1,125 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
Time-dependent transonic flow solutions for axial turbomachinery
Three-dimensional unsteady transonic flow through an axial turbomachine stage is described in terms of a pair of two-dimensional formulations pertaining to orthogonal surfaces, namely, a blade-to-blade surface and a hub-to-casing surface. The resulting systems of nonlinear, inviscid, compressible equations of motion are solved by an explicit finite-difference technique. The blade-to-blade program includes the periodic interaction between rotor and stator blade rows. Treatment of the boundary conditions and of the blade slipstream motion by a characteristic type procedure is discussed in detail. Harmonic analysis of the acoustic far field produced by the blade row interaction, including an arbitrary initial transient, is outlined. Results from the blade-to-blade program are compared with experimental measurements of the rotating pressure field at the tip of a high-speed fan. The hub-to-casing program determines circumferentially averaged flow properties on a meridional plane. Blade row interactions are neglected in this formulation, but the force distributions over the entire blade surface for both the rotor and stator are obtained. Results from the hub-to-casing program are compared with a relaxation method solution for a subsonic rotor. Results are also presented for a quiet fan stage which includes transonic flow in both the rotor and stator and a normal shock in the stator
Evolving Network With Different Edges
We proposed an evolving network model constituted by the same nodes but
different edges. The competition between nodes and different links were
introduced. Scale free properties have been found in this model by continuum
theory. Different network topologies can be generated by some tunable
parameters. Simulation results consolidate the prediction.Comment: 14 pages, 9 figures, some contents revised, fluctuation of x degree
adde
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 Quantum Lovasz Local Lemma
The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show
the existence of combinatorial objects meeting a prescribed collection of
"weakly dependent" criteria. We show that the LLL extends to a much more
general geometric setting, where events are replaced with subspaces and
probability is replaced with relative dimension, which allows to lower bound
the dimension of the intersection of vector spaces under certain independence
conditions. Our result immediately applies to the k-QSAT problem: For instance
we show that any collection of rank 1 projectors with the property that each
qubit appears in at most of them, has a joint satisfiable
state.
We then apply our results to the recently studied model of random k-QSAT.
Recent works have shown that the satisfiable region extends up to a density of
1 in the large k limit, where the density is the ratio of projectors to qubits.
Using a hybrid approach building on work by Laumann et al. we greatly extend
the known satisfiable region for random k-QSAT to a density of
. Since our tool allows us to show the existence of joint
satisfying states without the need to construct them, we are able to penetrate
into regions where the satisfying states are conjectured to be entangled,
avoiding the need to construct them, which has limited previous approaches to
product states.Comment: 19 page
Synchronization in Complex Systems Following the Decision Based Queuing Process: The Rhythmic Applause as a Test Case
Living communities can be considered as complex systems, thus a fertile
ground for studies related to their statistics and dynamics. In this study we
revisit the case of the rhythmic applause by utilizing the model proposed by
V\'azquez et al. [A. V\'azquez et al., Phys. Rev. E 73, 036127 (2006)]
augmented with two contradicted {\it driving forces}, namely: {\it
Individuality} and {\it Companionship}. To that extend, after performing
computer simulations with a large number of oscillators we propose an
explanation on the following open questions (a) why synchronization occurs
suddenly, and b) why synchronization is observed when the clapping period
() is ( is the mean self period
of the spectators) and is lost after a time. Moreover, based on the model, a
weak preferential attachment principle is proposed which can produce complex
networks obeying power law in the distribution of number edges per node with
exponent greater than 3.Comment: 16 pages, 5 figure
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
Using graph concepts to understand the organization of complex systems
Complex networks are universal, arising in fields as disparate as sociology,
physics, and biology. In the past decade, extensive research into the
properties and behaviors of complex systems has uncovered surprising
commonalities among the topologies of different systems. Attempts to explain
these similarities have led to the ongoing development and refinement of
network models and graph-theoretical analysis techniques with which to
characterize and understand complexity. In this tutorial, we demonstrate
through illustrative examples, how network measures and models have contributed
to the elucidation of the organization of complex systems.Comment: v(1) 38 pages, 7 figures, to appear in the International Journal of
Bifurcation and Chaos v(2) Line spacing changed; now 23 pages, 7 figures, to
appear in the Special Issue "Complex Networks' Structure and Dynamics'' of
the International Journal of Bifurcation and Chaos (Volume 17, Issue 7, July
2007) edited by S. Boccaletti and V. Lator
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