Abstract: In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl1QP.

Abstract: We address the problem of building watertight 3D models from surfaces that contain holes - for example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as known-empty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold non-interpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes.

Abstract: We study the panel DOLS estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual-specific time trends, individual-specific fixed effects and time-specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T approaches infinity, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of linear constraints has a limiting chi-square distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T go to infinity then letting N go to infinity. In a series of Monte Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel dynamic OLS to estimate coefficients of the long-run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e.=0.26) and the estimated interest rate semi-elasticity is -0.02 (asymptotic s.e.=0.01).

Abstract: We formulate an algorithm for the calculation of stable phase relations of a system with constrained bulk composition as a function of its environmental variables. The basis of this algorithm is the approximate representation of the free energy composition surfaces of solution phases by inscribed polyhedra. This representation leads to discretization of high variance phase fields into a continuous mesh of smaller polygonal fields within which the composition and physical properties of the phases are uniquely determined. The resulting phase diagram sections are useful for understanding the phase relations of complex metamorphic systems and for applications in which it is necessary to establish the variations in rock properties such as density, seismic velocities and volatile-content through a metamorphic cycle. The algorithm has been implemented within a computer program that is general with respect to both the choice of variables and the number of components and phases possible in a system, and is independent of the structure of the equations of state used to describe the phases of the system.

Abstract: We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where the flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function fi(q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences fi(Qi)-f-1(Qi-1) into eigenvectors of an approximate Jacobian matrix. This method is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities. Balance laws $q_t+f(q,x)_x=\psi(q,x)$ are also considered, in which case the source term is used to modify the flux difference before performing the wave decomposition, and an additional term is derived that must also be included to obtain full accuracy. This method is particularly useful for quasi-steady problems close to steady state.

Abstract: We consider the scattering of time-harmonic plane waves by an inhomogeneous medium. The far field patterns u? of the scattered waves depend on the index of refraction 1 + q, the frequency, and directions and of observation and incidence, respectively. The inverse problem which is studied in this paper is to determine the support ? of q from the knowledge of u? (, ) for all , where the frequency is fixed (and known). Our new approach is based on the far field operator F which is the integral operator with kernel u? (, ). It depends on the data only and is therefore known (at least approximately). The MUSIC algorithm in signal processing uses the discrete version of F, i.e. the matrix F = (u? ( i, j)) N?N, and determines the locations of the point scatterers. The key idea in both cases is to factorize F and F in the forms where the operator S and the matrix S are 'more explicit' than F and F, respectively, and T, T are suitable isomorphisms. In a first theoretical result we show that the ranges of S and F# coincide, where F# is some suitable combination of the real and imaginary parts of F. In the finite dimensional case a simple argument from matrix theory yields that the ranges of S and F coincide. Since F# is known from the data we can decide for every function on the unit sphere whether it belongs to the range of S or not. We apply this test to the far field patterns of point sources and arrive at an explicit test whether a point z belongs to ? or not. We will demonstrate that this method also leads to a fast visualization of the obstacle.

Abstract: PREFACE A-Z DICTIONARY STATISTICAL NOTATION Mathematical Notation Greek Letters Cumulative Probabilities for the Bionormal Distribution Cumulative Probabilities for the Poisson Distribution The Standard Normal Distribution Function Upper-Tail Percentage Points for the Standard-Normal Distribution Percentage Points for the t-Distribution Percentage Points for the Chi-Squared Distribution Percentage Points for the F-Distribution Critical Values for the Product-Moment Correlation Coefficient, r Critical Values for Spearman's Rank Correlation Coefficient Critical Values for Kendall Pseudo-Random Numbers Selected Landmarks in the Development of Statistics FURTHER REFERENCE

Abstract: The field of property testing studies algorithms that distinguish, using a small number of queries, between inputs which satisfy a given property, and those that are 'far' from satisfying the property. Testing properties that are defined in terms of monotonicity has been extensively investigated, primarily in the context of the monotonicity of a sequence of integers, or the monotonicity of a function over the n-dimensional hypercube {1,…,m}n. These works resulted in monotonicity testers whose query complexity is at most polylogarithmic in the size of the domain.We show that in its most general setting, testing that Boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory. These problems include: testing that a Boolean assignment of variables is close to an assignment that satisfies a specific 2-CNF formula, testing that a set of vertices is close to one that is a vertex cover of a specific graph, and testing that a set of vertices is close to a clique.We then investigate the query complexity of monotonicity testing of both Boolean and integer functions over general partial orders. We give algorithms and lower bounds for the general problem, as well as for some interesting special cases. In proving a general lower bound, we construct graphs with combinatorial properties that may be of independent interest.

Abstract: We construct a parametrization of deep-inelastic structure functions which retains information on experimental errors and correlations, and which does not introduce any theoretical bias while interpolating between existing data points. We generate a Monte Carlo sample of pseudo-data configurations and we train an ensemble of neural networks on them. This effectively provides us with a probability measure in the space of structure functions, within the whole kinematic region where data are available. This measure can then be used to determine the value of the structure function, its error, point-to-point correlations and generally the value and uncertainty of any function of the structure function itself. We apply this technique to the determination of the structure function F2 of the proton and deuteron, and a precision determination of the isotriplet combination F2[p?d]. We discuss in detail these results, check their stability and accuracy, and make them available in various formats for applications.

Abstract: Presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software.

Abstract: A criterion for a function to belong to or to is given. Various integral conditions under which a measurable function is constant are discussed.

Abstract: Simulated granular packings with different particle friction coefficient $\ensuremath{\mu}$ are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces $P(f)$ are computed and compared with existing experimental data. Here $f\ensuremath{\equiv}F/\overline{F}$ is the contact force F normalized by the average value $\overline{F}.$ $P(f)$ exhibits exponential-like decay at large forces, a plateau/peak near $f=1,$ with additional features at forces smaller than the average that depend on $\ensuremath{\mu}.$ Additional information beyond the one-point force distribution functions is provided in the form of the force-force spatial distribution function and the contact point radial distribution function. These quantities indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three-dimensional, unloaded packings.

Abstract: When solving non-stationary problems of mathematical physics, a particular attention is paid to schemes with weighted factors. Assume that we solve the Cauchy problem for the first-order evolution equation \(\frac{{du}}{{dt}} + Au = f(t),0 < t < T,u(0) = {u_0}\) where f (t),u 0 are given, whilst u(t) is the unknown function with values in a finite-dimensional Hilbert space H.

Abstract: This letter introduces a two-dimensional bilinear mapping operator referred to as the cubic phase (CP) function. For first-, second-, or third-order polynomial phase signals, the energy of the CP function is concentrated along the frequency rate law of the signal. The function, thus, has an interpretation as a time-frequency rate representation. The peaks of the CP function yield unbiased estimates of the instantaneous (angular) frequency rate (IFR) and, hence, can be used as the basis for an IFR estimation algorithm. The letter defines an IFR estimation algorithm and theoretically analyzes it. The estimation is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios. Simulations are provided to verify the theoretical claims.

Abstract: The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper (Haubold and Mathai, 2000).

Abstract: We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann-Hilbert problem related to the Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore [1] obtained from the mode coupling approximation.

Abstract: This letter exploits the cyclic prefix to create a blind adaptive globally convergent channel-shortening algorithm, with a complexity like least mean squares. The cost function is related to that of the shortening signal-to-noise solution of Melsa et al. (see IEEE Trans. Commun., vol.44, p.1662-72, Dec. 1996), and simulations are provided to demonstrate the performance of the algorithm.

Abstract: For the first time, a running time analysis of population-based multi-objective evolutionary algorithms for a discrete optimization problem is given To this end, we define a simple pseudo-Boolean bi-objective problem (LOTZ: leading ones - trailing zeroes) and investigate time required to find the entire set of Pareto-optimal solutions It is shown that different multi-objective generalizations of a (1+1) evolutionary algorithm (EA) as well as a simple population-based evolutionary multi-objective optimizer (SEMO) need on average at least �(n3) steps to optimize this function We propose the fair evolutionary multi-objective optimizer (FEMO) and prove that this algorithm performs a black box optimization in �(n2 log n) function evaluations where n is the number of binary decision variables

Abstract: This paper presents a new simple algorithm for minimizing submodular functions. For integer valued submodular functions, the algorithm runs in O(n6EO log nM) time, where n is the cardinality of the ground set, M is the maximum absolute value of the function value, and EO is the time for function evaluation. The algorithm can be improved to run in O ((n4EO+n5)log nM) time. The strongly polynomial version of this faster algorithm runs in O((n5EO + n6) log n) time for real valued general submodular functions. These are comparable to the best known running time bounds for submodular function minimization. The algorithm can also be implemented in strongly polynomial time using only additions, subtractions, comparisons, and the oracle calls for function evaluation. This is the first fully combinatorial submodular function minimization algorithm that does not rely on the scaling method.

Abstract: Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be formulated in terms of kappa-deformed exponential functions together with the associated deduced logarithmic functions.

Abstract: Since the seminal paper of Kydland and Prescott (1982) and King, Plosser and Rebelo (1988), it has become commonplace in macroeconomics to approximate the solution to nonlinear, dynamic general equilibrium models using linear methods. Linear approximation methods are useful to characterize certain aspects of the dynamic properties of complicated models. First-order approximation techniques are not however, well suited to handle questions such as welfare comparisons across alternative stochastic of policy environments. The problem with using linearized decision rules to evaluate second-order approximations to the objective function is that some second-order terms of the objective function are ignored when using a linearized decision rule. Such problems do not arise when the policy function is approximated to second-order or higher. In this paper we derive a second order approximation to the policy function of a dynamic, rational expectations model. Our approach follows the perturbation method described in Judd (1998) and developed further by Collard and Juillard (2001). We follow Collard and Juillard closely in notation and methodology. An important difference separates this Paper from the work of Collard and Juillard. Namely, Collard and Juillard apply what they call a bias reduction procedure to capture the fact that the policy function depends on the variance of the underlying shocks. Instead, we explicitly incorporate a scale parameter for the variance of the exogenous shocks as an argument of the policy function. In approximating the policy function, we take a second order Taylor expansion with respect to the state variables as well as this scale parameter. To illustrate its applicability, the method is used to solve the dynamics of a simple neoclassical model. The Paper closes with a brief description of a set of MATLAB programs designed to implement the method.