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In this paper, by means of the null set defined by Wu (J Math Anal Appl. 2019;472:1741–1761), we introduce a set-valued equilibrium problem based on the null set, where the objective mapping takes values in a hyperspace equipped with a convex cone. Moreover, we obtain new existence results for set-valued equilibrium problems defined on compact or noncompact sets. Some applications are given to set optimization problems, to a set-valued variational inequality, to saddle point theorems for set-valued mappings, and to a generalized noncooperative game [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship of the metric mean dimension between a topological dynamical system (X , T , d) and the induced hyperspace topological dynamical system (2 X , 2 T , d H). Specially, for the topological dynamical system with metric mean dimension is zero, we give three different examples to show that the metric mean dimension of hyperspace dynamical system is zero, finite positive number and infinity, respectively. [ABSTRACT FROM AUTHOR]

First reported in the early 2000s, a new generation of metals called 'high-entropy alloys' (HEAs) have the potential to outperform conventional alloys that rely on a primary base metal. The plethora of five or more metallic elements when alloyed in equiatomic or near equiatomic creates a vast HEA material hyperspace that can lead to exceptional technical properties. This paper provides insights into HEAdevelopment in Australia; in particular, the additive manufacturing of HEA deposits through thermal spray and laser-based methods. [ABSTRACT FROM AUTHOR]

We study stronger forms of sensitivity on the arbitrary product of semiflows on Hausdorff uniform spaces. Moreover, Devaney chaos, Poincaré chaos, and their related properties are studied on product semiflows. Furthermore, we study relations between the chaos-related properties of a semiflow and that of its induced hyperspatial semiflow. Some results regarding stronger forms of sensitivity are also obtained on hyperspatial semiflows. [ABSTRACT FROM AUTHOR]

A multi-objective algorithm is always favoured over a single objective algorithm as it considers different aspects of a dataset in the form of various objectives. In this article, a multi-objective clustering algorithm has been proposed based on Differential Evolution. Here, three objectives have been considered to handle different complex datasets. In addition to this, a kernel function is hybridised with the objectives to evaluate the data on a hyperspace for reducing the impact of nonlinearity on cluster formation. Moreover, to get the best compromised solution from the Pareto front an effective fuzzy concept has been followed. Five metaheuristic approaches have been taken into consideration for performance comparison. These methodologies have been applied to twelve datasets and the result reveals the efficacy of the proposed model in data clustering. [ABSTRACT FROM AUTHOR]

In this article we introduce a stability concept for the coercivity of multivariate polynomials . In particular, we consider perturbations of f by polynomials up to the so-called degree of stable coercivity, and we analyze this stability concept in terms of the corresponding Newton polytopes at infinity. For coercive polynomials we also introduce the order of coercivity as a measure expressing the order of growth of f, and we identify a broad class of multivariate polynomials for which the order of coercivity and the degree of stable coercivity coincide. For these polynomials we give a geometric interpretation of this phenomenon in terms of their Newton polytopes at infinity, which we call the degree of convenience. We relate our results to the existing literature and we illustrate them with some examples. As applications we show that the gradient maps corresponding to a broad class of polynomials are always subjective, we establish Hölder type global error bounds for such polynomials, and we link our results to the existence of solutions in the calculus of variations. [ABSTRACT FROM AUTHOR]

This article focuses on Bourdieu’s topological conception of social space to expand on it and develop an alternative model. Bourdieu describes social space as topological because it consists of a set of relative positions. Individuals in similar positions can come together to form social groups, so that differences between groups reveal or at least reflect the different positions in space. For this reason, it is convenient to think of social space as Bourdieu understands it as a space of groups. Yet there are other kinds of geometry beside topology. The article examines the difference between topology and Euclidean geometry to determine how we can modify Bourdieu’s model to uncover other potential features of social space. Rather than conceptualizing social space as a space of groups, we can envision a flow that is created as individuals relay one another so that the flow can go on even though the same individuals never stay put. Flows can arise by finding support on other flows. Thus arise structures in space that cannot be ‘mapped onto’ social actors occupying different positions because actors only sustain the flows through their perpetual turnover. [ABSTRACT FROM AUTHOR]

Symbolic dynamic is an important model of a general systems. This paper is devoted to the study of hyperspace dynamical systems of such systems. More precisely, we investigate the expansivity, topological entropy of the induced hyperspace dynamical system of a symbolic dynamical system . [ABSTRACT FROM AUTHOR]

A continuous map f on a compact metric space X induces in a natural way the map on the hyperspace of all closed non-empty subsets of X. We study the question of transmission of chaos between f and . We deal with generic, generic -, dense and dense -chaos for interval maps. We prove that all four types of chaos transmit from f to , while the converse transmission from to f is true for generic, generic - and dense -chaos. Moreover, the transmission of dense - and generic -chaos from to f is true for maps on general compact metric spaces. [ABSTRACT FROM AUTHOR]

Expectile, first introduced by Newey and Powell in1987in the econometrics literature, has recently become increasingly popular in risk management and capital allocation for financial institutions due to its desirable properties such as coherence and elicitability. The current standard tool for expectile regression analysis is the multiple linear expectile regression proposed by Newey and Powell in1987. The growing applications of expectile regression motivate us to develop a much more flexible nonparametric multiple expectile regression in a reproducing kernel Hilbert space. The resulting estimator is called KERE, which has multiple advantages over the classical multiple linear expectile regression by incorporating nonlinearity, nonadditivity, and complex interactions in the final estimator. The kernel learning theory of KERE is established. We develop an efficient algorithm inspired by majorization-minimization principle for solving the entire solution path of KERE. It is shown that the algorithm converges at least at a linear rate. Extensive simulations are conducted to show the very competitive finite sample performance of KERE. We further demonstrate the application of KERE by using personal computer price data. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar’s theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary and sufficient condition which allows to state this direction of Sklar’s theorem in Hilbert spaces. We consider copulas with densities and specifically construct copulas in a Hilbert space by a family of pairwise copulas with densities. [ABSTRACT FROM PUBLISHER]

The Möbius polynomial is an invariant of ranked posets, closely related to the Möbius function. In this paper, we study the Möbius polynomial of face posets of convex polytopes. We present formulas for computing the Möbius polynomial of the face poset of a pyramid or a prism over an existing polytope, or of the gluing of two or more polytopes in terms of the Möbius polynomials of the original polytopes. We also present general formulas for calculating Möbius polynomials of face posets of simplicial polytopes and of Eulerian posets in terms of theirf-vectors and some additional constraints. [ABSTRACT FROM PUBLISHER]

We give an elementary proof of the Jordan Brouwer separation theorem for smooth hypersurfaces using the divergence theorem and the inverse function theorem. [ABSTRACT FROM AUTHOR]

Analyzing on-line drug communities provides important insights into the connection between computer-mediated communication and drug use in contemporary society. Drawing on social learning theory, we analyze conversations within the on-line communityDMT-Nexus. We find that the on-line context affects the social learning process concerning drug use in distinct ways and identify how users gain relevant knowledge and interpretive strategies and acquire credibility. Based on these findings, we propose an expansion of Becker’s social learning model of drug use reflecting the unique constraints and opportunities of on-line contexts including the importance of vivid textual descriptions and modes of communication. [ABSTRACT FROM PUBLISHER]

In this paper, we construct a deterministic fractal in fuzzy metric space using generalized fuzzy contraction mapping and its fixed-point theorem in hyper-space of non-empty compact sets. Moreover, we present the self-similar group of H-contraction in fuzzy metric space and prove some familiar results of self-similar group for fuzzy metric space. [ABSTRACT FROM AUTHOR]

The polynomial bound of a Hilbert space operatoris the quantity. One of the Halmos ‘Ten problems’ asked whetherimplies thatis similar to a contraction. This question was settled in the negative by Pisier after many years. The finite–dimensional version of the problem asks to what extentcan be exceeded by. We establish some general criteria for the equalityand show thatcan occur even formatrices. [ABSTRACT FROM PUBLISHER]

Letbe ancomplex matrix such that every row and every column has at most one non-zero entry. We determine permutations of the non-zero entries ofso that the resulting matrix has maximum numerical radius. Extension of the results to operators acting on separable Hilbert spaces are also obtained. Related results and additional problems are also mentioned. [ABSTRACT FROM PUBLISHER]

Abstract—This article presents a statistical learning-based method for preventive control of microgrids against isolating from the main grid. Based on the stability criteria, the microgrid pre-islanding conditions are divided into secure and insecure classes. Critical variables regarding microgrid dynamic security are first selected via a feature selection procedure known as RELIEF. An unsupervised learning method, the pattern discovery method, is then applied to the space of the critical variables to extract the detailed structure knowledge called patterns. The patterns are in hyperspace and can effectively encode the microgrid security boundaries. The extracted patterns are used as preventive control laws to change the pre-islanding microgrid operating point if it is in the insecure region. Applying the proposed preventive control strategy guarantees that the microgrid can be isolated from the main grid without any instability problem. The studies are conducted in the time domain using the developed program in a MATLAB environment (The MathWorks, Natick, Massachusetts, USA). The results demonstrate the effectiveness and accuracy of the proposed preventive control method of microgrid against islanding in comparison with the decision tree based method. [ABSTRACT FROM PUBLISHER]

In this article the author takes as a point of departure certain discursive practices employed by physicists credited with popularizing the field of quantum mechanics in order to posit the relationship between space, learning, and the perception of pedagogical realities as trans-local phenomena. More specifically, through this article the author attempts to understand how the physicist's language describing the universe and its uncertainties within a hypothetical “hyperspace” may contribute to what we commonly understand and frame as curriculum and pedagogy. The author concludes by addressing the linguistic challenges present when we attempt to frame curriculum and pedagogy as a form of transgression into both the domains of the social and the physical sciences. This move unequivocally translates into establishing an epistemological framework advancing possibilities in educational research resultant from the work that is done at the edge of one's knowledge. [ABSTRACT FROM PUBLISHER]

Powered by a growing environmental awareness and the perception of ending fossil-based energy sources, wind energy has evolved as a reliable, mature and increasingly price-competitive alternative to fossil and nuclear energy sources. Along with incremental technological progress, the wind industry, i.e. the development and manufacturing of wind turbines, has developed very dynamically both with respect to organization and location. Originating mainly in small and medium-sized enterprises in a core region of Northern Europe, the wind industry is now a global industry with an increasing significance of Chinese turbine manufacturers. Informed by evolutionary thinking and recent discussions on the concept of path dependence, we will trace this organizational change and geographical shift over time and space. We will show that the development of the wind industry is an example of on-path evolution in which the accumulation of small and incremental change has led to fundamentally new structures. The main drivers of this development have been politics and various types of public policies as well as, more recently, the globalization of knowledge production in global innovation networks—thus illustrating the need to better integrate the role of the state and of institutions at multiple levels into evolutionary thinking. [ABSTRACT FROM PUBLISHER]

The accumulation of knowledge is a key driver of technological change and economic growth. Significant attention has been directed to the processes of knowledge production in a spatial context, but little attention has been given to the type of knowledge produced within specific places. The objectives of the present study are to map the US technology/knowledge space, to examine the evolution of that space over the time period 1975–2005, and to investigate the character of knowledge cores within US cities. The knowledge space is based on the proximity of technology classes, utilizing measures derived from co-classification information contained in patent documents. Results show that over time, patents increasingly cluster within technology classes that are located close to one another in technology space. They also reveal considerable heterogeneity in measures of technological specialization across US metropolitan areas. In general, smaller cities tend to display higher levels of knowledge relatedness, often because invention is controlled by a small number of firms with a limited range of technological know-how. Larger cities generate knowledge that is more broadly dispersed across the US knowledge space. Some cities maintain their technological coherence over time, the technological trajectories of others fracture and dissipate, while yet in other cities new technology cores emerge and develop. Higher levels of technological relatedness (specialization) in cities are linked to faster rates of knowledge production and to distinctive trajectories of knowledge evolution. [ABSTRACT FROM PUBLISHER]

In Landscape with Rowers: Poetry From the Netherlands, J. M. Coetzee (2004) has collected his own translations of poetic cycles and sequences by six poets: Gerrit Achterberg, Sybren Polet, Hugo Claus, Cees Nooteboom, Hans Faverey, and Rutger Kopland. I argue that with this rather anachronistic collection of poems, all predating the 1990s and to a greater or lesser extent associated with the artistic drive during the third and part of the fourth quarter of the twentieth century toward exploring more 'objective' compositional methods and in several instances also the 'hyperreal', Coetzee has not attempted to introduce the world to a representative set of modern Dutch poems - much rather, he has utilized a very specific selection of poems from a small continental literature to produce, in Peircean terms, a higher translation or, to borrow St-Pierre's (2007: 6) formulation in In Translation - Reflections, Refractions, Transformations, 'a new reading, a new writing'. Drawing on, amongst others, Amit Pinchevski's (2005) By Way of Interruption and Slavoj Z ˇizˇek's Welcome to the Desert of the Real, I show that Landscape with Rowers can be seen as a conscious and conscientious interruption tailor made for the decade(s) following the historic interruption that 9/11 constituted. [ABSTRACT FROM AUTHOR]

Over the past two decades, Dutch housing policy has become more market-oriented and neoliberal. This sea change is reflected in the architecture of owner-occupied houses, whose production has been increasingly accompanied by theming. Theming has often been criticized as an action to maximize profit through the commercialization of spaces and the resulting hyperreal, and hence fake, architecture. In the Netherlands, building professionals also develop theming in order to realize inward-looking, hyperreal residential spaces with an ambience that opposes the surrounding "real" space. Developers invent new strategies to engage with home buyers' unconscious thoughts on manageable community life and feelings of insecurity. References to the traditional small town, whether of Western or non-Western origin, are particularly powerful instruments to appeal to buyers' insecurities. Yet the profit imperative complicates the actual practice of theming. Creating different themed ambiences for disparate target groups strains the capacity of standardized housing production systems, necessitating additional investment. Architects and developers struggle to perfect a "convincing ambience" for prospective residents, while seeking to avoid producing the "fake architecture" that will stigmatize their work among professional colleagues. [ABSTRACT FROM AUTHOR]

Istanbul is the largest city in Turkey and is the most important socio-economic, cultural and touristic centre of the country. As the historical capital of three empires, its very rich cultural and social legacy is reflected in its public spaces. Despite its rapid growth and the transformation of its physical and social structures during the second half of the twentieth century, its public spaces still preserve much of their traditional social interactions, a quality which is difficult to find in many industrial cities. The purpose of this paper is to investigate the changes that have occurred through time in the social and physical characteristics of public spaces of the city. In the analysis, some distinguished streets, squares and waterfronts were chosen from different parts of the city and compared and contrasted with their previous and current physical and social characteristics. The results of this study illustrate that location, social and historical backgrounds, accessibility and investments for their redesign have played important roles in the successful transformation of these public spaces. [ABSTRACT FROM AUTHOR]

We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present a new interpretation of this order which allows to generalize to this setting many known results for matrices: functional calculus, semi-lattice properties, shorted operators and orthogonal decompositions. We also show several properties for general Hilbert spaces regarding the star order and its relationship with the functional calculus and the polar decomposition, which were unknown even in the finite-dimensional setting. We also study the existence of strong limits of star-monotone sequences and nets. [ABSTRACT FROM AUTHOR]

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas-Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules. [ABSTRACT FROM AUTHOR]

We propose a general form to analyze the space-time interdependency of continuous space-time stochastic processes. We present a new space-time approach based on the intensity function of the underlying point process. These formulations can be, to some extent, analytically solved to obtain explicit formulae of interest. We define a general function that controls the space-time interaction and allows for closed forms depending on the particular choice of several mathematical tools playing a role in this interaction function. In particular, we make use of copulas and Laplace transforms to provide interesting examples of the dynamics of the random intensity function and, in turn, of the number of points contained in a given region. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the general rheonomic mechanical systems using the Lagrange geometry. We will construct the time-dependent Lagrange space for the mechanical system, its canonical semispray and the nonlinear connection, which are determined only by the given mechanical system. One studies the rheonomic holonomic mechanical systems with external forces, using the geometry of the rheonomic Lagrange space endowed with the canonical semispray determined by the external forces. The geometry of the canonical semispray is the geometry of the rheonomic mechanical system. [ABSTRACT FROM AUTHOR]

We use norm inequalities for operators, such as Cauchy-Schwarz inequality and Minkowski inequality, to establish sharp norm inequalities for the absolute value of operators. Among other inequalities, it is shown that if A, B and X are operators on a Hilbert space, such that X is self-adjoint, and r ≥ 1, then [image omitted] This inequality generalizes some earlier related results. Other related inequalities are also discussed. [ABSTRACT FROM AUTHOR]

Two forms of Hrebicek's conjecture (formulated and explained in Hrebicek, 1992, 1994, 1997, 1998, 2002) about the fractal structure of language are clarified in terms of a precise mathematical formalism. This allows us, among other things, a more detailed understanding of Kohler's objections to the conjectures (Kohler, 1995, 1997). The approach using iterated function systems and the Moran-Hutchinson formula is newly applied to analyze and visualize linguistic structures. The role of a hyperspace is indicated in reply to questions posed in Leopold (2001). Some open problems are finally formulated in concluding remarks. [ABSTRACT FROM AUTHOR]

In this article, we discuss the application of arithmetic average discretization alternating group explicit (A-AGE) method to a new two-level implicit variable mesh formula of O(k2hl- 1+ khl + hl3) for the solution of non-linear parabolic equation uxx = F(x,t,u,ux, ut) subject to appropriate initial and Dirichlet boundary conditions, where k > 0 and hl > 0 are the variable step lengths in time and space directions, respectively. The proposed technique is also useful to solve parabolic singular problems. Our discretization procedure requires only 3-spatial grid points. A-AGE and Newton-A-AGE algorithms are discussed in detail. Comparison of numerical results of these methods with the corresponding successive over relaxation (SOR) and Newton-SOR methods is also included. [ABSTRACT FROM AUTHOR]

This paper deals with the averaging and diffusion approximation for occupation time of general phase space semi-Markov processes under split with simple and double merging in a series scheme. These results seem to be particularly interesting since the variance coefficient is obtained in a simple form. The method of proof of weak convergence results here is based on the construction of the compensating operator of the extended Markov renewal processes and on the solution of the singular perturbation problem of this operator acting on test functions. [ABSTRACT FROM AUTHOR]

Brownian motion has been used to derive stopping boundaries for group sequential trials, however, when we observe dependent increment in the data, fractional Brownian motion is an alternative to be considered to model such data. In this article we compared expected sample sizes and stopping times for different stopping boundaries based on the power family alpha spending function under various values of Hurst coefficient. Results showed that the expected sample sizes and stopping times will decrease and power increases when the Hurst coefficient increases. With same Hurst coefficient, the closer the boundaries are to that of O'Brien-Fleming, the higher the expected sample sizes and stopping times are; however, power has a decreasing trend for values start from H = 0.6 (early analysis), 0.7 (equal space), 0.8 (late analysis). We also illustrate study design changes using results from the BHAT study. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of a C1, 1 solution of the Qk flow in the viscosity sense for compact convex hypersurfaces Σt embedded in Rn+1 (n ≥ 2). The solution exists up to the time T < ∞ at which the enclosed volume becomes zero. In particular, for compact convex hypersurfaces with flat sides we show that, under a certain non-degeneracy initial condition, the interface separating the flat from the strictly convex side, becomes smooth, and it moves by the Qk-1 flow at least for a short time. [ABSTRACT FROM AUTHOR]

The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities. [ABSTRACT FROM AUTHOR]

We consider a system of three surfaces, graphs over a bounded domain in 2, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to 2π/3.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic Holder spaces), for sufficiently regular initial data satisfying a compatibility condition. [ABSTRACT FROM AUTHOR]

We consider a second-order parabolic equation in d+1 with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Holder continuous in the space variables. We show that global Schauder estimates hold even in this case. The proof introduces a new localization procedure. Our results show that the constant appearing in the classical Schauder estimates is in fact independent of the L∞-norms of the lower order coefficients. We also give a proof of uniqueness which is of independent interest even in the case of bounded coefficients. [ABSTRACT FROM AUTHOR]

We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface. [ABSTRACT FROM AUTHOR]

We consider a Cauchy problem for an overdetermined system of nonlinear partial differential equations, and give necessary and sufficient conditions for solvability of this Cauchy problem for all data. As an application, we find all real tube hypersurfaces in complex space whose Levi number is maximal. [ABSTRACT FROM AUTHOR]

Given a countable subset Λ of a set Ω, we investigate the construction of all the reproducing kernel Hilbert (resp. Banach) spaces on Ω that have Λ as a sampling (resp. p-sampling) set. Unlike the general p-frames, we prove that every p-sampling set for a reproducing kernel Banach space yields a reconstruction formula. Some applications are given to demonstrate the general construction. [ABSTRACT FROM AUTHOR]

A hypermedia application offers its users much freedom to navigate through a large hyperspace. Adaptive hypermedia (AH) offers personalized content, presentation, and navigation support. Many adaptive hypermedia systems (AHS) are tightly integrated with one specific application and/or use a limited number of techniques and methods. This makes it difficult to capture all of them in one generic model. In this paper we examine adaptation questions stated in the very beginning of the AH era and elaborate on their recent interpretations. We will reconsider design issues for application independent generic AHS, review open questions of system extensibility introduced in adjacent research fields and try to come up with an up-to-date taxonomy of adaptation techniques and an extensive set of requirements for a new adaptive system reference model or architecture, to be developed in the future. [ABSTRACT FROM AUTHOR]

AdaBoost.M1 has been successfully applied to improve the accuracy of a learning algorithm for multi-class classification problems. However, it may be hard to satisfy the required conditions in some practical cases. An improved algorithm called AdaBoost.MK is developed to solve this problem. Early proposed support vector machines (SVM)-based, multi-class classification algorithms work by splitting the original problem into a set of two-class subproblems. The amount of time and space required by these algorithms is very demanding. We develop a multi-class classification algorithm by incorporating one-class SVMs with a well-designed discriminant function. Finally, a hybrid method integrating AdaBoost.MK and one-class SVMs is proposed to solve multi-class classification problems. Experimental results on data sets from UCI and Statlog show that the proposed approach outperforms other multi-class algorithms, such as support vector data descriptions (SVDDs) and AdaBoost.M1 with one-class SVMs, and the improvement is found to be statistically significant. [ABSTRACT FROM AUTHOR]

Classic time geography is powerful but rigid, admitting only uniform travel velocities. Computational time geographic methods that resolve the uniform velocity assumption through transportation networks or isochrones only partially address this weakness and do not have a rigorous theoretical foundation. This article develops an analytical time geographic theory for the case where travel velocities vary continuously across space. Using the continuous transportation or “urban fields” tradition in quantitative geography and regional science, this article formulates analytical definitions of the space-time path and prism for the case where unobserved components are characterized by minimum cost curves through an inverse velocity field rather than straight line segments through a uniform velocity plane. This provides a geometrically and visually oriented approach to capturing complex velocities that complements existing methods. Time geographic fields also generalize time geography as the classic and isochrone versions are special cases; these now have a rigorous analytical foundation. It also can extend the network approach by treating links as regions with continuously varying velocities. Time geographic fields are also useful for nonnetwork-constrained phenomena such as movement through terrain, water, and air. This article illustrates the approach using a computational implementation based on a lattice approximation. [ABSTRACT FROM AUTHOR]

The decision-tree (DT) algorithm is a very popular and efficient data-mining technique. It is non-parametric and computationally fast. Besides forming interpretable classification rules, it can select features on its own. In this article, the feature-selection ability of DT and the impacts of feature-selection/extraction on DT with different training sample sizes were studied by using AVIRIS hyperspcetral data. DT was compared with three other feature-selection methods; the results indicated that DT was an unstable feature selector, and the number of features selected by DT was strongly related to the sample size. Trees derived with and without feature-selection/extraction were compared. It was demonstrated that the impacts of feature selection on DT were shown mainly as a significant increase in the number of tree nodes (14.13-23.81%) and moderate increase in tree accuracy (3.5-4.8%). Feature extraction, like Non-parametric Weighted Feature Extraction (NWFE) and Decision Boundary Feature Extraction (DBFE), could enhance tree accuracy more obviously (4.78-6.15%) and meanwhile a decrease in the number of tree nodes (6.89-16.81%). When the training sample size was small, feature-selection/extraction could increase the accuracy more dramatically (6.90-15.66%) without increasing tree nodes. [ABSTRACT FROM AUTHOR]

In this essay, I engage the L.A.--Chicago debate by repositioning both area-specific constraints and visual orders as intermediary variables. This leads the discussion to two considerations that in turn reposition the meaning of the familiar differences attributed to Los Angeles and Chicago. First, a focus on the particular implications of translocal processes for an area allows us to establish that agglomeration and dispersal might both be part of a given firm's or sector's chain of operations and that they might be distributed across very different types of geographic areas. The main implication for a comparison of the L.A. and Chicago models is that it makes problematic the notion that geographic dispersal à la L.A. is the new spatial form corresponding to today's new economy, and agglomeration à la Chicago belongs to an earlier modernity. The second focus is on the limits of homogenization and convergence in urban landscapes as explanations in comparative studies. I recode these homogenized landscapes--the hyperspace of global business--as an infrastructure: they are necessary but indeterminate in that they can be used for different purposes. This shifts the emphasis to what inhabits that built environment. A key underlying economic dynamic I find in my research is that the global economy thrives on the specialized differences of countries, regions, and cities. But it does need homogenized standards (e.g., of production, of financial reporting, of accounting, and the like), and, I add, it also needs standardized built environments. [ABSTRACT FROM AUTHOR]

Joel E. Cohen (Annals of Probability, 9(1981):899-901) conjectured that any stochastic matrix P = {pi, j} could be represented by some circle rotation f in the following sense: For some partition {Si} of the circle into sets consisting of finite unions of arcs, we have (*)pi, j = μ(f(Si) ∩ Sj)/μ(Si), where μ denotes arc length. In this article we show how cycle decomposition techniques originally used (Alpern, Annals of Probability, 11(1983):789-794) to establish Cohen's conjecture can be extended to give a short simple proof of the Coding Theorem, that any mixing (that is, PN > 0 for some N) stochastic matrix P can be represented (in the sense of * but with Si merely measurable) by any aperiodic measure preserving bijection (automorphism) of a Lesbesgue probability space. Representations by pointwise and setwise periodic automorphisms are also established. While this article is largely expository, all the proofs, and some of the results, are new. [ABSTRACT FROM AUTHOR]

Stochastic convolutions [image omitted] driven by a local martingale M in a Hilbert space are studied in the case when S(t) is a strongly continuous semigroup of contractions. Very simple proofs of the maximal inequality and exponential tail estimates are given by using unitary dilations and Zygmund's extrapolation theorem. Applications to stochastic convolutions driven by Poisson random measures are provided. A part of the results is then generalized to stochastic convolutions in Lq-spaces. [ABSTRACT FROM AUTHOR]

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as |x|→∞ is considered. Hence the total positive charge, total negative charge, and total energy are infinite. Smooth solutions with appropriate asymptotic behavior for large |x|, which were previously shown to exist locally in time, are continued globally for spherically symmetric data. This is done by showing that the charge density decays at least as fast as |x|-4. Finally, an increased decay rate of |x|-6 is shown in the general case without the assumption of spherical symmetry. [ABSTRACT FROM AUTHOR]

Manipulation of superpositions of discrete quantum states has a mathematical counterpart in the motion of a unit-length statevector in an N-dimensional Hilbert space. Any such statevector motion can be regarded as a succession of two-dimensional rotations. But the desired statevector change can also be treated as a succession of reflections, the generalization of Householder transformations. In multidimensional Hilbert space such reflection sequences offer more efficient procedures for statevector manipulation than do sequences of rotations. We here show how such reflections can be designed for a system with two degenerate levels - a generalization of the traditional two-state atom - that allows the construction of propagators for angular momentum states. We use the Morris-Shore transformation to express the propagator in terms of Morris-Shore basis states and Cayley-Klein parameters, which allows us to connect properties of laser pulses to Hilbert-space motion. Under suitable conditions on the couplings and the common detuning, the propagators within each set of degenerate states represent products of generalized Householder reflections, with orthogonal vectors. We propose physical realizations of this novel geometrical object with resonant, near-resonant and far-off-resonant laser pulses. We give several examples of implementations in real atoms or molecules. [ABSTRACT FROM AUTHOR]

The iMac G5 represents a contemporary trend in the design of new media objects, whereby technology is rendered invisible by its seamless penetration of the surfaces of everyday life. This effacement of technological objects has economic and cultural implications: it helps prevent seeing connections between the circulation of global capital and the use of media in a local context. We argue that the ostensibly neutral form of media is implicated with social inequality, so reconfiguring our relationship to the materiality of new media within our immediate surroundings is critical. [ABSTRACT FROM AUTHOR]