continuous pole placement for delay equations in this paper we describe a stabilization method for linear time delay systems which extends the classical pole placement method for ordinary differential equations unlike methods based on finite spectrum assignment our method does not render the closed loop system finite dimensional but consists of controlling the rightmost eigenvalues because these are moved to the left half plane in a quasi continuous way we refer to our method as continuous pole placement we explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems

on stability of lms methods and characteristic roots of delay differential equations we investigate the use of linear multistep lms methods for computing characteristic roots of systems of linear delay differential equations ddes with multiple fixed discrete delays these roots are important in the context of stability and bifurcation analysis we prove convergence orders for the characteristic root approximations and analyze under what condition for the steplength the discrete integration scheme retains certain delay independent stability properties of the original equations unlike existing results we concentrate on the recovery of both stability and instability we illustrate our findings with a number of numerical test results

dna electrophoresis studied with the cage model the cage model for polymer reptation proposed by evans and edwards and its recent extension to model dna electrophoresis are studied by numerically exact computation of the drift velocities for polymers with a length l of up to 15 monomers the computations show the nernst einstein regime v e followed by a regime where the velocity decreases exponentially with the applied electric field strength in agreement with de gennes reptation arguments we find that asymptotically for large polymers the diffusion coefficient d decreases quadratically with polymer length for the cage model the proportionality coefficient is dl2 0 175 2 additionally we find that the leading correction term for finite polymer lengths scales as n 1 2 where n l 1 is the number of bonds

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

the exact distribution of the hansen jagannathan bound under the assumption of multivariate normality of asset returns this paper presents a geometric interpretation and the finite sample distributions of the sample hansen jagannathan bounds on the variance of admissible stochastic discount factors with and without the nonnegativity constraint on the stochastic discount factors in addition since the sample hansen jagannathan bounds can be very volatile we propose a simple method to construct confidence intervals for the population hansen jagannathan bounds finally we show that the analytical results in the paper are robust to departures from the normality assumption

linear multistep methods for impulsive delay differential equations abstract this paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations numerical experiments show that the simpson s rule and two step bdf method are of order p 0 when applied to impulsive delay differential equations an improved linear multistep numerical process is proposed convergence and stability conditions of the numerical solutions are given in the paper numerical experiments are given in the end to illustrate the conclusion

asymptotic stability contractivity and dissipativity of one leg θ method for non autonomous delay functional differential equations abstract this paper focuses on asymptotic stability contractivity and dissipativity of non autonomous nonlinear delay functional differential equations with bounded lag and the corresponding dynamical properties of one leg method sufficient conditions for these delay functional differential equations to be dissipative asymptotically stable and contractive are established one leg method is constructed to solve such equations numerically an important result on the growth of solution of a class of difference inequalities with variable coefficients is obtained finally it is proved that the one leg method is asymptotically stable contractive and dissipative if and only if 1 numerical examples are given to confirm our theoretical results

improving the run time and quality of nested dissection ordering when performing sparse matrix factorization the ordering of matrix rows and columns has a dramatic impact on the factorization time this paper describes an approach to the reordering problem that produces significantly better orderings than prior methods the algorithm is a hybrid of nested dissection and minimum degree ordering and combines an assortment of different algorithmic advances new or improved algorithms are described for graph compression multilevel partitioning and separator improvement when these techniques are combined the resulting orderings average 39 better than minimum degree over a suite of test matrices while requiring roughly 2 7 times the run time of liu s multiple minimum degree

the numerical stability of linear multistep methods for delay differential equations with many delays this paper deals with the stability analysis of linear multistep methods for the numerical solution of delay differential equations ddss with many delays we focus on the stability behaviour of such methods when they are applied to a scalar linear dde with many constant delays and complex coefficients the concept of gp m stability is introduced under a sufficient condition for the test equation to be stable the linear multistep method when combined with a certain lagrange interpolation must be stable for all stepsizes it is proven that a linear multistep method is gp m stable if and only if it is a stable for ordinary differential equations odes

bartlett adjustment of empirical discrepancy statistics summary we introduce two classes of empirical discrepancy statistics that extend empirical likelihood and establish simple conditions under which they admit bartlett adjustment

nonparametric assessment of hedge fund performance abstract we propose a new class of performance measures for hedge fund hf returns based on a family of empirically identifiable stochastic discount factors sdfs the sdf based measures incorporate no arbitrage pricing restrictions and naturally embed information about higher order mixed moments between hf and benchmark factors returns we provide a full asymptotic theory for our sdf estimators to test for the statistical significance of each fund s performance and for the relevance of individual benchmark factors within each proposed measure we apply our methodology to a panel of 4815 individual hedge funds our empirical analysis reveals that fewer funds have a statistically significant positive alpha compared to the jensen s alpha obtained by the traditional linear regression approach moreover the funds rankings vary considerably between the two approaches performance also varies between the members of our family because of a different fund exposure to higher order moments of the benchmark factors highlighting the potential heterogeneity across investors in evaluating performance

economic implications of nonlinear pricing kernels based on a family of discrepancy functions we derive nonparametric stochastic discount factor bounds that naturally generalize variance entropy and higher moment bounds these bounds are especially useful to identify how parameters affect pricing kernel dispersion in asset pricing models in particular they allow us to distinguish between models where dispersion comes mainly from skewness from models where kurtosis is the primary source of dispersion we analyze the admissibility of disaster disappointment aversion and long run risk models with respect to these bounds this paper was accepted by jerome detemple finance

hypergraph partitioning based models and methods for exploiting cache locality in sparse matrix vector multiplication sparse matrix vector multiplication spmxv is a kernel operation widely used in iterative linear solvers the same sparse matrix is multiplied by a dense vector repeatedly in these solvers matric

cache oblivious sparse matrix vector multiplication by using sparse matrix partitioning methods in this article we introduce a cache oblivious method for sparse matrix vector multiplication our method attempts to permute the rows and columns of the input matrix using a recursive hypergraph based sparse matrix partitioning scheme so that the resulting matrix induces cache friendly behavior during sparse matrix vector multiplication matrices are assumed to be stored in row major format by means of the compressed row storage crs or its variants incremental crs and zig zag crs the zig zag crs data structure is shown to fit well with the hypergraph metric used in partitioning sparse matrices for the purpose of parallel computation the separated block diagonal sbd form is shown to be the appropriate matrix structure for cache enhancement we have implemented a run time cache simulation library enabling us to analyze cache behavior for arbitrary matrices and arbitrary cache properties during matrix vector multiplication within a k way set associative idealized cache model the results of these simulations are then verified by actual experiments run on various cache architectures in all these experiments we use the mondriaan sparse matrix partitioner in one dimensional mode the savings in computation time achieved by our matrix reorderings reach up to 50 percent in the case of a large link matrix

a bayesian approach to diagnosis of asset pricing models a large literature has arisen which exploits a particular portfolio on the mean variance frontier determining a minimum variance bound on the set of stochastic discount factors state price to probability ratios this paper proposes a new variational characterization of the closely related set of state price densities based on minimization of the kullback leibler information criterion in contrast to the variance bound the resulting information bound automatically satisfies an important positivity constraint furthermore the information bound is determined by a portfolio which maximizes expected cara utility several interpretations of the information bound are given and empirical uses of it are illustrated

estimations on numerically stable step size for neutral delay differential systems with multiple delays we derive two estimations of numerically stable step size for systems of neutral delay differential equations with multiple delays the stable step size for numerical integration of nddes with multiple delays can be easily selected by means of the logarithmic norm and the spectral radius of certain matrices both explicit linear multistep methods and explicit runge kutta methods are considered

spline collocation methods for solving delay differential equations the convergence and stability analysis of seventh c 3 spline collocation methods if applied to delay differential equations ddes will be considered letting the interior collocation points x i 1 c j x i 1 c jh j 1 3 be dependent on three parameters c 1 c 2 c email protected 0 1 it will be shown that these methods for ddes possess convergence rate of order seven if 0 7279115

assessing misspecified asset pricing models with empirical likelihood estimators abstract hansen and jagannathan 1997 compare misspecified asset pricing models based on least square projections on a family of admissible stochastic discount factors we extend their fundamental contribution by considering minimum discrepancy projections where misspecification is measured by a family of convex functions that take into account higher moments of asset returns the minimum discrepancy problems are solved on dual spaces producing a family of estimators that captures the least square problem as a particular case we derive the asymptotic distributions of the estimators for the cressie read family of discrepancies and illustrate their use with an assessment of the consumption asset pricing model

hypergraph based unsymmetric nested dissection ordering for sparse lu factorization in this paper we discuss a hypergraph based unsymmetric nested dissection hund ordering for reducing the fill in incurred during gaussian elimination it has several important properties it takes a global perspective of the entire matrix as opposed to local heuristics it takes into account the asymmetry of the input matrix by using a hypergraph to represent its structure it is suitable for performing gaussian elimination in parallel with partial pivoting this is possible because the row permutations performed due to partial pivoting do not destroy the column separators identified by the nested dissection approach the hypergraph nested dissection approach is essentially equivalent to graph nested dissection on the matrix a t a but we need only the original matrix a and never form the usually denser matrix a t a the usage of hypergraphs in our approach is fairly standard and hund can be implemented by calling an existing hypergraph partitioner that uses recursive bisection our implementation uses local reordering constrained column approximate minimum degree ccolamd to further improve the ordering we also explain how weighted matching hsl routine mc64 can be used in this context experimental results on 27 medium and large size matrices with highly unsymmetric structures compare our approach to four other well known reordering algorithms the results show that it provides a robust reordering algorithm in the sense that it is the best or close to the best often within 10 of all the other methods in particular on matrices with highly unsymmetric structures

asymptotic stability of numerical methods for linear delay parabolic differential equations this paper is concerned with the asymptotic stability property of some numerical processes by discretization of parabolic differential equations with a constant delay these numerical processes include forward and backward euler difference schemes and crank nicolson difference scheme which are obtained by applying step by step methods to the resulting systems of delay differential equations sufficient and necessary conditions for these difference schemes to be delay independently asymptotically stable are established it reveals that an additional restriction on time and spatial stepsizes of the forward euler difference scheme is required to preserve the delay independent asymptotic stability due to the existence of the delay term numerical experiments have been implemented to confirm the asymptotic stability of these numerical methods

permuting sparse rectangular matrices into block diagonal form we investigate the problem of permuting a sparse rectangular matrix into block diagonal form block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem as recently investigated in the context of mathematical programming lu factorization and qr factorization to represent the nonzero structure of a matrix we propose bipartite graph and hypergraph models that reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning respectively our experiments on a wide range of matrices using the state of the art graph and hypergraph partitioning tools metis and patoh revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime

using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution previously hansen and jagannathan 1990a derived and computed mean standard deviation frontiers for intertemporal marginal rates of substitution imrs implied by asset market data these frontiers give the lower bounds on the standard deviations as a function of the mean in this paper we develop a strategy for utilizing conditioning information efficiently and hence improve on the standard deviation bounds computed by hansen and jagannathan we implement this strategy empirically by using the seminonparametric snp methodology suggested by gallant and tauchen 1989 to estimate the conditional distribution of a vector of monthly asset payoffs we use the fitted conditional distributions to calculate both conditional and unconditional standard deviation bounds for the imrs the unconditional bounds are as sharp as possible subject to robustness considerations we also use the fitted distributions to compute the moments of various candidate marginal rates of substitution suggested by economic theory and in particular the time nonseparable preferences of dunn and singleton 1986 and eichenbaum and hansen 1990 for these preferences our findings suggest that habit persistence will put the moments of the imrs inside the frontier at reasonable values of the curvature parameter at the same time we uncover evidence that the implied imrs fails to satisfy all of the restrictions inherent in the euler equation the findings help explain why euler equation estimation methods typically find evidence in favor of local durability instead of habit persistence for monthly data

duality relationships for entropy like minimization problems this paper considers the minimization of a convex integral functional over the positive cone of an l p space subject to a finite number of linear equality constraints such problems arise in spectral estimation where the bjective function is often entropy like and in constrained approximation the lagrangian dual problem is finite dimensional and unconstrained under a quasi interior constraint qualification the primal and dual values are equal with dual attainment examples show the primal value may not be attained conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum these conditions are satisfied in many examples

robust estimation with exponentially tilted hellinger distance abstract this paper is concerned with estimation of parameters defined by moment equalities we introduce the exponentially tilted hellinger distance ethd estimator which is efficient under correct specification and robust to both global and local misspecification in the spirit of schennach 2007 ethd combines the hellinger distance and the kullback leibler information criterion we show that it achieves optimal minimax robust properties under local deviations from the model and remains well behaved under global misspecification

convergence of one leg methods for neutral delay integro differential equations the error analysis of one leg methods for a class of nonlinear neutral delay integro differential equations ndides is given it is proved that an a stable one leg method with an appropriate quadrature rule applied to ndides is convergent of order at least min p q 12 if the one leg method is consistent of order p2 in the classical sense for odes and the error order of the quadrature rule is o hq 1 numerical examples further confirm the theoretical results

convergence of runge kutta methods for neutral delay integro differential equations the present paper is concerned with the convergence of numerical methods to solve initial value problems of neutral delay integro differential equations ndides the error estimation of runge kutta methods for a class of nonlinear systems of ndides are derived some numerical experiments are given which confirm the theoretical results

a two dimensional data distribution method for parallel sparse matrix vector multiplication a new method is presented for distributing data in sparse matrix vector multiplication the method is two dimensional tries to minimize the true communication volume and also tries to spread the computation and communication work evenly over the processors the method starts with a recursive bipartitioning of the sparse matrix each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros the communication volume caused by the split is minimized after the matrix partitioning the input and output vectors are partitioned with the objective of minimizing the maximum communication volume per processor experimental results of our implementation mondriaan for a set of sparse test matrices show a reduction in communication volume compared to one dimensional methods and in general a good balance in the communication work experimental timings of an actual parallel sparse matrix vector multiplication on an sgi origin 3800 computer show that a sufficiently large reduction in communication volume leads to savings in execution time

partitioning hypergraphs in scientific computing applications through vertex separators on graphs the modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community leading to novel models and algorithms their applications and development of associated tools hypergraphs are now a standard tool in combinatorial scientific computing the modeling flexibility of hypergraphs however comes at a cost algorithms on hypergraphs are inherently more complicated than those on graphs which sometimes translates to nontrivial increases in processing times neither the modeling flexibility of hypergraphs nor the runtime efficiency of graph algorithms can be overlooked therefore the new research thrust should be how to cleverly trade off between the two this work addresses one method for this trade off by solving the hypergraph partitioning problem by finding vertex separators on graphs specifically we investigate how to solve the hypergraph partitioning problem by seeking a vertex separator on its net intersection graph nig where each net of the hypergraph is represented by a vertex and two vertices share an edge if their nets have a common vertex we propose a vertex weighting scheme to attain good node balanced hypergraphs since the nig model cannot preserve node balancing information vertex removal and vertex splitting techniques are described to optimize cut net and connectivity metrics respectively under the recursive bipartitioning paradigm we also developed implementations of our proposed hypergraph partitioning formulations by adopting and modifying a state of the art graph partitioning by vertex separator tool onmetis experiments conducted on a large collection of sparse matrices demonstrate the effectiveness of our proposed techniques