an index of tumorigenic potency a new index of tumorigenic potency is derived using a survival adjusted quantal response estimator given by bailer and portier 1988 biometrics 44 417 431 the small sample bias and mean squared error properties of this estimator are explored using computer simulations of animal carcinogenicity experiments and are compared to the characteristics of the td50 an estimator proposed by sawyer et al 1984 biometrics 40 27 40 it is observed that this new index tends to have smaller bias and mean squared error relative to the td50 over varying shapes of the tumor onset distribution levels of tumor lethality and levels of treatment lethality

brief paper stabilization of some fractional delay systems of neutral type in this note we give new stability tests which enable one to fully characterize the h stability of systems with transfer function g s r s p s q s e s h where h 0 and p q r are real polynomials in the variable s m for 0 p s q s 1

rigorous solution of the gardner problem we prove rigorously the well known result of gardner about the typical fractional volume of interactions between n spins which solve the problem of storing a given set of p random patterns the gardner formula for this volume in the limit n p p n is proven for all values of besides we prove a useful criterion for the factorisation of all correlation functions for a class of models of classical statistical mechanics

absence of self averaging of the order parameter in the sherrington kirkpatrick model we prove that if n is the sherrington kirkpatrick sk hamiltonian and the quantity bar q n n 1 sum left langle s l right rangle h 2 converges in the variance to a nonrandom limit asn then the mean free energy of the model converges to the expression obtained by sk since this expression is known not to be correct in the low temperature region our result implies the non self averaging of the order parameter of the sk model this fact is an important ingredient of the parisi theory which is widely believed to be exact we also prove that the variance of the free energy of the sk model converges to zero asn i e the free energy has the self averaging property

the free energy of a class of hopfield models we show that in the limitp n 0 p n 0 the limit free energy of the hopfield model equals in probability the curie weiss free energy we prove also that the free energy of the hopfield model is self averaging for any finite

a linearized stability theorem for nonlinear delay fractional differential equations in this paper we prove a theorem of linearized asymptotic stability for nonlinear fractional differential equations with a time delay by using the method of linearization of a nonlinear equation along an orbit lyapunov s first method we show that an equilibrium of a nonlinear caputo fractional delay differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable our approach is based on a technique that converts the linear part of the equation into a diagonal one then by using the properties of generalized mittag leffler functions the construction of an associated lyapunov perron operator and the banach contraction mapping theorem we obtain the desired result

estimation of the proportional hazard in two treatment group clinical trials two easily computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared by simulation with the partial maximum likelihood cml estimator which assumes the cox model with no covariates the two methods studied are the mantel haenszel estimator and the o e method which employs the ratio of the relative death rates for the two treatments uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a weibull distribution with shape parameter 2 the o e method is biased but within the range of values of the ratio of the hazard rates of interest in clinical trials it is more efficient in terms of mean square error than either cml or the mantel haenszel method for all but the largest trials the mantel haenszel method is minimally biased gives answers very close to those obtained using cml and may be used to provide satisfactory approximate confidence intervals

calculation of carcinogenic potency from long term animal carcinogenesis experiments an index of carcinogenic potency for chemicals tested in chronic animal experiments is described by analogy with the well known lethal dose 50 ld50 of quantal bioassay a tumorigenic dose 50 td50 may be defined in the absence both of tumors in the control group and of intercurrent deaths as that daily dose of chemical which gives 50 of the test animals tumors by some fixed age tumors in the control zero dose group are handled exactly as for the ld50 and intercurrent deaths are handled by life table methods nonparametric procedures are developed for estimating the td50 and for constructing confidence intervals these are based on likelihoods which assume that the tumor hazard is linear in dose

brief analysis of fractional delay systems of retarded and neutral type this paper analyses several properties linked to the robust control of fractional differential systems with delays the bibo stability of both retarded and neutral fractional delay systems is related to the location of their poles in the particular case of retarded systems we give some properties of the poles of the system and the singular values of its hankel operator

a numerical algorithm for stability testing of fractional delay systems this paper presents an effective numerical algorithm for testing the bibo stability of fractional delay systems described by fractional order delay differential equations it is based on using cauchy s integral theorem and solving an initial value problem the algorithm has a reliable result which is illustrated by several examples and hence is practically useful in the analysis and design of feedback control for both integer and fractional order systems having time delays

intersecting random half spaces toward the gardner derrida formula gardner and derrida have introduced a natural version of the problem of the capacity of the binary perceptron with temperature and they proposed based on physical methods remarkable formulas for this model we give a complete rigorous proof that these formulas are correct at sufficiently high temperature for a much larger class of models

a computing method on stability intervals of time delay for fractional order retarded systems with commensurate time delays abstract this paper investigates the stability intervals of time delays for fractional order retarded time delay systems by the orlando formula the existence of the crossing frequencies is brought to verify the stability related to the commensurate time delay for each crossing frequency the corresponding critical time delays are determined by the generalized eigenvalues of two matrices constructed by the crossing frequency the commensurate fractional order and the coefficients of the characteristic function the root tendency rt is defined to provide a method to analyze the number of the unstable roots for a given crossing frequency and critical time delay based on the rt values and the number of the unstable roots for fractional order systems with no time delay a computing method on the stability intervals of time delay is proposed in this paper finally a numerical example is offered to validate the effectiveness of this method

stability and performance analysis for positive fractional order systems with time varying delays this paper addresses the stability and l infty gain analysis problem for continuous time positive fractional order delay systems with incommensurate orders between zero and one a necessary and sufficient condition is firstly given to characterize the positivity of continuous time fractional order systems with bounded time varying delays moreover by exploiting the monotonic and asymptotic property of the constant delay system by virtue of the positivity and comparing the trajectory of the time varying delay system with that of the constant delay system it is proved that the asymptotic stability of positive fractional order systems is not sensitive to the magnitude of delays in addition it is shown that the l infty gain of a positive fractional order system is independent of the magnitude of delays and fully determined by the system matrices finally a numerical example is given to show the validity of the theoretical results

rigorous results for the hopfield model with many patterns we perform a thorough investigation of the main aspects of the hopfield model with many patterns advances are made toward the validity of the replica symmetric solution strong evidence of the validity of this solution is given over the entire domain where this validity is conjectured complete proof is given in a subregion that contains strictly the ergodic region

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

the space of interactions in neural network models the typical fraction of the space of interactions between each pair of n ising spins which solve the problem of storing a given set of p random patterns as n bit spin configurations is considered the volume is calculated explicitly as a function of the storage ratio alpha p n of the value kappa 0 of the product of the spin and the magnetic field at each site and of the magnetisation m here m may vary between 0 no correlation and 1 completely correlated the capacity increases with the correlation between patterns from alpha 2 for correlated patterns with kappa 0 and tends to infinity as m tends to 1 the calculations use a saddle point method and the order parameters at the saddle point are assumed to be replica symmetric this solution is shown to be locally stable a local iterative learning algorithm for updating the interactions is given which will converge to a solution of given kappa provided such solutions exist

a measure of tumorigenic potency incorporating dose response shape many researchers have considered the problem of ranking chemical agents based on their carcinogenic potency sawyer et al 1984 biometrics 40 27 40 proposed a carcinogenic potency estimate that incorporates both intercurrent mortality and background tumor rates since then many authors have either generalized the method outlined by sawyer et al or developed their own method based on a slightly different adjustment for treatment related changes in survival none of these methods however has estimated the shape of the dose response curve and incorporated such an estimate in potency estimation in this manuscript a measure of tumorigenic potency is proposed that utilizes the estimated shape of the dose response relationship in addition to estimated dose effects in order to rank chemicals on the basis of carcinogenic risk comparison of this new measure to that of sawyer et al is done using a large database of animal carcinogenicity experiments from the national cancer institute and the national toxicology program

an algorithm for stabilization of fractional order time delay systems using fractional order pid controllers this technical note presents a solution to the problem of stabilizing a given fractional order system with time delay using fractional order pllambdadmu controllers it is based on determining a set of global stability regions in the kp ki kd space corresponding to the fractional orders lambda and mu in the range of 0 2 and then choosing the biggest global stability region in this set this method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements the algorithm is simple and has reliable result which is illustrated by an example and hence is practically useful in the analysis and design of fractional order control systems

the replica symmetric solution without replica trick for the hopfield model we derive the saddle point equations for the order parameters of the hopfield model in the case of replica symmetry without using the replica trick but assuming that the edwards anderson parameter is a self averaging quantity

necessary and sufficient conditions for bibo stability of some fractional delay systems of neutral type in this note bounded input bounded output bibo stability of a large class of neutral type fractional delay systems is investigated necessary and sufficient conditions of bibo stability are presented for the intended class of systems the sufficient conditions have been provided for a more general case in the previous studies two lemmas are provided for checking a prerequisite imposed on the considered class of systems finally two numerical examples are given to illustrate the obtained results