3,943 research outputs found
Sorting photons by radial quantum number
The Laguerre-Gaussian (LG) modes constitute a complete basis set for
representing the transverse structure of a {paraxial} photon field in free
space. Earlier workers have shown how to construct a device for sorting a
photon according to its azimuthal LG mode index, which describes the orbital
angular momentum (OAM) carried by the field. In this paper we propose and
demonstrate a mode sorter based on the fractional Fourier transform (FRFT) to
efficiently decompose the optical field according to its radial profile. We
experimentally characterize the performance of our implementation by separating
individual radial modes as well as superposition states. The reported scheme
can, in principle, achieve unit efficiency and thus can be suitable for
applications that involve quantum states of light. This approach can be readily
combined with existing OAM mode sorters to provide a complete characterization
of the transverse profile of the optical field
Improved Bounds for 3SUM, -SUM, and Linear Degeneracy
Given a set of real numbers, the 3SUM problem is to decide whether there
are three of them that sum to zero. Until a recent breakthrough by Gr{\o}nlund
and Pettie [FOCS'14], a simple -time deterministic algorithm for
this problem was conjectured to be optimal. Over the years many algorithmic
problems have been shown to be reducible from the 3SUM problem or its variants,
including the more generalized forms of the problem, such as -SUM and
-variate linear degeneracy testing (-LDT). The conjectured hardness of
these problems have become extremely popular for basing conditional lower
bounds for numerous algorithmic problems in P.
In this paper, we show that the randomized -linear decision tree
complexity of 3SUM is , and that the randomized -linear
decision tree complexity of -SUM and -LDT is , for any odd
. These bounds improve (albeit randomized) the corresponding
and decision tree bounds
obtained by Gr{\o}nlund and Pettie. Our technique includes a specialized
randomized variant of fractional cascading data structure. Additionally, we
give another deterministic algorithm for 3SUM that runs in time. The latter bound matches a recent independent bound by Freund
[Algorithmica 2017], but our algorithm is somewhat simpler, due to a better use
of word-RAM model
Cascading Quivers from Decaying D-branes
We use an argument analogous to that of Kachru, Pearson and Verlinde to argue
that cascades in L^{a,b,c} quiver gauge theories always preserve the form of
the quiver, and that all gauge groups drop at each step by the number M of
fractional branes. In particular, we demonstrate that an NS5-brane that sweeps
out the S^3 of the base of L^{a,b,c} destroys M D3-branes.Comment: 11 pages, 1 figure; v2: references adde
Holographic dual of the Standard Model on the throat
We apply recent techniques to construct geometries, based on local Calabi-Yau
manifolds, leading to warped throats with 3-form fluxes in string theory, with
interesting structure at their bottom. We provide their holographic dual
description in terms of RG flows for gauge theories with almost conformal
duality cascades and infrared confinement. We describe a model of a throat with
D-branes at its bottom, realizing a 3-family Standard Model like chiral sector.
We provide the explicit holographic dual gauge theory RG flow, and describe the
appearance of the SM degrees of freedom after confinement. As a second
application, we describe throats within throats, namely warped throats with
discontinuous warp factor in different regions of the radial coordinate, and
discuss possible model building applications.Comment: 46 pages, 21 figures, reference adde
Network hierarchy evolution and system vulnerability in power grids
(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.Peer ReviewedPostprint (author's final draft
An Efficient Data Structure for Dynamic Two-Dimensional Reconfiguration
In the presence of dynamic insertions and deletions into a partially
reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of
developing efficient approaches to dynamic defragmentation and reallocation.
One key aspect is to develop efficient algorithms and data structures that
exploit the two-dimensional geometry of a chip, instead of just one. We propose
a new method for this task, based on the fractal structure of a quadtree, which
allows dynamic segmentation of the chip area, along with dynamically adjusting
the necessary communication infrastructure. We describe a number of algorithmic
aspects, and present different solutions. We also provide a number of basic
simulations that indicate that the theoretical worst-case bound may be
pessimistic.Comment: 11 pages, 12 figures; full version of extended abstract that appeared
in ARCS 201
Spatial and performance optimality in power distribution networks
(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Complex network theory has been widely used in vulnerability analysis of power networks, especially for power transmission ones. With the development of the smart grid concept, power distribution networks are becoming increasingly relevant. In this paper, we model power distribution systems as spatial networks. Topological and spatial properties of 14 European power distribution networks are analyzed, together with the relationship between geographical constraints and performance optimization, taking into account economic and vulnerability issues. Supported by empirical reliability data, our results suggest that power distribution networks are influenced by spatial constraints which clearly affect their overall performance.Peer ReviewedPostprint (author's final draft
The -Center Problem in Tree Networks Revisited
We present two improved algorithms for weighted discrete -center problem
for tree networks with vertices. One of our proposed algorithms runs in
time. For all values of , our algorithm
thus runs as fast as or faster than the most efficient time
algorithm obtained by applying Cole's speed-up technique [cole1987] to the
algorithm due to Megiddo and Tamir [megiddo1983], which has remained
unchallenged for nearly 30 years. Our other algorithm, which is more practical,
runs in time, and when it is
faster than Megiddo and Tamir's time algorithm
[megiddo1983]
Branes and fluxes in special holonomy manifolds and cascading field theories
We conduct a study of holographic RG flows whose UV is a theory in 2+1
dimensions decoupled from gravity, and the IR is the N=6,8 superconformal fixed
point of ABJM. The solutions we consider are constructed by warping the
M-theory background whose eight spatial dimensions are manifolds of special
holonomies sp(1) times sp(1) and spin(7). Our main example for the spin(7)
holonomy manifold is the A8 geometry originally constructed by Cvetic, Gibbons,
Lu, and Pope. On the gravity side, our constructions generalize the earlier
construction of RG flow where the UV was N=3 Yang-Mills-Chern-Simons matter
system and are simpler in a number of ways. Through careful consideration of
Page, Maxwell, and brane charges, we identify the discrete and continuous
parameters characterizing each system. We then determine the range of the
discrete data, corresponding to the flux/rank for which the supersymmetry is
unbroken, and estimate the dynamical supersymmetry breaking scale as a function
of these data. We then point out the similarity between the physics of
supersymmetry breaking between our system and the system considered by
Maldacena and Nastase. We also describe the condition for unbroken
supersymmetry on class of construction based on a different class of spin(7)
manifolds known as B8 spaces whose IR is different from that of ABJM and
exhibit some interesting features.Comment: 51 pages, 12 figures. Update in quantization of G4 on B8 in equations
(5.12) and (5.13
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