52,485 research outputs found
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings
We propose a method for effectively upscaling incompressible viscous flow in
large random polydispersed sphere packings: the emphasis of this method is on
the determination of the forces applied on the solid particles by the fluid.
Pore bodies and their connections are defined locally through a regular
Delaunay triangulation of the packings. Viscous flow equations are upscaled at
the pore level, and approximated with a finite volume numerical scheme. We
compare numerical simulations of the proposed method to detailed finite element
(FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A
good agreement is found both in terms of forces exerted on the solid particles
and effective permeability coefficients
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
We present two graph-based algorithms for multiclass segmentation of
high-dimensional data. The algorithms use a diffuse interface model based on
the Ginzburg-Landau functional, related to total variation compressed sensing
and image processing. A multiclass extension is introduced using the Gibbs
simplex, with the functional's double-well potential modified to handle the
multiclass case. The first algorithm minimizes the functional using a convex
splitting numerical scheme. The second algorithm is a uses a graph adaptation
of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates
between diffusion and thresholding. We demonstrate the performance of both
algorithms experimentally on synthetic data, grayscale and color images, and
several benchmark data sets such as MNIST, COIL and WebKB. We also make use of
fast numerical solvers for finding the eigenvectors and eigenvalues of the
graph Laplacian, and take advantage of the sparsity of the matrix. Experiments
indicate that the results are competitive with or better than the current
state-of-the-art multiclass segmentation algorithms.Comment: 14 page
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Agent based modeling of energy networks
Attempts to model any present or future power grid face a huge challenge because a power grid is a complex system, with feedback and multi-agent behaviors, integrated by generation, distribution, storage and consumption systems, using various control and automation computing systems to manage electricity flows.
Our approach to modeling is to build upon an established model of the low voltage electricity network which is tested and proven, by extending it to a generalized energy model.
But, in order to address the crucial issues of energy efficiency, additional processes like energy conversion and storage, and further energy carriers, such as gas, heat, etc., besides the traditional electrical one, must be considered. Therefore a more powerful model, provided with enhanced nodes or conversion points, able to deal with multidimensional flows, is being required.
This article addresses the issue of modeling a local multi-carrier energy network. This problem can be considered as an extension of modeling a low voltage distribution network located at some urban or rural geographic area. But instead of using an external power flow analysis package to do the power flow calculations, as used in electric networks, in this work we integrate a multiagent algorithm to perform the task, in a concurrent way to the other simulation tasks, and not only for the electric fluid but also for a number of additional energy carriers. As the model is mainly focused in system operation, generation and load models are not developed
Complex networks analysis in socioeconomic models
This chapter aims at reviewing complex networks models and methods that were
either developed for or applied to socioeconomic issues, and pertinent to the
theme of New Economic Geography. After an introduction to the foundations of
the field of complex networks, the present summary adds insights on the
statistical mechanical approach, and on the most relevant computational aspects
for the treatment of these systems. As the most frequently used model for
interacting agent-based systems, a brief description of the statistical
mechanics of the classical Ising model on regular lattices, together with
recent extensions of the same model on small-world Watts-Strogatz and
scale-free Albert-Barabasi complex networks is included. Other sections of the
chapter are devoted to applications of complex networks to economics, finance,
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issues, including results for opinion and citation networks.
Finally, some avenues for future research are introduced before summarizing the
main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared
for Complexity and Geographical Economics - Topics and Tools, P.
Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published
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