scaling for orthogonality in updating algorithms where orthogonal transformations are accumulated it is important to preserve the orthogonality of the product in the presence of rounding error moonen et al ibid vol 39 p 1911 13 1991 have pointed out that simply normalizing the columns of the product tends to preserve orthogonality though not as degroat ibid vol 39 p 1913 14 1991 points out to working precision the authors discuss the previous work and give an analysis of the phenomenon

urv esprit for tracking time varying signals esprit is an algorithm for determining the fixed directions of arrival of a set of narrowband signals at an array of sensors unfortunately its computational burden makes it unsuitable for real time processing of signals with time varying directions of arrival the authors develop a new implementation of esprit that has potential for real time processing it is based on a rank revealing urv decomposition rather than the eigendecomposition or singular value decomposition used in previous esprit algorithms the authors demonstrate its performance on simulated data representing both constant and time varying signals they find that the urv based esprit algorithm is effective for estimating time varying directions of arrival at considerable computational savings over the svd based algorithm

bounded linear logic a modular approach to polynomial time computability typing is a way of describing the interactive behavior of algorithms usual typing systems are mainly concerned with input output specifications e g given terms f a b and a a the computation of f a by normalization yields a result of type b however one can dream of more refined typings that would not only ensure ethereal termination but would for instance yield feasible resource bounds it seems that time complexity does not lend itself naturally to modular manipulation we seek something more primitive

set relations and optimality conditions in set valued maps abstract problems in set valued optimization can be solved via set optimization in this paper properties of set optimization are investigated conditions for existence of solutions are established directional derivatives are studied for set valued mappings necessary and sufficient conditions in the existence of solutions are showed with directional derivatives

generating plans in linear logic ii a geometry of conjunctive actions abstract after the proof theoretic study given in masseron 1991 we propose a new geometric characterization of actions in the spirit of girard s proof nets and bibel s connection graphs in the conjunctive case

hadamard s theorem for locally lipschitzian maps if the derivativef p of a continuously differentiable mapffrom r into itself is an invertible linear transformation for each p then by the classical inverse function theorem f is a local homeomorphism every p has a neighborhood u mapped homeomorphically onto its image f u a natural and intriguing question under what further conditions will f be a homeomorphism of r onto itself was answered in one way by hadamard 8 in 1906 using a condition on the norms b max bh h i of the inverses b f p

connection methods in linear logic and proof nets construction linear logic ll is the logical foundation of some type theoretic languages and also of environments for specification and theorem proving in this paper we analyse the relationships between the proof net notion of ll and the connection notion used for efficient proof search in different logics aiming at using proof nets as a tool for automated deduction in linear logic we define a connection based characterization of provability in multiplicative linear logic mll we show that an algorithm for proof net construction can be seen as a proof search connection method this central result is illustrated with a specific algorithm that is able to construct for a provable mll sequent a set of connections a proof net and a sequent proof from these results we expect to extend to other ll fragments we analyse what happens with the additive connectives of ll by tackling the additive fragment in a similar way

reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

approximations of nondifferentiable functions and local topological equivalence a concept of local approximation of a function is introduced this concept is defined via directional derivatives in consequence the local approximation is carried out by a positively homogeneous mapping we obtain local approximations for functions that are not necessarily locally lipschitzian nor continuous this is the case of some large classes of functions such as stable functions or contingently epidifferentiable and directionally lipschitzian functions using the concept of topological equivalence we establish the existence of a local coordinate transformation between the original function and the positively homogeneous function this investigation is developed for contingently epidifferentiable functions around a noncritical point and for noncontingently epidifferentiable functions under particular conditions

on proof normalization in linear logic abstract we present a proof theoretic foundation for automated deduction in linear logic at first we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a proof then we discuss the naturally arising question of the redundancy reduction and investigate the possibilities of proof normalization which depend on the proof search strategy and the fragment we consider thus we can define the concept of normal proof that might be the basis of works about automatic proof construction and design of logic programming languages based on linear logic

global invertibility of nonsmooth mappings on etend le theoreme de hadamard d inversibilite globale a la classe des applications localement continues de lipschitz

local topological equivalence of nonsmooth functions in hilbert spaces in this paper we investigate the relation between nonsmooth functions with domain in a hilbert space and their local approximations we consider lipschitz functions and define an approximation model with directional derivatives the qualitative behaviour of the approximation is studied by means of the concept of topological equivalence using this concept we establish the existence of a local coordinate transformation between the original function and the local approximation

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

program development in constructive type theory abstract we present the program development concept in a logical framework including constructive type theory and then show how to use such theories to derive programs from proofs of formal specifications we are interested in two important facts that are the mechanization of the proof construction and the possibility to express in the theory significant concepts for programming like inductively defined types and general recursion we give here a survey on some results and problems appearing in logical frameworks devoted to the programming with proofs approach

structural analysis of nonsmooth mappings inverse functions and metric projections abstract it is known that a locally lipschitz continuous function r n r n which is strongly b differentiable at a point x0 r n is a lipschitz homeomorphism in a neighborhood of x0 if and only if its b derivative at x0 is a lipschitz homeomorphism we show that strongly b differentiability is a rather restrictive requirement for piecewise differentiable functions however it turns out that generically a piecewise differentiable function can be locally transformed into a strongly b differentiable function by means of a piecewise differentiable homeomorphism the corresponding criteria yield structural inverse function theorems for piecewise differentiable functions the results are applied to the metric projection onto a convex set

ramification and causality abstract in formal systems for reasoning about actions the ramification problem denotes the problem of handling indirect effects these effects are not explicitly represented in action specifications but follow from general laws describing dependencies among components of the world state an adequate treatment of indirect effects requires a suitably weakened version of the general law of persistence it also requires a method to avoid unintuitive changes suggested by the aforementioned dependency laws we propose a solution to the ramification problem that uses directed relations between two single effects stating the circumstances under which the occurrence of the first causes the second we argue for the necessity of an approach based on causality by elaborating the limitations of common paradigms employed to handle ramifications the principle of categorization and the policy of minimal change our abstract solution is realized on the basis of a particular action calculus namely the fluent calculus

a quasi newton adaptive algorithm for generalized symmetric eigenvalue problem we first recast the generalized symmetric eigenvalue problem where the underlying matrix pencil consists of symmetric positive definite matrices into an unconstrained minimization problem by constructing an appropriate cost function we then extend it to the case of multiple eigen vectors using an inflation technique based on this asymptotic formulation we derive a quasi newton based adaptive algorithm for estimating the required generalized eigen vectors in the data case the resulting algorithm is modular and parallel and it is globally convergent with probability one we also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices in the pencil on the resulting eigenstructure simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank one updating algorithm of karasalo 1986 further the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems

a note on efficient numerically stabilized rank one eigenstructure updating and reply in the above named paper r d degroat and r a roberts see ibid vol 38 no 2 p 301 16 feb 1990 developed a reorthogonalization scheme for stabilizing eigenstructure updating algorithms the commenters show that only part of this scheme namely the renormalization is essential for the stability so that a cheaper scheme with roughly half as many computations can perform equally well degroat addresses two points raised by the commenters work

proff search in type theoretic languages an introduction we introduce the main concepts and problems in the theory of proof search in type theoretic languages and survey some specific connected topics we do not claim to cover all of the theoretical and implementation issues in the study of proof search in type theoretic languages rather we present some key ideas and problems starting from well motivated points of departure such as a definition of a type theoretic language or the relationship between languages and proof objects the strong connections between different proof search methods in logics type theories and logical frameworks together with their impact on programming and implementation issues are central in this context

optimality conditions for a nonconvex set valued optimization problem in this paper we study necessary and sufficient optimality conditions for a set valued optimization problem convexity of the multifunction and the domain is not required a definition of k approximating multifunction is introduced this multifunction is the differentiability notion applied to the problem a characterization of weak minimizers is obtained for invex and generalized k convexlike multifunctions using the lagrange multiplier rule

a typed calculus based on a fragment of linear logic abstract linear logic we concisely write ll has been introduced recently by jean yves girard in theoretical computer science 50 1987 born from the semantics of second order lambda calculus ll is more expressive than traditional logic both classical and intuitionistic due to the absence of structural rules and to a particular treatment of negation which is denoted by proofs in ll do not have a directional character the constructive meaning of a proof of a b is a function mapping all proofs of a into proofs of b in ll a b has a similar meaning but b a represents the same formula and has the same proofs so one of such proofs can map a proof of a into one of b as well as a proof of b into one of a in this paper we are interested in the multiplicative second order subsystem ll of linear logic we introduce a calculus called v calculus whose terms are canonical representations of proofs the aim of the calculus is to give a better comprehension of the computational aspects of the process of cut elimination we prove that the v calculus obeys strong normalization and the church rosser properties

optimality conditions for set valued maps with set optimization abstract problems in set valued optimization can be solved via set optimization in this paper optimality conditions are studied for set valued maps with set optimization optimality requirements are established for continuous selections using directional derivatives necessary and sufficient conditions for the existence of solutions are shown for set valued maps under generalized convexity assumptions and with the notion of the contingent derivative

computational interpretations of linear logic abstract we study girard s linear logic from the point of view of giving a concrete computational interpretation of the logic based on the curry howard isomorphism in the case of intuitionistic linear logic this leads to a refinement of the lambda calculus giving finer control over order of evaluation and storage allocation while maintaining the logical content of programs as proofs and computation as cut elimination in the classical case it leads to a concurrent process paradigm with an operational semantics in the style of berry and boudol s chemical abstract machine this opens up a promising new approach to the parallel implementation of functional programming languages and offers the prospect of typed concurrent programming in which correctness is guaranteed by the typing

representing scope in intuitionistic deductions abstract intuitionistic proofs can be segmented into scopes which describe when assumptions can be used in standard descriptions of intuitionistic logic these scopes occupy contiguous regions of proofs this leads to an explosion in the search space for automated deduction because of the difficulty of planning to apply a rule inside a particular scoped region of the proof this paper investigates an alternative representation which assigns scope explicitly to formulas and which is inspired in part by semantics based translation methods for modal deduction this calculus is simple and is justified by direct proof theoretic arguments that transform proofs in the calculus so that scopes match standard descriptions a herbrand theorem established straightforwardly lifts this calculus to incorporate unification the resulting system has no impermutabilities whatsoever rules of inference may be used equivalently anywhere in the proof nevertheless a natural specification describes how terms are to be extracted from its deductions

homeomorphisms and generalized derivatives when d is open in r f d rk is said to be lipschitzian provided each point in d has a neighborhood where f is lipschitz continuous for such maps the derivative f p may not exist everywhere in d but one can at least assign to each p a certain collection f p of linear transformations from r into r k called the generalized derivative for the definition see section 4 reading clarke 3 or pourciau 20 j one finds this notion of differentiability enjoys many nice properties but only the following extension of the inverse function theorem needs to be singled out here supposing f has values in r if af p is invertible that is if each linear transformation in af p is invertible at every p then f is a local homeomorphism of course local homeomorphisms are not generally homeomorphisms and in this paper we seek additional conditions on the generalized derivative and the boundary behavior of the map forcing f to be a homeomorphism in mathematical economics theorems of this type are crucial for establishing the uniqueness of competitive equilibrium points in abstract economies for such applications theorems that require the image off to satisfy a difficult to verify condition like simple connectedness are not very useful involving boundary restrictions and covering spaces our results at first are topological but then in section 4 we blend these topological ideas with properties of the generalized derivative to obtain analytic conditions when the map is lipschitzian throughout we suppose d is a domain with compact closure k in euclidean n space r b is the boundary k d f is a continuous map from k into r and f is the restriction f d our path will take us through covering spaces we call f d m a covering if each point of fz has an open neighborhood v whose preimage f v is the pairwise disjoint union of open sets each of which f maps homeomorphically onto v when f is a covering it is a local homeomorphism yet not all local homeomorphisms are coverings

nonsmooth calculus in finite dimensions the notion of subgradient originally defined for convex functions has in recent years been extended via the upper subderivative to cover functions that are not necessarily convex or even continuous a number of calculus rules have been proven for these generalized subgradients this paper develops the finite dimensional generalized subdifferential calculus for strictly lower semicontinuous functions under considerably weaker hypotheses than those previously used the most general finite dimensional convex subdifferential calculus results are recovered as corollaries other corollaries given include new necessary conditions for optimality in a nonsmooth mathematical program various chain rule formulations are considered equality in the subdifferential calculus formulae is proven under hypotheses weaker than the usual subdifferential regularity assumptions

generating plans in linear logic i actions as proofs abstract there is an increasing interest in the relation between logic and the changes involved in reasoning and specifically in plan generation up to now several attempts in this direction have been made either by embedding actions into a classical framework or by using nonstandard formalisms we think that these attempts though promising miss their objectives for a lack of a suitable logic and that the effort must be pursued in this paper we show how to obtain a strong and clean correspondence between proofs and sequences of actions by using only girard s linear logic eliminating from the classical logic the structural rules which are not adapted to our purpose a theorem is presented which expresses the new adequacy between proofs and actions