practical aspects of higher order numerical schemes for wave propagation phenomena this paper examines practical issues related to the use of compact difference based fourth and sixth order schemes for wave propagation phenomena with focus on maxwell s equations of electromagnetics an outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches transformed plane method and physical space differencing in the first technique the truncation error expansion for the sixth order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available physical space differencing formulas are derived for the five point stencil by expressing the coefficients in terms of local spacing ratios the order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes to ensure stability for a broad range of problems fourier analysis is employed to develop a single parameter family of up to tenth order tridiagonal based spatial filters the implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1 d cavity where they are employed to suppress a late time instability the paper concludes after demonstrating the application of the scheme to several 3 d canonical problems utilizing cartesian as well as curvilinear meshes published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

compact location problems we consider the problem of placing a specified number p of facilities on the nodes of a network so as to minimize some measure of the distances between facilities this formulation models a number of problems arising in facility location statistical clustering pattern recognition and also a processor allocation problem in multiprocessor systems

broadband time domain impedance models the modeling of a set of impedance values given either experimentally or heuristically for implementation as a time domain impedance equivalent boundary condition tdibc is discussed it is shown that impedance as defined by the reflection of plane harmonic waves when extended for broadband time domain applications can correspond to mathematically feasible but physically unacceptable noncausal reflection processes given a set of impedance data on a finite positive and real frequency range it is possible to construct causal time domain models that render efficient implementation of tdibc for broadband reflections however these models defined by measurement of harmonic waves may not be valid for the reflection of impulses for which measurement of transient reflections is warranted

segmentation problems we study a novel genre of optimization problems which we call segmentation problems motivated in part by certain aspects of clustering and data mining for any classical optimization problem the corresponding segmentation problem seeks to partition a set of cost vectors into several segments so that the overall cost is optimized we focus on two natural and interesting but maxsnp complete problems in this class the hypercube segmentation problem and the catalog segmentation problem and present approximation algorithms for them we also present a general greedy scheme which can be specialized to approximate any segmentation problem

computing maximally separated sets in the plane let s be a set of n points in reals 2 given an integer 1 le k le n we wish to find a maximally separated subset i subseteq s of size k this is a subset for which the minimum among the k choose 2 pairwise distances between its points is as large as possible the decision problem associated with this problem is to determine whether there exists i subseteq s i k so that all k choose 2 pairwise distances in i are at least 2 this problem can also be formulated in terms of disk intersection graphs let d be the set of unit disks centered at the points of s the disk intersection graph g of d has as edges all pairs of disks with nonempty intersection any set i with the above properties is then the set of centers of disks that form an independent set in the graph g this problem is known to be np complete if k is part of the input in this paper we first present a linear time eps approximation algorithm for any constant k next we give exact algorithms for the cases k 3 and k 4 that run in time o n 4 3 polylog n we also present a simpler n o sqrt k time exact algorithm as compared with the recent algorithm in j alber and j fiala j algorithms 52 2004 pp 134 151 for arbitrary values of k

covering moving points with anchored disks consider a set of mobile clients represented by n points in the plane moving at constant speed along n different straight lines we study the problem of covering all mobile clients using a set of k disks centered at k fixed centers each disk exists only at one instant and while it does covers any client within its coverage radius the task is to select an activation time and a radius for each disk such that every mobile client is covered by at least one disk in particular we study the optimization problem of minimizing the maximum coverage radius first we prove that although the static version of the problem is polynomial the kinetic version is np hard moreover we show that the problem is not approximable by a constant factor unless p np we then present a generic framework to solve it for fixed values of k which in turn allows us to solve more general optimization problems our algorithms are efficient for constant values of k

ectropy of diversity measures for populations in euclidean space measures to evaluate the diversity of a set of points population in euclidean space play an important role in a variety of areas of science and engineering well known measures are often used without a clear insight into their quality and many of them do not appropriately penalize populations with a few distant groups of collocated or closely located points to the best of our knowledge there is a lack of rigorous criteria to compare diversity measures and help select an appropriate one in this work we define a mathematical notion of ectropy for classifying diversity measures in terms of the extent to which they tend to penalize point collocation we investigate the advantages and disadvantages of several known measures and we propose some novel ones that exhibit a good ectropic behavior in particular we introduce a quasi entropy measure based on a geometric covering problem three measures based on discrepancy from uniform distribution and one based on euclidean minimum spanning trees all considered measures are tested and compared on a large set of random and structured populations special attention is also devoted to the complexity of computing the measures most of the novel measures compare favorably with the classical ones in terms of ectropy the measure based on euclidean minimum spanning trees turns out to be the most promising one in terms of the tradeoff between the ectropic behavior and the computational complexity

improved combinatorial algorithms for facility location problems we present improved combinatorial approximation algorithms for the uncapacitated facility location problem two central ideas in most of our results are cost scaling and greedy improvement we present a simple greedy local search algorithm which achieves an approximation ratio of 2 414 epsilon in tilde o n 2 epsilon time this also yields a bicriteria approximation tradeoff of 1 gamma 1 2 gamma for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to jain and vazirani we get an approximation ratio of 1 853 in tilde o n 3 time this is very close to the approximation guarantee of the best known algorithm which is linear programming lp based further combined with the best known lp based algorithm for facility location we get a very slight improvement in the approximation factor for facility location achieving 1 728 we also consider a variant of the capacitated facility location problem and present improved approximation algorithms for this

on min max r gatherings we consider a min max version of the previously studied r gathering problem with unit demands the problem we consider is a metric facility location problem in which each open facility must serve at least r customers and the maximum of all the facility and connection costs should be minimized rather than their sum this problem is motivated by scenarios in which r customers are required for a facility to be worth opening and the costs represent the time until the facility connection will be available i e we want to have the complete solution ready as soon as possible we present a 3 approximation algorithm for this problem and prove that it cannot be approximated better assuming p np next we consider this problem with the additional natural requirement that each customer will be assigned to a nearest open facility and present a 9 approximation algorithm we further consider previously introduced special cases and variants and obtain improved algorithmic and hardness results

fcm based model selection algorithms for determining the number of clusters clustering is an important research topic that has practical applications in many fields it has been demonstrated that fuzzy clustering using algorithms such as the fuzzy c means fcm has clear advantages over crisp and probabilistic clustering methods like most clustering algorithms however fcm and its derivatives need the number of clusters in the given data set as one of their initializing parameters the main goal of this paper is to develop an effective fuzzy algorithm for automatically determining the number of clusters after a brief review of the relevant literature we present a new algorithm for determining the number of clusters in a given data set and a new validity index for measuring the goodness of clustering experimental results and comparisons are given to illustrate the performance of the new algorithm

parameterized approximation algorithms for some location problems in graphs we develop efficient parameterized with additive error approximation algorithms for the connected r domination problem and the connected p center problem for unweighted and undirected graphs given a graph g we show how to construct a connected big r mathcal o mu big dominating set d with d le d efficiently here d is a minimum connected r dominating set of g and mu is our graph parameter which is the tree breadth or the cluster diameter in a layering partition of g additionally we show that a mathcal o mu approximation for the connected p center problem on g can be computed in polynomial time our interest in these parameters stems from the fact that in many real world networks including internet application networks web networks collaboration networks social networks biological networks and others and in many structured classes of graphs these parameters are small constants

online unit covering in euclidean space abstract we revisit the online unit covering problem in higher dimensions given a set of n points in r d that arrive one by one cover the points by balls of unit radius so as to minimize the number of balls used in this paper we work in r d using the euclidean distance i we give an online deterministic algorithm with competitive ratio o 1 321 d thereby improving on the previous record o 2 d d log d due to charikar et al 2004 by an exponential factor in particular the competitive ratios are 5 in the plane and 12 in 3 space the previous ratios were 7 and 21 respectively for d 3 the ratio of our online algorithm matches the ratio of the current best offline algorithm for the same problem due to biniaz et al 2017 which is remarkable and rather unusual ii we show that the competitive ratio of every deterministic online algorithm for unit covering in r d under the l 2 norm is at least d 1 for every d 1 this greatly improves upon the previous best lower bound log d log log log d due to charikar et al 2004 iii we generalize the above result to unit covering in r d under the l c norm where c is a centrally symmetric convex body via the illumination number iv we obtain lower bounds of 4 and 5 for the competitive ratio of any deterministic algorithm for online unit covering in r 2 and r 3 respectively the previous best lower bounds were 3 for both cases v when the input points are from the square or hexagonal lattice in r 2 we give deterministic online algorithms for unit covering with an optimal competitive ratio of 3 for the cubic lattice in r 3 we give a deterministic online algorithm with a competitive ratio of 5

kinetic clustering of points on the line the problem of clustering a set of points moving on the line consists of the following given positive integers n and k the initial position and the velocity of n points find an optimal k clustering of the points we consider two classical quality measures for the clustering minimizing the sum of the clusters diameters and minimizing the maximum diameter of a cluster for the former we present polynomial time algorithms under some assumptions and for the latter a 2 71 e approximation

finite difference solution to the parabolic wave equation in this article an implicit finite difference ifd scheme is introduced for solving underwater acoustic wave propagation problems this scheme is applied to the parabolic wave equation model for the acoustic problem with a free surface and arbitrary bottom and bottom boundary conditions the mathematical theory of the implicit finite difference method as applied to the parabolic equation is developed and a computer model to implement the ifd is introduced representative problems are presented to demonstrate the capability of the ifd model advantages and limitations of the ifd are discussed

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

nonlinear dimensionality reduction by locally linear inlaying high dimensional data is involved in many fields of information processing however sometimes the intrinsic structures of these data can be described by a few degrees of freedom to discover these degrees of freedom or the low dimensional nonlinear manifold underlying a high dimensional space many manifold learning algorithms have been proposed here we describe a novel algorithm locally linear inlaying lli which combines simple geometric intuitions and rigorously established optimality to compute the global embedding of a nonlinear manifold using a divide and conquer strategy lli gains some advantages in itself first its time complexity is linear in the number of data points and hence lli can be implemented efficiently second lli overcomes problems caused by the nonuniform sample distribution third unlike existing algorithms such as isometric feature mapping isomap local tangent space alignment ltsa and locally linear coordination llc lli is robust to noise in addition to evaluate the embedding results quantitatively two criteria based on information theory and kolmogorov complexity theory respectively are proposed furthermore we demonstrated the efficiency and effectiveness of our proposal by synthetic and real world data sets

a compact difference scheme for the navier stokes equations in vorticity velocity formulation this paper presents a new numerical method for solving the incompressible unsteady navier stokes equations in vorticity velocity formulation the method is applicable to spatial simulations of transitional and turbulent boundary layer flows it is based on a compact difference discretization of the streamwise and wall normal derivatives in cartesian coordinates a fourier collocation approach is used for the spanwise derivatives important new features of the numerical method are the use of nonequidistant differences in the wall normal direction the use of split compact differences in the streamwise direction a new fast iteration for a semi implicit time integration of the wall normal diffusion terms and an improvement of the buffer domain technique to prevent reflections of waves at the outflow boundary results of test calculations are presented to verify the improvements obtained by the use of these new techniques

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

an approach to multiple attribute decision making based on fuzzy preference information on alternatives this paper investigates the multiple attribute decision making madm problem with preference information on alternatives a new approach is proposed to solve the madm problem where the decision maker gives his her preference on alternatives in a fuzzy relation to reflect the decision maker s preference information an optimization model is constructed to assess the attribute weights and then to select the most desirable alternatives finally an example is used to illustrate the proposed approach

basic renewal theorems for random walks with widely dependent increments abstract in this paper we derive some basic renewal theorems for random walks with widely dependent increments which contain some common negatively dependent random variables r v s some positively dependent r v s and some others for this purpose we investigate uniform integrability for related counting processes and the strong law of large numbers for the widely dependent r v s

a probabilistic analysis of em for mixtures of separated spherical gaussians we show that given data from a mixture of k well separated spherical gaussians in d a simple two round variant of em will with high probability learn the parameters of the gaussians to near optimal precision if the dimension is high d ln k we relate this to previous theoretical and empirical work on the em algorithm

a nearly linear time approximation scheme for the euclidean k median problem this paper provides a randomized approximation scheme for the k median problem when the input points lie in the d dimensional euclidean space the worst case running time is o 2 o log 1 epsilon varepsilon d 1 n log d 6 n which is nearly linear for any fixed varepsilon and d moreover our method provides the first polynomial time approximation scheme for and uncapacitated facility location instances in d dimensional euclidean space for any fixed d 2 our work extends techniques introduced originally by arora for the euclidean traveling salesman problem tsp to obtain the improvement we develop a structure theorem to describe hierarchical decomposition of solutions the theorem is based on an adaptive decomposition scheme which guesses at every level of the hierarchy the structure of the optimal solution and accordingly modifies the parameters of the decomposition we believe that our methodology is of independent interest and may find applications to further geometric problems

generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites abstract the linguistic term set is an applicable and flexible technique in qualitative decision making qdm to further develop the linguistic term set this paper proposes a generalized asymmetric linguistic term set galts based on the asymmetric sigmoid semantics which belongs to an asymmetric and non uniform linguistic term set and can be used to address the qdm problems involving risk appetites of the decision maker dm then a value at risk fitting varf approach is designed for obtaining the risk appetite parameters of the galts and six desirable properties of the galts are analyzed i e asymmetry non uniformity generality variability range consistency and diminishing utility based on the above approaches and the generalized asymmetric linguistic preference relations galprs a qdm process involving risk appetites of the dm is designed because the galprs consist of subjective information provided by the dm the process is not perfectly consistent and is usually difficult to change or repeat thus a transitivity improvement approach is investigated and the corresponding calculation steps are provided finally an example dealing with the problem of investment decision making is provided and the results fully demonstrate the validity of the proposed methods for qdm involving risk appetites

spectral generalized multi dimensional scaling multidimensional scaling mds is a family of methods that embed a given set of points into a simple usually flat domain the points are assumed to be sampled from some metric space and the mapping attempts to preserve the distances between each pair of points in the set distances in the target space can be computed analytically in this setting generalized mds is an extension that allows mapping one metric space into another that is mds into target spaces in which distances are evaluated numerically rather than analytically here we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition where the surfaces are treated as sampled metric spaces the resulting spectral gmds procedure enables efficient embedding by incorporating smoothness of the metric structure into the problem thereby substantially reducing the complexity involved in its solution while practically overcoming its non convex nature the method is compared to existing techniques that compute dense correspondence between shapes numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state of the art approaches especially when isometry invariance is a dominant property

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

fast euler solver for transonic airfoils i theory ii applications equations written in terms of generalized riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices using an implicit euler solver that is based on the lambda formulation the solution is found on a c grid whose boundaries are very close to the airfoil the fast solver is then applied to the computation of several flowfields on a naca 0012 airfoil at various mach number and alpha values yielding results that are primarily concerned with transonic flows the effects of grid fineness and boundary distances are analyzed the code is found to be robust and accurate as well as fast

an indication of unification for different clustering approaches the question of finding generic concepts and properties common to the different clustering approaches is a current problem this inquire is addressed most thoroughly in kleinberg s paper on the impossibility theorem see 1 kleinberg introduced the notion of clustering function a function that takes a dissimilarity measure defined on a data set s and returns a partition of s and a set of simple properties for the study of such functions scale invariance richness and consistency the main result of 1 is the impossibility theorem there is no clustering method satisfying all these properties this study has been accepted as a rigorous proof of the difficulty in finding a unified framework for different clustering approaches our goal in this paper is to provide primary concepts and results for the formal study of the various clustering approaches to accomplish this we discuss and expand on the ideas introduced by kleinberg our guiding philosophy is to incorporate a crucial fact overlooked in the study conducted in 1 clustering methods not only depend on the dissimilarity measure but also on other parameters such as dissimilarity thresholds centroids stop criteria among others this paper gives a formal definition of clustering method and reformulates the afore mentioned properties even it introduces some new contrary to the result obtained in 1 many of the methods discussed here satisfy all of our properties with all these grounds in hand we glimpse a clue of unification among the different clustering approaches

topology invariant similarity of nonrigid shapes this paper explores the problem of similarity criteria between nonrigid shapes broadly speaking such criteria are divided into intrinsic and extrinsic the first referring to the metric structure of the object and the latter to how it is laid out in the euclidean space both criteria have their advantages and disadvantages extrinsic similarity is sensitive to nonrigid deformations while intrinsic similarity is sensitive to topological noise in this paper we approach the problem from the perspective of metric geometry we show that by unifying the extrinsic and intrinsic similarity criteria it is possible to obtain a stronger topology invariant similarity suitable for comparing deformed shapes with different topology we construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set valued distance numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail

a bad instance for k means k means is a seeding technique for the k means method with an expected approximation ratio of o logk where k denotes the number of clusters examples are known on which the expected approximation ratio of k means is w logk showing that the upper bound is asymptotically tight however it remained open whether k means yields a constant approximation with probability 1 poly k or even with constant probability we settle this question and present instances on which k means achieves an approximation ratio no better than 2 email protected logk with probability exponentially close to 1

nonlinear dimensionality reduction by topologically constrained isometric embedding many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space the embedding process usually relies on distances between neighboring features mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non convexity distortions resulting from using long geodesics indiscriminately lead to a known limitation of the isomap algorithm when used to map non convex manifolds presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries the resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold thus avoiding an inherent limitation of the isomap algorithm since the proposed algorithm matches non local structures it is robust to strong noise we show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques both global and local in nature

ecmdd evidential c medoids clustering with multiple prototypes in this work a new prototype based clustering method named evidential c medoids ecmdd which belongs to the family of medoid based clustering for proximity data is proposed as an extension of fuzzy c medoids fcmdd on the theoretical framework of belief functions in the application of fcmdd and original ecmdd a single medoid prototype which is supposed to belong to the object set is utilized to represent one class for the sake of clarity this kind of ecmdd using a single medoid is denoted by secmdd in real clustering applications using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance in order to address this problem a variation of ecmdd using multiple weighted medoids denoted by wecmdd is presented unlike secmdd in wecmdd objects in each cluster carry various weights describing their degree of representativeness for that class this mechanism enables each class to be represented by more than one object experimental results in synthetic and real data sets clearly demonstrate the superiority of secmdd and wecmdd moreover the clustering results by wecmdd can provide richer information for the inner structure of the detected classes with the help of prototype weights

the consistency of the nearest neighbor estimator of the density function based on wod samples abstract in this paper the consistency of the nearest neighbor estimator of the density function based on widely orthant dependent wod in short samples is investigated the convergence rate of strong consistency the complete consistency the uniformly complete consistency and uniformly strong consistency of the nearest neighbor estimator of the density function based on wod samples are established our results established in the paper generalize or improve the corresponding ones for independent samples and some negatively dependent samples

approximating uniform triangular meshes in polygons we consider the problem of triangulating a convex polygon using n steiner points under the following optimality criteria 1 minimizing the overall edge length ratio 2 minimizing the maximum edge length and 3 minimizing the maximum triangle perimeter we establish a relation of these problems to a certain extreme packing problem based on this relationship we develop a heuristic producing constant approximations for all the optimality criteria above provided n is chosen sufficiently large that is the produced triangular mesh is uniform in these respects the method is easy to implement and runs in o n2log n time and o n space the observed runtime is much less moreover for criterion 1 the method works within the same complexity and approximation bounds for arbitrary polygons with possible holes and for criteria 2 and 3 it does so for a large subclass

active clustering of biological sequences given a point set s and an unknown metric d on s we study the problem of efficiently partitioning s into k clusters while querying few distances between the points in our model we assume that we have access to one versus all queries that given a point s s return the distances between s and all other points we show that given a natural assumption about the structure of the instance we can efficiently find an accurate clustering using only o k distance queries our algorithm uses an active selection strategy to choose a small set of points that we call landmarks and considers only the distances between landmarks and other points to produce a clustering we use our procedure to cluster proteins by sequence similarity this setting nicely fits our model because we can use a fast sequence database search program to query a sequence against an entire data set we conduct an empirical study that shows that even though we query a small fraction of the distances between the points we produce clusterings that are close to a desired clustering given by manual classification

constrained clustering by constraint programming cluster analysis is an important task in data mining with hundreds of different approaches in the literature since the last decade the cluster analysis has been extended to constrained clustering also called semi supervised clustering so as to integrate previous knowledge on data to clustering algorithms in this dissertation we explore constraint programming cp for solving the task of constrained clustering the main principles in cp are 1 users specify declaratively the problem in a constraint satisfaction problem 2 solvers search for solutions by constraint propagation and search relying on cp has two main advantages the declarativity which enables to easily add new constraints and the ability to find an optimal solution satisfying all the constraints when there exists one we propose two models based on cp to address constrained clustering tasks the models are flexible and general and supports instance level constraints and different cluster level constraints it also allows the users to choose among different optimization criteria in order to improve the efficiency different aspects have been studied in the dissertation experiments on various classical datasets show that our models are competitive with other exact approaches we show that our models can easily be embedded in a more general process and we illustrate this on the problem of finding the pareto front of a bi criterion optimization process

clustering to minimize the maximum intercluster distance the problem of clustering a set of points so as to minimize the maximum intercluster distance is studied an o kn approximation algorithm where n is the number of points and k is the number of clusters that guarantees solutions with an objective function value within two times the optimal solution value is presented this approximation algorithm succeeds as long as the set of points satisfies the triangular inequality we also show that our approximation algorithm is best possible with respect to the approximation bound if pz np

a context quantization approach to universal denoising we revisit the problem of denoising a discrete time continuous amplitude signal corrupted by a known memoryless channel by modifying our earlier approach to the problem we obtain a scheme that is much more tractable than the original one and at the same time retains the universal optimality properties the universality refers to the fact that the proposed denoiser asymptotically with increasing block length of the data achieves the performance of an optimum denoiser that has full knowledge of the distribution of a source generating the underlying clean sequence the only restriction being that the distribution is stationary the optimality in a sense we will make precise of the denoiser also holds in the case where the underlying clean sequence is unknown and deterministic and the only source of randomness is in the noise the schemes involve a simple preprocessing step of quantizing the noisy symbols to generate quantized contexts the quantized context value corresponding to each sequence component is then used to partition the unquantized symbols into subsequences a universal symbol by symbol denoiser for unquantized sequences is then separately employed on each of the subsequences we identify a rate at which the context length and quantization resolution should be increased so that the resulting scheme is universal the proposed family of schemes is computationally attractive with an upper bound on complexity which is independent of the context length and the quantization resolution initial experimentation seems to indicate that these schemes are not only superior from a computational viewpoint but also achieve better denoising in practice

asymmetric k center is log n hard to approximate in the asymmetric k center problem the input is an integer k and a complete digraph over n points together with a distance function obeying the directed triangle inequality the goal is to choose a set of k points to serve as centers and to assign all the points to the centers so that the maximum distance of any point from its center is as small as possible we show that the asymmetric k center problem is hard to approximate up to a factor of log n o 1 unless np dtime nlog log n since an o log n approximation algorithm is known for this problem this resolves the asymptotic approximability of asymmetric k center this is the first natural problem whose approximability threshold does not polynomially relate to the known approximation classes we also resolve the approximability threshold of the metric symmetric k center problem with costs

uniform asymptotics of the finite time ruin probability for all times abstract in this paper we study the asymptotics of the finite time ruin probability for a generalized renewal risk model with independent strong subexponential claim sizes and widely lower orthant dependent inter occurrence times this widely lower orthant dependence structure can include some common negative dependent random variables r v s such as negatively lower orthant dependent r v s some positive dependent r v s and some other dependent r v s for this generalized renewal risk model we show that the asymptotics of the finite time ruin probability hold uniformly for all times in the sense that the magnitude of the initial reserve of some insurance portfolio does not influence the length of the operating time further the uniform asymptotics of the random time ruin probability in the above model have been obtained

spectral representation and reduced order modeling of the dynamics of stochastic reaction networks via adaptive data partitioning dynamical analysis tools are well established for deterministic models however for many biochemical phenomena in cells the molecule count is low leading to stochastic behavior that causes deterministic macroscale reaction models to fail the main mathematical framework representing these phenomena is based on jump markov processes that model the underlying stochastic reaction network conventional dynamical analysis tools do not readily generalize to the stochastic setting due to nondifferentiability and absence of explicit state evolution equations we developed a reduced order methodology for dynamical analysis that relies on the karhunen loeve decomposition and polynomial chaos expansions the methodology relies on adaptive data partitioning to obtain an accurate representation of the stochastic process especially in the case of multimodal behavior as a result a mixture model is obtained that represents the reduced order dynamics of the system the schlogl model is used as a prototype bistable process that exhibits time scale separation and leads to multimodality in the reduced order model

large group decision making incorporating decision risk and risk attitude a statistical approach abstract in this study we propose a statistical method incorporating decision risk and risk attitude into large group decision making the decision making groups are divided into subgroups based on their attitudes to risk and the evaluation information for the decision makers within the same subgroup is combined to form the sample dataset next the internal decision risk levels of all subgroups are measured using sample standard deviations and reduced through a feedback mechanism significance testing is used to determine the criterion weights and to measure the external decision risk levels of subgroups the internal and external decision risk levels are then combined to yield the subgroup weights confidence interval is used to transform the sample data into interval numbers which are then aggregated and analyzed to yield the decision making results meanwhile risk attitudes are taken into account throughout the decision making process by various means a case study and comparison analyses along with sensitivity analyses are used to illustrate the feasibility and rationality of the proposed method our experiments suggest that decision risk and risk attitude matter in large group decision making

low dispersion finite difference methods for acoustic waves in a pipe a new algorithm for computing one dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial boundary value problem conventional dissipation free second order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength using the signal generated by a piston in a duct as an example transient acoustic computations are presented using a new compact three point algorithm which allows about 60 fewer mesh points per wave length both pulse and harmonic excitation are considered coupling of the acoustic signal with the pipe resonant modes are shown to generate a complex transient wave with rich harmonic content

generalized p center problems complexity results and approximation algorithms abstract in an earlier paper two alternative p center problems where the centers serving costumers must be chosen so that exactly one node from each of p prespecified disjoint pairs of nodes is selected were shown to be np complete this paper considers a generalized version of these problems in which the nodes from which the p servers are to be selected are partitioned into k sets and the number of servers selected from each set must be within a prespecified range we refer to these problems as the set p center problems we establish that the triangle inequality inequality versions of these problems in which the edge weights are assumed to satisfy the triangle inequality are also np complete we also provide a polynomial time approximation algorithm for the two inequality set p center problems that is optimal for one of the problems in the sense that no algorithm with polynomial running time can provide a better constant factor performance guarantee unless p np for the special case alternative p center problems which we refer to as the pair p center problems we extend the previous results in several ways for example the results mentioned above for the set p center problems also apply to the pair p center problems furthermore we establish and exploit a correspondence between satisfiability and the dominating set type of problems that naturally arise when considering the decision versions of the pair p center problems

fault tolerant k center problems the basic k center problem is a fundamental facility location problem where we are asked to locate k facilities in a graph and to assign vertices to facilities so as to minimize the maximum distance from a vertex to the facility to which it is assigned this problem is known to be np hard and several optimal approximation algorithms that achieve an approximation factor of 2 have been developed for it we focus our attention on a generalization of this problem where each vertex is required to have a set of k centers close to it in particular we study two different versions of this problem in the first version each vertex is required to have at least centers close to it in the second version each vertex that does not have a center placed on it is required to have at least centers close to it for both these versions we are able to provide polynomial time approximation algorithms that achieve constant approximation factors for any for the first version we give an algorithm that achieves an approximation factor of 3 for any and achieves an approximation factor of 2 for 4 for the second version we provide algorithms with approximation factors of 2 for any the best possible approximation factor for even the basic k center problem is 2 assuming p np in addition we give a polynomial time approximation algorithm for a generalization of the k supplier problem where a subset of at most k supplier nodes must be selected as centers so that every demand node has at least centers close to it for this version our approximation factor is 3 the best possible approximation factor for even the basic k supplier problem is 3 assuming p np

implicit high order compact algorithm for computational acoustics accurate solution of the linearized multidimensional euler equations for aeroacoustics as a system of simple wave equations is demonstrated if organized this system has unambiguous easily implemented boundary conditions allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions thus the task of designing a complex multidimensional scheme with approximate boundary conditions reduces to the design of accurate schemes for the simple wave equation in particular an implicit compact finite difference scheme and a characteristically exact but numerically nth order accurate boundary condition are used this low dispersion scheme has a third order spatial accuracy for various types of nonuniform meshes fourth order accuracy on uniform meshes and by choice a temporal accuracy of second order for algorithmic simplicity as the crank nicolson scheme the robustness and accuracy of the scheme and the validity of the system decoupling are demonstrated through a series of numerical experiments and comparisons with published results including the recent institute for computer applications in science and engineering nasa langley research center benchmark problems of acoustic and convective wave propagation in cartesian and cylindrical domains and reflection at stationary and or moving boundaries

hybrid manifold embedding in this brief we present a novel supervised manifold learning framework dubbed hybrid manifold embedding hyme unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions the hyme aims to provide a more general nonlinear explicit mapping function by performing a two layer learning procedure in the first layer a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity in the second layer a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low dimensional space by integrating these two layers in a unified mapping function a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace experiments on various data sets validate the effectiveness of the proposed method

a general framework of hierarchical clustering and its applications hierarchical clustering problem is a traditional topic in computer science which aims to discover a consistent hierarchy of clusters with different granularities one of the most important open questions on hierarchical clustering is the identification of the meaningful clustering levels in the hierarchical structure in this paper we answer this question from algorithmic point of view in particular we derive a quantitative analysis on the impact of the low level clustering costs on high level clusters when agglomerative algorithms are run to construct the hierarchy this analysis enables us to find meaningful clustering levels which are independent of the clusters hierarchically beneath it we thus propose a general agglomerative hierarchical clustering framework which automatically constructs meaningful clustering levels this framework is proven to be generally applicable to any k clustering problem in any relaxed metric space in which strict triangle inequality is relaxed within some constant factor to fully utilize the hierarchical clustering framework we conduct some case studies on k median and k means clustering problems in both of which our framework achieves better approximation factor than the state of the art methods we also extend our framework to handle the data stream clustering problem which allows only one scan on the whole data set by incorporating our framework into guha s data stream clustering algorithm the clustering quality is greatly enhanced with only small extra computation cost incurred the extensive experiments show that our proposal is superior to the distance based agglomerative hierarchical clustering and data stream clustering algorithms on a variety of data sets

impedance and its time domain extensions the classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex valued quantity akin to plane harmonic waves and the analysis of their ree ections a new look at this classical quantity irrespective of the type of incident waves is presented it points out that a direct operational inversion of impedance into time domain boundary operators will in general lead to an unstable system whereas the inversion of the corresponding ree ection coefe cient will result in stable easily implementable boundary operators for time domain prediction of wave ree ection it reveals the equivalent pulselike causal process of time convoluting the incident wave into the ree ected wave excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations

optimization on lie manifolds and pattern recognition several pattern recognition problems can be reduced in a natural way to the problem of optimizing a nonlinear function over a lie manifold however optimization on lie manifolds involves in general a large number of nonlinear equality constraints and is hence one of the hardest optimization problems we show that exploiting the special structure of lie manifolds allows one to devise a method for optimizing on lie manifolds in a computationally efficient manner the new method relies on the differential geometry of lie manifolds and the underlying connections between lie groups and their associated lie algebras we describe an application of the new lie group method to the problem of diagnosing malignancy in the cytological extracts of breast tumors the diagnosis method that we present has a mean sensitivity of 98 086 and a predictive index of 0 0602 making it the most accurate and reliable diagnostic method reported thus far

asymmetric fuzzy preference relations based on the generalized sigmoid scale and their application in decision making involving risk appetites numerical preference relations constitute a useful decision making technique and can be classified into two types on the basis of the 0 1 0 9 and 1 9 scales however these numerical scales cannot fully describe some desired properties such as asymmetry consistency variability and diminishing utility in accordance with the preference relations to address this issue we first develop a generalized sigmoid function and define a continuous preference set on the basis of which we propose the generalized sigmoid scale then we introduce the optimal discrete fitting and risk preference selection approaches to solve the risk appetite parameters in the generalized sigmoid scale using these new methods we further propose the asymmetric fuzzy preference relation afpr examine its additive transitivity property and some weak transitivity properties and design an approximate consistency test the corresponding five step modeling process under an asymmetric fuzzy preference environment is constructed which can be applied in decision making involving different risk appetites finally two examples are used to demonstrate the properties and advantages of these new methods the first example is simple and shows the differences between the traditional fuzzy preference relations and the afprs while the second is a practical case and is used to illustrate the feasibility and reasonability of the afprs

a potential theoretic method for far field sound radiation calculations abstract the far field acoustic radiation due to the interaction of upstream unsteady vortical disturbances with an airfoil in subsonic compressible flow is calculated using potential theory a kirchhoff surface is placed in the near field surrounding the airfoil and the pressure on this surface is calculated from the unsteady flow field obtained using a second order finite difference code the governing equation is reduced to the helmholtz equation in the frequency domain and the solution is written in terms of an integral over the kirchhoff surface involving the free space green s function and an unknown single layer density function the single layer density is then determined from the boundary condition on the kirchhoff surface this method is presented as an alternative to classical kirchhoff methods it has the advantage of being able to accommodate arbitrarily shaped kirchhoff surfaces and is also readily extendable to three dimensional problems numerical results are presented for thin symmetric and loaded airfoils thin airfoil results are compared to the analytical solution and thick airfoil results are checked for numerical convergence and compared to results obtained from a time domain euler solver

a nonparametric statistical approach to clustering via mode identification a new clustering approach based on mode identification is developed by applying new optimization techniques to a nonparametric density estimator a cluster is formed by those sample points that ascend to the same local maximum mode of the density function the path from a point to its associated mode is efficiently solved by an em style algorithm namely the modal em mem this method is then extended for hierarchical clustering by recursively locating modes of kernel density estimators with increasing bandwidths without model fitting the mode based clustering yields a density description for every cluster a major advantage of mixture model based clustering moreover it ensures that every cluster corresponds to a bump of the density the issue of diagnosing clustering results is also investigated specifically a pairwise separability measure for clusters is defined using the ridgeline between the density bumps of two clusters the ridgeline is solved for by the ridgeline em rem algorithm an extension of mem based upon this new measure a cluster merging procedure is created to enforce strong separation experiments on simulated and real data demonstrate that the mode based clustering approach tends to combine the strengths of linkage and mixture model based clustering in addition the approach is robust in high dimensions and when clusters deviate substantially from gaussian distributions both of these cases pose difficulty for parametric mixture modeling a c package on the new algorithms is developed for public access at http www stat psu edu jiali hmac

spectral multidimensional scaling an important tool in information analysis is dimensionality reduction there are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks the efficiency of dimension reduction tools is measured in terms of memory and computational complexity which are usually a function of the number of the given data points sparse local operators that involve substantially less than quadratic complexity at one end and faithful multiscale models with quadratic cost at the other end make the design of dimension reduction procedure a delicate balance between modeling accuracy and efficiency here we combine the benefits of both and propose a low dimensional multiscale modeling of the data at a modest computational cost the idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its laplace beltrami operator there embedding into a small dimensional euclidean space is accomplished while optimizing for a small number of coefficients we provide a theoretical support and demonstrate that working in the natural eigenspace of the data one could reduce the process complexity while maintaining the model fidelity as examples we efficiently canonize nonrigid shapes by embedding their intrinsic metric into a method often used for matching and classifying almost isometric articulated objects finally we demonstrate the method by exposing the style in which handwritten digits appear in a large collection of images we also visualize clustering of digits by treating images as feature points that we map to a plane

a framework for evaluating approximation methods for gaussian process regression gaussian process gp predictors are an important component of many bayesian approaches to machine learning however even a straightforward implementation of gaussian process regression gpr requires o n2 space and o n3 time for a data set of n examples several approximation methods have been proposed but there is a lack of understanding of the relative merits of the different approximations and in what situations they are most useful we recommend assessing the quality of the predictions obtained as a function of the compute time taken and comparing to standard baselines e g subset of data and fitc we empirically investigate four different approximation algorithms on four different prediction problems and make our code available to encourage future comparisons

a time domain method for duct acoustics this paper reports the development of a time accurate method for prediction of acoustics in lined ducts the multi dimensional euler equations are dimensionally split into a system of uni directional simple wave equations which are discretized and solved using an implicit compact high order finite difference scheme the split equations are closed and coupled through the concept of impedance at domain boundaries time domain extensions of the impedance boundary condition and their efficient implementation are introduced for broadband and monotone waves the method is benchmarked by the modal solution of a monopole in the lined duct and used to investigate wall interference on the acoustic fields of realistic sources excellent agreement is found in the comparison with classical solutions and the discrepancy found in the comparison with experiment is ascribable to experimental uncertainty