution, endosymbiosis,
and lateral gene transfer). A major goal in systematic biology is to infer
evolutionary relationships, and while phylogenetic trees can be uniquely
determined from various simple combinatorial data on , for networks the
reconstruction question is much more subtle. Here we ask when can a network be
uniquely reconstructed from its `ancestral profile' (the number of paths from
each ancestral vertex to each element in ). We show that reconstruction
holds (even within the class of all networks) for a class of networks we call
`orchard networks', and we provide a polynomial-time algorithm for
reconstructing any orchard network from its ancestral profile. Our approach
relies on establishing a structural theorem for orchard networks, which also
provides for a fast (polynomial-time) algorithm to test if any given network is
of orchard type. Since the class of orchard networks includes tree-sibling
tree-consistent networks and tree-child networks, our result generalise
reconstruction results from 2008 and 2009. Orchard networks allow for an
unbounded number of reticulation vertices, in contrast to tree-sibling
tree-consistent networks and tree-child networks for which is at most
and , respectively.Comment: 21 pages, 5 figure
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