6,289 research outputs found
Dynamical system analysis and forecasting of deformation produced by an earthquake fault
We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.Comment: 30 pages, 12 figure
Price Dispersion and Accessibility: A Case study of Fast Food
This study examines spatial variation in the price and accessibility of fast food across a major urban area. We use novel data on the price of a representative fast food meal and the location of fast food restaurants belonging to one of three major chains in the District of Columbia and its surrounding suburbs. These data are used to test a structural model of spatial competition. The results of this study are easily interpreted and compared with a past analysis. We find that spatial differences in costs and demand conditions drive variation in the number of firms operating in a market, which in turn affects prices.food prices, food accessibility, spatial competition, price dispersion, fast food
Characterizing the community structure of complex networks
Community structure is one of the key properties of complex networks and
plays a crucial role in their topology and function. While an impressive amount
of work has been done on the issue of community detection, very little
attention has been so far devoted to the investigation of communities in real
networks. We present a systematic empirical analysis of the statistical
properties of communities in large information, communication, technological,
biological, and social networks. We find that the mesoscopic organization of
networks of the same category is remarkably similar. This is reflected in
several characteristics of community structure, which can be used as
``fingerprints'' of specific network categories. While community size
distributions are always broad, certain categories of networks consist mainly
of tree-like communities, while others have denser modules. Average path
lengths within communities initially grow logarithmically with community size,
but the growth saturates or slows down for communities larger than a
characteristic size. This behaviour is related to the presence of hubs within
communities, whose roles differ across categories. Also the community
embeddedness of nodes, measured in terms of the fraction of links within their
communities, has a characteristic distribution for each category. Our findings
are verified by the use of two fundamentally different community detection
methods.Comment: 15 pages, 20 figures, 4 table
A generalized asynchronous computability theorem
We consider the models of distributed computation defined as subsets of the
runs of the iterated immediate snapshot model. Given a task and a model
, we provide topological conditions for to be solvable in . When
applied to the wait-free model, our conditions result in the celebrated
Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate
the utility of our characterization, we consider a task that has been shown
earlier to admit only a very complex -resilient solution. In contrast, our
generalized computability theorem confirms its -resilient solvability in a
straightforward manner.Comment: 16 pages, 5 figure
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