46,237 research outputs found
Stochastic analysis of different rough surfaces
This paper shows in detail the application of a new stochastic approach for
the characterization of surface height profiles, which is based on the theory
of Markov processes. With this analysis we achieve a characterization of the
scale dependent complexity of surface roughness by means of a Fokker-Planck or
Langevin equation, providing the complete stochastic information of multiscale
joint probabilities. The method is applied to several surfaces with different
properties, for the purpose of showing the utility of this method in more
details. In particular we show the evidence of Markov properties, and we
estimate the parameters of the Fokker-Planck equation by pure, parameter-free
data analysis. The resulting Fokker-Planck equations are verified by numerical
reconstruction of conditional probability density functions. The results are
compared with those from the analysis of multi-affine and extended multi-affine
scaling properties which is often used for surface topographies. The different
surface structures analysed here show in details advantages and disadvantages
of these methods.Comment: Minor text changes to be identical with the published versio
Modelling network travel time reliability under stochastic demand
A technique is proposed for estimating the probability distribution of total network travel time, in the light of normal day-to-day variations in the travel demand matrix over a road traffic network. A solution method is proposed, based on a single run of a standard traffic assignment model, which operates in two stages. In stage one, moments of the total travel time distribution are computed by an analytic method, based on the multivariate moments of the link flow vector. In stage two, a flexible family of density functions is fitted to these moments. It is discussed how the resulting distribution may in practice be used to characterise unreliability. Illustrative numerical tests are reported on a simple network, where the method is seen to provide a means for identifying sensitive or vulnerable links, and for examining the impact on network reliability of changes to link capacities. Computational considerations for large networks, and directions for further research, are discussed
Network Density of States
Spectral analysis connects graph structure to the eigenvalues and
eigenvectors of associated matrices. Much of spectral graph theory descends
directly from spectral geometry, the study of differentiable manifolds through
the spectra of associated differential operators. But the translation from
spectral geometry to spectral graph theory has largely focused on results
involving only a few extreme eigenvalues and their associated eigenvalues.
Unlike in geometry, the study of graphs through the overall distribution of
eigenvalues - the spectral density - is largely limited to simple random graph
models. The interior of the spectrum of real-world graphs remains largely
unexplored, difficult to compute and to interpret.
In this paper, we delve into the heart of spectral densities of real-world
graphs. We borrow tools developed in condensed matter physics, and add novel
adaptations to handle the spectral signatures of common graph motifs. The
resulting methods are highly efficient, as we illustrate by computing spectral
densities for graphs with over a billion edges on a single compute node. Beyond
providing visually compelling fingerprints of graphs, we show how the
estimation of spectral densities facilitates the computation of many common
centrality measures, and use spectral densities to estimate meaningful
information about graph structure that cannot be inferred from the extremal
eigenpairs alone.Comment: 10 pages, 7 figure
On Modeling Economic Default Time: A Reduced-Form Model Approach
In the aftermath of the global financial crisis, much attention has been paid
to investigating the appropriateness of the current practice of default risk
modeling in banking, finance and insurance industries. A recent empirical study
by Guo et al.(2008) shows that the time difference between the economic and
recorded default dates has a significant impact on recovery rate estimates. Guo
et al.(2011) develop a theoretical structural firm asset value model for a firm
default process that embeds the distinction of these two default times. To be
more consistent with the practice, in this paper, we assume the market
participants cannot observe the firm asset value directly and developed a
reduced-form model to characterize the economic and recorded default times. We
derive the probability distribution of these two default times. The numerical
study on the difference between these two shows that our proposed model can
both capture the features and fit the empirical data.Comment: arXiv admin note: text overlap with arXiv:1012.0843 by other author
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