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56
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 406 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
How to Get an Exact Sample From a Generic Markov Chain and Sample a Random Spanning Tree From a Directed Graph, Both Within the Cover Time
 In Proceedings of the Seventh Annual ACMSIAM Symposium on Discrete Algorithms
, 1996
"... This paper shows how to obtain unbiased samples from an unknown Markov chain by observing it for O(T c ) steps, where T c is the cover time. This algorithm improves on several previous algorithms, and there is a matching lower bound. Using the techniques from the sampling algorithm, we also show how ..."
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Cited by 13 (2 self)
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This paper shows how to obtain unbiased samples from an unknown Markov chain by observing it for O(T c ) steps, where T c is the cover time. This algorithm improves on several previous algorithms, and there is a matching lower bound. Using the techniques from the sampling algorithm, we also show how to sample random directed spanning trees from a weighted directed graph, with arcs directed to a root, and probability proportional to the product of the edge weights. This tree sampling algorithm runs within 18 cover times of the associated random walk, and is more generally applicable than the algorithm of Broder and Aldous. 1 Introduction Random sampling of combinatorial objects has found numerous applications in computer science and statistics. Examples include approximate enumeration and estimation of the expected value of quantities. Usually there is a finite space X of objects, and a probability distribution ß on X , and we wish to sample object x 2 X with probability ß(x). One ef...
In defence of naiveté: The conceptual status of lagrangian quantum field theory
 SYNTHESE 151
, 2001
"... I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive ’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conc ..."
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Cited by 9 (5 self)
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I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive ’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too illdefined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.
Towards a Paradigm Change in Computer Science and Software Engineering: A Synthesis
 THE KNOWLEDGE ENGINEERING REVIEW
, 2004
"... In this paper, we identify and analyze a set of characteristics that increasingly distinguish today's complex software systems from "traditional" ones. Several examples in different areas show that these characteristics are not limited to a few application domains but are widespread. Then, we discus ..."
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Cited by 8 (0 self)
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In this paper, we identify and analyze a set of characteristics that increasingly distinguish today's complex software systems from "traditional" ones. Several examples in different areas show that these characteristics are not limited to a few application domains but are widespread. Then, we discuss how these characteristics are likely to impact dramatically the very way software systems are modeled and engineered. In particular, we appear to be on the edge of a radical shift of paradigm, about to change our very attitudes in software systems modeling and engineering.
A Renormalization Group approach to relativistic Cosmology
"... We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a “3+1 ” formalism and invokes the coarse graining arguments, provided and supported by the realspace Renormalization Group (RG) methods, in parallel with lattice models of Statistical Mechanic ..."
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Cited by 7 (3 self)
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We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a “3+1 ” formalism and invokes the coarse graining arguments, provided and supported by the realspace Renormalization Group (RG) methods, in parallel with lattice models of Statistical Mechanics. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the RicciHamilton equations studied in connection with the geometry of threemanifolds. The possible relevance of the RicciHamilton flow in implementing the averaging in cosmology has been previously advocated, but the physical motivations behind this suggestion were not clear. The RG interpretation provides us with such physical motivations. The properties of the RicciHamilton flow make it possible to study a critical behaviour of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheetlike structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant
The Evolutionary Unfolding of Complexity
, 1999
"... We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution  a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of chang ..."
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Cited by 7 (2 self)
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We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution  a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach  statistical dynamics  combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current "landscape" models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher tness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.
Mission Impossible: Find a Random Pseudorandom Number Generator
 Computers in Physics, Vol.9
, 1995
"... In this column, we present some practical aspects about constructing a new test bench for random number sequences. The tests are based on two commonly used physical models in studies of statistical mechanics, namely the twodimensional Ising spin model and random walks. We illustrate by a few examp ..."
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Cited by 6 (0 self)
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In this column, we present some practical aspects about constructing a new test bench for random number sequences. The tests are based on two commonly used physical models in studies of statistical mechanics, namely the twodimensional Ising spin model and random walks. We illustrate by a few examples the sensitivity of the tests by showing their ability to find rather weak correlations in some commonly used pseudorandom number generators. 1 Email addresses of the authors are Ilpo.Vattulainen@csc.fi and ala@phcu.helsinki.fi. Introduction Random numbers have a wide variety of practical uses in modern applications. For example, in Monte Carlo (MC) simulations random numbers have been used since the late 1940's to model stochastic elements of nature, in telecommunication systems such as GSM (Global System for Mobile communications) random numbers are used to prevent eavesdropping, and in several kinds of optimization problems random numbers have a lot of use. We must note, however, ...
Monte Carlo without Chains
"... A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; er ..."
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Cited by 5 (3 self)
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A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the EdwardsAnderson spin glass in three dimensions.
Exact renormalization group flow equations for free energies and Npoint functions in uniform external fields
 MUMTHP 98/001 hepth/9801124
, 1998
"... The exact Wilson/Polchinski renormalization group equation is projected onto its uniform external field dependent effective free energy and connected Green’s functions. The result is a hierarchy of equations which admits a choice of “natural ” truncation and closure schemes for nonperturbative appro ..."
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Cited by 3 (0 self)
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The exact Wilson/Polchinski renormalization group equation is projected onto its uniform external field dependent effective free energy and connected Green’s functions. The result is a hierarchy of equations which admits a choice of “natural ” truncation and closure schemes for nonperturbative approximate solution. In this way approximation schemes can be generated which avoid power series expansions in either fields or momenta. When following one closure scheme the lowest order equation is the mean field approximation, while another closure scheme gives the “local potential approximation.” Extension of these closure schemes to higher orders leads to interesting new questions regarding truncation schemes and the convergence of nonperturbative approximations. One scheme, based on a novel “momentum cluster decomposition ” of the connected Green’s functions, seems to offer new possibilities for accurate nonperturbative successive appproximation. 1
Exact Sampling with Markov Chains
 Ph.D. Dissertation, M.I.T., http://dimacs.rutgers.edu/∼dbwilson
, 1996
"... Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution ß from which we wish to sample. After the Markov chain has been ..."
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Cited by 3 (0 self)
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Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution ß from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to ß. The principal problem with this approach is that it is often difficult to determine how long to run the Markov chain. In this thesis we present several algorithms that use Markov chains to return samples distributed exactly according to ß. The algorithms determine on their own how long to run the Markov chain. Two of the algorithms may be used with any Markov chain, but are useful only if the state space is not too large. Nonetheless, a spinoff of these two algorithms is a procedure for sampling random spanning trees of a directed graph that runs more quickly than the Aldous/Broder algorithm. Another of the exact sa...