11,717 research outputs found
Hashing for Similarity Search: A Survey
Similarity search (nearest neighbor search) is a problem of pursuing the data
items whose distances to a query item are the smallest from a large database.
Various methods have been developed to address this problem, and recently a lot
of efforts have been devoted to approximate search. In this paper, we present a
survey on one of the main solutions, hashing, which has been widely studied
since the pioneering work locality sensitive hashing. We divide the hashing
algorithms two main categories: locality sensitive hashing, which designs hash
functions without exploring the data distribution and learning to hash, which
learns hash functions according the data distribution, and review them from
various aspects, including hash function design and distance measure and search
scheme in the hash coding space
Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics
(SEASD), a novel computational method for dynamic simulations of polydisperse
colloidal suspensions with full hydrodynamic interactions. SEASD is based on
the framework of Stokesian Dynamics (SD) with extension to compressible
solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J.
Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet
the performance requirement of dynamic simulations, we use Graphic Processing
Units (GPU) to evaluate the suspension mobility, and achieve an order of
magnitude speedup compared to a CPU implementation. For further speedup, we
develop a novel far-field block-diagonal preconditioner to reduce the far-field
evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of
the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118
(2003) 10323]. We extensively discuss implementation and parameter selection
strategies in SEASD, and demonstrate the spectral accuracy in the mobility
evaluation and the overall computation scaling. We
present three computational examples to further validate SEASD and SEASD-nf in
monodisperse and bidisperse suspensions: the short-time transport properties,
the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear
Brownian rheology. Our validation results show that the agreement between SEASD
and SEASD-nf is satisfactory over a wide range of parameters, and also provide
significant insight into the dynamics of polydisperse colloidal suspensions.Comment: 39 pages, 21 figure
Khovanov-Rozansky homology via a canopolis formalism
In this paper, we describe a canopolis (i.e. categorified planar algebra)
formalism for Khovanov and Rozansky's link homology theory. We show how this
allows us to organize simplifications in the matrix factorizations appearing in
their theory. In particular, it will put the equivalence of the original
definition of Khovanov-Rozansky homology and the definition using Soergel
bimodules in a more general context, allow us to give a new proof of the
invariance of triply graded homology and give new analysis of the behavior of
triply graded homology under the Reidemeister IIb move.Comment: 24 pages, 7 figures. v3: edited introduction and fixed diagram 1,
plus minor change
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling
The goal of decentralized optimization over a network is to optimize a global
objective formed by a sum of local (possibly nonsmooth) convex functions using
only local computation and communication. It arises in various application
domains, including distributed tracking and localization, multi-agent
co-ordination, estimation in sensor networks, and large-scale optimization in
machine learning. We develop and analyze distributed algorithms based on dual
averaging of subgradients, and we provide sharp bounds on their convergence
rates as a function of the network size and topology. Our method of analysis
allows for a clear separation between the convergence of the optimization
algorithm itself and the effects of communication constraints arising from the
network structure. In particular, we show that the number of iterations
required by our algorithm scales inversely in the spectral gap of the network.
The sharpness of this prediction is confirmed both by theoretical lower bounds
and simulations for various networks. Our approach includes both the cases of
deterministic optimization and communication, as well as problems with
stochastic optimization and/or communication.Comment: 40 pages, 4 figure
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