General Class Of Models Research Articles

Dynamical and gravitational lensing properties of a new phenomenological model of elliptical galaxies

Recent observations of the line of sight velocity profile of elliptical galaxies have furnished controversial results with some works favouring the presence of a large amount of dark matter in the outer regions and others arguing in favour of no dark matter at all. In order to shed new light on this controversy, we propose here a new phenomenological description of the total mass profile of galaxies. Under the hypothesis of spherical symmetry, we assume a double power-law expression for the global M/L ratio Upsilon(r)= Upsilon_0(r/r_0) ^{alpha}(1+r/r_0)^{beta}. In particular, Upsilon propto r^{alpha} for r/r_0 >1), Upsilon propto r^{alpha+beta} thus showing that models with alpha+beta=0 have an asymptotically constant M/L ratio. A wide range of possibilities is obtained by varying the slope parameters in the range we determine on the basis of physical considerations. Choosing a general expression for the luminosity density profile j(r), we work out an effective galaxy model that accounts for all the phenomenology observed in real elliptical galaxies. We derive the main dynamics and lensing properties of such an effective model. We analyze a general class of models, able to take into account different dynamical trends. We are able to obtain analytical expressions for the main dynamical and lensing quantities. We show that constraining the values of alpha+beta makes it possible to analyze the problem of the dark matter in elliptical galaxies. Indeed, positive values of alpha+beta would be a strong evidence for dark matter. Finally we indicate possible future approaches in order to face the observational data, in particular using velocity dispersion profiles and lensed quasar events.

Dynamic Modeling and Statistical Analysis of Event Times

This review article provides an overview of recent work in the modelling and analysis of recurrent events arising in engineering, reliability, public health, biomedical, and other areas. Recurrent event modelling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the inter-event times within a unit cannot be ignored, and the effects of performed interventions after each event occurrence need to be factored in. A recent general class of models for recurrent events which simultaneously accommodates these aspects is described. Statistical inference methods for this class of models are presented and illustrated through applications to real data sets. Some existing open research problems are described.

Pairwise likelihood inference for ordinal categorical time series

Ordinal categorical time series may be analyzed as censored observations from a suitable latent stochastic process, which describes the underlying evolution of the system. This approach may be considered as an alternative to Markov chain models or to regression methods for categorical time series data. The problem of parameter estimation is solved through a simple pseudolikelihood, called pairwise likelihood. This inferential methodology is successfully applied to the class of autoregressive ordered probit models. Potential usefulness for inference and model selection within more general classes of models are also emphasized. Illustrations include simulation studies and two simple real data applications.

Harvesting in a random environment: Itô or Stratonovich calculus?

We extend to harvesting stochastic differential equation (SDE) models in a random environment our previous work on models without harvesting concerning the resolution of the Itô–Stratonovich controversy. The resolution is obtained for the very general class of models d N/d t= N ( r( N)− h( N)+ σε( t)), where N= N( t) is the population size at time t, r( N) is the (density-dependent) “mean” per capita growth rate, h( N) is the (density-dependent) harvesting effort, ε( t) is a standard white noise (representing environmental random fluctuations), and σ is a noise intensity parameter. Itô and Stratonovich calculus in the resolution of SDEs apparently give different qualitative and quantitative results, leading to controversy on which calculus is more appropriate and creating an obstacle on the use of this modeling approach. We show that the apparent difference between the two calculi is due to a semantic confusion based on the fallacious assumption that we are working with the same type of mean rates. After clearing the confusion, the two calculi yield exactly the same results and we obtain important common conditions for extinction and for existence of a stationary density. The resolution of the controversy is intertwined with and sheds light on the estimation issues.

Semiparametric inference for a general class of models for recurrent events

Procedures for estimating the parameters of the general class of semiparametric models for recurrent events proposed by Peña and Hollander [(2004). Models for recurrent events in reliability and survival analysis. In: Soyer R., Mazzuchi T., Singpurwalla N. (Eds.), Mathematical Reliability: An Expository Perspective. Kluwer Academic Publishers, Dordrecht, pp. 105–123 (Chapter 6)] are developed. This class of models incorporates an effective age function encoding the effect of changes after each event occurrence such as the impact of an intervention, it models the impact of accumulating event occurrences on the unit, it admits a link function in which the effect of possibly time-dependent covariates are incorporated, and it allows the incorporation of unobservable frailty components which induce dependencies among the inter-event times for each unit. The estimation procedures are semiparametric in that a baseline hazard function is nonparametrically specified. The sampling distribution properties of the estimators are examined through a simulation study, and the consequences of mis-specifying the model are analyzed. The results indicate that the flexibility of this general class of models provides a safeguard for analyzing recurrent event data, even data possibly arising from a frailty-less mechanism. The estimation procedures are applied to real data sets arising in the biomedical and public health settings, as well as from reliability and engineering situations. In particular, the procedures are applied to a data set pertaining to times to recurrence of bladder cancer and the results of the analysis are compared to those obtained using three methods of analyzing recurrent event data.

Saturation for a General Class of Models

Implicit techniques for construction and representation of the reachability set of a high-level model have become quite efficient for certain types of models. In particular, previous work developed a "saturation" algorithm that exploits asynchronous behavior to efficiently construct the reachability set using multiway decision diagrams, but using a Kronecker product expression to represent each model event. For models whose events do not naturally fall into this category, use of the saturation algorithm requires adjusting the model by combining components or splitting events into subevents until a Kronecker product expression is possible. In practice, this can lead to additional overheads during reachability set construction. This paper presents a new version of the saturation algorithm that works for a general class of models: models whose events are not necessarily expressible as Kronecker products, models containing events with complex priority structures, and models whose state variables have unknown bounds. Experimental results are given for several examples

Spatial and functional modeling of carnivore and insectivore molariform teeth

The interaction between the two main competing geometric determinants of teeth (the geometry of function and the geometry of occlusion) were investigated through the construction of three-dimensional spatial models of several mammalian tooth forms (carnassial, insectivore premolar, zalambdodont, dilambdodont, and tribosphenic). These models aim to emulate the shape and function of mammalian teeth. The geometric principles of occlusion relating to single- and double-crested teeth are reviewed. Function was considered using engineering principles that relate tooth shape to function. Substantial similarity between the models and mammalian teeth were achieved. Differences between the two indicate the influence of tooth strength, geometric relations between upper and lower teeth (including the presence of the protocone), and wear on tooth morphology. The concept of "autocclusion" is expanded to include any morphological features that ensure proper alignment of cusps on the same tooth and other teeth in the tooth row. It is concluded that the tooth forms examined are auto-aligning, and do not require additional morphological guides for correct alignment. The model of therian molars constructed by Crompton and Sita-Lumsden ([1970] Nature 227:197-199) is reconstructed in 3D space to show that their hypothesis of crest geometry is erroneous, and that their model is a special case of a more general class of models.

Topological mass mechanism and exact fields mapping

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of [1] for arbitrary dimensions.

Towards a high-energy theory for the Higgs phase of gravity

Spontaneous Lorentz violation due to a time-dependent expectation value for a massless scalar has been suggested as a method for dynamically generating dark energy. A natural candidate for the scalar is a Goldstone boson arising from the spontaneous breaking of a U(1) symmetry. We investigate the low-energy effective action for such a Goldstone boson in a general class of models involving only scalars, proving that if the scalars have standard kinetic terms then at the {\em classical} level the effective action does not have the required features for spontaneous Lorentz violation to occur asymptotically $(t \to \infty)$ in an expanding FRW universe. Then we study the large $N$ limit of a renormalizable field theory with a complex scalar coupled to massive fermions. In this model an effective action for the Goldstone boson with the properties required for spontaneous Lorentz violation can be generated. Although the model has shortcomings, we feel it represents progress towards finding a high energy completion for the Higgs phase of gravity.

A time‐dependent discrimination index for survival data

To derive models suitable for outcome prediction, a crucial aspect is the availability of appropriate measures of predictive accuracy, which have to be usable for a general class of models. The Harrell's C discrimination index is an extension of the area under the ROC curve to the case of censored survival data, which owns a straightforward interpretability. For a model including covariates with time-dependent effects and/or time-dependent covariates, the original definition of C would require the prediction of individual failure times, which is not generally addressed in most clinical applications. Here we propose a time-dependent discrimination index Ctd where the whole predicted survival function is utilized as outcome prediction, and the ability to discriminate among subjects having different outcome is summarized over time. Ctd is based on a novel definition of concordance: a subject who developed the event should have a less predicted probability of surviving beyond his/her survival time than any subject who survived longer. The predicted survival function of a subject who developed the event is compared to: (1) that of subjects who developed the event before his/her survival time, and (2) that of subjects who developed the event, or were censored, after his/her survival time. Subjects who were censored are involved in comparisons with subjects who developed the event before their observed times. The index reduces to the previous C in the presence of separation between survival curves on the whole follow-up. A confidence interval for Ctd is derived using the jackknife method on correlated one-sample U-statistics.The proposed index is used to evaluate the discrimination ability of a model, including covariates having time-dependent effects, concerning time to relapse in breast cancer patients treated with adjuvant tamoxifen. The model was obtained from 596 patients entered prospectively at Istituto Nazionale per lo Studio e la Cura dei Tumori di Milano (INT). The model discrimination ability was validated on an independent testing data set of 175 patients provided by Centro Regionale Indicatori Biochimici di Tumore (CRIBT) in Venice.

Global asymptotic stability for the disease free equilibrium for epidemiological models

For a general class of models, we prove the global asymptotic stability (GAS) of the disease free equilibrium (DFE) under general assumptions. These conditions are related to the basic reproductive ratio R 0 . We also give a practical algorithm to compute a threshold condition equivalent to R 0 ⩽ 1 . We show that these two results can be applied to numerous epidemiological models from the literature. To cite this article: J.C. Kamgang, G. Sallet, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The diffusive vesicle supply center model for tip growth in fungal hyphae

We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151–164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.

Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality

A welfare analysis of policies for risk averse preferences is handicapped within linear or linearized models and their certainty equivalence property. I calculate the optimal policy in a nonlinear stochastic dynamic general equilibrium model. Then I estimate the posterior density of structural parameters and the marginal likelihood within a nonlinear state space model. The computational challenges are considerable and I concentrate on the numerics and statistics for a simple model of dynamic consumption and labor choice. It is estimated on simulated data in order to test the routines with known true parameters. The code is written for a general model class. The policy function is approximated by Smolyak Chebyshev polynomials and the rational expectation integral by Smolyak Gaussian quadrature. The Smolyak operator is used to extend univariate approximation and integration operators to many dimensions. It is also called boolean method, hyperbolic cross points, discrete or sparse grids, fully symmetrical integration rules or complete polynomials. It reduces the curse of dimensionality from exponential to polynomial growth. The likelihood integrals are evaluated by a Gaussian quadrature and Gaussian quadrature particle filter. The bootstrap or sequential importance resampling particle filter, based on a Monte Carlo integration, is used as an accuracy benchmark. The posterior is estimated by the Gaussian filter and a Metropolis-Hastings algorithm. I propose a genetic extension of the standard Metropolis-Hastings algorithm by parallel random walk sequences. The candidate parameter vectors are constructed by innovation from the parallel sequences in addition to the usual random walk shocks. This improves the robustness of start values and the global maximization properties. Moreover it simplifies a cluster implementation and the random walk variances decision is reduced to only two parameters so that almost no trial sequences are needed. Finally the marginal likelihood is calculated as a criterion for nonnested and quasi-true models in order to select between the nonlinear estimates and a first order perturbation solution combined with the Kalman filter.

ICA based identification of dynamical systems generating synthetic and real world time series

Independent Component Analysis (ICA) is a recent and well known technique used to separate mixtures of signals. While in general the researchers put their attention on the type of signals and of mixing, we focus our attention on a quite general class of models which act as sources of the time series, the dynamical systems. In this paper we focus our attention on the general problem to understand the behaviour of ICA methods with respect to the time series deriving from a specific dynamical system, selecting large classes of them, and using ICA to make separation. This study gives some interesting results that are very useful both to highlight some properties related to dynamical systems and to clarify some general aspects of ICA, by using both synthetic and real data.From one hand we study the features of the linear (simple and coupled) and non-linear (single and coupled) dynamical systems, stochastic resonances, chaotic and real dynamical systems. We have to stress that we obtain information about the separation of these systems and substantially how from the entropy of the complete system we can obtain the entropies of the single dynamical systems (so that we also could obtain a more realistic analogic circuit).On the other hand these results show the high capability of the ICA method to recognize the dynamical systems independently from their complexity and in the case of stochastic series ICA perfectly recognizes the different dynamical systems also where the Fourier Transform is irresolute.We also note that in the case of real dynamical systems we showed that ICA permits to recognize the information connected to the sources and to associate to it a phenomenological dynamical system that reproduce it (i.e. Organ Pipe, Stromboli Volcano, Aerosol Index).

On the Newtonian limit of generalized modified gravity models

We consider the Newtonian limit of modified theories of gravity that include inverse powers of the curvature in the action in order to explain the cosmic acceleration. It has been shown that the simplest models of this kind are in conflict with observations at the Solar System level. In this Letter we point out that when one adds to the action inverse powers of curvature invariants that do not vanish for the Schwarzschild geometry one generically recovers an acceptable Newtonian limit at small distances. Gravity is however modified at large distances. We compute the first correction to the Newtonian potential in a quite general class of models. The characteristic distance entering in these modifications is of the order of 10 pc for the Sun and of the order of 102 kpc for a galaxy.

Prior Learning and Convex-Concave Regularization of Binary Tomography

Abstract In our previous work, we introduced a convex-concave regularization approach to the reconstruction of binary objects from few projections within a limited range of angles. A convex reconstruction functional, comprising the projections equations and a smoothness prior, was complemented with a concave penalty term enforcing binary solutions. In the present work we investigate alternatives to the smoothness prior in terms of probabilistically learnt priors encoding local object structure. We show that the difference-of-convex-functions DC-programming framework is flexible enough to cope with this more general model class. Numerical results show that reconstruction becomes feasible under conditions where our previous approach fails.

On mechanics and thermodynamics of a stellar galaxy in a two-component virial system and the Fundamental Plane

The paper confirms the existence of a special configuration (among the infinitive number of a priori possible virial states) which a B stellar (Baryonic) component may assume inside a given D dark halo potential well. This satisfies the d’Alembert Principle of virtual works and its typical dimension works as a scale length (we call tidal radius) induced on the gravitational field of the bright component by the dark one. Its dynamic and thermodynamic properties are here analyzed in connection with the physical reason for the existence of the Fundamental Plane (FP) for ellipticals and, in general, for two-component virialized systems. The analysis is performed by using two-component models with two power-law density profiles and two homogeneous cores. The outputs of this kind of models, at the special configuration, are summarized and compared with some observable scaling relations for pressure supported ellipticals. The problem of extending the results to a general class of models with Zhao (1996) [MNRAS 278, 488] profiles, which are more suitable for an elliptical galaxy system, is also taken into account. The virial equilibrium stages of the two-component system have to occur after a previous violent relaxation phase. If the stellar B component is allowed to cool slowly its virial evolution consists of a sequence of contractions with enough time to rearrange the virial equilibrium after any step. The thermodynamic process during the dynamical evolution is so divided into a sequence of transformations which are irreversible but occur between two quasi-equilibrium stages. Then, it is possible to assign: a mean temperature to the whole B component during this quasi-static sequence and the entropy variation between two consecutive virial steps. The analysis allows the conclusion that the induced scale length is a real confinement for the stellar system. This follows from the application of the Io Thermodynamics Principle under the virial equilibrium constraint, by checking how larger configurations turn out to be forbidden, according to the IIo Thermodynamics Principle. The presence of this specific border on the space of the baryonic luminous component has to be regarded as the physical reason why a stellar galaxy belongs to the FP and why astrophysical objects, with a completely different history and formation, but characterized by a tidal radius (as the globular clusters are) lie on the same FP. An other problem addressed is how this special configuration may be reached. This is strictly connected with the problem of the end state of the collisionless stellar system after a violent relaxation phase. Even if degeneracy towards the initial conditions is present on the FP, the mechanic and thermodynamic properties of the special configuration suggest this state may be the best candidate for the beginning of the B component virial evolution, and also give a possible explanation for why an elliptical is not completely relaxed in respect to its dark halo.

BAYESIAN METHODS FOR CONTROL LOOP PERFORMANCE ASSESSMENT IN CROSS-DIRECTIONAL CONTROL

The minimum variance (MV) lower bound has been applied to many multivariable control systems in order to assess their performance based on routine operating data. However, such analysis often depends on the selection of a suitable dynamic model of the data and for multivariable systems, there can be many candidate models. Also, uncertainty is often not considered, because standard approximations do not exist for the sampling distribution of these multivariable performance indices. This paper addresses these two issues by using the Bayesian approach to vector autoregression (VAR) modelling with Markov Chain Monte Carlo (MCMC) numerical methods. Dynamic model selection is carried out by using Reversible Jump (RJ) MCMC and it is shown that MCMC can be used to the estimate the non-standard distributions that exist in multivariable MV performance indices. The approach is applied to data from an industrial cross-directional (CD) control system by using a more general class of model than has previously been studied for these systems.

Is the Observed Persistence Spurious? A Test for Fractional Integration Versus Short Memory and Structural Breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood

We propose a simulated maximum likelihood estimator for dynamic models based on non-parametric kernel methods. Our method is designed for models without latent dynamics from which one can simulate observations but cannot obtain a closed-form representation of the likelihood function. Using the simulated observations, we nonparametrically estimate the density - which is unknown in closed form - by kernel methods, and then construct a likelihood function that can be maximized. We prove for dynamic models that this nonparametric simulated maximum likelihood (NPSML) estimator is consistent and asymptotically efficient. NPSML is applicable to general classes of models and is easy to implement in practice.