90 research outputs found
Community detection in temporal multilayer networks, with an application to correlation networks
Networks are a convenient way to represent complex systems of interacting
entities. Many networks contain "communities" of nodes that are more densely
connected to each other than to nodes in the rest of the network. In this
paper, we investigate the detection of communities in temporal networks
represented as multilayer networks. As a focal example, we study time-dependent
financial-asset correlation networks. We first argue that the use of the
"modularity" quality function---which is defined by comparing edge weights in
an observed network to expected edge weights in a "null network"---is
application-dependent. We differentiate between "null networks" and "null
models" in our discussion of modularity maximization, and we highlight that the
same null network can correspond to different null models. We then investigate
a multilayer modularity-maximization problem to identify communities in
temporal networks. Our multilayer analysis only depends on the form of the
maximization problem and not on the specific quality function that one chooses.
We introduce a diagnostic to measure \emph{persistence} of community structure
in a multilayer network partition. We prove several results that describe how
the multilayer maximization problem measures a trade-off between static
community structure within layers and larger values of persistence across
layers. We also discuss some computational issues that the popular "Louvain"
heuristic faces with temporal multilayer networks and suggest ways to mitigate
them.Comment: 42 pages, many figures, final accepted version before typesettin
The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market
We investigate triangular arbitrage within the spot foreign exchange market
using high-frequency executable prices. We show that triangular arbitrage
opportunities do exist, but that most have short durations and small
magnitudes. We find intra-day variations in the number and length of arbitrage
opportunities, with larger numbers of opportunities with shorter mean durations
occurring during more liquid hours. We demonstrate further that the number of
arbitrage opportunities has decreased in recent years, implying a corresponding
increase in pricing efficiency. Using trading simulations, we show that a
trader would need to beat other market participants to an unfeasibly large
proportion of arbitrage prices to profit from triangular arbitrage over a
prolonged period of time. Our results suggest that the foreign exchange market
is internally self-consistent and provide a limited verification of market
efficiency
Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion
Extending our previous work on 2D growth for the Laplace equation we study
here {\it multidimensional} growth for {\it arbitrary elliptic} equations,
describing inhomogeneous and anisotropic pattern formations processes. We find
that these nonlinear processes are governed by an infinite number of
conservation laws. Moreover, in many cases {\it all dynamics of the interface
can be reduced to the linear time--dependence of only one ``moment" }
which corresponds to the changing volume while {\it all higher moments, ,
are constant in time. These moments have a purely geometrical nature}, and thus
carry information about the moving shape. These conserved quantities (eqs.~(7)
and (8) of this article) are interpreted as coefficients of the multipole
expansion of the Newtonian potential created by the mass uniformly occupying
the domain enclosing the moving interface. Thus the question of how to recover
the moving shape using these conserved quantities is reduced to the classical
inverse potential problem of reconstructing the shape of a body from its
exterior gravitational potential. Our results also suggest the possibility of
controlling a moving interface by appropriate varying the location and strength
of sources and sinks.Comment: CYCLER Paper 93feb00
Singular Laplacian Growth
The general equations of motion for two dimensional Laplacian growth are
derived using the conformal mapping method. In the singular case, all
singularities of the conformal map are on the unit circle, and the map is a
degenerate Schwarz-Christoffel map. The equations of motion describe the
motions of these singularities. Despite the typical fractal-like outcomes of
Laplacian growth processes, the equations of motion are shown to be not
particularly sensitive to initial conditions. It is argued that the sensitivity
of this system derives from a novel cause, the non-uniqueness of solutions to
the differential system. By a mechanism of singularity creation, every solution
can become more complex, even in the absence of noise, without violating the
growth law. These processes are permitted, but are not required, meaning the
equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.
Bayesian genome assembly and assessment by Markov Chain Monte Carlo sampling
Most genome assemblers construct point estimates, choosing a genome sequence
from among many alternative hypotheses that are supported by the data. We
present a Markov Chain Monte Carlo approach to sequence assembly that instead
generates distributions of assembly hypotheses with posterior probabilities,
providing an explicit statistical framework for evaluating alternative
hypotheses and assessing assembly uncertainty. We implement this approach in a
prototype assembler and illustrate its application to the bacteriophage
PhiX174.Comment: 17 pages, 5 figure
A theory for the impact of a wave breaking onto a permeable barrier with jet generation
We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall
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Hybrid Parallelism for Volume Rendering on Large, Multi- and Many-core Systems
With the computing industry trending towards multi- and many-core processors, we study how a standard visualization algorithm, ray-casting volume rendering, can benefit from a hybrid parallelism approach. Hybrid parallelism provides the best of both worlds: using distributed-memory parallelism across a large numbers of nodes increases available FLOPs and memory, while exploiting shared-memory parallelism among the cores within each node ensures that each node performs its portion of the larger calculation as efficiently as possible. We demonstrate results from weak and strong scaling studies, at levels of concurrency ranging up to 216,000, and with datasets as large as 12.2 trillion cells. The greatest benefit from hybrid parallelism lies in the communication portion of the algorithm, the dominant cost at higher levels of concurrency. We show that reducing the number of participants with a hybrid approach significantly improves performance
Detecting a Currency's Dominance or Dependence using Foreign Exchange Network Trees
In a system containing a large number of interacting stochastic processes,
there will typically be many non-zero correlation coefficients. This makes it
difficult to either visualize the system's inter-dependencies, or identify its
dominant elements. Such a situation arises in Foreign Exchange (FX) which is
the world's biggest market. Here we develop a network analysis of these
correlations using Minimum Spanning Trees (MSTs). We show that not only do the
MSTs provide a meaningful representation of the global FX dynamics, but they
also enable one to determine momentarily dominant and dependent currencies. We
find that information about a country's geographical ties emerges from the raw
exchange-rate data. Most importantly from a trading perspective, we discuss how
to infer which currencies are `in play' during a particular period of time
A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation
We present a new class of exact solutions for the so-called {\it Laplacian
Growth Equation} describing the zero-surface-tension limit of a variety of 2D
pattern formation problems. Contrary to common belief, we prove that these
solutions are free of finite-time singularities (cusps) for quite general
initial conditions and may well describe real fingering instabilities. At long
times the interface consists of N separated moving Saffman-Taylor fingers, with
``stagnation points'' in between, in agreement with numerous observations. This
evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file
H5hut: A high-performance I/O library for particle-based simulations
Particle-based simulations running on large high-performance computing systems over many time steps can generate an enormous amount of particle- and field-based data for post-processing and analysis. Achieving high-performance I/O for this data, effectively managing it on disk, and interfacing it with analysis and visualization tools can be challenging, especially for domain scientists who do not have I/O and data management expertise. We present the H5hut library, an implementation of several data models for particle-based simulations that encapsulates the complexity of HDF5 and is simple to use, yet does not compromise performance
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