Maximum <Emphasis Type="Italic">k</Emphasis>-Splittable <Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">t</Emphasis>-Flows

Given a graph with a source and a sink node, the NP-hard maximum k-splittable s,t-flow (M k SF) problem is to find a flow of maximum value from s to t with a flow decomposition using at most k paths. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k-splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values for the paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Usually the routing is considered before the packing. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal M k SF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed ε>0, the computed set of alternatives contains a packing used by a (1−ε)-approximate solution. The latter result is based on the observation that (1−ε)-approximate flows only require constantly many different flow values. We believe that this observation is of interest in its own right. (ii) Based on (i), we prove that, for constant k, the M k SF problem can be solved in polynomial time on graphs of bounded treewidth. If k is part of the input, this problem is still NP-hard and we present a polynomial time approximation scheme for it.     

Heidegger on technology and <Emphasis Type="Italic">Gelassenheit</Emphasis>: <Emphasis Type="Italic">wabi</Emphasis>-<Emphasis Type="Italic">sabi</Emphasis> and the art of <Emphasis Type="Italic">Verfallenheit</Emphasis>

The question of the contemporary relevance of Heidegger’s reflections on technology to today’s advanced technology is here explored with reference to the notion of “entanglement” towards a review of Heidegger’s understanding of technology and media, including the entertainment industry and modern digital life. Heidegger’s reflections on Gelassenheit have been connected with the aesthetics of the tea ceremony, disputing the material aesthetics of porcelain versus plastic. Here by approaching the art of wabi-sabi as the art of Verfallenheit, I argue that Gelassenheit may be understood in these terms.     

Variations for the <Emphasis Type="Italic">Q</Emphasis>- and <Emphasis Type="Italic">H</Emphasis>-factors in the polar decomposition

In this paper, the variations of both subunitary polar factors and Hermitian positive semidefinite polar factors in the polar decomposition are studied. New perturbation bounds of both polar factors are given without the restriction that A and its perturbed matrix à have the same rank. These improve recent results.     

Construction and Arithmetics of <Emphasis Type="Italic">H</Emphasis>-Matrices

In previous papers hierarchical matrices were introduced which are data-sparse and allow an approximate matrix arithmetic of nearly optimal complexity. In this paper we analyse the complexity (storage, addition, multiplication and inversion) of the hierarchical matrix arithmetics. Two criteria, the sparsity and idempotency, are sufficient to give the desired bounds. For standard finite element and boundary element applications we present a construction of the hierarchical matrix format for which we can give explicit bounds for the sparsity and idempotency.     

EP<Emphasis Type="Italic">n</Emphasis>P: An Accurate <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) Solution to the P<Emphasis Type="Italic">n</Emphasis>P Problem

We propose a non-iterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n ⁵) or even O(n ⁸), without being more accurate. Our method is applicable for all n≥4 and handles properly both planar and non-planar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12×12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data.     

Adaptive Geometrically Balanced Clustering of <Emphasis Type="Italic">H</Emphasis>-Matrices

In [8], a class of (data-sparse) hierarchical (-) matrices is introduced that can be used to efficiently assemble and store stiffness matrices arising in boundary element applications. In this paper, we develop and analyse modifications in the construction of an -matrix that will allow an efficient application to problems involving adaptive mesh refinement. In particular, we present a new clustering algorithm such that, when an -matrix has to be updated due to some adaptive grid refinement, the majority of the previously assembled matrix entries can be kept whereas only a few new entries resulting from the refinement have to be computed. We provide an efficient implementation of the necessary updates and prove for the resulting -matrix that the storage requirements as well as the complexity of the matrix-vector multiplication are almost linear, i.e., AMS Subject Classifications: 65F05, 65F30, 65N38, 65N50.     

Corepresentation of a sylow <Emphasis Type="Italic">p</Emphasis>-subgroup of a group <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The corepresentation of a Sylow p-subgroup of a symmetric group in the form of generating relations is investigated, and a Sylow subgroup of a group , i.e., an n-fold wreath product of regular cyclic groups of prime order, that is isomorphic to the group of automorphisms of a spherically homogeneous root tree is also studied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 27–41, January–February 2009.     

Intuitionistic (<Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-fuzzy hyperquasigroups

The concept of intuitionistic fuzzy subhyperquasigroups in a hyperquasigroup with respect to an s-norm and a t-norm on intuitionistic fuzzy sets is introduced and their properties of such hyperquasigroups are studied. Intuitionistic (S, T)-fuzzy relations on a hyperquasigroup G are discussed. In particular, we investigate connections hyperquasigroups with binary quasigroups.     

Low-density incomplete <Emphasis Type="Italic">LDL</Emphasis><Superscript><Emphasis Type="Italic">T</Emphasis></Superscript> factorizations

A particular class of incomplete factorizations is proposed as preconditioners for the linear system Ax = b where A is a symmetric, large and sparse matrix. The ILDL ^T< (p) factorization (p = 1,2,3, …) determines the density of the lower triangular matrix L selecting the p largest off-diagonal entries of each column during the Gaussian elimination process. This selection may be computationally expensive, but the effectiveness of the preconditioner allows us to choose very low-density factors to reduce both work time and storage requirements. This incomplete factorization can be performed reliably on H-matrices. When A is a positive definite matrix, but not an H-matrix, one can perform an incomplete factorization if positive off-diagonal entries are removed or reduced and diagonally compensated. Numerical results for a variety of problems and comparisons with other incomplete factorizations are presented. Received: August 2002 / Accepted: December 2002 RID="*" ID="*"This work was supported by the Spanish grant BFM 2001-2641.     

Bose-Mesner algebra on finite <Emphasis Type="Italic">G</Emphasis>/<Emphasis Type="Italic">H</Emphasis> coset graphs and its application on continuous time quantum walks

Continuous-time quantum walk (CTQW) over finite group schemes is investigated, where it is shown that some properties of a CTQW over a group scheme defined on a finite group G induces a CTQW over group scheme defined on G/H, where H is a normal subgroup of G with prime index. This reduction can be helpful in analyzing CTQW on underlying graphs of group schemes. Even though this claim is proved for normal subgroups with prime index (using the Clifford’s theorem from representation theory), it is checked in some examples that for other normal subgroups or even non-normal subgroups, the result is also true! Moreover, it is shown that the Bose-Mesner (BM) algebra associated with the group scheme over G is isomorphic to the corresponding BM algebra of the association scheme defined over the coset space G/H up to the scale factor |H|. In fact, we show that the underlying graph defined over group G is a covering space for the quotient graph defined over G/H, so that CTQW over the graph on G, starting from any arbitrary vertex, is isomorphic to the CTQW over the quotient graph on G/H if we take the sum of the amplitudes corresponding to the vertices belonging to the same cosets.     

<Emphasis Type="Italic">I-Quest</Emphasis>: an <Emphasis Type="Italic">i</Emphasis>ntelligent <Emphasis Type="Italic">que</Emphasis>ry <Emphasis Type="Italic">st</Emphasis>ructuring based on user browsing feedback for semantic retrieval of video data

In spite of significant improvements in video data retrieval, a system has not yet been developed that can adequately respond to a user’s query. Typically, the user has to refine the query many times and view query results until eventually the expected videos are retrieved from the database. The complexity of video data and questionable query structuring by the user aggravates the retrieval process. Most previous research in this area has focused on retrieval based on low-level features. Managing imprecise queries using semantic (high-level) content is no easier than queries based on low-level features due to the absence of a proper continuous distance function. We provide a method to help users search for clips and videos of interest in video databases. The video clips are classified as interesting and uninteresting based on user browsing. The attribute values of clips are classified by commonality, presence, and frequency within each of the two groups to be used in computing the relevance of each clip to the user’s query. In this paper, we provide an intelligent query structuring system, called I-Quest, to rank clips based on user browsing feedback, where a template generation from the set of interesting and uninteresting sets is impossible or yields poor results.

The servicing system <Emphasis Type="Italic">MAP</Emphasis>(<Emphasis Type="Italic">PH</Emphasis>)+<Emphasis Type="Italic">MAP/PH/N/R</Emphasis> as a model of optimizing an <Emphasis Type="Italic">HTTP</Emphasis> server with blockings

We consider a multiline queueing system with joint or single queries. The number of queries in a connection is random and is not known when the connection is established. Queries arriving during each connection are described by the phase type input steam. Accepting a connection in the system is restricted by tokens. Connections arriving when no free tokens are present are refused. Single queries arrive without tokens. If the number of free slots in the system is not enough, the system is blocked.     

Emergence of anti-<Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity in type-IV bouncing cosmology as due to <Emphasis Type="Italic">M</Emphasis><Subscript>0</Subscript>-brane

Recently, some authors considered the origin of a type-IV singular bounce in modified gravity and obtained the explicit form of F(R) which can produce this type of cosmology. In this paper, we show that during the contracting branch of type-IV bouncing cosmology, the sign of gravity changes, and antigravity emerges. In our model, M0 branes get together and shape a universe, an anti-universe, and a wormhole which connects them. As time passes, this wormhole is dissolved in the universes, F(R) gravity emerges, and the universe expands. When the brane universes become close to each other, the squared energy of their system becomes negative, and some tachyonic states are produced. To remove these states, universes are assumed to be compact, the sign of compacted gravity changes, and anti-F(R) gravity arises, which causes getting away of the universes from each other. In this theory, a Type-IV singularity occurs at t = t _s , which is the time of producing tachyons between expansion and contraction branches.     

The <Emphasis Type="Italic">POINT</Emphasis> approach to represent <Emphasis Type="Italic">now</Emphasis> in bitemporal databases

Most modern database applications involve a significant amount of time dependent data and a significant portion of this data is now-relative. Now-relative data are a natural and meaningful part of every temporal database as well as being the focus of most queries. Previous studies indicate that the choice of the representation of now significantly influences the efficiency of accessing bitemporal data. In this paper we propose and experimentally evaluate a novel approach to represent now that we termed the POINT approach, in which now-relative facts are represented as points on the transaction-time and/or valid-time line. Furthermore, in the POINT approach we propose a logical query transformation that relies on the above representation and on the geometry features of spatial access methods. Such a logical query transformation enables off-the-shelf spatial indexes to be used. We empirically prove that the POINT approach is efficient on now-relative bitemporal data, outperforming the maximum timestamp approach that has been proven to the best approach to now-relative data in the literature, independently of the indexing methodology (B ⁺- tree vs R ^*- tree) being used. Specifically, if spatial indexing is used, the POINT approach outperforms the maximum timestamp approach to the extent of factor more than 10, both in number of disk accesses and CPU usage.     

High frequency curvature oscillations in <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

It is argued that F(R) modified gravity generically leads to high frequency curvature oscillations in astrophysical systems with rising mass/energy density. Potentially observational manifestations of such oscillations are discussed. In particular, gravitational repulsion in finite-size objects, forbidden in standard General Relativity, is shown to exist. Also an alternation of density perturbation evolution is found out. The latter is induced by excitation of a parametric resonance and by the so-called antifriction phenomenon. These new features could lead to strong reshaping of the usual Jeans instability.     

Extension of <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis> log <Emphasis Type="Italic">n</Emphasis>) Filtering Algorithms for the Unary Resource Constraint to Optional Activities

Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edge-finding and not-first/not-last are the most popular filtering algorithms for unary resources. In this paper we introduce new O(n log n) versions of these two filtering algorithms and one more O(n log n) filtering algorithm called detectable precedences. These algorithms use a special data structures Θ-tree and Θ-Λ-tree. These data structures are especially designed for “what-if” reasoning about a set of activities so we also propose to use them for handling so called optional activities, i.e. activities which may or may not appear on the resource. In particular, we propose new O(n log n) variants of filtering algorithms which are able to handle optional activities: overload checking, detectable precedences and not-first/not-last.     

Supporting top-<Emphasis Type="Italic">k</Emphasis><Emphasis Type="Italic">join</Emphasis> queries in relational databases

Ranking queries, also known as top-k queries, produce results that are ordered on some computed score. Typically, these queries involve joins, where users are usually interested only in the top-k join results. Top-k queries are dominant in many emerging applications, e.g., multimedia retrieval by content, Web databases, data mining, middlewares, and most information retrieval applications. Current relational query processors do not handle ranking queries efficiently, especially when joins are involved. In this paper, we address supporting top-k join queries in relational query processors. We introduce a new rank-join algorithm that makes use of the individual orders of its inputs to produce join results ordered on a user-specified scoring function. The idea is to rank the join results progressively during the join operation. We introduce two physical query operators based on variants of ripple join that implement the rank-join algorithm. The operators are nonblocking and can be integrated into pipelined execution plans. We also propose an efficient heuristic designed to optimize a top-k join query by choosing the best join order. We address several practical issues and optimization heuristics to integrate the new join operators in practical query processors. We implement the new operators inside a prototype database engine based on PREDATOR. The experimental evaluation of our approach compares recent algorithms for joining ranked inputs and shows superior performance.Received: 23 December 2003, Accepted: 31 March 2004, Published online: 12 August 2004Edited by: S. AbiteboulExtended version of the paper published in the Proceedings of the 29th International Conference on Very Large Databases, VLDB 2003, Berlin, Germany, pp 754-765     

I—SATCHMORE：An Improvement of A—SATCHMORE

This paper presents an improvement of A-SATCHMORE (SATCHMORE with Availability).A-SATCHMORE incorporates relevancy testing and availability checking into SATCHMO to prune away irrelevant forward chaining.However ,considering every consequent atom of those non-Horn clauses being derivable,A-SATCHMORE may suffer from a potential explosion of the search space when some of such consequent atoms are actually underivable.This paper introduces a solution for this problem and shows its correctness.     

3D virtual mosaics: <Emphasis Type="Italic">Opus Palladium</Emphasis> and <Emphasis Type="Italic">mixed</Emphasis> styles

One of the oldest art forms, mosaics are built by careful selection and placement of small pieces called tiles. Although 2D mosaics have attracted attention in computer graphics research, 3D virtual mosaic sculptures are less common. In this work, we present a method to simulate mosaic sculptures using tiles with irregular shapes, a method known by mosaicists as Opus Palladium, or simply “crazy paving,” due to the inherent freedom of mixing the tiles. In order to add expressiveness and emphasize some features, artists distribute the tiles following a high-level design over the shape. We use Voronoi polygons to represent the tiles computed from a distribution of points on the surface of the 3D object. We also address the simulation of mixed mosaics, where both irregular and squared-shape tiles are used on the same object. Previous works on such surface mosaics have used only square-shaped tiles, with fixed or variable size. Special mosaic-like effects are obtained with the help from texture maps, which control the high-level design of the tile distribution.