The <Emphasis Type="Italic">MAP</Emphasis> + <Emphasis Type="Italic">MAP/PH</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis> queuing system with single and batch arrivals of customers

The single-server queuing system with finite buffer was considered. The customers may arrive one-by-one or in batches. Arrivals of single customers and their batches obey the Markov input processes. The customers from a batch taken for servicing come one at a time at the exponentially distributed time intervals. The numbers of customers in batches are distributed geometrically. The time of customer servicing has a phase-type distribution. The numbers of batches and single customers that may be simultaneously accepted by the system are controllable parameters. The joint distribution of the number of batches and the number of customers in system, loss probabilities, distribution of the time of batch sojourn, and problems of optimization were analyzed.     

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.     

Local gravity constraints and power law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) theories

There is a conformal equivalence between power law f(R) theories and scalar field theories in which the scalar degree of freedom evolves under the action of an exponential potential function. In the scalar field representation, there is a strong coupling of the scalar field with the matter sector due to the conformal transformation. We use the chameleon mechanism to implement constraints on the potential function of the scalar field in order that the resulting model be in accord with Solar System experiments. Investigation of these constraints reveals that there may be no possibility to distinguish between a power law f(R) function and the usual Einstein-Hilbert Lagrangian density.     

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.     

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.     

A multiserver MAP/PH/<Emphasis Type="Italic">N</Emphasis> system with controlled broadcasting by unreliable servers

A multiserver queuing system with an unlimited buffer is considered. The customer arrival is described by the Markov arrival process. The service time has a phase-type distribution. The service may occur with errors. The service strategy is as follows. If the number of busy servers is higher than a certain threshold value at the moment of the customer arrival, then the customer is copied, and the copies are serviced by all the free servers. If the number of busy servers is not higher than this threshold at the moment of the customer arrival, then the customer is serviced by one server. Stationary distributions of the number of customers and the residence time within the system are obtained. The threshold’s influence on the main parameters of the system’s productivity is numerically investigated.     

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.     

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.     

An <Emphasis Type="Italic">R</Emphasis> || <Emphasis Type="Italic">C</Emphasis><Subscript>max</Subscript> Quantum Scheduling Algorithm

Grover’s search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which show a square root speedup over their classical counterparts. In this paper, we discuss a systematic way to formulate such problems and give as an example a quantum scheduling algorithm for an R||C_max problem. R||C_max is representative for a class of scheduling problems whose goal is to find a schedule with the shortest completion time in an unrelated parallel machine environment. Given a deadline, or a range of deadlines, the algorithm presented in this paper allows us to determine if a solution to an R||C_max problem with N jobs and M machines exists, and if so, it provides the schedule. The time complexity of the quantum scheduling algorithm is while the complexity of its classical counterpart is .     

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.     

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.     

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.     

States on <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> algebras

The aim of this paper is to introduce the notion of states on R ₀ algebras and investigate some of their properties. We prove that every R ₀ algebra possesses at least one state. Moreover, we investigate states on weak R ₀ algebras and give some examples to show that, in contrast to R ₀ algebras, there exist weak R ₀ algebras which have no states. We also derive the condition under which finite linearly ordered weak R ₀ algebras have a state. This work is supported by NSFC (No.60605017).     

Transit cosmological models with domain walls in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R,T</Emphasis>) gravity

We study the physical behavior of the transition of a 5D perfect fluid universe from an early decelerating phase to the current accelerating phase in the framework of f(R, T) theory of gravity in the presence of domain walls. The fifth dimension is not observed because it is compact. To determine the solution of the field equations, we use the concept of a time-dependent deceleration parameter which yields the scale factor a(t) = sinh^1/n(αt), where n and α are positive constants. For 0 < n ≤ 1, this generates a class of accelerating models, while for n > 1 the universe attains a phase transition from an early decelerating phase to the present accelerating phase, consistent with the recent observations. Some physical and geometric properties of the models are also discussed.     

Some high-rate linear codes over <Emphasis Type="Italic">GF</Emphasis>(5) and <Emphasis Type="Italic">GF</Emphasis>(7)

Let an [n, k, d] _q code be a linear code of length n, dimension k, and with minimum Hamming distance d over GF(q). The ratio R = k/n is called the rate of a code. In this paper, [62, 53, 6]₅, [62, 48, 8]₅, [71, 56, 8]₅, [124, 113, 6]₅, [43, 36, 6]₇, [33, 23, 7]₇, and [27, 18, 7]₇ high-rate codes and new codes with parameters [42, 14, 19]₅, [42, 15, 18]₅, [48, 13, 24]₅, [52, 12, 28]₅, [71, 15, 38]₅, [71, 16, 36]₅, [72, 12, 41]₅, [78, 10, 50]₅, [88, 11, 54]₅, [88, 13, 51]₅, [124, 14, 77]₅, [32, 12, 15]₇, [32, 10, 17]₇, [36, 10, 20]₇, and [48, 10, 29]₇ are constructed. The codes with parameters [62, 53, 6]₅ and [43, 36, 6]₇ are optimal.     

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.     

(1+4)-dimensional spherically symmetric black holes in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>)

New non-vacuum spherically symmetric solutions in (1+4)-dimensional space-time are derived using the field equations of f(T) theory, where T is the torsion scalar defined as \(T\mathop = \limits^{def} {T^\mu }_{\nu \rho }S_\mu ^{\nu \rho }\). The energy density, radial and transversal pressures in these solutions are shown to satisfy the energy conditions. Other interesting solutions are obtained under the constraint of vanishing radial pressure for different choices of f(T). Impositions are provided to reproduce the (1+4)-dimensional AdS-Schwarzschild solution. In the quadratic case, i.e., f(T) ∝ T ², other impositions are derived and have shown to satisfy the non-diagonal components of the field equations of f(T) theory. The physics relevant to the resulting models is discussed.     

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.     

Exact 3-satisfiability is decidable in time <Emphasis Type="Italic">O</Emphasis>(2<Superscript>0.16254<Emphasis Type="Italic">n</Emphasis></Superscript>)

Let F=C ₁C _m be a Boolean formula in conjunctive normal form over a set V of n propositional variables, s.t. each clause C _i contains at most three literals l over V. Solving the problem exact 3-satisfiability (X3SAT) for F means to decide whether there is a truth assignment setting exactly one literal in each clause of F to true (1). As is well known X3SAT is NP-complete [6]. By exploiting a perfect matching reduction we prove that X3SAT is deterministically decidable in time O(2^0.18674n ). Thereby we improve a result in [2,3] stating X3SATO(2^0.2072n ) and a bound of O(2^0.200002n ) for the corresponding enumeration problem #X3SAT stated in a preprint [1]. After that by a more involved deterministic case analysis we are able to show that X3SATO(2^0.16254n ).     

<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.