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In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]

Let f be a positive smooth function on a closed Riemann surface (M, g). The f-energy of a map u from M to a Riemannian manifold (N, h) is defined as $$ E_f(u)=\int_Mf|\nabla u|^2dV_g, $$ and its L2-gradient is: $$ \tau_f(u) = f\tau(u)+ \nabla f\cdot\nabla u. $$ We will study the blow-up properties of some approximate f-harmonic map sequences in this paper. For a sequence uk : M → N with |τf(uk)|L2 < C1 and Ef(uk) < C2, we will show that, if the sequence is not compact, then it must blow-up at some critical points of f or some concentrate points of |τf(uk)|2dVg. For a minimizing α-f-harmonic map sequence in some homotopy class of maps from M into N we show that, if the sequence is not compact, the blow-up points must be the minimal point of f and the energy identity holds true. [ABSTRACT FROM AUTHOR]

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k-strict pseudo-contraction non-self mapping in Hilbert space. By the viscosity approximation algorithms, under suitable conditions , some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper extend and improve some recent results of Marino and Xu [G.Marino,H.K.Xu, Weak and strong convergence theorems for k-strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-349], Zhou [H.Zhou, Convergence theorems of fixed Points for k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 69 (2008) 456-462], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506- 515], Ceng,Homidan,etc [L. C. Ceng, S.A.Homidan, Q.H.Ansari, J. C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967-974]. [ABSTRACT FROM AUTHOR]

The aim of this paper is threefold: 1) to propose a simple accurate closed-form approximation to the probability density function of the sum of arbitrarily distributed Nakagami-m random variables; 2) to propose a simple accurate closed-form approximation to the level crossing rate for the sum of Nakagami-m random processes; and 3) to show some possible applications for the proposed formulations. With such an aim, we choose the α-μ distribution for which the parameters are estimated from the sum of the Nakagami-m envelopes. As shall be shown from sample representative examples, the proposed approximations are simple, versatile, and highly accurate. The approach used here can easily be extended to other applications such as bit error rate and channel capacity calculations among others. [ABSTRACT FROM AUTHOR]

The univariate spline quasi-interpolants (QIs) studied in this paper are approximation operators using B-spline expansions with coefficients that are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find QIs that have both good approximation orders and uniform norms which are bounded independently of the given partition. Near-best QIs are obtained by minimizing an upper bound for the infinity norm of QIs depending on a certain number of free parameters, thus reducing this norm. This paper is devoted to the study of some families of near-best discrete quasi-interpolants (dQIs) of approximation order 3. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems. [ABSTRACT FROM AUTHOR]

In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established. [ABSTRACT FROM AUTHOR]

This paper presents an efficient technique for synthesis and optimization of the polynomials over GF(2m), where m is a nonzero positive integer. The technique is based on a graph-based decomposition and factorization of the polynomials, followed by efficient network factorization and optimization. A technique for efficiently computing the coefficients of the polynomials over GF(pm), where p is a prime number, is first presented. The coefficients are stored as polynomial graphs over GF(pm). The synthesis and optimization is initiated from this graph-based representation. The technique has been applied to minimize multipliers over the fields GF(2κ ), where k = 2,..., 8, generated with all the 51 primitive polynomials in the 0.18-/~m CMOS technology with the help of the Synopsys design compiler. It has also been applied to minimize combinational exponentiation circuits, parallel integer adders and multipliers, and other multivariate bit- as well as word-level polynomials. The experimental results suggest that the proposed technique can reduce area, delay, and power by significant amounts. We also observed that the technique is capable of producing 100% testable circuits for stuck-at faults. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of the details of mathematical and computational aspects of the Galerkin/least-squares and the Galerkin/weak form least-squares finite element process within the mathematical and computational framework [1, 2, 3] based on h, p, k as independent computational parameters and requiring that the integral forms be variationally consistent (VC). Higher-order global differentiability of order (k-1) defined by the order k of the approximation space is essential for incorporating correct physics of the processes in the computations and that k is an independent parameter in addition to h and p in all finite element computations. In this paper the attributes of the Galerkin method, the Galerkin method with weak form, and least-squares processes in h, p, k framework with variationally consistent (VC) or variationally inconsistent (VIC) integral forms are utilized to investigate the mathematical features of the Galerkin/least-squares processes (GAL/LSP) and Galerkin/weak form least-squares process (GAL/WF/LSP) to establish (1) when such processes have a sound mathematical basis (2) role of functionals resulting from the Galerkin method, the Galerkin method with weak form and least-squares processes in GAL/LSP and GAL/WF/LSP (3) Importance of minimally conforming spaces and role of higher order spaces in GAL/LSP and GAL/WF/LSP. It is concluded that GAL/LSP only have sound mathematical basis for self adjoint differential operators when viewed within h,p,k framework with the requirement that the integral forms be variationally consistent. For non-self adjoint and non-linear differential operators GAL/LSP and GAL/WF/LSP do not have a sound mathematical basis within the proposed framework. Currently used finite element processes based on GAL/WF/LSP utilizing local approximations of class C0 violate basic mathematical principles, are in violation with physics and hence do not provide a valid and mathematically sound approach. Investigation of the GAL/LSP and GAL/WF/LSP when the local approximations are in minimally conforming spaces or in spaces of order higher than minimally conforming spaces, shows that the functionals from GAL and GAL/WF processes only have detrimental affect on the LSP process. Numerical studies are presented to demonstrate various aspects and features. [ABSTRACT FROM AUTHOR]

In this paper, we consider algorithms for constructing n-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences. [ABSTRACT FROM AUTHOR]

Abstract  In this paper we consider the problem of the approximation of the integral of a smooth enough function f(x,y) on the standard simplex $${\int\limits_{\Delta _{2} } {f{\left( {x,y} \right)}dxdy} } = {\sum\limits_{\alpha = 1}^3 {{\sum\limits_{i,j} {A_{{\alpha ij}} \frac{{\alpha ^{{i j}} }}{{\alpha x^{i} \alpha y^{j} }}f{\left( {x_{\alpha } ,y_{\alpha } } \right)} E{\left( f \right)}} }} }$$ where the nodes are the vertices of the simplex. Such kind of quadratures belong to a more general class of formulas for numerical integration, which are called boundary-type quadrature formulas. We discuss three classes of such formulas that are exact for algebraic polynomials and generate embedded pairs. We give bounds for the truncation errors and conditions for convergence. Finally, we show how to organize an algorithm for the automatic computation of the quadratures with estimate of the errors and provide some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we show that approximation spaces are basic structures for knowledge discovery from multi-relational data. The utility of approximation spaces as fundamental objects constructed for concept approximation is emphasized. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings. [ABSTRACT FROM AUTHOR]

We study the transformation of "predicate introduction" in non-monotonic logics. By this, we mean the act of replacing a complex formula by a newly defined predicate. From a knowledge representation perspective, such transformations can be used to eliminate redundancy or to simplify a theory. From a more practical point of view, they can also be used to transform a theory into a normal form imposed by certain inference programs or theorems. In a companion paper, we developed an algebraic theory that considers predicate introduction within the framework of "approximation theory", a fixpoint theory for non-monotone operators that generalizes all main semantics of various non-monotonic logics, including logic programming, default logic and autoepistemic logic. We then used these results to show that certain logic programming transformations are equivalence preserving under, among others, both the stable and well-founded semantics. In this paper, we now apply the same algebraic results to autoepistemic logic and prove that a transformation to reduce the nesting depth of modal operators is equivalence preserving under a family of semantics for this logic. This not only provides useful theorems for autoepistemic logic, but also demonstrates that our algebraic theory does indeed capture the essence of predicate introduction in a generally applicable way. [ABSTRACT FROM AUTHOR]

This paper tests the hypothesis that optimal perturbations in quasigeostrophic turbulence are excited sufficiently strongly and frequently to account for the energy-containing eddies. Optimal perturbations are defined here as singular vectors of the propagator, for the energy norm, corresponding to the equations of motion linearized about the time-mean flow. The initial conditions are drawn from a numerical solution of the nonlinear equations associated with the linear propagator. Experiments confirm that energy is concentrated in the leading evolved singular vectors, and that the average energy in the initial singular vectors is within an order of magnitude of that required to explain the average energy in the evolved singular vectors. Furthermore, only a small number of evolved singular vectors (4 out of 4000) are needed to explain the dominant eddy structure when total energy exceeds a predefined threshold. The initial singular vectors explain only 10% of such events, but this discrepancy was similar to that of the full propagator, suggesting that it arises primarily due to errors in the propagator. In the limit of short lead times, energy conservation can be expressed in terms of suitable singular vectors to constrain the energy distribution of the singular vectors in statistically steady equilibrium. This and other connections between linear optimals and nonlinear dynamics suggests that the positive results found here should carry over to other systems, provided the propagator and initial states are chosen consistently with respect to the nonlinear system. [ABSTRACT FROM AUTHOR]

In this paper, the so-called η-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function η. In this method, an equivalent η-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated η-approximated vector optimization problem. Finally, the description of the η-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented. [ABSTRACT FROM AUTHOR]

In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems where α, β, c > 0 are parameters. Those systems model two-dimensional small amplitude long wavelength water waves. For α ≤ 1, this equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every β, c and almost every α ≤ 1, it admits solutions that are quasiperiodic in time. The proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the Boussinesq system to the center manifold, uses arguments of classical perturbation theory by considering the Hamiltonian formulation of the problem and studying the Birkhoff normal form. [ABSTRACT FROM AUTHOR]

This paper considers the problem of approximating an integrable function by piecewise linear functions that keep the integral and positivity of the original function. [ABSTRACT FROM AUTHOR]

This paper offers a sparse, multiscale representation of objects. It captures the object appearance by selection from a very large dictionary of Gaussian differential basis functions. The learning procedure results from the matching pursuit algorithm, while the recognition is based on polynomial approximation to the bases, turning image matching into a problem of polynomial evaluation. The method is suited for coarse recognition between objects and, by adding more bases, also for fine recognition of the object pose. The advantages over the common representation using PCA include storing sampled points for recognition is not required, adding new objects to an existing data set is trivial because retraining other object models is not needed, and significantly in the important case where one has to scan an image over multiple locations in search for an object, the new representation is readily available as opposed to PCA projection at each location. The experimental result on the COIL-100 data set demonstrates high recognition accuracy with real-time performance. [ABSTRACT FROM AUTHOR]

In this paper we investigate numerical methods for solving hyperbolic conservation laws based on finite volumes and optimal recovery. These methods can, for example, be applied in certain ENO schemes. Their approximation properties depend in particular on the reconstruction from cell averages. Hence, this paper is devoted to prove convergence results for such reconstruction processes from cell averages. [ABSTRACT FROM AUTHOR]

In our papers [Inverse Problems, 15 (1999), pp. 309--327] and [Numer. Math., 88 (2001), pp. 347--365] we proposed algorithm {\tt REGINN}, an inexact Newton iteration for the stable solution of nonlinear ill-posed problems. {\tt REGINN} consists of two components: the outer iteration, which is a Newton iteration stopped by the discrepancy principle, and an inner iteration, which computes the Newton correction by solving the linearized system. The convergence analysis presented in both papers covers virtually any linear regularization method as inner iteration, especially Landweber iteration, $\nu$-methods, and Tikhonov--Phillips regularization. In the present paper we prove convergence rates for {\tt REGINN} when the conjugate gradient method, which is nonlinear, serves as inner iteration. Thereby we add to a convergence analysis of {Hanke}, who had previously investigated {\tt REGINN} furnished with the conjugate gradient method [Numer. Funct. Anal. Optim., 18 (1997), pp. 971--993]. By numerical experiments we illustrate that the conjugate gradient method outperforms the $\nu$-method as inner iteration. [ABSTRACT FROM AUTHOR]

The top part of Figure 1.1 shows some classes from the (truth-table) bounded-query and boolean hierarchies. It is well known that if either of these hierarchies collapses at a given level, then all higher levels of that hierarchy collapse to that same level. This is a standard "upward translation of equality" that has been known for over a decade. The issue of whether these hierarchies can translate equality downwards has proven vastly more challenging. In particular, with regard to Figure 1.1, consider the following claim: \[ \psigkmtt = \psigkmponett \implies \diffmsigk = \codiffmsigk = \bh(\sigmak). (*) \] This claim, if true, says that equality translates downwards between levels of the bounded-query hierarchy and the boolean hierarchy levels that (before the fact) are immediately below them. Until recently, it was not known whether (*)ever held, except for the degenerate cases m = 0 and k = 0. Then Hemaspaandra, Hemaspaandra, and Hempel [SIAM J. Comput., 28 (1999), pp. 383--393] proved that (*) holds for all m, for k > 2. Buhrman and Fortnow [J. Comput. System Sci., 59 (1999), pp. 182--199] then showed that, when k = 2, (*) holds for the case m = 1. In this paper, we prove that for the case k = 2, (*) holds for all values of m. Since there is an oracle relative to which "for k = 1, (*) holds for all m" fails (see Buhrman and Fortnow), our achievement of the k = 2 case cannot be strengthened to k = 1 by any relativizable proof technique. The new downward translation we obtain also tightens the collapse in the polynomial hierarchy implied by a collapse in the bounded-query hierarchy of the second level of the polynomial hierarchy. [ABSTRACT FROM AUTHOR]

In this paper, we continue the development of state feedback boundary control laws based on the backstepping methodology, for the stabilization of unstable, parabolic partial differential equations. We consider the linearized Ginzburg--Landau equation, which models, for instance, vortex shedding in bluff body flows. Asymptotic stabilization is achieved by means of boundary control via state feedback in the form of an integral operator. The kernel of the operator is shown to be twice continuously differentiable, and a series approximation for its solution is given. Under certain conditions on the parameters of the Ginzburg--Landau equation, compatible with vortex shedding modelling on a semi-infinite domain, the kernel is shown to have compact support, resulting in partial state feedback. Simulations are provided in order to demonstrate the performance of the controller. In summary, the paper extends previous work in two ways: (1) it deals with two coupled partial differential equations, and (2) under certain circumstances handles equations defined on a semi-infinite domain. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the couniform (or dual Goldie) dimension of a module under various polynomial extensions. For a ring automorphism s ? Aut( R ), we use the notion of a s-compatible module M R to obtain results on the couniform dimension of the polynomial modules M [ x ], M [ x -1 ], and M [ x , x -1 ] over suitable skew extension rings. [ABSTRACT FROM AUTHOR]

Letbe a unit sphere of thed-dimensional Euclidean space Rd and let(0 < p= 1) denote the real Hardy space onFor 0 < p= 1 andletEj(f,Hp) (j= 0, 1, ...) be the best approximation offby spherical polynomials of degree less than or equal toj, in the spaceGiven a distributionfonits Cesàro mean of order d>-1 is denoted byFor 0p. In this paper, the following result is proved:TheoremLet0N(f)˜BN(f)means that there’s a positive constant C, independent of N and f, such thatIn the cased= 2,this result was proved by Belinskii in 1996. [ABSTRACT FROM AUTHOR]

This paper extends Pawlak's rough set onto the basis of a fuzzy partition of the universe of discourse. Some basic properties of partition-based fuzzy approximation operators are examined. To measure uncertainty in generalized fuzzy rough sets, a new notion of entropy of a fuzzy set is introduced. The notion is demonstrated to be adequate for measuring the fuzziness of a fuzzy event. The entropy of a fuzzy partition and conditional entropy are also proposed. These kinds of entropy satisfy some basic properties similar to those of Shannon's entropy. It is proved that the measure of fuzziness of a partition-based fuzzy rough set, FR( A ), is equal to zero if and only if the set A is crisp and definable. [ABSTRACT FROM AUTHOR]

In the analysis of steel structures, several modern codes such as LRFD and Eurocode 3 provide for second-order approximate analysis. This paper presents a method of optimization for use in design that is directed toward improving the overall stability and strength of moment-resistant building frames. The method makes use of codified expressions for approximate second-order analysis. The objective function used in the optimization is the dominant eigenvalue of the linearized buckling problem. Only a first-order analysis is required, along with the calculation of the first eigenvalue of the linearized buckling problem of the structure. This new method provides a story by story procedure that is easily visualized. Several examples are provided to illustrate applications of the procedure. [ABSTRACT FROM AUTHOR]

In this paper we show that a generalization of a popular motion planning puzzle called Lunar Lockout is computationally intractable. In particular, we show that the problem is PSPACE-complete. We begin with a review of NP-completeness and polynomial-time reductions, introduce the class PSPACE, and motivate the significance of PSPACE-complete problems. Afterwards, we prove that determining whether a given instance of a generalized Lunar Lockout puzzle is solvable is PSPACE-complete. [ABSTRACT FROM AUTHOR]

Average-case analysis provides knowledge about the quality of estimation algorithms in the case when the influence of outliers (exceptionally difficult elements) is to be neglected. This is in contrast with the worst-case analysis, where exceptionally difficult elements are of particular interest. In this paper we consider the average behavior of estimation algorithms based on corrupted information, with values in a subspace of the problem element space. We study two local average errors, with respect to probability measures defined by a class of weight functions. We define the optimal algorithm and derive exact error formulas, in Euclidean norms in problem element and information spaces. The formulas explicitly show the dependence of the errors on basic components of the problem, in particular on the weights. Attention is paid to the class of isotropic weight functions, examples of which are provided by truncated Gaussian weight functions. An extension of the results to non-Euclidean norms in the information space in a special case is shown. [ABSTRACT FROM AUTHOR]

The paper establishes lower bounds on the provability of D = NP and the MRDP theorem in weak fragments of arithmetic. The theory I[sup 5] E[sub l] is shown to be unable to prove D = NP. This non-provability result is used to show that I[sup 5] E[sub 1] cannot prove the MRDP theorem. On the other hand it is shown that I¹ E[sub1] proves D contains all predicates of the form (∀i ≤ |b|) P(i, x) ο Q(i, x) where ο is =, <, or ≤, and I[sup 0] E[sub1] proves D contains all predicates of the form (∀i ≤ b) P(i, x) = Q(i, x). Here P and Q are polynomials. A conjecture is made that D contains NLOGTIME. However, it is shown that this conjecture would not be sufficient to imply D = NP. Weak reductions to equality are then considered as a way of showing D = NP. It is shown that the bit-wise less than predicate, ≤2, and quality are both co-NLOGTIME complete under FDLOGTIME reductions. This is used to show that if the FDLOGTIME functions are definable in D then D = NP. [ABSTRACT FROM AUTHOR]

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

In this paper we consider domain decomposition methods for solving the radial basis function interpolation equations. There are three interwoven threads to the paper. The first thread provides good ways of setting up and solving small- to medium-sized radial basis function interpolation problems. These may occur as subproblems in a domain decomposition solution of a larger interpolation problem. The usual formulation of such a problem can suffer from an unfortunate scale dependence not intrinsic in the problem itself. This scale dependence occurs, for instance, when fitting polyharmonic splines in even dimensions. We present and analyze an alternative formulation, available for all strictly conditionally positive definite basic functions, which does not suffer from this drawback, at least for the very important example previously mentioned. This formulation changes the problem into one involving a strictly positive definite symmetric system, which can be easily and efficiently solved by Cholesky factorization. The second section considers a natural domain decomposition method for the interpolation equations and views it as an instance of von Neumann's alternating projection algorithm. Here the underlying Hilbert space is the reproducing kernel Hilbert space induced by the strictly conditionally positive definite basic function. We show that the domain decomposition method presented converges linearly under very weak nondegeneracy conditions on the possibly overlapping subdomains. The last section presents some algorithmic details and numerical results of a domain decomposition interpolatory code for polyharmonic splines in 2 and 3 dimensions. This code has solved problems with 5 million centers and can fit splines with 10,000 centers in approximately 7 seconds on very modest hardware. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present an algorithm for finding a saddle point to the constrained minimax problem. The initial problem is transformed into an equivalent equality constrained problem, and then the interior point approach is used. To satisfy the original inequality constraints a logarithmic barrier function is used and special care is given to step size parameter to keep the variables within permitted boundaries. Numerical results illustrating the method are given. [ABSTRACT FROM AUTHOR]

The basic diagrams for the lift and drag of a wing and the lift-to-drag ratio are common in texts on aeronautics and how to fly. However, what is not normally given is the use of these diagrams to illustrate other aspects of flying - the speed required to fly straight and level (for each angle of attack of the wing) or the power required at each speed setting. This paper discusses these aspects, and grounds them in reality by using data from the Wright brothers' experiments on gliders. It also approximates the data with simple polynomial expressions, and shows that the main features of the curves derived are not sensitive to this sort of approximation. The paper uses little more than GCSE mathematics, but provides a real-life application of forces, moments and power that may appeal to many students. [ABSTRACT FROM PUBLISHER]

As one of data mining techniques, outlier detection aims to discover outlying observations that deviate substantially from the reminder of the data. Recently, the Local Outlier Factor (LOF) algorithm has been successfully applied to outlier detection. However, due to the computational complexity of the LOF algorithm, its application to large data with high dimension has been limited. The aim of this paper is to propose grid-based algorithm that reduces the computation time required by the LOF algorithm to determine the k-nearest neighbors. The algorithm divides the data spaces in to a smaller number of regions, called as a “grid”, and calculates the LOF value of each grid. To examine the effectiveness of the proposed method, several experiments incorporating different parameters were conducted. The proposed method demonstrated a significant computation time reduction with predictable and acceptable trade-off errors. Then, the proposed methodology was successfully applied to real database transaction logs of Korea Atomic Energy Research Institute. As a result, we show that for a very large dataset, the grid-LOF can be considered as an acceptable approximation for the original LOF. Moreover, it can also be effectively used for real-time outlier detection. [ABSTRACT FROM AUTHOR]

In this paper, we consider the finite-dimensional approximations of Tikhonov regularization for nonlinear ill-posed problems with approximately given right-hand sides. We propose an a posteriori parameter choice strategy, which is a modified form of Morozov's discrepancy principle, to choose the regularization parameter. Under certain assumptions on the nonlinear operator, we obtain the convergence and rates of convergence for Tikhonov regularized solutions. This paper extends the results, which were developed by Plato and Vainikko in 1990 for solving linear ill-posed equations, to nonlinear problems. [ABSTRACT FROM AUTHOR]

Mean-field Boltzmann machine learning is recognized as a practical method to circumvent the difficulty that Boltzmann machine learning is very time-consuming. However, its theoretical meaning is still not clear. In this paper, based on information geometry, we give an information-theoretic interpretation of mean-field Boltzmann machine learning and a clear geometrical explanation of the approximation used there. Based on this interpretation, computer simulations for evaluating the effectiveness of mean-field Boltzmann machine learning are carried out for two-unit Boltzmann machines. The necessity of geometrical analysis in demonstrating the effectiveness of mean-field Boltzmann machine learning is discussed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(8): 30–39, 1999 [ABSTRACT FROM AUTHOR]

In the design of two channel perfect reconstruction filter banks, most of the conventional methods optimize the frequency response of each filter to meet the perfect reconstruction condition. However, quantization of the filter coefficients results in some errors in the frequency response, so it is not guaranteed that the perfect reconstruction condition is still satisfied. In this paper, we present a new method for designing biorthogonal FIR linear phase filter banks with structurally perfect reconstruction. From the perfect reconstruction condition, we first describe a class of structurally perfect reconstruction implementations. Since the proposed filter banks structurally satisfy the perfect reconstruction condition, the design problem becomes the magnitude approximation of the analysis or synthesis filters. Design of these filters can be reduced to the design of half-band filters. We then give a new method to design FIR linear phase half-band filters with arbitrary flatness. Therefore, the proposed filter banks can be designed easily by using the proposed method. Additionally, the magnitude responses of the low- and high-pass filters can be arbitrarily controlled by using two different half-band filters. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 1–8, 1999 [ABSTRACT FROM AUTHOR]

This paper develops an information decision system for new product pricing based on Bayesian updating of prior estimates of demand distribution parameter values and on optimization by dynamic programming. The model considers the interaction of production and pricing decisions and emphasizes the simultaneous making of both decisions. After presentation of the basic model, approximate techniques are introduced which obtain most of the benefit of the approach while requiring only a fraction of the computer cost and input data. Numerical examples using growing demand and price sensitivity are given to demonstrate the high computer cost of the first model and the relative performance (on a profit basis) of the approximate techniques. [ABSTRACT FROM AUTHOR]

When a person is working with large scale Markov Decision Processes, he normally uses the policy iteration approach developed by Howard and modified by White. White's modification makes use of the method of successive approximations. Computational experience has shown that for many processes, the rate of convergence of the successive approximation is very slow. In this paper, techniques for speeding convergence are discussed. Numerical examples and computational experience which show the relative merits of the various approaches are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the link between a certain class of discrete-velocity models (DVMs) and the Boltzmann equation. Those models possess an infinite number of velocities laying on a regular grid of step h in R3. Our aim is to prove that it is possible to construct models consistent with the Boltzmann equation, i.e., such that the discrete collision term can be seen as an approximation of the collision integral of the Boltzmann equation. [ABSTRACT FROM AUTHOR]

The time-series analysis (called indirect method) based on the Perron-Frobenius operator is well known as a theoretical method which can determine the statistics for various chaos in one-dimensional distance dynamical systems without determining the trajectory. However, it is rare that a strict solution for the statistics can be determined explicitly and consequently, the indirect method is not practical at present. To remedy this situation, previously we proposed an indirect method based on Galerkin's approximation to the operator, and verified its usefulness. However, the method was not effective for the intermittent chaos with 1/f power spectrum. This paper extends the indirect method using Galerkin's method by introducing the singular function in the approximation to the unbounded invariant density. As a result, the power spectrum is density. As a result, the power spectrum is obtained which agrees fairly well with the data calculated directly from the trajectory over a wide frequency range. An interesting result was obtained by the recent study wherein the spectrum of the intermittent chaos has the form of 1/fdelta; in the limit of zero frequency, where the exponent δ is related explicitly to the nonlinearity of the one-dimensional discrete dynamical system. However, the forementioned result refers only to the spectrum of the chaos in the limit. By contrast, the proposed method can serve as a practical method to estimate the power spectrum of 1/f noise over a wide range. [ABSTRACT FROM AUTHOR]

In vitro studies have previously found a class of vestibular nuclei neurons to exhibit a bidirectional afterhyperpolarization (AHP) in their membrane potential, due to calcium and calcium-activated potassium conductances. More recently in vivo studies of such vestibular neurons were found to exhibit a boosting nonlinearity in their input-output tuning curves. In this paper, a Hodgkin-Huxley (HH) type neuron model, originally developed to reproduce the in vitro AHP, is shown to produce a boosting nonlinearity similar to that seen in vivo for increased the calcium conductance. Indicative of a bifurcation, the HH model is reduced to a generalized integrate-and-fire (IF) model that preserves the bifurcation structure and boosting nonliearity. By then projecting the neuron model’s phase space trajectories into 2D, the underlying geometric mechanism relating the AHP and boosting nonlinearity is revealed. Further simplifications and approximations are made to derive analytic expressions for the steady steady state firing rate as a function of bias current, μ, as well as the gain (i.e. its slope) and the position of its peak at μ = μ*. Finally, although the boosting nonlinearity has not yet been experimentally observed in vitro, testable predictions indicate how it might be found. [ABSTRACT FROM AUTHOR]

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical computation of null controls for the wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [ Cîndea, Fernández-Cara & Münch, Numerical controllability of the wave equation through primal methods and Carleman estimates, 2013], a so called primal method is described leading to a strongly convergent approximation of boundary controls: the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality condition. In this work, we adapt the method to approximate the control of minimal square-integrable norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and its adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner controllability. For simplicity, we present the approach in the one dimensional case. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance of static solutions for two-stage adjustable robust linear optimization problems with uncertain constraint and objective coefficients and give a tight characterization of the adaptivity gap. Computing an optimal adjustable robust optimization problem is often intractable since it requires to compute a solution for all possible realizations of uncertain parameters (Feige et al. in Lect Notes Comput Sci 4513:439-453, ). On the other hand, a static solution is a single (here and now) solution that is feasible for all possible realizations of the uncertain parameters and can be computed efficiently for most dynamic optimization problems. We show that for a fairly general class of uncertainty sets, a static solution is optimal for the two-stage adjustable robust linear packing problems. This is highly surprising in view of the usual perception about the conservativeness of static solutions. Furthermore, when a static solution is not optimal for the adjustable robust problem, we give a tight approximation bound on the performance of the static solution that is related to a measure of non-convexity of a transformation of the uncertainty set. We also show that our bound is at least as good (and in many case significantly better) as the bound given by the symmetry of the uncertainty set (Bertsimas and Goyal in Math Methods Oper Res 77(3):323-343, ; Bertsimas et al. in Math Oper Res 36(1):24-54, ). [ABSTRACT FROM AUTHOR]