how colored environmental noise affects population extinction environmental noise can cause an exponential reduction in the mean time to extinction mte of an isolated population we study this effect on an example of a stochastic birth death process with rates modulated by a colored that is correlated gaussian noise a path integral formulation yields a transparent way of evaluating the mte and finding the optimal realization of the environmental noise that determines the most probable path to extinction the population size dependence of the mte changes from exponential in the absence of the environmental noise to a power law for a short correlated noise and to no dependence for long correlated noise we also establish the validity domains of the white noise limit and adiabatic limit

extending the archimedean copula methodology to model multivariate survival data grouped in clusters of variable size summary for the analysis of clustered survival data two different types of model that take the association into account are commonly used frailty models and copula models frailty models assume that conditionally on a frailty term for each cluster the hazard functions of individuals within that cluster are independent these unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster copula models in contrast assume that the joint survival function of the individuals within a cluster is given by a copula function evaluated in the marginal survival function of each individual it is the copula function which describes the association between the lifetimes within a cluster a major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal to set up manageable estimation procedures for the different model parameters we describe a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of archimedean copulas with completely monotone generator we develop both one and two stage estimators for the copula parameters furthermore we show the consistency and asymptotic normality of these estimators finally we perform a simulation study to investigate the finite sample properties of the estimators we illustrate the method on a data set containing the time to first insemination in cows with cows clustered in herds

on multivariate rayleigh and exponential distributions in this paper expressions for multivariate rayleigh and exponential probability density functions pdfs generated from correlated gaussian random variables are presented we first obtain a general integral form of the pdfs and then study the case when the complex gaussian generating vector is circular we consider two specific circular cases the exchangeable case when the variates are evenly correlated and the exponentially correlated case expressions for the multivariate pdf in these cases are obtained in integral form as well as in the form of a series of products of univariate pdfs we also derive a general expression for the multivariate exponential characteristic function cf in terms of determinants in the exchangeable and exponentially correlated cases cf expressions are obtained in the form of a series of products of univariate gamma cfs the cf of the sum of exponential variates in these cases is obtained in closed form finally the bivariate case is presented mentioning its main features while the integral forms of the multivariate pdfs provide a general analytical framework the series and determinant expressions for the exponential cfs and the series expressions for the pdfs can serve as a useful tool in the performance analysis of digital modulation over correlated rayleigh fading channels using diversity combining

local and global controllability for nonlinear systems a technique to study local and global controllability properties for a wide class of nonlinear systems is presented in addition to an extensive study of systems on r2 we propose as an application of our method a new criterion for global controllability of systems with polynomial drift term defined on rn in the case of linear systems the criterion reduces to the classical kalman condition a study of local controllability at the equilibrium point of the drift term of systems defined on r2 enables us not only to rederive a local controllability result derived by hermes 4 5 but also to extend this result when no assumptions are made on the boundedness of the controls

a local stabilization theorem for interconnected systems abstract we prove that if a nonlinear control system is locally asymptotically stabilizable at its equilibrium by means of a continuous feedback then adding an integrator the resulting system is also locally asymptotically stabilizable by means of a feedback law which is smooth except possibly at the equilibrium our approach is based on previous works of arstein sontag and the author

mrc performance for binary signals in nakagami fading with general branch correlation exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with l correlated branches in nakagami fading bit error rates are evaluated for both coherent and noncoherent binary phase shift keying and frequency shift keying signals starting from the l variate moment generating function of the random input power vector the new formulation presented for the bit error rate in which the covariance matrix of the fading at the l branches explicitly appears allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches results are presented for evaluation of the outage probability for integer values of fading severity as well as for the effect of the presence of unbalanced channels with arbitrary correlation

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

local dependence functions for some families of bivariate distributions and total positivity the purpose of this paper is to investigate a very useful application of a certain local dependence function c f x y which was considered recently by holland and wang 20 an interesting property of c f x y is that the underlying joint density f x y is tp 2 that is totally positive of order 2 if and only if c f x y 0 this gives an elegant way to investigate the tp 2 property of any bivariate distribution for the saramanov family the ali mikhail haq family of bivariate distributions and the family of bivariate elliptical distributions we derive the local dependence function and obtain conditions for f x y to be tp 2 these families are quite rich and include many other large classes of bivariate distributions as their special cases similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with pareto conditionals

generalized sliding mode control for multi input nonlinear systems the purpose of this paper is to present a framework for the design of sliding mode based controllers for multi input affine nonlinear systems in this framework the control effort goes to zero as the state approaches the sliding surface a key feature for practical implementation the sliding surface is a submanifold with codimension equal to the dimension of the involutive distribution g generated by the controlled vector fields rather than the dimension of their linear span we also allow nonzero vectors in g to be tangent to the sliding surface the singular case in sliding mode control

outage probability of diversity systems over generalized fading channels outage probability is an important performance measure of communication systems operating over fading channels relying on a simple and accurate algorithm for the numerical inversion of the laplace transforms of cumulative distribution functions we develop a moment generating function based numerical technique for the outage probability evaluation of maximal ratio combining mrc and postdetection equal gain combining egc in generalized fading channels for which the fading in each diversity path need not be independent identically distributed nor even distributed according to the same family of distributions the method is then extended to coherent egc but only for the case of nakagami m fading channels the mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of mrc and egc systems

analysis of hybrid selection maximal ratio combining in correlated nakagami fading we present an analysis of a hybrid selection maximal ratio combining diversity system over an evenly correlated slow frequency nonselective nakagami fading channel where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same and all average branch signal to noise ratios snrs are equal in this system the l branches with the largest instantaneous snr out of n available branches are selected and combined using maximal ratio combining from the joint characteristic function cf of the instantaneous branch snrs we obtain an expression for the cf of the combiner output snr as a series of elementary cfs the expression can be conveniently used to obtain the symbol error probability of coherent detection of different m ary modulation schemes we illustrate our methodology using m ary phase shift keying as an example

global robust controllability of the triangular integro differential volterra systems a solution of the global controllability problem for a class of nonlinear control systems of the volterra integro differential equations is presented it is proven that there exists a family of continuous controls that solve the global controllability problem for this class the constructed controls depend continuously on the initial and the terminal states it makes possible to prove the global controllability of the uniformly bounded perturbations of these systems under the global lipschitz condition for the unperturbed system with respect to the states and the controls

extinction rates for fluctuation induced metastabilities a real space wkb approach the extinction of a single species due to demographic stochasticity is analyzed the discrete nature of the individual agents and the poissonian noise related to the birth death processes result in local extinction of a metastable population as the system hits the absorbing state the fokker planck formulation of that problem fails to capture the statistics of large deviations from the metastable state while approximations appropriate close to the absorbing state become in general invalid as the population becomes large to connect these two regimes a real space wkb method based on the master equation is presented and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state the details of the underlying microscopic process smeared out in a mean field treatment are shown to be crucial for an exact determination of the extinction exponent this general scheme is shown to reproduce the known results in the field to yield new corollaries and to fit quite precisely the numerical solutions moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

demographic stochasticity and extinction in populations with allee effect we study simple stochastic scenarios based on birth and death markovian processes that describe populations with the allee effect to account for the role of demographic stochasticity in the mean field deterministic limit we recover well known deterministic evolution equations widely employed in population ecology the mean time to extinction is in general obtained by the wentzel kramers brillouin wkb approximation for populations with the strong and weak allee effects an exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics we study the conditions for the validity of the wkb solution and analyze the boundary between the weak and strong allee effect by comparing exact solutions with numerical simulations

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

uniform stabilization of nonlinear systems with arbitrary switchings and dynamic uncertainties we solve the problem of global uniform input to state stabilization of nonlinear switched systems with time varying and periodic dynamics with dynamic uncertainties and with external disturbances the switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form gtf with non invertible input output maps in our first and most general result we prove that if the dynamic uncertainty is treated as external disturbance then the general triangular form system can be stabilized with arbitrarily small gain w r t the dynamic uncertainty by means of a switching independent smooth and periodic feedback hence using a suitable extension of the well known small gain theorem to our case of switched systems with arbitrary switchings we obtain the uniform input to state stabilization of the entire interconnected system the second part of the paper addresses a more special case of triangular form tf switched systems with right invertible input output i o maps with unknown switchings and with dynamic uncertainties we show that the design becomes simpler and more constructive and the controllers become time invariant if the dynamics is autonomous in this special case finally we consider an example with explicit design of the stabilizing controllers

pairwise dependence diagnostics for clustered failure time data frailty and copula models specify a parametric dependence structure for multivariate failure time data estimation of some joint quantities can be highly sensitive to the assumed parametric form and hence model fit is an important issue this paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models the approach is based on the cumulative sum of residuals that are calculated in bivariate time the residuals reflect the difference between the observed and expected bivariate association structures the proposed model checking process is interpretable with a limiting distribution which can be approximated using the bootstrap simulations and a data example illustrate the practical application of the method

gaussian class multivariate weibull distributions theory and applications in fading channels ascertaining on the suitability of the weibull distribution to model fading channels a theoretical framework for a class of multivariate weibull distributions originated from gaussian random processes is introduced and analyzed novel analytical expressions for the joint probability density function pdf moment generating function mgf and cumulative distribution function cdf are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers two specific distributions with arbitrary number of correlated variates are considered and studied with exponential and with constant correlation where their pdfs are introduced both cases assume equal average fading powers but not necessarily identical fading parameters for the multivariate weibull distribution with exponential correlation useful corresponding formulas as for the bivariate case are derived the presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection equal gain and maximal ratio combining mrc techniques operating over correlated weibull fading channels for these diversity receivers several useful performance criteria such as the moments of the output signal to noise ratio snr including average output snr and amount of fading and outage probability are analytically derived moreover the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach the proposed mathematical analysis is complemented by various evaluation results showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance

performance of digital linear modulations on weibull slow fading channels a closed form expression is derived for the moment generating function of the weibull distribution valid when its fading parameter assumes integer values expressions for average signal to noise ratio signal outage and average symbol error rate are derived for single channel reception and independent multichannel diversity reception operating on flat weibull slow fading channels

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

on the extension of the korobov s class of linearizable triangular systems by nonlinear control systems of the class c1 abstract we give the complete description of nonlinear control systems of the class c 1 with one dimensional control which are feedback linearizable by means of a change of the control of the class c 1 and a change of variables of the class c 2 as well as the control systems which are linearizable by means of a change of variables only the both results are originated from the approach proposed by v i korobov in 1973 for the linearization of triangular control systems

feedback classification of multi input nonlinear control systems we study the feedback group action on multi input nonlinear control systems with uncontrollable mode we follow slightly an approach proposed in kang and krener w kang and a j krener siam j control optim 30 1992 pp 1319 1337 which consists of analyzing the system and the feedback group step by step we construct a normal form which generalizes on one hand the results obtained in the single input case and on the other hand those recently obtained by the same author in the controllable case we illustrate our results by studying the caltech multi vehicle wireless testbed mvwt and the prototype of planar vertical takeoff and landing aircraft pvtol we also study the notion of bifurcation of controllability for systems with one nonzero uncontrollable mode we first show that the equilibria for those systems is a p dimensional submanifold p equals number of inputs provided that one term in their normal form is nonzero we show that these systems are linearly controllable hence stabilizable at any nearby equilibrium point of the origin

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

two interpretations of the discrimination parameter in this paper we propose two interpretations for the discrimination parameter in the two parameter logistic model 2plm the interpretations are based on the relation between the 2plm and two stochastic models in the first interpretation the 2plm is linked to a diffusion model so that the probability of absorption equals the 2plm the discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given for the second interpretation the 2plm is connected to a specific type of race model in the race model the discrimination parameter is inversely related to the dependency of the information used in the decision process extended versions of both models with person to person variability in the difficulty parameter are considered when fitted to a data set it is shown that a generalization of the race model that allows for dependency between choices and response times rts is the best fitting model

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

on decomposition of nonlinear control systems in this paper the problem is studied when the system x i k 1 u t g t x x 0 x 0 defined on an n dimensional analytic manifold can be decomposed into either independent subsystems or a cascade of subsystems necessary and sufficient conditions for the existence of such local decompositions are given in terms of lie algebras generated by the system

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

failure time models with matched data summary holt prentice 1974 adapted the proportional hazards model to give failure time models for matched pairs in which a member of the ith pair with covariate z has hazard function aoi t exp bz with full data more efficient estimators of b can be obtained if a weibull specialization ai qt11 of the baseline hazard can be assumed but these estimators are unavailable for censored data estimates of formed by assuming the ai s are independent gamma variates are investigated the resulting estimators are found to be more efficient than those obtained by holt prentice when the ai s are in fact gamma to be available for censored data and to perform well under a number of very different unimodal alternatives to a gamma distribution for the ai s

colonization of a territory by a stochastic population under a strong allee effect and a low immigration pressure we study the dynamics of colonization of a territory by a stochastic population at low immigration pressure we assume a sufficiently strong allee effect that introduces in deterministic theory a large critical population size for colonization at low immigration rates the average precolonization population size is small thus invalidating the wkb approximation to the master equation we circumvent this difficulty by deriving an exact zero flux solution of the master equation and matching it with an approximate nonzero flux solution of the pertinent fokker planck equation in a small region around the critical population size this procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization for a wide range of immigration rates at sufficiently high immigration rates our results agree with wkb results obtained previously at low immigration rates the results can be very different

population extinction risk in the aftermath of a catastrophic event we investigate how a catastrophic event modeled as a temporary fall of the reproduction rate increases the extinction probability of an isolated self regulated stochastic population using a variant of the verhulst logistic model as an example we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe this quantity is given by the eikonal action computed over the optimal path instanton of an effective classical hamiltonian system with a time dependent hamiltonian for a general catastrophe the eikonal equations can be solved numerically for simple models of catastrophic events analytic solutions can be obtained one such solution becomes quite simple close to the bifurcation point of the verhulst model the eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation

immigration extinction dynamics of stochastic populations how high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population become extinct is there any relation between the population size distributions with and without immigration under what conditions can one justify the simple patch occupancy models which ignore the population distribution and its dynamics in a patch and treat a patch simply as either occupied or empty we answer these questions by exactly solving a simple stochastic model obtained by adding a steady immigration to a variant of the verhulst model a prototypical model of an isolated stochastic population

new representations for the gaussian class multivariate weibull distribution with constant correlation and applications novel single integral representations for the multivariate probability density functions pdfs and cumulative distribution functions cdfs of the gaussian class weibull distribution are derived the solutions are expressed in terms of familiar mathematical functions which are available in common mathematical software the well known equal constant correlation model is considered a special linear transformation of independent gaussian random variables is used to generate correlated weibull random variables the advantage of the new representation is that only a single integral computation is needed to compute a n dimensional distribution the new representation of the cdf is used for the performance evaluation of a selection diversity combiner operating in equally correlated weibull fading channels the new pdf representation is also used for an analysis of the moments of the output signal to noise ratio of an equal gain diversity combiner operating in equally correlated weibull fading channels

equivalence of nonlinear systems to triangular form the singular case the problem of state equivalence of a given nonlinear system to a triangular form is considered here the solution of this problem has been known for the regular case i e when there exists a certain nested sequence of regular and involutive distributions it is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback this paper deals with the singular case i e when the nested sequence of involutive distributions of the system contains singular distributions special attention is paid to the so called bijective triangular form geometric coordinates free criteria for the solution of the above problem as well as constructive verifiable procedures are given these results are used to obtain a result in the nonsmooth stabilization problem

extinction of metastable stochastic populations we investigate the phenomenon of extinction of a long lived self regulating stochastic population caused by intrinsic demographic noise extinction typically occurs via one of two scenarios depending on whether the absorbing state n 0 is a repelling scenario a or attracting scenario b point of the deterministic rate equation in scenario a the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n 0 in scenario b there is an intermediate repelling point n n 1 between the attracting point n 0 and another attracting point n n 2 in the vicinity of which the metastable population resides the crux of the theory is a dissipative variant of wkb wentzel kramers brillouin approximation which assumes that the typical population size in the metastable state is large starting from the master equation we calculate the quasistationary probability distribution of the population sizes and the exponentially long mean time to extinction for each of the two scenarios when necessary the wkb approximation is complemented i by a recursive solution of the quasistationary master equation at small n and ii by the van kampen system size expansion valid near the fixed points of the deterministic rate equation the theory yields both entropic barriers to extinction and pre exponential factors and holds for a general set of multistep processes when detailed balance is broken the results simplify considerably for single step processes and near the characteristic bifurcations of scenarios a and b

performance of dual diversity predetection egc in correlated rayleigh fading with unequal branch snrs the bit error probability bep for coherent detection of binary signals with dual diversity predetection equal gain combining is derived using the beaulieu 1991 series in particular we consider a correlated rayleigh fading channel with unequal branch signal to noise ratios the bep expression is in terms of the power correlation coefficient of the branches is easy to compute and depicts clearly the effect of correlated fading on the error performance

on p normal forms of nonlinear systems using the differential geometric control theory we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to via a change of coordinates and restricted smooth state feedback a generalized normal form called p normal form which includes brunovsky canonical form and feedback linearizable systems in a lower triangular form as its special cases we also give an algorithm for computing the appropriate coordinate transformations and feedback control laws

performance analysis of dual selection diversity in correlated weibull fading channels ascertaining the importance of the dual selection combining sc receivers and the suitability of the weibull model to describe mobile fading channels we study the performance of a dual sc receiver over correlated weibull fading channels with arbitrary parameters exact closed form expressions are derived for the probability density function the cumulative distribution function and the moments of the output signal to noise ratio snr important performance criteria such as average output snr amount of fading outage probability and average bit error probability for several modulation schemes are studied furthermore for these performance criteria novel closed form analytical expressions are derived the proposed analysis is complemented by various performance evaluation results including the effects of the input snr s unbalancing fading severity and fading correlation on the overall system s performance computer simulation results have verified the validity and accuracy of the proposed analysis

partial state global stabilization for general triangular systems abstract we deal with the partial state global stabilization problem for a wide class of nonlinear systems which contains those having triangular structure the sufficient conditions we propose guarantee global stabilization by means of an output smooth feedback integrator

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

a new asymptotic analysis technique for diversity receptions over correlated lognormal fading channels prior asymptotic performance analyses are based on the series expansion of the moment generating function mgf or the probability density function pdf of channel coefficients however these techniques fail for lognormal fading channels because the taylor series of the pdf of a lognormal random variable is zero at the origin and the mgf does not have an explicit form although lognormal fading model has been widely applied in wireless communications and free space optical communications few analytical tools are available to provide elegant performance expressions for correlated lognormal channels in this paper we propose a novel framework to analyze the asymptotic outage probabilities of selection combining sc equal gain combining egc and maximum ratio combining mrc over equally correlated lognormal fading channels based on these closed form results we show 1 the outage probability of egc or mrc becomes an infinitely small quantity compared to that of sc at high signal to noise ratio snr 2 channel correlation can cause an infinite performance loss at high snr and 3 negatively correlated lognormal channels can outperform the independent lognormal channels the analyses reveal insights into the long standing problem of asymptotic performance analyses over correlated lognormal channels and circumvent the time consuming monte carlo simulation and numerical integration

effect of reaction step size noise on the switching dynamics of stochastic populations in genetic circuits when the messenger rna lifetime is short compared to the cell cycle proteins are produced in geometrically distributed bursts which greatly affects the cellular switching dynamics between different metastable phenotypic states motivated by this scenario we study a general problem of switching or escape in stochastic populations where influx of particles occurs in groups or bursts sampled from an arbitrary distribution the fact that the step size of the influx reaction is a priori unknown and in general may fluctuate in time with a given correlation time and statistics introduces an additional nondemographic reaction step size noise into the system employing the probability generating function technique in conjunction with hamiltonian formulation we are able to map the problem in the leading order onto solving a stationary hamilton jacobi equation we show that compared to the usual case of single step influx bursty influx exponentially decreases the population s mean escape time from its long lived metastable state in particular close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst size distribution our results are demonstrated on several realistic distributions and compare well with numerical monte carlo simulations

the identifiability of the competing risks model summary this paper considers the consequences for identifiability of introducing regressors into the competing risks model of multistate duration analysis we establish conditions under which access to regressors overturns the nonidentification theorem of cox and tsiatis for both proportional and accelerated failure time models

persistence of instanton connections in chemical reactions with time dependent rates the evolution of a system of chemical reactions can be studied in the eikonal approximation by means of a hamiltonian dynamical system the fixed points of this dynamical system represent the different states in which the chemical system can be found and the connections among them represent instantons or optimal paths linking these states we study the relation between the phase portrait of the hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time we show that the topology of the phase space is robust for small time dependent perturbations in concrete examples and state general results when possible this robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time dependent situation

on the multivariate nakagami m distribution with exponential correlation capitalizing on the proof of a theorem presented by l e blumenson and k s miller see ann math statist vol 34 p 903 10 1963 we propose a useful closed formula for the exponentially correlated n variate nakagami m probability density function moreover an infinite series approach for the corresponding cumulative distribution function is presented bounds on the error resulting from the truncation of the infinite series are also derived finally in order to check the accuracy of the proposed formulation numerical results are presented

infinite series representations of the bivariate rayleigh and nakagami m distributions despite the usefulness of the bivariate correlated nakagami m cumulative distribution function cdf in communications systems analysis an infinite series for the computation of this function is not known in this letter an infinite series representation of the bivariate cdf is derived bounds on the error resulting from truncation of the infinite series are also derived

nonregular feedback linearization a nonsmooth approach in this note we address the problem of exact linearization via nonsmooth nonregular feedback a criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs and its application to nonholonomic systems is briefly discussed

the trivariate and quadrivariate weibull fading distributions with arbitrary correlation and their applications to diversity reception the statistical characteristics of the trivariate and quadrivariate weibull fading distribution with arbitrary correlation non identical fading parameters and average powers are analytically studied novel expressions for important joint statistics are derived using the weibull power transformation these expressions are used to evaluate the performance of selection combining sc and maximal ratio combining mrc diversity receivers in the presence of such fading channels

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

robust stabilization of the generalized triangular form nonlinear systems with disturbances we investigate the problem of global uniform input to state stabilization of nonlinear generalized triangular form gtf control systems of ode with time varying and periodic dynamics and with external essentially bounded disturbances our first main result is a statement which is a kind of extension of theorems on adding an integrator to the case of input to state stabilization of gtf systems as a corollary we immediately obtain our second main result on global uniform input to state stabilzation of gtf systems w r t the external disturbances the latter is a generalization of the recent result devoted to the global asymptotic stabilization of the gtf systems without disturbances it is essential that the proof of the main result is based on the converse iss lyapunov theorems for the time varying systems which allows to simplify construction proposed our recent work

positive dependence of a class of multivariate exponential distributions the positive dependence of a subclass of multivariate exponential distributions is examined this class is characterized by an index vector k and a parameter vector lambda which are used as an ordering to yield degrees of positive dependence the results presented have a direct implication on the reliability function of a system and the survival probability function of a shock model and consequently on the optimal assembly of systems

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

population extinction in a time modulated environment the extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment we investigate this effect using as an example a stochastic branching annihilation process with a time dependent branching rate the population extinction is treated in eikonal approximation where it is described as an instanton trajectory of a proper reaction hamiltonian the modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase we calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations the techniques include a first order theory with respect to the modulation amplitude a second order theory in the spirit of the kapitsa pendulum effect and adiabatic theory valid for low modulation frequencies

population switching under a time varying environment we study the switching dynamics of a stochastic population subjected to a deterministically time varying environment our approach is demonstrated on a problem of population establishment which is important in ecology at the deterministic level the model we study gives rise to a critical population size beyond which the system experiences establishment notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations here we consider two prototypical examples of a time varying environment a temporary change in the environment and a periodically varying environment by employing a semiclassical approximation we compute within exponential accuracy the change in the establishment probability and mean establishment time of the population due to the environmental variability our analytical results are verified by using a modified gillespie algorithm which accounts for explicitly time dependent reaction rates importantly our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations

asymptotic analysis and tight performance bounds of diversity receptions over beckmann fading channels with arbitrary correlation prior results on exact error rates and outage probabilities of diversity receptions over arbitrarily correlated fading channels involve intractable nested integrals which makes the performance analyses challenging to carry out in this paper we derive asymptotic expressions and asymptotically tight bounds for error rates and outage probabilities of diversity receptions including maximal ratio combining selection combining and equal gain combining over arbitrarily correlated beckmann fading channels these new asymptotic performance expressions reveal insights into the diversity systems over arbitrarily correlated beckmann fading channels and the accuracy of the asymptotic performance expressions is explicitly quantified by the performance bounds using these analytical tools one can assess the performance of the diversity reception systems over arbitrarily correlated beckmann fading channels without resorting to time consuming monte carlo simulation or numerical multifold integration

performance analysis of triple selection diversity over exponentially correlated nakagami m fading channels an approach to the performance analysis of a triple selection diversity system over exponentially correlated nakagami m fading channels is presented closed form expressions of converged sums for both outage and average error probabilities are derived numerical results are presented to point out the effect of the fading correlation the fading severity as well as the improvement achieved by the triple selection combining compared with the corresponding dual diversity case

global properties of the triangular systems in the singular case we introduce a new class of the triangular multi input and multi output control systems of o d e which are not feedback linearizable and investigate its global behavior the triangular form introduced is a generalization of the classes of triangular systems considered before for our class we solve the problem of global robust controllability combining our main result with that of f h clarke yu s ledyaev e d sontag a i subbotin asymptotic controllability implies feedback stabilization ieee trans automat control 42 1997 1394 1407 we obtain a corollary on the global discontinuous sampled stabilization an example showing that global smooth stabilization can be irrelevant to the singular case is considered to prove our main result we apply a certain back stepping algorithm and combine the technique proposed in v i korobov s s pavlichkov w h schmidt global robust controllability of the triangular integro differential volterra systems j math anal appl 309 2005 743 760 with solving a specific problem of global practical stabilization by means of a discontinuous time varying feedback law

global stabilization of the generalized mimo triangular systems with singular input output links this work is devoted to the problem of global stabilization for a class of the general multi input and multi output mimo triangular systems which are not feedback linearizable to solve the problem we develop a specific backstepping procedure and generalize some existing results since we deal with the global stabilization for the singular and mimo case the technique of the proof differs from the standard backstepping algorithms

novel simple representations for gaussian class multivariate distributions with generalized correlation novel single integral representations for the multivariate probability density functions and cumulative distribution functions of gaussian class distributions rayleigh rician weibull nakagami m and generalized rician are derived the solutions are expressed in terms of well known functions which are available in common mathematical software the marginal random variables are not necessarily identically distributed as is the case for some past solutions a generalized correlation structure based on a special linear transformation of independent gaussian random variables is used in this study the advantage of the new representation is that only a single integral computation is needed to compute an n dimensional distribution

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

equal gain diversity receiver performance in wireless channels performance analysis of equal gain combining egc diversity systems is notoriously difficult only more so given that the closed form probability density function pdf of the egc output is only available for dual diversity combining in rayleigh fading a powerful frequency domain approach is therefore developed in which the average error rate integral is transformed into the frequency domain using parseval s theorem such a transformation eliminates the need for computing or approximating the egc output pdf which is unknown but instead requires the knowledge of the corresponding characteristic function which is readily available the frequency domain method also circumvents the need to perform multiple fold convolution integral operations usually encountered in the calculation of the pdf of the sum of the received signal amplitudes we then derive integral expressions for the average symbol error rate of an arbitrary two dimensional signaling scheme with egc reception in rayleigh rician nakagami m 1960 and nakagami q fading channels for practically important cases of second and third order diversity systems in nakagami fading both coherent and noncoherent detection methods for binary signaling are analyzed using the appell hypergeometric function a number of closed form solutions are derived in which the results put forward by zhang see ibid vol 45 p 270 73 1997 are shown to be special cases

a multivariate distribution with weibull connections a simple form of multivariate distribution is defined which for certain parameter values has weibull marginals the distribution has a single parameter governing association between the variates which may be positive negative or zero the simple forms for marginal and conditional distributions hazard functions and densities make it attractive for practical application and interpretation

n ast nakagami a novel stochastic model for cascaded fading channels a generic and novel distribution referred to as nakagami constructed as the product of n statistically independent but not necessarily identically distributed nakagami m random variables rvs is introduced and analyzed the proposed distribution turns out to be a very convenient tool for modelling cascaded nakagami m fading channels and analyzing the performance of digital communications systems operating over such channels the moments generating probability density cumulative distribution and moments functions of the n nakagami distribution are developed in closed form using the meijer s g function using these formulas generic closed form expressions for the outage probability amount of fading and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the n nakagami fading and the additive white gaussian noise channel are presented complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation the suitability of the n nakagami fading distribution to approximate the lognormal distribution is also being investigated using kolmogorov smirnov tests the rate of convergence of the central limit theorem as pertaining to the multiplication of nakagami m rvs is quantified

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

the bivariate generalized κ κ g distribution and its application to diversity receivers the correlated bivariate generalized k kg distribution with not necessarily identical shaping and scaling parameters is introduced and studied this composite distribution is convenient for modeling multipath shadowing correlated fading environments when the correlations between the signal envelopes and their powers are different generic infinite series expressions are derived for the probability density function pdf the cumulative distribution function cdf and the joint moments assuming identical shaping parameters simpler expressions for the pdf cdf and the characteristic function cf are provided while the joint moments are derived in closed form furthermore the pdfs of the product and ratio of two correlated kg random variables are obtained capitalizing on these theoretical expressions for the statistical characteristics of the correlated kg distribution the performance analysis of various diversity reception techniques such as maximal ratio combining mrc equal gain combining egc and selection diversity sd over bivariate kg fading channels is presented for the sd the outage probability is studied while for the mrc and egc the average bit error probability is obtained the proposed analysis is accompanied by numerical results clearly demonstrating the usefulness of the theoretical approach as well as the appropriateness of the kg distribution to model multipath shadowing fading channels

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

constructive nonsmooth stabilization of triangular systems the problem of local asymptotic continuous feedback stabilization of single input nonlinear systems is considered here the aim is to explicitly construct a continuous asymptotically stabilizing feedback for a class of nonlinear systems that is known to be continuous feedback asymptotically stabilizable but for which the known results do not provide an effective method to compute the stabilizer computer simulations are included to show practical applicability of our approach

statistical analysis and characterization of the indoor propagation channel this paper presents statistical analysis of data obtained by measuring narrowband path loss at dect digital enhanced cordless telecommunications frequency 1 89 ghz in an indoor environment specific goodness of fit tests are applied to the data the tests assess whether the data generating source belongs to a known family of random variables results obtained support that local path loss distribution can be represented as weibull or nakagami in most environments the close resemblance between such distributions and rice distribution with rayleigh as a special case confirms that rice rayleigh description of fading can be applied to indoor environments that similarity leads to a general simple approximate expression for the cumulative distribution function of the signal to interference ratio the expression can be used without limitations to the number and the parameters of the rice interferers

reducing the extinction risk of stochastic populations via nondemographic noise we consider nondemographic noise in the form of uncertainty in the reaction step size and reveal a dramatic effect this noise may have on the stability of self regulating populations employing the reaction scheme ma ka but allowing e g the product number k to be a priori unknown and sampled from a given distribution we show that such nondemographic noise can greatly reduce the population s extinction risk compared to the fixed k case our analysis is tested against numerical simulations and by using empirical data of different species we argue that certain distributions may be more evolutionary beneficial than others

dynamics of simple gene network motifs subject to extrinsic fluctuations cellular processes do not follow deterministic rules even in identical environments genetically identical cells can make random choices leading to different phenotypes this randomness originates from fluctuations present in the biomolecular interaction networks most previous work has been focused on the intrinsic noise in of these networks yet especially for high copy number biomolecules extrinsic or environmental noise en has been experimentally shown to dominate the variation here we develop an analytical formalism that allows for calculation of the effect of en on gene expression motifs we introduce a method for modeling bounded en as an auxiliary species in the master equation the method is fully generic and is not limited to systems with small en magnitudes we focus our study on motifs that can be viewed as the building blocks of genetic switches a nonregulated gene a self inhibiting gene and a self promoting gene the role of the en properties magnitude correlation time and distribution on the statistics of interest are systematically investigated and the effect of fluctuations in different reaction rates is compared due to its analytical nature our formalism can be used to quantify the effect of en on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single cell gene expression experiments

feedback classification of nonlinear single input control systems with controllable linearization normal forms canonical forms and invariants we study the feedback group action on single input nonlinear control systems we follow an approach of kang and krener based on analyzing step by step the action of homogeneous transformations on the homogeneous part of the same degree of the system we construct a dual normal form and dual invariants with respect to those obtained by kang we also propose a canonical form and a dual canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms resp their dual canonical forms coincide we give an explicit construction of transformations bringing the system to its normal dual normal canonical and dual canonical forms we illustrate our results by simple examples on mathbb r 3 and mathbb r 4

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

population extinction under bursty reproduction in a time modulated environment in recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations for example nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size or environmental variability in the form of time varying reaction rates have been separately found to dramatically impact the extinction risk of isolated populations in this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation using the so called momentum space wentzel kramers brillouin wkb approach and accounting for the explicit time dependence in the reaction rates we arrive at a set of time dependent hamilton equations to this end we evaluate the population s extinction risk by finding the instanton of the time perturbed hamiltonian numerically whereas analytical expressions are presented in particular limits using various perturbation techniques we focus on two classes of time varying environments periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe all our theoretical results are tested against numerical monte carlo simulations with time dependent rates and also against a numerical solution of the corresponding time dependent hamilton equations

ber performance of dual predetection egc in correlative nakagami m fading in this letter an approach to the evaluation of the error performance in dual predetection equal gain combining egc systems over correlated nakagami m fading channels is presented deriving an infinite series representation for the characteristic function of the sum of two correlated nakagami m variables a closed form formula is extracted for binary phase shift keying and coherent binary frequency shift keying while several other modulation schemes are studied capitalizing on a parsevals s theorem based approach previously published numerical results and simulations are also presented to illustrate the proposed mathematical analysis and to point out the effect of the input signal to noise ratio unbalancing the fading severity and the fading correlation on the system s error performance

noise driven unlimited population growth demographic noise causes unlimited population growth in a broad class of models which without noise would predict a stable finite population we study this effect on the example of a stochastic birth death model which includes immigration binary reproduction and death the unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution mpd of the population we develop a systematic wkb theory complemented by the van kampen system size expansion for the mpd and for the decay time important signatures of the mpd are a power law tail such that all the distribution moments except the zeroth one diverge and the presence in the solution of two different wkb modes