logic test pattern generation using linear codes logic testing of today s integrated circuits is a task of increasing difficulty as the number of circuits or transistors packed onto a single chip grows higher and higher exhaustive pattern testing with adequate partitioning of logic has been explored regarding its potential in solving the problems in test pattern generation and fault coverage in this paper we propose a new method of simultaneously generating exhaustive test patterns for all possible input subsets each corresponding to an output up tq a specified size the method is based on the structure of linear polynomial codes and can be easily implemented by modifying existing shift registers in an lssd or scan path design to embody additional feedback connections this is particularly attractive since the implementation is compatible with the approach of self testing using pseudorandom patterns thus a very reasonable strategy is to combine limited exhaustive pattern testing with pseudorandom pattern testing ini cases where complete exhaustive testing is not practical

bayesian age period cohort models with versatile interactions and long term predictions mortality and population in finland 1878 2050 age period cohort apc models are widely used for studying time trends of disease incidence or mortality model identifiability has become less of a problem with bayesian apc models these models are usually based on random walk rw1 rw2 smoothing priors for long and complex time series and for long predicted periods these models as such may not be adequate we present two extensions for the apc models first we introduce flexible interactions between the age period and cohort effects based on a two dimensional conditional autoregressive smoothing prior on the age period plane our second extension uses autoregressive integrated ari models to provide reasonable long term predictions to illustrate the utility of our model framework we provide stochastic predictions for the finnish male and female population in 2010 2050 for that we first study and forecast all cause male and female mortality in finland 1878 2050 showing that using an interaction term is needed for fitting and interpreting the observed data we then provide population predictions using a cohort component model which also requires predictions for fertility and migration as our main conclusion ari models have better properties for predictions than the simple rw models do but mixing these prediction models with rw1 or rw2 smoothing priors for observed periods leads to a model that is not fully consistent further research with our model framework will concentrate on using a more consistent model for smoothing and prediction such as autoregressive integrated moving average models with state space methods or gaussian process priors

pricing and hedging asian basket spread options asian options basket options and spread options have been extensively studied in the literature however few papers deal with the problem of pricing general asian basket spread options this paper aims to fill this gap in order to obtain prices and greeks in a short computation time we develop approximation formulae based on comonotonicity theory and moment matching methods we compare their relative performances and explain how to choose the best approximation technique as a function of the asian basket spread characteristics we also give explicitly the greeks for our proposed methods in the last section we extend our results to options denominated in foreign currency

linear dependencies in linear feedback shift registers linear feedback shift registers have been proposed to generate test patterns for the self test of logic networks the probability of linear dependence among k bit positions of a subset of k bits in a maximum length shift register sequence is an outstanding problem in this correspondence we derive a formula for the calculation of the probability

moment matching approximation of asian basket option prices in this paper we propose some moment matching pricing methods for european style discrete arithmetic asian basket options in a black scholes framework we generalize the approach of m curran valuing asian and portfolio by conditioning on the geometric mean price management science 40 1994 1705 1711 and of g deelstra j liinev m vanmaele pricing of arithmetic basket options by conditioning insurance mathematics economics 34 2004 55 57 in several ways we create a framework that allows for a whole class of conditioning random variables which are normally distributed we moment match not only with a lognormal random variable but also with a log extended skew normal random variable we also improve the bounds of g deelstra i diallo m vanmaele bounds for asian basket options journal of computational and applied mathematics 218 2008 215 228 numerical results are included and on the basis of our numerical tests we explain which method we recommend depending on moneyness and time to maturity

max algebra and pairwise comparison matrices abstract this paper is a continuation of our 2004 paper max algebra and pairwise comparison matrices in which the max eigenvector of a symmetrically reciprocal matrix was used to approximate such a matrix by a transitive matrix this approximation was based on minimizing the maximal relative error in a later paper by dahl a different error measure was used and led to a slightly different approximating transitive matrix here some geometric properties of this approximation problem are discussed these lead among other results to a new characterization of a max eigenvector of an irreducible nonnegative matrix the case of toeplitz matrices is discussed in detail and an application to music theory that uses toeplitz symmetrically reciprocal matrices is given

default probabilities of a holding company with complete and partial information abstract this paper studies the valuation of credit risk for firms that own several subsidiaries or business lines we provide simple analytical approximating expressions for probabilities of default and for equity debt market values both in the case when the information is available in continuous time as well as in the case that it is not instantaneously available the total firm s asset value being modeled as a sum of lognormal random variables we use convex upper and lower approximations to infer these analytical approximating expressions we extend the model to firms financed by multiple stochastic liabilities and conclude by numerical illustrations

quickest drift change detection in levy type force of mortality model abstract in this paper we give solution to the quickest drift change detection problem for a levy process consisting of both a continuous gaussian part and a jump component we consider here bayesian framework with an exponential a priori distribution of the change point using an optimality criterion based on a probability of false alarm and an expected delay of the detection our approach is based on the optimal stopping theory and solving some boundary value problem paper is supplemented by an extensive numerical analysis related with the construction of the generalized shiryaev roberts statistics in particular we apply this method after appropriate calibration to analyse polish life tables and to model the force of mortality in this population with a drift changing in time

pmax1 and smax properties and asymptotic stability in the max algebra abstract in this work we introduce the class of p max 1 matrices for the max algebra and derive some properties of these that echo similar results for p matrices in the conventional algebra in analogy with 1 we define the row p max 1 property and the smax property of a finite set of nonnegative matrices moreover we relate these concepts to stability questions for sets of matrices and difference inclusions in the max algebra

modeling repeated functional observations we introduce a new methodological framework for repeatedly observed and thus dependent functional data aiming at situations where curves are recorded repeatedly for each subject in a sample our methodology covers the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies where the timing of recordings is often sparse and random the proposed models lead to an interpretable and straightforward decomposition of the inherent variation in repeatedly observed functional data and are implemented through a straightforward two step functional principal component analysis we provide consistency results and asymptotic convergence rates for the estimated model components we compare the proposed model with an alternative approach via a two dimensional karhunen loeve expansion and illustrate it through the analysis of longitudinal mortality data from period lifetables that are repeatedly observed for a sample of countries over ma

bayesian forecasting of cohort fertility there are signs that fertility in rich countries may have stopped declining but this depends critically on whether women currently in reproductive ages are postponing or reducing lifetime fertility analysis of average completed family sizes requires forecasts of remaining fertility for women born 1970 1995 we propose a bayesian model for fertility that incorporates a priori information about patterns over age and time we use a new dataset the human fertility database hfd to construct improper priors that give high weight to historically plausible rate surfaces in the age dimension cohort schedules should be well approximated by principal components of hfd schedules in the time dimension series should be smooth and approximately linear over short spans we calibrate priors so that approximation residuals have theoretical distributions similar to historical hfd data our priors use quadratic penalties and imply a high dimensional normal posterior distribution for each country s fertility surface

functional inequalities for spectral radii of nonnegative matrices abstract let p n denote the set of all square n n nonnegative matrices for a k a k ij n i j 1 k 1 m k not a power we set f a 1 a m f a 1 ij a m ij n i j 1 for each a p n we let a denote its spectral radius this paper is concerned with the characterization of those functions f r m r satisfying either f a 1 a m f a 1 a m 1 or f a 1 a m f a 1 a m 2 for all a 1 a m p n and every n e n we totally characterize all functions satisfying 1 we delineate various classes of functions which satisfy 2 if f 0 0 and f is bounded above in some neighborhood of any eint r m then we totally characterize all f satisfying 2

limit eigenvalues of nonnegative matrices abstract in this paper we give a simple closed formula for a certain limit eigenvalue of a nonnegative matrix we bound the spectral radius of a nonnegative matrix in terms of this limit eigenvalue

universal unification of life death evolution post evolution and extinction abstract a general law of universal maximally rapid entropy decrease unifies metabolism mortality and evolution yields their quantitatively accurate universal laws and singularities proves that accidental premature mortality is relatively small and quantifies it predicts that evolution may be continuous or followed by weak and strong spurts leads to a definition of post evolution and considers its probability suggests an absolute instability of technological terrestrial and extra terrestrial civilizations and allows for computer simulations of mortality and evolution

barabanov norms lipschitz continuity and monotonicity for the max algebraic joint spectral radius abstract we present several results describing the interplay between the max algebraic joint spectral radius jsr for compact sets of matrices and suitably defined matrix norms in particular we extend a classical result for the conventional algebra showing that the max algebraic jsr can be described in terms of induced norms of the matrices in the set we also show that for a set generating an irreducible semigroup in a cone theoretic sense a monotone barabanov norm always exists this fact is then used to show that the max algebraic jsr is locally lipschitz continuous on the space of compact irreducible sets of matrices with respect to the hausdorff distance we then prove that the max algebraic jsr is locally hoelder continuous on the space of compact sets of nonnegative matrices finally we prove a strict monotonicity property for the max algebraic jsr that echoes a fact for the classical jsr the single matrix characterisation of the max algebraic jsr plays a vital role in our proofs

functional inequalities for max eigenvalues of nonnegative matrices let pn denote the set of all n n nonnegative matrices for a function f r m r and matrices ak aijk i j 1n k 1 m define f a1 am f aij1 aijm ij 1n for each a pn we denote its spectral radius by a and its max eigenvalue by a in a previous paper all functions f which satisfy f a1 am f a1 am n n a1 am pn and some functions which satisfy f a1 am f a1 am n n a1 am pn were characterized here for an interval i in r we characterize those functions f satisfying f a1 am f a1 am n n a1 am inn as well as the functions satisfying f 0 0 and f a1 am f a1 am n n a1 am inn

on the spectrum in max algebra abstract we give new proofs of several fundamental results of spectral theory in max algebra this includes the description of the spectrum in max algebra of a given non negative matrix via local spectral radii the spectral theorem and the spectral mapping theorem in max algebra the latter result is also generalized to the setting of power series in max algebra by applying certain continuity properties of the spectrum in max algebra our methods enable us to obtain some related results for the usual spectrum of complex matrices and distinguished spectrum for non negative matrices

inference on factor structures in heterogeneous panels this paper develops an estimation and testing framework for a stationary large panel model with observable regressors and unobservable common factors we allow for slope heterogeneity and for correlation between the common factors and the regressors we propose a two stage estimation procedure for the unobservable common factors and their loadings based on common correlated effects estimator and the principal component estimator we also develop two tests for the null of no factor structure one for the null that loadings are cross sectionally homogeneous and one for the null that common factors are homogeneous over time our tests are based on using extremes of the estimated loadings and common factors the test statistics have an asymptotic gumbel distribution under the null and have power versus alternatives where only one loading or common factor differs from the others monte carlo evidence shows that the tests have the correct size and good power

modifying the power method in max algebra in the max algebra system the eigenequation for an n n irreducible nonnegative matrix a aij is a x a x here a x i maxjaijxj and a is the maximum circuit geometric mean the complexity of the power method given in l elsner p van den driessche linear algebra appl to appear to compute a and x is considered under some assumptions on the critical matrix it is shown that the algorithm may have time complexity o n4 a modified power method based on karp s formula is presented for this new algorithm with no assumptions on the critical matrix a and x can be computed in o n3 time furthermore this algorithm can be used to compute all linearly independent eigenvectors corresponding to a

modeling hazard rates as functional data for the analysis of cohort lifetables and mortality forecasting as world populations age the analysis of demographic mortality data and demographic predictions of future mortality have met with increasing interest the study of mortality patterns and the forecasting of future mortality with its associated impacts on social welfare health care and societal planning has become a more pressing issue an ideal set of data to study patterns of change in long term mortality is the well known historical swedish cohort mortality data because of its high quality and long span of more than two centuries we explore the use of functional data analysis to model these data and to derive mortality forecasts specifically we address the challenge of flexibly modeling these data while including the effect of the birth year by regarding log hazard functions derived from observed cohort lifetables as random functions a functional model for the analysis of these cohort log hazard functions extending functional principal component approaches by introducing time varying eigenfunc

the analytic hierarchy process max algebra and multi objective optimisation the analytic hierarchy process ahp is widely used for decision making involving multiple criteria elsner and van den driessche 2004 2010 10 11 introduced a max algebraic approach to the single criterion ahp we extend this to the multi criteria ahp by considering multi objective generalisations of the single objective optimisation problem solved in these earlier papers we relate the existence of globally optimal solutions to the commutativity properties of the associated matrices we relate min max optimal solutions to the generalised spectral radius and we prove that pareto optimal solutions are guaranteed to exist

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

stochastic population forecasts for the united states beyond high medium and low abstract conventional population projections use high medium and low scenarios to indicate uncertainty but probability interpretations are rarely given and in any event the resulting ranges for vital rates births deaths age groups sizes age ratios and population size cannot possibly be probabilistically consistent with one another this article presents and implements a new method for making stochastic population forecasts that provide consistent probability intervals we blend mathematical demography and statistical time series methods to estimate stochastic models of fertility and mortality based on u s data back to 1900 and then use the theory of random matrix products to forecast various demographic measures and their associated probability intervals to the year 2065 our expected total population sizes agree quite closely with the census medium projections and our 95 percent probability intervals are close to the census high and low scenarios but census intervals in 2065 for ages 65

bounds for the price of discrete arithmetic asian options in this paper the pricing of european style discrete arithmetic asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds in our approach we use a general technique for deriving upper and lower bounds for stop loss premiums of sums of dependent random variables as explained in kaas et al ins math econom 27 2000 151 168 and additionally the ideas of rogers and shi j appl probab 32 1995 1077 1088 and of nielsen and sandmann j financial quant anal 38 2 2003 449 473 we are able to create a unifying framework for european style discrete arithmetic asian options through these bounds that generalizes several approaches in the literature as well as improves the existing results we obtain analytical and easily computable bounds the aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters investigate the effect of different conditioning variables and compare their efficiency numerically several sets of numerical results are included we also discuss hedging using these bounds moreover our methods are applicable to a wide range of pricing problems involving a sum of dependent random variables

a comonotonicity based valuation method for guaranteed annuity options we consider the valuation of a guaranteed annuity option gao under a generalised modelling setup where both interest and mortality risks are stochastic and correlated changes of probability measures are employed to obtain more implementable valuation formulae for mortality linked contracts comonotonicity theory is applied to derive upper and lower bounds for the annuity rate in the convex order sense these bounds provide accurate approximations for the value of gaos numerical illustrations are included to show the accuracy and practical applicability of our comonotonic approximations for the gao values

the law of invariant mortality abstract a concept of invariance is applied to mortality data it predicts an exact law of invariant mortality consequences of this law are presented and some are tested the most intriguing consequence is that mortality might be predominantly related to a thermodynamic mechanism and may be reversed simultaneously for all ages to its value at a much younger age

continuity of the generalized spectral radius in max algebra abstract let be an induced matrix norm associated with a monotone norm on r n and be the collection of all nonempty closed and bounded subsets of n n nonnegative matrices under this matrix norm for the hausdorff metric h between and is given by h max sup a inf b a b sup b inf a a b the max algebra system consists of the set of nonnegative numbers with sum a b max a b and the standard product ab for a b 0 for n n nonnegative matrices a b their product is denoted by a b where a b ij max 1 k n a ik b kj for each the max algebra version of the generalized spectral radius of is limsup m sup a m a 1 m where m a 1 a 2 a m a i here a is the maximum circuit geometric mean in this paper we prove that the max algebra version of the generalized spectral radius is continuous on the hausdorff metric space h the notion of the max algebra version of simultaneous nilpotence of matrices is also proposed necessary and sufficient conditions for the max algebra version of simultaneous nilpotence of matrices are presented as well

polynomial convolutions in max plus algebra abstract recently in a work that grew out of their exploration of interlacing polynomials marcus spielman and srivastava 21 and marcus 20 studied certain combinatorial polynomial convolutions these convolutions preserve real rootedness and capture expectations of characteristic polynomials of unitarily invariant random matrices thus providing a link to free probability we explore analogues of these types of convolutions in the setting of max plus algebra in this setting the max permanent replaces the determinant the maximum is the analogue of the expected value and real rootedness is replaced by full canonical form our results resemble those of marcus et al however in contrast to the classical setting we obtain an exact and simple description of all roots of the convolution of p x and q x in terms of the roots of p x and q x

bounds for the perron root using max eigenvalues abstract using the techniques of max algebra a new proof of al pin s lower and upper bounds for the perron root of a nonnegative matrix is given the bounds depend on the row sums of the matrix and its directed graph if the matrix has zero main diagonal entries then these bounds may improve the classical row sum bounds this is illustrated by a generalized tournament matrix

on the continuity of the generalized spectral radius in max algebra abstract given a bounded set of n n non negative matrices let and denote the generalized spectral radius of and its max version respectively we show that sup t 0 n 1 t 1 t where t denotes the hadamard power of we apply this result to give a new short proof of a known fact that is continuous on the hausdorff metric space h of all nonempty compact collections of n n non negative matrices

comonotonic bounds on the survival probabilities in the lee carter model for mortality projection in the lee carter framework future survival probabilities are random variables with an intricate distribution function in large homogeneous portfolios of life annuities value at risk or conditional tail expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities this paper aims to derive some bounds in the increasing convex or stop loss sense on these random survival probabilities these bounds are obtained with the help of comonotonic upper and lower bounds on sums of correlated random variables

comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior the computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits the current market practice of monte carlo simulation often requires intensive computations which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner in an attempt to find low cost and efficient alternatives we explore the techniques of comonotonic bounds to produce closed form approximation of risk measures for variable annuity guaranteed benefits the techniques are further developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic policyholder behavior which involves very complex path dependent structures in several numerical examples the method of comonotonic approximation is shown to run several thousand times faster than simulations with only minor compromise of accuracy

stochastic approximations in cbd mortality projection models comonotonicity has been successfully applied to derive various approximations in the single factor mortality projection model proposed by lee and carter 1992 after denuit and dhaene 2007 however this approach appears to lead to inaccurate approximations in the multi factor mortality projection models developed by cairns et al 2006 therefore we propose in this paper an alternative approach which consists in keeping the correlation structure within the time factors unchanged for every calendar year proceeding in this way we provide accurate approximations useful for insurance practitioners avoiding them the simulations within simulations problem whatever the size of their portfolios

forecasting age specific breast cancer mortality using functional data models accurate estimates of future age specific incidence and mortality are critical for allocation of resources to breast cancer control programmes and evaluation of screening programmes the purpose of this study is to apply functional data analysis techniques to model age specific breast cancer mortality time trends and forecast entire age specific mortality functions using a state space approach we use annual unadjusted breast cancer mortality rates in australia from 1921 to 2001 in 5 year age groups 45 to 85 we use functional data analysis techniques where mortality and incidence are modelled as curves with age as a functional covariate varying by time data are smoothed using non parametric smoothing methods then decomposed using principal components analysis to estimate basis functions that represent the functional curve period effects from the fitted coefficients are forecast then multiplied by the basis functions resulting in a forecast mortality curve with prediction intervals to forecast we adopt a state space approach and an automatic modelling framework for selecting among exponential smoothing methods overall breast cancer mortality rates in australia remained relatively stable from 1960 to the late 1990s but have declined over the last few years a set of four basis functions minimized the mean integrated squared forecasting error and account for 99 3 per cent of variation around the mean mortality curve twenty year forecasts suggest a continuing decline but at a slower rate and stabilizing beyond 2010 forecasts show a decline in all age groups with the greatest decline in older women the proposed methods have the potential to incorporate important covariates such as hormone replacement therapy and interventions to represent mammographic screening this would be particularly useful for evaluating the impact of screening on mortality and incidence from breast cancer

a generalized eigenvalue problem in the max algebra abstract we consider the generalized eigenvalue problem a x b x x 0 x 0 where a and b are entrywise nonnegative n n matrices and the max product satisfies a x i max m 1 n a im x m the case b i has been studied by several authors and for irreducible e g positive a there is exactly one eigenvalue in the above max sense the generalized problem is different and for example neither existence nor uniqueness of eigenvalues is guaranteed even for 2 2 positive matrices a and b which can be analysed by graphical methods for general n existence and uniqueness are discussed by different methods including degree theory

permanents max algebra and optimal assignment abstract the max algebra consists of the set of real numbers together with equipped with two binary operations maximization and addition for a square matrix its permanent over the max algebra is simply the maximum diagonal sum of the matrix several results are proved for the permanent over the max algebra which are analogs of the corresponding results for the permanent of a nonnegative matrix these include alexandroff inequality bregman s inequality cauchy binet formula and a bebianotype expansion

modeling and forecasting u s mortality abstract time series methods are used to make long run forecasts with confidence intervals of age specific mortality in the united states from 1990 to 2065 first the logs of the age specific death rates are modeled as a linear function of an unobserved period specific intensity index with parameters depending on age this model is fit to the matrix of u s death rates 1933 to 1987 using the singular value decomposition svd method it accounts for almost all the variance over time in age specific death rates as a group whereas e 0 has risen at a decreasing rate over the century and has decreasing variability k t declines at a roughly constant rate and has roughly constant variability facilitating forecasting k t which indexes the intensity of mortality is next modeled as a time series specifically a random walk with drift and forecast the method performs very well on within sample forecasts and the forecasts are insensitive to reductions in the length of the base period from 90 to 30

efficient simulation of tail probabilities for sums of log elliptical risks in the framework of dependent risks it is a crucial task for risk management purposes to quantify the probability that the aggregated risk exceeds some large value u motivated by asmussen et al 2011 1 in this paper we introduce a modified asmussen kroese estimator for simulation of the rare event that the aggregated risk exceeds u we show that in the framework of log gaussian risks our novel estimator has the best possible performance i e it has asymptotically vanishing relative error for the more general class of log elliptical risks with marginal distributions in the gumbel max domain of attraction we propose a modified rojas nandayapa estimator of the rare events of interest which for specific importance sampling densities has a good logarithmic performance our numerical results presented in this paper demonstrate the excellent performance of our novel asmussen kroese algorithm

a provisioning problem with stochastic payments abstract we consider the problem of determining the minimal requirement one must establish in order to meet a series of future random payments it is shown in a very general setting that this problem can be recast as a chance constrained model and how the technique of sample average approximation can be employed to find solutions we also use comonotonic theory to analyze analytical approximations in a restricted gaussian setting our numerical illustrations demonstrate that the sample average approximation is a viable and efficient way to solve the stated problem generally and outperforms the analytical approximations in passing we present a result that is related to stein s famous lemma stein 1981 and is of interest in itself

a max version of the generalized spectral radius theorem abstract let be a bounded set of n n nonnegative matrices in max algebra in this paper we propose the notions of the max algebra version of the generalized spectral radius of and the max algebra version of the joint spectral radius of the max algebra version of the generalized spectral radius theorem is established we propose the relationship between the generalized spectral radius of in the sense of daubechies and lagarias and its max algebra version moreover a generalization of elsner and van den driessche s lemma is presented as well

optimal approximations for risk measures of sums of lognormals based on conditional expectations in this paper we investigate the approximations for the distribution function of a sum s of lognormal random variables these approximations are obtained by considering the conditional expectation e s l of s with respect to a conditioning random variable l the choice of l is crucial in order to obtain accurate approximations the different alternatives for l that have been proposed in the literature to date are global in the sense that l is chosen such that the entire distribution of the approximation e s l is close to the corresponding distribution of the original sum s in an actuarial or a financial context one is often only interested in a particular tail of the distribution of s therefore in this paper we propose approximations e s l which are only locally optimal in the sense that the relevant tail of the distribution of e s l is an accurate approximation for the corresponding tail of the distribution of s numerical illustrations reveal that local optimal choices for l can improve the quality of the approximations in the relevant tail significantly we also explore the asymptotic properties of the approximations e s l and investigate links with results from s asmussen rojas nandayapa sums of dependent lognormal random variables asymptotics and simulation stochastic series at department of mathematical sciences university of aarhus research report number 469 2005 finally we briefly address the sub optimality of asian options from the point of view of risk averse decision makers with a fixed investment horizon

multiple seed tpg structures linear feedback shift registers lfsrs are popular mechanisms for built in test pattern generation tpg they are normally used with a primitive characteristic polynomial because in that case only one initialization state seed is required we show that if the characteristic polynomial is nonprimitive irreducible the required seeds can still be efficiently generated we establish a formula that shows how the seeds of any nonprimitive irreducible polynomial relate to each other this leads to an efficient hardware implementation with small hardware overhead irrespective of the number of seeds and enhances the choices available for the design of appropriate tpg structures in the case of pseudoexhaustive tpg that were previously limited to primitive characteristic polynomials only

spectral theorem for convex monotone homogeneous maps and ergodic control we consider convex maps f rn rn that are monotone i e that preserve the product ordering of rn and nonexpansive for the sup norm this includes convex monotone maps that are additively homogeneous i e that commute with the addition of constants we show that the fixed point set of f when it is nonempty is isomorphic to a convex inf subsemilattice of rn whose dimension is at most equal to the number of strongly connected components of a critical graph defined from the tangent affine maps of f this yields in particular an uniqueness result for the bias vector of ergodic control problems this generalizes results obtained previously by lanery romanovsky and schweitzer and federgruen for ergodic control problems with finite state and action spaces which correspond to the special case of piecewise affine maps f we also show that the length of periodic orbits of f is bounded by the cyclicity of its critical graph which implies that the possible orbit lengths of f are exactly the orders of elements of the symmetric group on n letters

error models for official mortality forecasts abstract the office of the actuary u s social security administration produces alternative forecasts of mortality to reflect uncertainty about the future appropriate probabilistic interpretations of the intervals have not been provided however because explicit stochastic models are not used in this article we identify the components and assumptions of the official forecasts and approximate them by stochastic parametric models we estimate parameters of the models from past data derive statistical intervals for the forecasts and compare them with the official high low intervals we use the models to evaluate the forecasts rather than to develop different predictions of the future analysis of data from 1972 to 1985 shows that the official intervals for mortality forecasts for males or females aged 45 70 have approximately a 95 chance of including the true mortality rate in any year for other ages the chances are much less than 95 the office of the actuary s interval estimates of age and cause

conservation laws of metabolism and mortality abstract quantitatively accurate laws of metabolism and mortality which are the same for species with different evolutionary history e g humans and flies are derived and extensively verified such conservation with respect to evolution i e in non stationary and heterogeneous conditions laws are unique for self organized live systems they impose restrictions on biological heterogeneity establish two universal ways of its evolution predict a new kind of rapid compared to lifespan adaptation and reversible mortality which may be directed predictions agree with experimental data exact criterion unravels universal conservation law in non universal experimental dependences and accurately divides a heterogeneous population into non universal groups which yield the law with 5 mean accuracy this allows to approximate and forecast mortality in different countries and resolves a two century old controversy with the universal law of mortality

the influence of the marked reduced graph of a nonnegative matrix on the jordan form and on related properties a survey abstract for a nonnegative matrix p we discuss the relation of its marked reduced graph to that part of the jordan form that is associated with the perron frobenius root to the nonnegativity of the eigenvectors and generalized eigenvectors to the nonnegativity of solutions of linear equations and to the asymptotic growth of powers of the matrix results are often stated in terms of m matrices and standard results on irreducible matrices are assumed we give examples to illustrate the theorems surveyed

transitory mortality jump modeling with renewal process and its impact on pricing of catastrophic bonds abstract a number of stochastic mortality models with transitory jump effects have been proposed for the securitization of catastrophic mortality risks most of the studies on catastrophic mortality risk modeling assumed that the mortality jumps occur once a year or used a poisson process for their jump frequencies although the timing and the frequency of catastrophic events are unknown the history of the events might provide information about their future occurrences in this paper we propose a specification of the lee carter model by using the renewal process and we assume that the mean time between jump arrivals is no longer constant our aim is to find a more realistic mortality model by incorporating the history of catastrophic events we illustrate the proposed model with mortality data from the us the uk switzerland france and italy our proposed model fits the historical data better than the other jump models for all countries furthermore we price hypothetical mortality bonds and show that the renewal process has a significant impact on the estimated prices

max balancing weighted directed graphs and matrix scaling a weighted directed graph g is a triple v a g where v a is a directed graph and g is an arbitrary real valued function defined on the arc set a let g be a strongly connected simple weighted directed graph we say that g is max balanced if for every nontrivial subset of the vertices w the maximum weight over arcs leaving w equals the maximum weight over arcs entering w we show that there exists a up to an additive constant unique potential pv for v v such that v a gp is max balanced where gap pu ga pv for a u v a we describe an o v 2 a algorithm for computing p using an algorithm for computing the maximum cycle mean of g finally we apply our principal result to the similarity scaling of nonnegative matrices

on visualization scaling subeigenvectors and kleene stars in max algebra abstract the purpose of this paper is to investigate the interplay arising between max algebra convexity and scaling problems the latter which have been studied in nonnegative matrix theory are strongly related to max algebra one problem is that of strict visualization scaling defined as for a given nonnegative matrix a a diagonal matrix x such that all elements of x 1 ax are less than or equal to the maximum cycle geometric mean of a with strict inequality for the entries which do not lie on critical cycles in this paper such scalings are described by means of the max algebraic subeigenvectors and kleene stars of nonnegative matrices as well as by some concepts of convex geometry

on linear dependencies in subspaces of lfsr generated sequences the probability of linear dependency in subsequences generated by linear feedback shift registers is examined it is shown that this probability for a short subsequence e g a sequence defined by the length of a scan chain can be much higher than that for an entire m sequence

time trends and forecasts of body mass index from repeated cross sectional data a different approach in this paper we report a case study on a technical generalization of the lee carter model originally developed to project mortality to forecast body mass index bmi kg m2 we present the method on an annually repeated cross sectional data set the dutch health survey covering years between 1981 and 2008 we applied generalized additive models for location scale and shape semi parametric regression models to estimate the probability distribution of bmi for each combination of age gender and year assuming that bmi follows a box cox power exponential distribution we modelled and extrapolated the distribution parameters as a function of age and calendar time using the lee carter model the projected parameters defined future bmi distributions from which we derived the prevalence of normal weight overweight and obesity our analysis showed that important changes occurred not only in the location and scale of the bmi distribution but also in the shape of it the bmi distribution became flatter and more shifted to the right assuming that past trends in the distribution of bmi will continue in the future we predicted a stable or slow increase in the prevalence of overweight until 2020 among men and women we conclude that our adaptation of the lee carter model provides an insightful and flexible way of forecasting bmi and that ignoring changes in the shape of the bmi distribution would likely result in biased forecasts

bayesian model comparison for the order restricted rc association model association models constitute an attractive alternative to the usual log linear models for modeling the dependence between classification variables they impose special structure on the underlying association by assigning scores on the levels of each classification variable which can be fixed or parametric under the general row column rc association model both row and column scores are unknown parameters without any restriction concerning their ordinality however when the classification variables are ordinal order restrictions on the scores arise naturally under such restrictions we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the bayesian approach to achieve that we have constructed a reversible jump markov chain monte carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging the proposed methodology is evaluated through a simulation study and illustrated using actual datasets

the spectra of irreducible matrices over completed idempotent semifields motivated by some spectral results in the characterization of concept lattices we investigate the spectra of reducible matrices over complete idempotent semifields in the framework of naturally ordered semirings or dioids we find non null eigenvectors for every non null element in the semifield and conclude that the notion of spectrum has to be refined to encompass that of the incomplete semifield case so as to include only those eigenvalues with eigenvectors that have finite coordinates considering special sets of eigenvectors brings out finite complete lattices in the picture and we contend that such structure may be more important than standard eigenspaces for matrices over completed idempotent semifields

on the max version of the generalized spectral radius theorem abstract let be a bounded set of n n non negative matrices recently the max algebra version of the generalized spectral radius of was introduced we show that lim t i t 1 t where denotes the generalized spectral radius and t the hadamard power of this provides a description of that uses no max terminology as an application we give a short proof of the max version of the generalized spectral radius theorem

on the asymptotic stability of nonnegative matrices in max algebra abstract in the max algebra system for an n n nonnegative matrix a a ij the eigenequation for max eigenvalue and corresponding max eigenvector x is a x x where a x i max 1 j n a ij x j and a is the maximum circuit geometric mean it is shown that the following conditions are mutually equivalent i a r n ii a 1 iii a lim k a k 0 where a max x 1 x 0 a x and a limsup k a k 1 k

a max version of the perron frobenius theorem abstract if a an n n nonnegative irreducible matrix then there exists a 0 and a positive vector x such that maxjaijxj a xi i 1 2 n furthermore a is the maximum geometric mean of a circuit in the weighted directed graph corresponding to a this theorem which we refer to as the max version of the perron frobenius theorem is well known in the context of matrices over the max algebra and also in the context of matrix scalings in the present work which is partly expository we bring out the intimate connection between this result and the perron frobenius theory we present several proofs of the result some of which use the perron frobenius theorem structure of max eigenvalues and max eigenvectors is described possible ways to unify the perron frobenius theorem and its max version are indicated some inequalities for a are proved

on bootstrapping panel factor series this paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series two main results are shown firstly a bootstrap invariance principle is derived pointwise in i obtaining an upper bound for the order of truncation of the ar polynomial that depends on n and t consistent estimation of the long run variances is also studied for n t secondly joint bootstrap asymptotics is also studied investigating the conditions under which the bootstrap is valid in particular the extent of cross sectional dependence which can be allowed for is investigated whilst we show that for general forms of cross dependence consistent estimation of the long run variance and therefore validity of the bootstrap is fraught with difficulties however we show that one cross sectional unit at a time resampling schemes yield valid bootstrap based inference under weak forms of cross sectional dependence

some monotonicity properties of schur powers of matrices and related inequalities abstract a series of inequalities are developed relating the spectral radius a b of the schur product a b of two nonnegative matrices a and b with those of a a and b b yielding a b a a b b 1 2 as a corollary it is proved that the spectral radius of the schur powers r a r a r a a a r factors satisfies 1 r log r is decreasing while 1 r 1 log r is increasing the latter provided a is a stochastic matrix the entropy of a finite stationary markov chain is identified with d r dr r 1 a number of majorization comparisons for the spectral radius of schur powers is given

operational time and in sample density forecasting in this paper we consider a new structural model for in sample density forecasting in sample density forecasting is to estimate a structured density on a region where data are observed and then re use the estimated structured density on some region where data are not observed our structural assumption is that the density is a product of one dimensional functions with one function sitting on the scale of a transformed space of observations the transformation involves another unknown one dimensional function so that our model is formulated via a known smooth function of three underlying unknown one dimensional functions we present an innovative way of estimating the one dimensional functions and show that all the estimators of the three components achieve the optimal one dimensional rate of convergence we illustrate how one can use our approach by analyzing a real dataset and also verify the tractable finite sample performance of the method via a simulation study

generic uniqueness of the bias vector of finite stochastic games with perfect information mean payoff zero sum stochastic games can be studied by means of a nonlinear spectral problem when the state space is finite the latter consists in finding an eigenpair u solution of t u e u where t rn rn is the shapley or dynamic programming operator is a scalar e is the unit vector and u rn the scalar yields the mean payoff per time unit and the vector u called the bias allows one to determine optimal stationary strategies the existence of the eigenpair u is generally related to ergodicity conditions a basic issue is to understand for which classes of games the bias vector is unique up to an additive constant in this paper we consider perfect information zero sum stochastic games with finite state and action spaces thinking of the transition payments as variable parameters transition probabilities being fixed we show that the bias vector thought of as a function of the transition payments is generically unique up to an additive constant the proof uses techniques of max plus or tropical algebra and nonlinear perron frobenius theory as an application of our results we obtain a perturbation scheme allowing one to solve degenerate instances of stochastic games by policy iteration

bounds for asian basket options in this paper we propose pricing bounds for european style discrete arithmetic asian basket options in a black and scholes framework we start from methods used for basket options and asian options first we use the general approach for deriving upper and lower bounds for stop loss premia of sums of non independent random variables as in kaas et al upper and lower bounds for sums of random variables insurance math econom 27 2000 151 168 or dhaene et al the concept of comonotonicity in actuarial science and finance theory insurance math econom 31 1 2002 3 33 we generalize the methods in deelstra et al pricing of arithmetic basket options by conditioning insurance math econom 34 2004 55 57 and vanmaele et al bounds for the price of discrete sampled arithmetic asian options j comput appl math 185 1 2006 51 90 afterwards we show how to derive an analytical closed form expression for a lower bound in the non comonotonic case finally we derive upper bounds for asian basket options by applying techniques as in thompson fast narrow bounds on the value of asian options working paper university of cambridge 1999 and lord partially exact and bounded approximations for arithmetic asian options j comput finance 10 2 2006 1 52 numerical results are included and on the basis of our numerical tests we explain which method we recommend depending on moneyness and time to maturity

on the power method in max algebra abstract the eigenvalue problem for an irreducible nonnegative matrix a a ij in the max algebra system is a otimes x lambda x where a otimes x i mathop max j a ij x j and lambda turns out to be the maximum circuit geometric mean mu a a power method algorithm is given to compute mu a and eigenvector x the algorithm is developed by using results on the convergence of max powers of a which are proved using nonnegative matrix theory in contrast to an algorithm developed in 4 this new method works for any irreducible nonnegative a and calculates eigenvectors in a simpler and more efficient way some asymptotic formulas relating mu a the spectral radius and norms are also given

the markov chain tree theorem in commutative semirings and the state reduction algorithm in commutative semifields we extend the markov chain tree theorem to general commutative semirings and we generalize the state reduction algorithm to general commutative semifields this leads to a new universal algorithm whose prototype is the state reduction algorithm which computes the markov chain tree vector of a stochastic matrix

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated

generalized spectral radius and its max algebra version abstract let c n n and r n n be bounded subsets and let and denote the generalized spectral radius of and the max algebra version of the generalized spectral radius of respectively we apply a single matrix description of to give a new elementary and straightforward proof of the berger wang formula in max algebra and consequently a new short proof of the original berger wang formula in the case of bounded subsets of n n non negative matrices we also obtain a new description of in terms of the schur hadamard product and prove new trace and max trace descriptions of and in particular we show that limsup m sup a m tr a 1 m limsup m sup a m tr a 1 m and limsup m sup b m tr b 1 m limsup m sup b m tr b 1 m where tr a max i 1 n a ii and b b ij