Showing papers on "Bounded function published in 2004"
TL;DR: A variant of temporal logic tailored for specifying desired properties of continuous signals, based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions is introduced.
Abstract: In this paper we introduce a variant of temporal logic tailored for specifying desired properties of continuous signals. The logic is based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions. From formulae in this logic we create automatically property monitors that can check whether a given signal of bounded length and finite variability satisfies the property. A prototype implementation of this procedure was used to check properties of simulation traces generated by Matlab/Simulink.
1,067 citations
TL;DR: A nonlinear version of the recursive least squares (RLS) algorithm that uses a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples.
Abstract: We present a nonlinear version of the recursive least squares (RLS) algorithm. Our algorithm performs linear regression in a high-dimensional feature space induced by a Mercer kernel and can therefore be used to recursively construct minimum mean-squared-error solutions to nonlinear least-squares problems that are frequently encountered in signal processing applications. In order to regularize solutions and keep the complexity of the algorithm bounded, we use a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples. This sparsification procedure allows the algorithm to operate online, often in real time. We analyze the behavior of the algorithm, compare its scaling properties to those of support vector machines, and demonstrate its utility in solving two signal processing problems-time-series prediction and channel equalization.
1,011 citations
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TL;DR: In this paper, a new category C, called the cluster category, which is obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field, is introduced.
Abstract: We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field. We show that, in the simply-laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin-Zelevinsky cluster algebra. In this model, the tilting modules correspond to the clusters of Fomin-Zelevinsky. Using approximation theory, we investigate the tilting theory of C, showing that it is more regular than that of the module category itself, and demonstrating an interesting link with the classification of self-injective algebras of finite representation type. This investigation also enables us to conjecture a generalisation of APR-tilting.
652 citations
17 May 2004
TL;DR: In the presence of indivisibilities, it is shown that there exist allocations in which the envy is bounded by the maximum marginal utility, and an algorithm for computing such allocations is presented.
Abstract: We study the problem of fairly allocating a set of indivisible goods to a set of people from an algorithmic perspective. fair division has been a central topic in the economic literature and several concepts of fairness have been suggested. The criterion that we focus on is envy-freeness. In our model, a monotone utility function is associated with every player specifying the value of each subset of the goods for the player. An allocation is envy-free if every player prefers her own share than the share of any other player. When the goods are divisible, envy-free allocations always exist. In the presence of indivisibilities, we show that there exist allocations in which the envy is bounded by the maximum marginal utility, and present a simple algorithm for computing such allocations. We then look at the optimization problem of finding an allocation with minimum possible envy. In the general case the problem is not solvable or approximable in polynomial time unless P = NP. We consider natural special cases (e.g.additive utilities) which are closely related to a class of job scheduling problems. Approximation algorithms as well as inapproximability results are obtained. Finally we investigate the problem of designing truthful mechanisms for producing allocations with bounded envy.
514 citations
TL;DR: An inversion algorithm is provided (with proof) when the mean values are known for all spheres centered on the boundary of D, with radii in the interval [0, diam(D)/2].
Abstract: Suppose D is a bounded, connected, open set in Rn and f is a smooth function on Rn with support in $\overD$. We study the recovery of f from the mean values of f over spheres centered on a part or the whole boundary of D. For strictly convex $\overline{D}$, we prove uniqueness when the centers are restricted to an open subset of the boundary. We provide an inversion algorithm (with proof) when the mean values are known for all spheres centered on the boundary of D, with radii in the interval [0, diam(D)/2]. We also give an inversion formula when D is a ball in Rn, $n \geq 3$ and odd, and the mean values are known for all spheres centered on the boundary.
487 citations
11 Jan 2004
TL;DR: This work presents a simple deterministic data structure for maintaining a set S of points in a general metric space, while supporting proximity search and updates to S (insertions and deletions) and is essentially optimal in a certain model of distance computation.
Abstract: We present a simple deterministic data structure for maintaining a set S of points in a general metric space, while supporting proximity search (nearest neighbor and range queries) and updates to S (insertions and deletions). Our data structure consists of a sequence of progressively finer e-nets of S, with pointers that allow us to navigate easily from one scale to the next.We analyze the worst-case complexity of this data structure in terms of the "abstract dimensionality" of the metric S. Our data structure is extremely efficient for metrics of bounded dimension and is essentially optimal in a certain model of distance computation. Finally, as a special case, our approach improves over one recently devised by Karger and Ruhl [KR02].
424 citations
TL;DR: Two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities and the controller singularity problem is avoided perfectly in both approaches.
Abstract: In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.
404 citations
380 citations
TL;DR: It is shown that there are graphs with optimal labels of length 3 log n, such that if the authors use any labels with fewer than n bits per label, computing the distance function requires exponential time.
369 citations
13 Jun 2004
TL;DR: The Chebyshev polynomials are explored as a basis for approximating and indexing d-dimenstional trajectories and the key analytic result is the Lower Bounding Lemma, which shows that the Euclidean distance between two d-dimensional trajectories is lower bounded by the weighted Euclideans distance between the two vectors of ChebysHEv coefficients.
Abstract: In this paper, we attempt to approximate and index a d- dimensional (d ≥ 1) spatio-temporal trajectory with a low order continuous polynomial. There are many possible ways to choose the polynomial, including (continuous)Fourier transforms, splines, non-linear regressino, etc. Some of these possiblities have indeed been studied beofre. We hypothesize that one of the best possibilities is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. However, in general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown thta the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [16]. Thus, in this paper, we explore how to use the Chebyshev polynomials as a basis for approximating and indexing d-dimenstional trajectories.The key analytic result of this paper is the Lower Bounding Lemma. that is, we show that the Euclidean distance between two d-dimensional trajectories is lower bounded by the weighted Euclidean distance between the two vectors of Chebyshev coefficients. this lemma is not trivial to show, and it ensures that indexing with Chebyshev cofficients aedmits no false negatives. To complement that analystic result, we conducted comprehensive experimental evaluation with real and generated 1-dimensional to 4-dimensional data sets. We compared the proposed schem with the Adaptive Piecewise Constant Approximation (APCA) scheme. Our preliminary results indicate that in all situations we tested, Chebyshev indexing dominates APCA in pruning power, I/O and CPU costs.
361 citations
TL;DR: A novel robust optimization methodology is proposed, which when applied to mixed-integer linear programming (MILP) problems produces “robust” solutions which are in a sense immune against bounded uncertainty.
TL;DR: It is shown that a linear observer-based output feedback can globally regulate an equilibrium of strongly nonlinear systems, provided that a single high gain is appropriately tuned.
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TL;DR: In this article, the authors study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values, and they give necessary and sufficient conditions for time consistency in terms of the representing functionals.
Abstract: We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals.
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TL;DR: In the absence of arbitrage, the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T, where x is log-moneyness as discussed by the authors.
Abstract: Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T, where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying distribution. We prove the moment formula, which expresses explicitly this model-independent relationship. We prove also the reciprocal moment formula for the small-strike tail, and we exhibit the symmetry between the formulas. The moment formula, which evaluates readily in many cases of practical interest, has applications to skew extrapolation and model calibration.
TL;DR: The filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities and the set of desired robust filters is characterized in terms of some free parameters.
Abstract: This paper deals with a new filtering problem for linear uncertain discrete-time stochastic systems with randomly varying sensor delay. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. The system measurements are subject to randomly varying sensor delays, which often occur in information transmissions through networks. The problem addressed is the design of a linear filter such that, for all admissible parameter uncertainties and all probabilistic sensor delays, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. We show that the filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. We also characterize the set of desired robust filters in terms of some free parameters. An illustrative numerical example is used to demonstrate the usefulness and flexibility of the proposed design approach.
TL;DR: In the absence of arbitrage, the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T, where x is log-moneyness as discussed by the authors.
Abstract: Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T, where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying distribution. We prove the moment formula, which expresses explicitly this model-independent relationship. We prove also the reciprocal moment formula for the small-strike tail, and we exhibit the symmetry between the formulas. The moment formula, which evaluates readily in many cases of practical interest, has applications to skew extrapolation and model calibration.
TL;DR: An optimal interval estimate of the regression function is obtained, providing its uncertainty range for any assigned regressor values, and the set estimate allows to derive an optimal identification algorithm, giving estimates with minimal guaranteed L"p error on the assigned domain of the regressors.
TL;DR: The problem of globally uniformly asymptotically and locally exponentially stabilizing a family of nonlinear feedforward systems when there is a delay in the input is solved and explicit expressions of bounded control laws are determined.
Abstract: The problem of globally uniformly asymptotically and locally exponentially stabilizing a family of nonlinear feedforward systems when there is a delay in the input is solved. No limitation on the size of the delay is imposed. Explicit expressions of bounded control laws are determined.
TL;DR: For complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below, this paper showed that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfying a certain L p estimate in the same interval of p's.
Abstract: One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain L p estimate in the same interval of p's.
TL;DR: The robust stability of uncertain linear neutral systems with discrete and distributed delays is investigated and the proposed stability criteria are formulated in the form of a linear matrix inequality and it is easy to check the robust stability.
TL;DR: A delay-dependent stability criterion is obtained and formulated in the form of a linear matrix inequality that indicates the robust stability of uncertain linear neutral systems with time-varying discrete delay.
TL;DR: In this article, the authors presented time-domain, displacement-based governing equations of the perfectly matched layer (PML) model for linear wave equations on an unbounded domain.
Abstract: One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-of-incidence and of all non-zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192:1337-1375], the authors presented, inter alia, time-harmonic governing equations of PMLs for anti-plane and for plane-strain motion of (visco-)elastic media. This paper presents (a) corresponding time-domain, displacement-based governing equations of these PMLs and (b) displacement-based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti-plane PML is found to be symmetric, whereas that of the plane-strain PML is not. Numerical results are presented for the anti-plane motion of a semi-infinite layer on a rigid base, and for the classical soil-structure interaction problems of a rigid strip-footing on (i) a half-plane, (ii) a layer on a half-plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains.
TL;DR: In this paper, the authors studied the long time behavior of a family of singularly perturbed Cahn-Hilliard equations with singular (and, in particular, logarithmic) potentials.
Abstract: Our aim in this article is to study the long time behaviour of a family of singularly perturbed Cahn-Hilliard equations with singular (and, in particular, logarithmic) potentials. In particular, we are able to construct a continuous family of exponential attractors (as the perturbation parameter goes to 0). Furthermore, using these exponential attractors, we are able to prove the existence of the finite dimensional global attractor which attracts the bounded sets of initial data for all the possible values of the spatial average of the order parameter, hence improving previous results which required strong restrictions on the size of the spatial domain and to work on spaces on which the average of the order parameter is prescribed. Finally, we are able, in one and two space dimensions, to separate the solutions from the singular values of the potential, which allows us to reduce the problem to one with a regular potential. Unfortunately, for the unperturbed problem in three space dimensions, we need additional assumptions on the potential, which prevents us from proving such a result for logarithmic potentials. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors consider topological dynamical systems that arise from locally compact Abelian groups on compact spaces of translation bounded measures and show that such a system has a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
Abstract: Certain topological dynamical systems that arise from actions of -compact locally compact Abelian groups on compact spaces of translation bounded measures are considered. Such a measure dynamical system is shown to have a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
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TL;DR: In this article, the authors consider the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below and show that the Riesz transform is bounded on such a manifold, for $p$ ranging in an open interval above 2.
Abstract: One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is $L^p$ bounded on such a manifold, for $p$ ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain $L^p$ estimate in the same interval of $p$'s.
TL;DR: In this article, the authors consider the exponential stability of stochastic evolution with Lipschitz continuous non-linearities when zero is not a solution for these equations and prove the existence of a non-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift.
Abstract: We consider the exponential stability of stochastic evolution
equations with Lipschitz continuous non-linearities when zero is
not a solution for these equations. We prove the existence of a
non-trivial stationary solution which is exponentially stable,
where the stationary solution is generated by the composition of a
random variable and the Wiener shift. We also construct stationary
solutions with the stronger property of attracting bounded sets
uniformly. The existence of these stationary solutions follows
from the theory of random dynamical systems and their attractors.
In addition, we prove some perturbation results and formulate
conditions for the existence of stationary solutions for
semilinear stochastic partial differential equations with
Lipschitz continuous non-linearities.
TL;DR: In this paper, the authors considered the Dirichlet problem for positive solutions of the equation -Delta(m)(u) = f (u) in a bounded smooth domain Omega, with f locally Lipschitz continuous, and proved some regularity results for weak C-1( ) solutions.
01 Jan 2004
TL;DR: In this paper, the authors apply linear algebra techniques to precise interprocedural dataflow analysis, and describe analyses that determine for each program point identities that are valid among the program variables whenever control reaches that program point.
Abstract: We apply linear algebra techniques to precise interprocedural dataflow analysis. Specifically, we describe analyses that determine for each program point identities that are valid among the program variables whenever control reaches that program point. Our analyses fully interpret assignment statements with affine expressions on the right hand side while considering other assignments as non-deterministic and ignoring conditions at branches. Under this abstraction, the analysis computes the set of all affine relations and, more generally, all polynomial relations of bounded degree precisely. The running time of our algorithms is linear in the program size and polynomial in the number of occurring variables. We also show how to deal with affine preconditions and local variables and indicate how to handle parameters and return values of procedures.
TL;DR: In this article, it was shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate contractability and amenability, and the existence of suitable operator bounded approximate identities for the diagonal ideal.
TL;DR: The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in the earlier work with the provision that a magnitude bound on the unknown parameter be given.
Abstract: We propose a dynamic high-gain scaling technique and solutions to coupled Lyapunov equations leading to results on state-feedback, output-feedback, and input-to-state stable (ISS) appended dynamics with nonzero gains from all states and input. The observer and controller designs have a dual architecture and utilize a single dynamic scaling. A novel procedure for designing the dynamics of the high-gain parameter is introduced based on choosing a Lyapunov function whose derivative is negative if either the high-gain parameter or its derivative is large enough (compared to functions of the states). The system is allowed to contain uncertain terms dependent on all states and uncertain appended ISS dynamics with nonlinear gains from all system states and input. In contrast, previous results require uncertainties to be bounded by a function of the output and require the appended dynamics to be ISS with respect to the output, i.e., require the gains from other states and the input to be zero. The generated control laws have an algebraically simple structure and the associated Lyapunov functions have a simple quadratic form with a scaling. The design is based on the solution of two pairs of coupled Lyapunov equations for which a constructive procedure is provided. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given.