4,274 research outputs found
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Intangible Capital, Corporate Valuation and Asset Pricing
Recent studies have found unmeasured intangible capital to be large and important. In this paper we observe that by nature intangible capital is also very different from physical capital. We find it plausible to argue that the accumulation process for intangible capital differs significantly from the process by which physical capital accumulates. We study the implications of this hypothesis for rational firm valuation and asset pricing using a two-sector general equilibrium model. Our main finding is that the properties of firm valuation and stock prices are very dependent on the assumed accumulation process for intangible capital. If one entertains the possibility that intangible investments translates into capital stochastically, we find that plausible levels of macroeconomic volatility are compatible with highly variable corporate valuations, P/E ratios and stock returns.intangible capital; corporate valuation; stock return volatility
Steady-state analysis of google-like stochastic matrices with block iterative methods
A Google-like matrix is a positive stochastic matrix given by a convex combination of a sparse, nonnegative matrix and a particular rank one matrix. Google itself uses the steady-state vector of a large matrix of this form to help order web pages in a search engine. We investigate the computation of the steady-state vectors of such matrices using block iterative methods. The block partitionings considered include those based on block triangular form and those having triangular diagonal blocks obtained using cutsets. Numerical results show that block Gauss-Seidel with partitionings based on block triangular form is most often the best approach. However, there are cases in which a block partitioning with triangular diagonal blocks is better, and the Gauss-Seidel method is usually competitive. Copyright © 2011, Kent State University
Steady-state analysis of Google-like stochastic matrices
Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2007.Thesis (Master's) -- Bilkent University, 2007.Includes bibliographical references leaves 93-97.Many search engines use a two-step process to retrieve from the web pages related
to a user’s query. In the first step, traditional text processing is performed to find
all pages matching the given query terms. Due to the massive size of the web,
this step can result in thousands of retrieved pages. In the second step, many
search engines sort the list of retrieved pages according to some ranking criterion
to make it manageable for the user. One popular way to create this ranking is
to exploit additional information inherent in the web due to its hyperlink structure.
One successful and well publicized link-based ranking system is PageRank,
the ranking system used by the Google search engine. The dynamically changing
matrices reflecting the hyperlink structure of the web and used by Google
in ranking pages are not only very large, but they are also sparse, reducible,
stochastic matrices with some zero rows. Ranking pages amounts to solving for
the steady-state vectors of linear combinations of these matrices with appropriately
chosen rank-1 matrices. The most suitable method of choice for this task
appears to be the power method. Certain improvements have been obtained using
techniques such as quadratic extrapolation and iterative aggregation. In this thesis,
we propose iterative methods based on various block partitionings, including
those with triangular diagonal blocks obtained using cutsets, for the computation
of the steady-state vector of such stochastic matrices. The proposed iterative
methods together with power and quadratically extrapolated power methods are
coded into a software tool. Experimental results on benchmark matrices show
that it is possible to recommend Gauss-Seidel for easier web problems and block
Gauss-Seidel with partitionings based on a block upper triangular form in the
remaining problems, although it takes about twice as much memory as quadratically
extrapolated power method.Noyan, Gökçe NilM.S
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