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819
Generalized flows, intrinsic stochasticity, and turbulent transport
 Proc. Natl. Acad. Sci. USA
, 2000
"... ABSTRACT The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs which no longer satisfy the uniqueness theorem for ODEs. Two most natural r ..."
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Cited by 10 (1 self)
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ABSTRACT The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs which no longer satisfy the uniqueness theorem for ODEs. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field are considered. Whiteintime random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes characterized by their degrees of compressibility are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behavior for the structure functions of the passive scalar. Physically this means that the scaling depends on Prandtl number. In the other two regimes the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution ” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime which is the regime of inverse cascade. Existence and uniqueness of an invariant measure is also proved in these regimes when the transport equation is suitably forced. Finally incomplete selfsimilarity in the sense of BarenblattChorin is established.
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 639 (15 self)
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The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic
MODELING AND OPTIMAL CONTROL OF ESCHERICHIA COLI GENETIC CIRCUITS WITH INTRINSIC STOCHASTICITY
, 2006
"... This work considers aspects of the pathway performance optimization of Escherichia coli genetic circuits. A characteristic of such circuits is that some molecules are present in very low quantities. This leads to the use of a simulation environment, Stochastic Petri Nets (SPNs), which is appropria ..."
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This work considers aspects of the pathway performance optimization of Escherichia coli genetic circuits. A characteristic of such circuits is that some molecules are present in very low quantities. This leads to the use of a simulation environment, Stochastic Petri Nets (SPNs), which
Statistical mechanics for truncations of the BurgersHopf equation: a model for intrinsic stochastic behavior with scaling
 Milan Journal of Mathematics
"... Abstract. In this paper we consider both analytically and numerically several finitedimensional approximations for the inviscid BurgersHopf equation. Fourier Galerkin truncation is introduced and studied as a simple onedimensional model with intrinsic chaos and a welldefined mathematical structu ..."
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Cited by 17 (6 self)
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Abstract. In this paper we consider both analytically and numerically several finitedimensional approximations for the inviscid BurgersHopf equation. Fourier Galerkin truncation is introduced and studied as a simple onedimensional model with intrinsic chaos and a welldefined mathematical
LETTER Communicated by Andre ́ Longtin Irregular Firing of Isolated Cortical Interneurons in Vitro Driven by Intrinsic Stochastic Mechanisms
"... Pharmacologically isolated GABAergic irregular spiking and stuttering interneurons in the mouse visual cortex display highly irregular spike times, with high coefficients of variation ≈0.9–3, in response to a depolarizing, constant current input. This is in marked contrast to cortical pyramidal cel ..."
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Pharmacologically isolated GABAergic irregular spiking and stuttering interneurons in the mouse visual cortex display highly irregular spike times, with high coefficients of variation ≈0.9–3, in response to a depolarizing, constant current input. This is in marked contrast to cortical pyramidal cells, which spike quite regularly in response to the same current injection. We applied timeseries analysis methods to show that the irregular behavior of the interneurons was not a consequence of lowdimensional, deterministic processes. These methods were also applied to the Hindmarsh and Rose neuronal model to confirm that the methods are adequate for the types of data under investigation. This result has important consequences for the origin of fluctuations observed in the cortex in vivo. 1
Stochastic mRNA synthesis in mammalian cells
 PLOS BIOL
, 2006
"... Individual cells in genetically homogeneous populations have been found to express different numbers of molecules of specific proteins. We investigated the origins of these variations in mammalian cells by counting individual molecules of mRNA produced from a reporter gene that was stably integrated ..."
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Cited by 143 (15 self)
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and ending when they transition back to the inactive state. We show that these transitions are intrinsically random and not due to global, extrinsic factors such as the levels of transcriptional activators. Moreover, the gene activation causes burstlike expression of all genes within a wider genomic locus
Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations
 Biophys. J
, 2001
"... ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for t ..."
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Cited by 130 (1 self)
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for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative
Intrinsic heterogeneity in expectation formation.
 Journal of Economic Theory,
, 2006
"... Abstract We introduce the concept of Misspecification Equilibrium to dynamic macroeconomics. Agents choose between a list of misspecified econometric models and base their selection on relative forecast performance. A Misspecification Equilibrium is a stochastic process in which agents forecast opt ..."
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Cited by 48 (7 self)
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Abstract We introduce the concept of Misspecification Equilibrium to dynamic macroeconomics. Agents choose between a list of misspecified econometric models and base their selection on relative forecast performance. A Misspecification Equilibrium is a stochastic process in which agents forecast
Intrinsic simulations between stochastic cellular automata
, 2012
"... The paper proposes a simple formalism for dealing with deterministic, nondeterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the nondeterministic and ..."
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Cited by 4 (1 self)
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The paper proposes a simple formalism for dealing with deterministic, nondeterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the non
Stochastic determination of the intrinsic structure in Bayesian factor analysis
 STATISTICAL AND APPLIED MATHEMATICAL SCIENCES INSTITUTE
, 2004
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Results 1  10
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