Distance Problem Research Articles

On the Problem of Distance From a Point to the Subspace of Finite Codimension in Real Banach Space

In this paper,assuming X is Banach and L is a finite codimension subspace of X. Application of the dual method,there obtain the formula of distance and elements of best approximation from given a point to the subspace of finite codimension under some condition,and apply the formula to solve some of the specific optimal control problem.

Approximate Solutions of the Determinantal Assignment Problem and Distance Problems

The paper introduces the formulation of an exact algebrogeometric problem, the study of the Determinantal Assignment Problem (DAP) in the set up of design, where approximate solutions of the algebraic problem are sought. Integral part of the solution of the Approximate DAP is the computation of distance of a multivector from the Grassmann variety of a projective space. We examine the special case of the calculation of the minimum distance of a multivector in ∧2(ℝ5) from the Grassmann variety G2(ℝ5). This problem is closely related to the problem of decomposing the multivector and finding its best decomposable approximation. We establish the existence of the best decomposition in a closed form and link the problem of distance to the decomposition of multivectors. The uniqueness of this decomposition is then examined and several new alternative decompositions are presented that solve our minimization problem based on the structure of the problem.

Institutional Changes in Contemporary Theatre

Current processes in international theatre practice have been so different in artistic sense that they could hardly be combined in some unity. But there is anothercriterion, not purely artistic, according to which artistically different phenomena of contemporary theatre could be united in wholeness. It is an institutional kind of criterion. Contemporary state of theatre as a kind of art could not be clearly described and then productively investigated without interpretation of those strong and deep transformations that have happened to theatre as a kind of societal institution. The thing is that researchers usually do observe artistic and societal qualities of art separately. Of course, it is one of the results of knowledge coming into depth and getting specialized, but sometimes it seems as if in development of art there were two divided processes – artistic, on the one hand, and societal, on the other hand. In reality, this development is one and whole total process with many various aspects. To keep in mind the unity of artistic and societal transformations of theatrical art is the challenge for methodological discourse within any aesthetic investigation in this field. Institutional theory of art, according to the author’s point of view, is the very case of methodological attitude that allows a researcher stay realistic in relation to the abovementioned unity. There is the key point that demonstrates it – the approach of the institutional theory of art to the problem of psychical distance between performance and spectators, its historical institutionalization in the phenomenon of classical and the following changes within this institutional state that finally brought theatre from classical to non-classical aesthetic regime. Institutional theory looks at this transition as artistic in the inspiriting causes, but societal is focused on fixation of their results. So, this theory allows an aesthetic observer keep the balance on the blade of the artistic and the societal contents of the institutional state of contemporary theatre. This article is the author’s attempt to point out the most significant institutional changes in contemporary theatre.

入力の連続性を考慮したゲインスケジュールドリファレンスガバナを用いたハードディスクのロングシーク制御

In this paper, we propose a gain scheduled reference governor for control of systems with constraints on the state and/or input variables. We use the reference governor with outer feedback constructed via model following control method. We apply this control scheme to design of long seek control of hard disk drives. To achieve short seek time for long seek distance problems, we consider gain scheduling with the reference governor. With keeping the continuity of input, the control system switches feedback gains according to the location of the state. Moreover, we examine the usefulness of the proposed method by applying it to benchmark problems of hard disk drive control.

On Range Searching with Semialgebraic Sets. II

Let $P$ be a set of $n$ points in $\mathbb{R}^d$. We present a linear-size data structure for answering range queries on $P$ with constant-complexity semialgebraic sets as ranges, in time close to $O(n^{1-1/d})$. It essentially matches the performance of similar structures for simplex range searching, and, for $d\ge 5$, significantly improves earlier solutions by the first two authors obtained in 1994. This almost settles a long-standing open problem in range searching. The data structure is based on a partitioning technique of Guth and Katz [On the Erdös distinct distances problem in the plane, arXiv:1011.4105, 2010], which shows that for a parameter $r$, $1 < r \le n$, there exists a $d$-variate polynomial $f$ of degree $O(r^{1/d})$ such that each connected component of $\mathbb{R}^d\setminus Z(f)$ contains at most $n/r$ points of $P$, where $Z(f)$ is the zero set of $f$. We present an efficient randomized algorithm for computing such a polynomial partition, which is of independent interest and is likely to have additional applications.

Pattern Matching under Polynomial Transformation

We consider a class of pattern matching problems where a normalizing polynomial transformation can be applied at every alignment of the pattern and text. Normalized pattern matching plays a key role in fields as diverse as image processing and musical information processing, where application specific transformations are often applied to the input. By considering a wide range of such transformations, we provide fast algorithms and the first lower bounds for both new and old problems. Given a pattern of length $m$ and a longer text of length $n$, where both are assumed to contain integer values only, we first show $O(n\log m)$ time algorithms for pattern matching under linear transformations even when wildcard symbols can occur in the input. We then show how to extend the technique to polynomial transformations of arbitrary degree. Next we consider the problem of finding the minimum Hamming distance under polynomial transformation. We show that, for any $\varepsilon>0$, there cannot exist an $O(nm^{1-\varepsilon})$ time algorithm for additive and linear transformations conditional on the hardness of the classic 3Sum problem. Finally, we consider a version of the Hamming distance problem under additive transformations with a bound $k$ on the maximum distance that needs to be reported. We give a deterministic $O(nk\log k)$ time solution, which we then improve by careful use of randomization to $O(n\sqrt{k\log k}\log n)$ time for sufficiently small $k$. Our randomized solution outputs the correct answer at every position with high probability.

Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees

Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree edit distance problem is to determine the least cost sequence of insertions, deletions and substitutions that converts a tree into another given tree. Both problems are known to be hard to approximate within some constant factor in general.We tackle these problems from two perspectives: giving exact algorithms, either for special cases or in terms of some parameters; and approximation algorithms and hardness of approximation. We present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees. This is complemented with a tighter APX-hardness proof that holds when the trees are of height one and two, respectively. Furthermore, we present the first approximation algorithms for both problems. In particular, for the common subtree problem for t trees, we present an algorithm achieving a tlog2(bOPT+1) ratio, where bOPT is the number of branching nodes in the optimal solution. We also present constant factor approximation algorithms for both problems in the case of bounded height trees.

Empires of the Imagination: Transatlantic Histories of the Louisiana Purchase (review)

Empires of Imagination: Transatlantic Histories of Louisiana Purchase. Edited by Peter J. Kastor and Francois Weil. (Charlottesville, VA: University of Virginia Press, 2009. Pp. 376. Cloth, $40.00.)The Louisiana Purchase came as surprise on both sides of Atlantic, authors of Empires of Imagination remind us. The last addition to series of studies that commemorates bicentennial of what French call la vente de la Louisiane, this collection strives to revise Anglocentric vision of North American West (17). In synch with theme of imagination, well-established scholars explore mental constructs of people involved or affected by Purchase - including geopolitical imagination of Jefferson (Peter Onuf), prerevolutionary categories of Napoleon (Laurent Dubois), or conceptions of power of Choctaw Indians (Cecile Vidal). The essays are organized in three parts, respectively entitled Empire, Identity, and Memory. To get good grasp on historiography, however, very last essay of collection, written by Jacques Portes and Marie-Jeanne Rossignol, should be read first. Besides giving sense of very different treatment of Purchase in American and French historiographical traditions, two historians acutely pose problem of distance between academic knowledge and public celebration of historical events.Empires of Imagination grants significant place to diplomatic and political history, yet several essays examine Purchase from bottom up, trying to understand how it changed life in Louisiana. Opening first part of book, Richard White argues that life did not change much for several decades in pays d'en haut, haven for outlaws. In an inspired essay, White insists on the fictions of empire, presenting diplomacy as a form of pornography and Louisiana Purchase as historical event that blended, violence, desire, imaginary possession, and illicit sale (38). Building on work of White and other historians of Upper Louisiana, Cecile Vidal rejects cultural interpretations that have long lauded colonial genius of France when it came to dealing with Indians. Laurent Dubois moves narrative in French Atlantic, uncovering unpaid debts of United States to former slaves of Saint-Domingue. Dubois takes up argument of Robert L. Paquette and writes that Napoleon was forced to abandon his western design (and thus to sell Louisiana), since he was unwilling to accept end of slavery in Pearl of Caribbean.1 While France was trying to deal with insurgents, things were not easy in Washington. Spain's retrocession of Louisiana to France created great insecurities in early republic, notes James Lewis. While Federalists wanted to solve crisis by taking to arms, Jefferson chose to adopt diplomatic and peaceful course, animated by fears for still fragile union between states.The second part of book is concerned with questions of identity, mostly in Lower Louisiana. With his usual demographic approach, Paul Lachance examines censuses produced in decades surrounding Purchase to convey how successive authorities constructed and categorized people of Louisiana. …

POINT SET DISTANCE AND ORTHOGONAL RANGE PROBLEMS WITH DEPENDENT GEOMETRIC UNCERTAINTIES

Classical computational geometry algorithms handle geometric constructs whose shapes and locations are exact. However, many real-world applications require modeling and computing with geometric uncertainties, which are often coupled and mutually dependent. In this paper we address the relative position of points, point set distance problems, and orthogonal range queries in the plane in the presence of geometric uncertainty. The uncertainty can be in the locations of the points, in the query range, or both, and is possibly coupled. Point coordinates and range uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), a general and computationally efficient worst-case, first-order linear approximation of geometric uncertainty that supports dependence among uncertainties. We present efficient algorithms for relative points orientation, minimum and maximum pairwise distance, closest pair, diameter, and efficient algorithms for uncertain range queries: uncertain range/nominal points, nominal range/uncertain points, uncertain range/uncertain points, with independent/dependent uncertainties. In most cases, the added complexity is sub-quadratic in the number of parameters and points, with higher complexities for dependent point uncertainties.

MLPA-conservation mechanism in wireless sensor network environments

Abstract Transmission using excess power not only shortens the lifetime of sensor nodes, but also introduces interference. Packets should ideally be transmitted with moderate power. This study proposes a multi-level power adjustment (MLPA) mechanism for a wireless sensor network to prolong the lifetime of individual nodes and the overall network. In this study, we constructed an analytical model of the MLPA mechanism with m distinct power levels (m-LPA). For m-LPA, the closed-form expression of the optimal power setting was determined and the mean transmission power was minimized to one-third of the original fixed-transmission power. We found that the average power consumption of our proposed mechanism is 33.93% higher than that of fixed-transmission power. Thus, each node can extend the lifetime by 2.5 times. We have shown the relations between m and density in simulation results. Although the mechanism worked smoothly in this study, the sensors do not need to handle the distance and interference problem.

An explicit state-space solution to the one-block super-optimal distance problem

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control.

A Deterministic Reduction for the Gap Minimum Distance Problem

Determining the minimum distance of a linear code is one of the most important problems in algorithmic coding theory. The exact version of the problem was shown to be NP-complete by Vardy. The gap version of the problem was shown to be NP-hard for any constant factor under a randomized reduction in an earlier work. It was shown in the same paper that the minimum distance problem is not approximable in randomized polynomial time to the factor 2log1-ϵn unless NP ⊆ RTIME(2polylog(n)). In this paper, we derandomize the reduction and thus prove that there is no deterministic polynomial time algorithm to approximate the minimum distance to any constant factor unless P=NP. We also prove that the minimum distance is not approximable in deterministic polynomial time to the factor 2log1-ϵn unless NP ⊆ DTIME(2polylog(n)). As the main technical contribution, for any constant 2/3 <; ρ <; 1, we present a deterministic algorithm that given a positive integer s , runs in time poly(s) and constructs a code C of length poly(s) with an explicit Hamming ball of radius ρd(C), such that the projection at the first s coordinates sends the codewords in the ball surjectively onto a linear subspace of dimension s , where d(C) denotes the minimum distance of C. The codes are obtained by concatenating Reed-Solomon codes with Hadamard codes.

A clique-based method using dynamic programming for computing edit distance between unordered trees.

Many kinds of tree-structured data, such as RNA secondary structures, have become available due to the progress of techniques in the field of molecular biology. To analyze the tree-structured data, various measures for computing the similarity between them have been developed and applied. Among them, tree edit distance is one of the most widely used measures. However, the tree edit distance problem for unordered trees is NP-hard. Therefore, it is required to develop efficient algorithms for the problem. Recently, a practical method called clique-based algorithm has been proposed, but it is not fast for large trees. This article presents an improved clique-based method for the tree edit distance problem for unordered trees. The improved method is obtained by introducing a dynamic programming scheme and heuristic techniques to the previous clique-based method. To evaluate the efficiency of the improved method, we applied the method to comparison of real tree structured data such as glycan structures. For large tree-structures, the improved method is much faster than the previous method. In particular, for hard instances, the improved method achieved more than 100 times speed-up.

Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields

Abstract In this paper we study the extension problem, the averaging problem, and the generalized Erdős-Falconer distance problem associated with arbitrary homogeneous varieties in three dimensional vector spaces over finite fields. In the case when the varieties do not contain any plane passing through the origin, we obtain the best possible results on the aforementioned three problems. In particular, our result on the extension problem modestly generalizes the result by Mockenhaupt and Tao who studied the particular conical extension problem. In addition, investigating the Fourier decay on homogeneous varieties enables us to give complete mapping properties of averaging operators. Moreover, we improve the size condition on a set such that the cardinality of its distance set is nontrivial.

THE DEVELOPMENT OF GIS EDUCATIONAL RESOURCES SHARING AMONG CENTRAL TAIWAN UNIVERSITIES

Abstract. Using GIS in the classroom enhance students’ computer skills and explore the range of knowledge. The paper highlights GIS integration on e-learning platform and introduces a variety of abundant educational resources. This research project will demonstrate tools for e-learning environment and delivers some case studies for learning interaction from Central Taiwan Universities. Feng Chia University (FCU) obtained a remarkable academic project subsidized by Ministry of Education and developed e-learning platform for excellence in teaching/learning programs among Central Taiwan’s universities. The aim of the project is to integrate the educational resources of 13 universities in central Taiwan. FCU is serving as the hub of Center University. To overcome the problem of distance, e-platforms have been established to create experiences with collaboration enhanced learning. The e-platforms provide coordination of web service access among the educational community and deliver GIS educational resources. Most of GIS related courses cover the development of GIS, principles of cartography, spatial data analysis and overlaying, terrain analysis, buffer analysis, 3D GIS application, Remote Sensing, GPS technology, and WebGIS, MobileGIS, ArcGIS manipulation. In each GIS case study, students have been taught to know geographic meaning, collect spatial data and then use ArcGIS software to analyze spatial data. On one of e-Learning platforms provide lesson plans and presentation slides. Students can learn Arc GIS online. As they analyze spatial data, they can connect to GIS hub to get data they need including satellite images, aerial photos, and vector data. Moreover, e-learning platforms provide solutions and resources. Different levels of image scales have been integrated into the systems. Multi-scale spatial development and analyses in Central Taiwan integrate academic research resources among CTTLRC partners. Thus, establish decision-making support mechanism in teaching and learning. Accelerate communication, cooperation and sharing among academic units

Comparing Pedigree Graphs

Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution.

Simple Proofs of Classical Theorems in Discrete Geometry via the Guth–Katz Polynomial Partitioning Technique

Recently Guth and Katz ( arXiv:1011.4105, 2010) invented, as a step in their nearly complete solution of Erdős’s distinct distances problem, a new method for partitioning finite point sets in ℝ d , based on the Stone–Tukey polynomial ham-sandwich theorem. We apply this method to obtain new and simple proofs of two well known results: the Szemeredi–Trotter theorem on incidences of points and lines, and the existence of spanning trees with low crossing numbers. Since we consider these proofs particularly suitable for teaching, we aim at self-contained, expository treatment. We also mention some generalizations and extensions, such as the Pach–Sharir bound on the number of incidences with algebraic curves of bounded degree.

UniMoG—a unifying framework for genomic distance calculation and sorting based on DCJ

Summary: UniMoG is a software combining five genome rearrangement models: double cut and join (DCJ), restricted DCJ, Hannenhalli and Pevzner (HP), inversion and translocation. It can compute the pairwise genomic distances and a corresponding optimal sorting scenario for an arbitrary number of genomes. All five models can be unified through the DCJ model, thus the implementation is based on DCJ and, where reasonable, uses the most efficient existing algorithms for each distance and sorting problem. Both textual and graphical output is possible for visualizing the operations.Availability and implementation: The software is available through the Bielefeld University Bioinformatics Web Server at http://bibiserv.techfak.uni-bielefeld.de/dcj with instructions and example data.Contact: rhilker@cebitec.uni-bielefeld.de

The generalized Erdős–Falconer distance problems in vector spaces over finite fields

In this paper we study the generalized Erdos-Falconer distance problems in the finite field setting. The generalized distances are defined in terms of polynomials, and various formulas for sizes of distance sets are obtained. In particular, we develop a simple formula for estimating the cardinality of distance sets determined by diagonal polynomials. As a result, we generalize the spherical distance problems due to Iosevich and Rudnev and the cubic distance problems due to Iosevich and Koh. Moreover, our results are of higher dimensional version for Vu's work on two dimension. In addition, we set up and study the generalized pinned distance problems in finite fields. We give a nice generalization of some recent work in which the pinned distance problems related to spherical distances were investigated. Discrete Fourier analysis and exponential sum estimates play an important role in our proof.

Approximating distributional behaviour of LTI differential systems using Gaussian function and its derivatives

This article is concerned with the approximation of the distributional behaviour of linear, time-invariant (LTI) systems. First, we review the different types of approximations of distributions by smooth functions and explain their significance in characterising system properties. Second, we consider the problem of changing the state of controllable LTI differential systems in a very short time. Thus, we establish an interesting relation between the time and volatility parameters of the Gaussian function and its derivatives in the approximation of distributional solutions. An algorithm is then proposed for calculating the distributional input and its smooth approximation which minimises the distance to an arbitrary target state. The optimal choice of the volatility parameter for the state transition is also derived. Finally, some complementary distance problems are also considered. The main results of this article are illustrated by numerous examples.