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density functions of residence times for deterministic and stochastic compartmental systems

MATHEMATICAL BIOSCIENCES 2002年第Spe1期180卷 127-139页

作者： Jacquez, JA Univ Michigan Dept Physiol Ann Arbor MI 48104 USA Univ Michigan Dept Biostat Ann Arbor MI 48104 USA

A significant consideration in modeling systems with stages is to obtain models for the individual stages that have probability density functions (pdfs) of residence times that are close to those of the real system. Consequently, the theory of residence time distributions is important for modeling. Here I show first that linear deterministic compartmental systems with constant coefficients and their corresponding stochastic analogs (stochastic compartmental systems with linear rate laws) have the same pdfs of residence times for the same initial distributions of inputs. Furthermore, these are independent of inflows. Then I show that does not hold for non-linear deterministic systems and their stochastic analogs (stochastic compartmental systems with non-linear rate laws). In fact, for given initial distributions of inputs, the pdfs of non-linear determistic systems without inflows and of their stochastic analogs, are functions of the initial amounts injected. For systems with inflows, the pdfs change as the inflows influence the occupancies of the compartments of the system;they are state-dependent pdfs. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： compartmental systems residence times density functions

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density functions for entrainment and deposition rates of uniform sediment

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JOURNAL OF HYDRAULIC ENGINEERING 2007年第8期133卷 917-926页

作者： Elhakeem, Mohamed Mran, Jasim Univ Iowa Inst Hydraul Res Iowa City IA 52242 USA Univ S Carolina Dept Civil & Environm Engn Columbia SC 29208 USA

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related ) the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for 11 the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.

关键词： entrainment dunes probabilistic models bedforms sediment deposit Deposition rates Plankton entrainment Probabilistic Model dunes uniform sand bedforms Sediment deposits density functions Sediment properties

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density functions for navigation-function-based systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2008年第2期53卷 612-617页

作者： Loizou, Savvas G. Jadbabaie, Ali Natl Tech Univ Athens Dept Naval Architecture & Marine Engn Athens 15704 Greece Univ Penn Grasp Lab Philadelphia PA 19104 USA

In this paper, we present a scheme for constructing density functions for systems that are almost globally asymptotically stable (i.e., systems for which all trajectories converge to an equilibrium except for a set of measure zero) using navigation functions (NFs). Although recently-proven converse theorems guarantee the existence of density functions for such systems, such results are only existential and the construction of a density function for almost globally asymptotically stable systems remains a challenging task. We show that for a specific class of dynamical systems that are defined based on an NF, a density function can be easily derived from the system's underlying NF.

关键词： almost gas systems density functions dual Lyapunov techniques navigation functions (NFs)

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density functions of Periodic Sequences 2nd

Density Functions of Periodic Sequences

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2nd International Conference on Discrete Geometry and Mathematical Morphology (DGMM)

作者： Anosova, Olga Kurlin, Vitaliy Univ Liverpool Dept Comp Sci Liverpool L69 3BX Merseyside England

ISBN: (纸本)9783031198960;9783031198977

This paper contributes to the emergent area of Periodic Geometry, which studies continuous spaces of solid crystalline materials (crystals) by new methods of metric geometry. Since crystal structures are determined in a rigid form, their strongest practical equivalence is rigid motion or isometry preserving inter-point distances. The most fundamental model of any crystal is a periodic set of points at all atomic centers. The previous work introduced an infinite sequence of density functions that are continuous isometry invariants of periodic point sets. These density functions turned out to be highly non-trivial even in dimension 1 for periodic sequences of points in the line. This paper fully describes the density functions of any periodic sequence and their symmetry properties. The explicit description confirms coincidences of density functions that were previously computed via finite samples.

关键词： Periodic sequence Isometry invariant density functions

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Combination of Lyapunov and density functions for Stability of Rotational Motion

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第11期56卷 2599-2607页

作者： Vasconcelos, Jose Fernandes Rantzer, Anders Silvestre, Carlos Oliveira, Paulo Jorge Inst Super Tecn Inst Syst & Robot Lisbon Portugal Lund Univ Dept Automat Control Fac Engn S-22100 Lund Sweden

Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities.

关键词： Asymptotic stability density functions input-to-state stability Lyapunov methods

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Differentiability of Palmer's linearization theorem and converse result for density functions

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JOURNAL OF DIFFERENTIAL EQUATIONS 2015年第9期259卷 4634-4650页

作者： Castaneda, Alvaro Robledo, Gonzalo Univ Chile Fac Ciencias Dept Matemat Santiago Chile

We study differentiability properties in a particular case of the Palmer's linearization theorem, which states the existence of a homeomorpbism H between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that H is a C-2 preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Palmer's linearization theorem Hartman-Grobman theorem density functions Preserving orientation diffeomorphism

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Angle density functions for active sensor imaging

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IET RADAR SONAR AND NAVIGATION 2009年第3期3卷 224-232页

作者： Demirkol, A. Demir, Z. Emre, E. Sakarya Univ Dept Elect & Elect Engn Sakarya Turkey Sakarya Univ Dept Comp Engn Sakarya Turkey

A new target density function (TDF) is proposed for active sensor imaging. The TDF, called the angle density function, is studied by utilising the angular distribution of targets at a fixed range. Active sensor imaging based on the angle density function is achieved using a phased array radar system. The phased array system is arranged for stationary radar-stationary target configuration. The imaging algorithm is applied for the whole target area. Instead of pointwise imaging, an approach including the whole target area globally is developed. An advantage of the technique is the use of standard Fourier-based analysis. This makes it possible to use of simple functions for global radar imaging. Although the imaging is accomplished by way of the phased array radars, beamforming is not necessary with the proposed technique.

关键词： Angle Imaging Beamforming target configurations density functions phased array active sensor

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Notes on quantitative structureproperty relationships (QSPR), part 3: density functions origin shift as a source of quantum QSPR algorithms in molecular spaces

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JOURNAL OF COMPUTATIONAL CHEMISTRY 2013年第9期34卷 766-779页

作者： Carbo-Dorca, Ramon Univ Girona Inst Quim Computac Girona 17071 Catalonia Spain

A general algorithm implementing a useful variant of quantum quantitative structureproperty relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed. (c) 2012 Wiley Periodicals, Inc.

关键词： QSAR QSPR quantum QSPR molecular space QSPR dimensionality paradox in QSPR causality in QQSPR molecular quantum similarity density functions quantum object sets origin shifted DF nested do loops

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A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2010年第12期54卷 3404-3410页

作者： Ichimura, Tsuyoshi Fukuda, Daisuke Tokyo Inst Technol Dept Civil & Environm Engn Meguro Ku Tokyo 1528552 Japan

Nonparametric conditional density functions are widely used in applied econometric and statistical modelling because they provide enriched information summaries of the relationships between dependent and independent variables. Although least-squares cross-validation is considered to be the best criterion for bandwidth selection of the kernel estimator of the conditional density, the number of computations required for this procedure grows exponentially as the number of observations increases. A fast algorithm is proposed to reduce this computational cost, and its accuracy and efficiency are verified via numerical experiments. A practical application is also presented to demonstrate the algorithm's potential usefulness. (C) 2009 Elsevier B.V. All rights reserved.

关键词： statistical models (nuclear) A* Algorithm Fasting cross-validation density functions Independent Variables Conditional

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Analysis of positive invariance and almost regional attraction via density functions with converse results

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2007年第7期52卷 1329-1333页

作者： Masubuchi, Izumi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

This note is concerned with analysis of positive invariance of nonlinear systems and convergence of trajectories in a region of the state-space via density functions. If there exists a density function that is positive inside a set containing an equilibrium point and tends to zero as approaches to the boundary, the set is positively invariant and almost all of the trajectories starting from there converge to the equilibrium. Converse results are also provided to prove the existence of such density functions.

关键词： almost attraction density functions nonlinear systems positive invariance

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