43,692 research outputs found
Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce
The kernel -means is an effective method for data clustering which extends
the commonly-used -means algorithm to work on a similarity matrix over
complex data structures. The kernel -means algorithm is however
computationally very complex as it requires the complete data matrix to be
calculated and stored. Further, the kernelized nature of the kernel -means
algorithm hinders the parallelization of its computations on modern
infrastructures for distributed computing. In this paper, we are defining a
family of kernel-based low-dimensional embeddings that allows for scaling
kernel -means on MapReduce via an efficient and unified parallelization
strategy. Afterwards, we propose two methods for low-dimensional embedding that
adhere to our definition of the embedding family. Exploiting the proposed
parallelization strategy, we present two scalable MapReduce algorithms for
kernel -means. We demonstrate the effectiveness and efficiency of the
proposed algorithms through an empirical evaluation on benchmark data sets.Comment: Appears in Proceedings of the SIAM International Conference on Data
Mining (SDM), 201
Greybody factor of scalar fields from black strings
The greybody factor of massless, uncharged scalar fields is studied in the
background of cylindrically symmetric spacetimes, in the low-energy
approximation. We discuss two cases. In the first case we derive analytical
expression for the absorption probability when the spacetime is kinetically
coupled with the Einstein tensor. In the second case we do the analysis in the
absence of the coupling constant. For this purpose we analyze the wave equation
which is obtained from Klein-Gordon equation. The radial part of the wave
equation is solved in the form of the hypergeometric function in the near
horizon region, whereas in the far region the solution is of the form of
Bessel's function. Finally, considering continuity of the wave function we
smoothly match the two solutions in the low energy approximation to get the
formula for the absorption probability
Greybody factor of scalar field from Reissner-Nordstrom-de Sitter black hole
In this work we derive a general expression for the greybody factor of
non-minimally coupled scalar fields in Reissner-Nordstr\"om-de Sitter spacetime
in low frequency approximation. In particular case of zero momentum, greybody
factor tends to zero in low frequency limit as frequency squared goes to zero
for non-vanishing coupling. We also elaborate the significance of the results
by giving formulae of differential energy rate and general absorption cross
section. The greybody factor gives insight into the spectrum of Hawking
radiations
Global-local methodologies and their application to nonlinear analysis
An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified
- …