Testing list <Emphasis Type="Italic">H</Emphasis>-homomorphisms

In the List H- Homomorphism Problem, for a graph H that is a parameter of the problem, an instance consists of an undirected graph G with a list constraint \({L(v) \subseteq V(H)}\) for each variable \({v \in V(G)}\), and the objective is to determine whether there is a list H-homomorphism \({f:V(G) \to V(H)}\), that is, \({f(v) \in L(v)}\) for every \({v \in V(G)}\) and \({(f(u),f(v)) \in E(H)}\) whenever \({(u,v) \in E(G)}\).We consider the problem of testing list H-homomorphisms in the following weighted setting: An instance consists of an undirected graph G, list constraints L, weights imposed on the vertices of G, and a map \({f:V(G) \to V(H)}\) given as an oracle access. The objective is to determine whether f is a list H-homomorphism or far from any list H-homomorphism. The farness is measured by the total weight of vertices \({v \in V(G)}\) for which f(v) must be changed so as to make f a list H-homomorphism. In this paper, we classify graphs H with respect to the number of queries to f required to test the list H-homomorphisms. Specifically, we show that (i) list H-homomorphisms are testable with a constant number of queries if and only if H is a reflexive complete graph or an irreflexive complete bipartite graph and (ii) list H-homomorphisms are testable with a sublinear number of queries if and only if H is a bi-arc graph.     

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.     

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.     

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.     

<Emphasis Type="Italic">t</Emphasis>-Private and <Emphasis Type="Italic">t</Emphasis>-Secure Auctions

In most of the auction systems the values of bids are known to the auctioneer. This allows him to manipulate the outcome of the auction. Hence, one might be interested in hiding these values. Some cryptographically secure protocols for electronic auctions have been presented in the last decade. Our work extends these protocols in several ways. On the basis of garbled circuits, i.e., encrypted circuits, we present protocols for sealed-bid auctions that fulfill the following requirements： 1） protocols are information-theoretically t-private for honest but curious parties; 2） the number of bits that can be learned by malicious adversaries is bounded by the output length of the auction; 3） the computational requirements for participating parties are very low： only random bit choices and bitwise computation of the XOR-function are necessary. Note that one can distinguish between the protocol that generates a garbled circuit for an auction and the protocol to evaluate the auction. In this paper we address both problems. We will present a t-private protocol for the construction of a garbled circuit that reaches the lower bound of 2t ＋ 1 parties, and Finally, we address the problem of bid changes in an auction. a more randomness efficient protocol for （t ＋ 1）^2 parties     

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.     

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.     

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.     

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.     

<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.

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.     

On Interval Systems [<Emphasis Type="Italic">x</Emphasis>] = [<Emphasis Type="Italic">A</Emphasis>][<Emphasis Type="Italic">x</Emphasis>] + [<Emphasis Type="Italic">b</Emphasis>] and the Powers of Interval Matrices in Complex Interval Arithmetics

For the interval system of equations defined by [x] = [A][x] + [b] we derive necessary and sufficient criteria for the existence of solutions [x]. Furthermore we give necessary and sufficient criteria for the convergence of powers of [A]. In contrast to former results we treat complex interval arithmetics.     

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.     

Search for <Emphasis Type="Italic">C</Emphasis>-optimal routes in graphs

We propose search algorithms for paths in graphs that are optimal in the sense of a given choice function. As an example we consider the choice mechanism with respect to a binary relation that does not contain numerical criterial estimates.     

<Emphasis Type="Italic">LFTOP</Emphasis>: An <Emphasis Type="Italic">LF</Emphasis>-Based Approach to Domain-Specific Reasoning

A new approach to domain-specific reasoning is presented that is based on a type-theoretic logical framework(LF) but does not require the user to be an expert in type theory. The concepts of the domain and its related reasoning systems are formalized in LF, but the user works with the system through a syntax and interface appropriate to his/her work. A middle layer provides translation between the user syntax and LF, and allows additional support for reasoning(e.g., model checking). Thus, the complexity of the logical framework is hidden but the benefits of using type theory and its related tools are retained, such as precision and machine-checkable proofs. This approach is investigated through a number of case studies: here, the authors consider the verification of properties of concurrency. The authors have formalized a specification language (CCS) and logic (μ-calculus) in LF, together with useful lemmas, and a user-oriented syntax has been designed. The authors demonstrate the approach with simple examples. However, applying lemmas to objects introduced by the user may result in framework-level objects which cannot be translated back to the user level. The authors discuss this problem, define a notion of adequacy, and prove that in this case study, translation can always be reversed.     

Taut-String Algorithm and Regularization Programs with <Emphasis Type="Italic">G</Emphasis>-Norm Data Fit

In this paper we derive a unified framework for the taut-string algorithm and regularization with G-norm data fit. The G-norm data fit criterion (popularized in image processing by Y. Meyer) has been paid considerable interest in regularization models for pattern recognition. The first numerical work based on G-norm data fit has been proposed by Osher and Vese. The taut-string algorithm has been developed in statistics (Mammen and van de Geer and Davies and Kovac) for denoising of one dimensional sample data of a discontinuous function. Recently Hinterberger et al. proposed an extension of the taut-string algorithm to higher dimensional data by introducing the concept of tube methods. Here we highlight common features between regularization programs with a G-norm data fit term and taut-string algorithms (respectively tube methods). This links the areas of statistics, regularization theory, and image processing. Otmar Scherzer received his Ph.D. in Mathematics from the University of Linz, Austria, in 1990. Till 1999 he has been at the Industrial Mathematics Institute at the University of Linz. From 1999–2000 he visited the University of Munich (Germany) and from 2000–2001 he was Professor at the University of Bayreuth (Germany). Since 2001 he is Professor at the Department of Computer Science at the University of Innsbruck (Austria). From 1995 to 1996 he had an Erwin Schrödinger Scholarship of the Austrian Science Foundation (FWF) for visiting Texas A&M University and the University of Delaware (USA). Otmar Scherzer received the Award of the Austrian Mathematical Society (1998) and the START-price of the FWF in (1999). He is in the editorial board of Numerical Functional Analysis and Optimization and Inverse Problems. His research interest include image processing and inverse problems.This revised version was published online in June 2005 with correction to CoverDate     

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.     

Notes on wormhole existence in scalar-tensor and <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G _eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G _eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G _eff changes its sign.