Downloads & Free Reading Options - Results

This paper reports simulations allowing for stochastic accretion and mass loss within closed and open systems modeled using a previously developed multi-population, multi-zone (halo, thick disk, thin disk) treatment. The star formation rate is computed as a function of time directly from the model equations and all chemical evolution is followed without instantaneous recycling. Several types of simulations are presented here: (1) a closed system with bursty mass loss from the halo to the thick disk, and from the thick to the thin disk, in separate events to the thin disk; (2) open systems with random environmental (extragalactic) accretion, e.g. by infall of high velocity clouds directly to the thin disk; (3) schematic open system single and multiple collision events and intracluster stripping. For the open models, the mass of the Galaxy has been explicitly tracked with time. We present the evolution of the star formation rate, metallicity histories, and concentrate on the light elements. We find a wide range of possible outcomes, including an explanation for variations in the Galactic D/H ratio, and highlight the problems for uniquely reconstructing star forming histories from contemporary abundance measurements.

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

The optimal fire distribution policy obtained using a stochastic combat attrition model is compared with that for a deterministic one. The same optimal control problem for a homogeneous force in combat against a heterogeneous force of two homogeneous types is considered using two different models for the attrition mechanism in a fight-to-the-finish the Lanchester-type differential equation formulation and its analagous stochastic version of a continuous parameter Markov chain with stationary transition probabilities. Considering dynamic programming methodology, a computer program was developed to numerically determine the optimal fire distribution policy (closed-loop or feedback) for the stochastic attrition process. Numerical values are generated for several parameter sets and compared with the optimal fire distribution policy for the corresponding deterministic attrition process. Results indicate that the optimal fire distribution policy for the stochastic model is more complex than the deterministic one.

We analyze several aspects of a class of simple counting processes, that can emerge in some fields of applications where the presence of a change-point occurs. Under simple conditions we, in particular, prove a significant inequality for the stochastic intensity.

A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and the related Temperley-Lieb algebraic structures and representations are discussed. It is shown that corresponding to these $A_n$ symmetric integrable chain models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains whose spectra of the transition matrices (resp. intensity matrices) are the same as the ones of the corresponding integrable models.

ADA001248

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optimization. In addition, we develop a connection, for large time horizons, with a family of classical homothetic value function processes with random endowments.

A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating $S(f) \sim 1/f^\alpha$, thus offering a biophysical explanation for the ubiquitous $1/f$-type in neurological signals.

Gennady Samorodnitsky, Murad Taqqu Stable Non Gaussian Random Processes Stochastic Models With Infinite Variance ( Stochastic Modeling Series) Chapman And Hall CRC ( 1994)

We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the plane of parameters correspond to the Ising model, voter model and majority vote model. The dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing, annihilating, and branching random walkers. We use the freedom allowed by the space of parameters to measure, by numerical simulations, the persistence probability of a generic model in the low temperature phase, where the system coarsens. This probability is found to decay at large times as a power law with a seemingly constant exponent $\theta\approx 0.22$. We also discuss the connection between persistence and the nature of the interfaces between domains.

Quantitative Sociodynamics: Stochastic Methods and Models of Social Interaction Processes Author: Dirk Helbing Published by Springer Berlin Heidelberg ISBN: 978-3-642-11545-5 DOI: 10.1007/978-3-642-11546-2 Table of Contents: Introduction and Summary Dynamic Decision Behavior Master Equation in State Space Boltzmann-Like Equations Master Equation in Configuration Space The Fokker-Planck Equation Langevin Equations and Non-linear Dynamics Problems and Terminology Decision Theoretical Specification of the Transition Rates Opinion Formation Models Social Fields and Social Forces Evolutionary Game Theory Determination of the Model Parameters from Empirical Data

Quantitative Sociodynamics: Stochastic Methods and Models of Social Interaction Processes Author: Dirk Helbing Published by Springer Berlin Heidelberg ISBN: 978-3-642-11545-5 DOI: 10.1007/978-3-642-11546-2 Table of Contents: Introduction and Summary Dynamic Decision Behavior Master Equation in State Space Boltzmann-Like Equations Master Equation in Configuration Space The Fokker-Planck Equation Langevin Equations and Non-linear Dynamics Problems and Terminology Decision Theoretical Specification of the Transition Rates Opinion Formation Models Social Fields and Social Forces Evolutionary Game Theory Determination of the Model Parameters from Empirical Data

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Let us suppose that we are investigating a system whose state can be adequately specified by n real numbers x1, , x(n). We shall suppose that by some acceptable scientific theory it is predicted that, in the absence of disturbances from outside the system, the xi develop in time in accordance with certain differential equations, x(I) = g(I)0 (t,x), I-1,...,n. If there are disturbances or noises,n(1)(t),...n(r)(t), the underlying theory of such systems will often permit us to conclude that x(I) = g(I)0 (t,x) + sigma (sub p=1) g(I)p (t,x) n(p) (t), I = 1, ..., n, which g(I)p is the sensitivity of the ith coordinate to the pth noise.