Scalar Field Cosmology in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) Gravity with Λ

We study the behavior of cosmological parameters, massive and massless scalar fields (normal or phantom) with a scalar potential in f(R, T) theory of gravity for a flat Friedmann-Robertson-Walker (FRW) universe. To get exact solutions to the modified field equations, we use the f(R, T) = R + 2f(T) model by Harko et al. (T. Harko et al., Phys. Rev. D 84, 024020 (2011)), where R is the Ricci scalar and T is the trace of the energy momentum tensor. Our cosmological parameter solutions agree with the recent observational data. Finally, we discuss our results with various graphics.     

(<Emphasis Type="Italic">α</Emphasis>, <Emphasis Type="Italic">k</Emphasis>)-anonymous data publishing

Privacy preservation is an important issue in the release of data for mining purposes. The k-anonymity model has been introduced for protecting individual identification. Recent studies show that a more sophisticated model is necessary to protect the association of individuals to sensitive information. In this paper, we propose an (α, k)-anonymity model to protect both identifications and relationships to sensitive information in data. We discuss the properties of (α, k)-anonymity model. We prove that the optimal (α, k)-anonymity problem is NP-hard. We first present an optimal global-recoding method for the (α, k)-anonymity problem. Next we propose two scalable local-recoding algorithms which are both more scalable and result in less data distortion. The effectiveness and efficiency are shown by experiments. We also describe how the model can be extended to more general cases.     

The (<Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">q</Emphasis>, <Emphasis Type="Italic">r</Emphasis>, <Emphasis Type="Italic">l</Emphasis>) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean

This paper investigates a hill type economic production-inventory quantity (EPIQ) model with variable lead-time, order size and reorder point for uncertain demand. The average expected cost function is formulated by trading off costs of lead-time, inventory, lost sale and partial backordering. Due to the nature of the demand function, the frequent peak (maximum) and valley (minimum) of the expected cost function occur within a specific range of lead time. The aim of this paper is to search the lowest valley of all the valley points (minimum objective values) under fuzzy stochastic demand rate. We consider Intuitionistic fuzzy sets for the parameters and used Intuitionistic Fuzzy Aggregation Bonferroni mean for the defuzzification of the hill type EPIQ model. Finally, numerical examples and graphical illustrations are made to justify the model.     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.     

Equivalence between Closed Connected <Emphasis Type="Italic">n</Emphasis>-<Emphasis Type="Italic">G</Emphasis>-Maps without Multi-Incidence and <Emphasis Type="Italic">n</Emphasis>-Surfaces

Many combinatorial structures have been designed to represent the topology of space subdivisions and images. We focus here on two particular models, namely the n-G-maps used in geometric modeling and computational geometry and the n-surfaces used in discrete imagery. We show that a subclass of n-G-maps is equivalent to n-surfaces. To achieve this, we provide several characterizations of n-surfaces. Finally, the proofs being constructive, we show how to switch from one representation to another effectively.

A two-phase <Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 → ·/<Emphasis Type="Italic">PH</Emphasis>/1/0 system with losses

We find a stationary distribution and productivity characteristics for a two-phase queueing system with recurrent input flow. The servicing units are single-line on both phases. The servicing times have phase-type distributions. On the first phase, there is an infinite buffer. There is no intermediate buffer. In case the second phase device is busy at the time a claim has finished going through the first phase, this claim leaves the system unserved (is lost).     

Stochastic problems in <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> and <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

We consider stochastic control systems subjected simultaneously to stochastic and determinate perturbations. Stochastic perturbations are assumed to be state-multiplicative stochastic processes, while determinate perturbations can be any processes with finite energy on infinite time interval. The results of the determinate H _∞-theory are compared to their stochastic analogs. The determinate and stochastic theories are linked together by the lemma that establishes the equivalence between the stability and boundness of the ‖L‖_∞ < γ norm of the perturbation operator L, from one side, and the solvability of certain linear matrix inequalities (LMIs), from the other side. As soon as the stochastic version of the lemma is proven, the γ-controller analysis and design problems are solved, in general, identically in the frame of the united LMI methodology.     

What Is Context <Emphasis Type="Italic">For</Emphasis>? <Emphasis Type="Italic">Syntax in a Non-Abstract World</Emphasis>

An explanation for the uncertain progress of formalist linguistics is sought in an examination of the concept of syntax. The idea of analyzing language formally was made possible by developments in 20th century logic. It has been pointed out by many that the analogy between natural language and a formal system may be imperfect, but the objection made here is that the very concept of syntax, when applied to any non-abstract system of communication, is flawed as it is commonly used. Syntax is properly defined with respect to an individual transformation rule that might be applied to some message. Collections of syntax rules, however, are inevitably due to categories imposed by an observer, and do not correspond to functional features found in non-abstract systems. As such, these categories should not be relied upon as aids to understanding any natural system.     

The <Emphasis Type="Italic">k</Emphasis>-Homotopic Thinning and a Torus-Like Digital Image in <Emphasis Type="Bold">Z</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In order to discuss digital topological properties of a digital image (X,k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with k-adjacency. More precisely, let be a simple closed k _i -curve with l _i elements in . For some k-adjacency of the digital product which is a torus-like set, proceeding with the k-homotopic thinning of , we obtain its k-homotopic thinning set denoted by DT _k . Writing an algorithm for calculating the digital fundamental group of , we investigate the k-fundamental group of by the use of various properties of a digital covering (Z×Z,p ₁×p ₂,DT _k ), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property (contrary to the multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the view points of both digital k-homotopy theory and mathematical morphology.

Parallel Multi-Block ADMM with <Emphasis Type="Italic">o</Emphasis>(1 / <Emphasis Type="Italic">k</Emphasis>) Convergence

This paper introduces a parallel and distributed algorithm for solving the following minimization problem with linear constraints:

$$\begin{aligned} \text {minimize} ~~&f_1(\mathbf{x}_1) + \cdots + f_N(\mathbf{x}_N)\\ \text {subject to}~~&A_1 \mathbf{x}_1 ~+ \cdots + A_N\mathbf{x}_N =c,\\&\mathbf{x}_1\in {\mathcal {X}}_1,~\ldots , ~\mathbf{x}_N\in {\mathcal {X}}_N, \end{aligned}$$

where \(N \ge 2\), \(f_i\) are convex functions, \(A_i\) are matrices, and \({\mathcal {X}}_i\) are feasible sets for variable \(\mathbf{x}_i\). Our algorithm extends the alternating direction method of multipliers (ADMM) and decomposes the original problem into N smaller subproblems and solves them in parallel at each iteration. This paper shows that the classic ADMM can be extended to the N-block Jacobi fashion and preserve convergence in the following two cases: (i) matrices \(A_i\) are mutually near-orthogonal and have full column-rank, or (ii) proximal terms are added to the N subproblems (but without any assumption on matrices \(A_i\)). In the latter case, certain proximal terms can let the subproblem be solved in more flexible and efficient ways. We show that \(\Vert {\mathbf {x}}^{k+1} - {\mathbf {x}}^k\Vert _M^2\) converges at a rate of o(1 / k) where M is a symmetric positive semi-definte matrix. Since the parameters used in the convergence analysis are conservative, we introduce a strategy for automatically tuning the parameters to substantially accelerate our algorithm in practice. We implemented our algorithm (for the case ii above) on Amazon EC2 and tested it on basis pursuit problems with >300 GB of distributed data. This is the first time that successfully solving a compressive sensing problem of such a large scale is reported.

     

<Emphasis Type="Italic">κ</Emphasis>-<Emphasis Type="Italic">PMP</Emphasis>: Enhancing Physics-based Motion Planners with Knowledge-Based Reasoning

Physics-based motion planning is a challenging task, since it requires the computation of the robot motions while allowing possible interactions with (some of) the obstacles in the environment. Kinodynamic motion planners equipped with a dynamic engine acting as state propagator are usually used for that purpose. The difficulties arise in the setting of the adequate forces for the interactions and because these interactions may change the pose of the manipulatable obstacles, thus either facilitating or preventing the finding of a solution path. The use of knowledge can alleviate the stated difficulties. This paper proposes the use of an enhanced state propagator composed of a dynamic engine and a low-level geometric reasoning process that is used to determine how to interact with the objects, i.e. from where and with which forces. The proposal, called κ-PMP can be used with any kinodynamic planner, thus giving rise to e.g. κ-RRT. The approach also includes a preprocessing step that infers from a semantic abstract knowledge described in terms of an ontology the manipulation knowledge required by the reasoning process. The proposed approach has been validated with several examples involving an holonomic mobile robot, a robot with differential constraints and a serial manipulator, and benchmarked using several state-of-the art kinodynamic planners. The results showed a significant difference in the power consumption with respect to simple physics-based planning, an improvement in the success rate and in the quality of the solution paths.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for linear infinite-dimensional systems

In this paper, we consider mixed H ₂/H _∞ control problems for linear infinite-dimensional systems. The first part considers the state feedback control for the H ₂/H _∞ control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H ₂/H _∞ control problem for linear infinitedimensional systems are presented in terms of the solutions of the coupled operator Riccati equations and coupled differential operator Riccati equations. The second part addresses the observer-based H ₂/H _∞ control of linear infinite-dimensional systems with infinite horizon and finite horizon costs. The solutions for the observer-based H ₂/H _∞ control problem of linear infinite-dimensional systems are represented in terms of the solutions of coupled operator Riccati equations. The first-order partial differential system examples are presented for illustration. In particular, for these examples, the Riccati equations are represented in terms of the coefficients of first-order partial differential systems.     

Approximate Pattern Matching with the <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> and <Emphasis Type="Italic">L</Emphasis><Subscript>∞</Subscript> Metrics

Given an alphabet Σ={1,2,…,|Σ|} text string T∈Σ ⁿ and a pattern string P∈Σ ^m , for each i=1,2,…,n−m+1 define L _p (i) as the p-norm distance when the pattern is aligned below the text and starts at position i of the text. The problem of pattern matching with L _p distance is to compute L _p (i) for every i=1,2,…,n−m+1. We discuss the problem for d=1,2,∞. First, in the case of L ₁ matching (pattern matching with an L ₁ distance) we show a reduction of the string matching with mismatches problem to the L ₁ matching problem and we present an algorithm that approximates the L ₁ matching up to a factor of 1+ε, which has an O(\frac1e²nlogmlog|S|)O(\frac{1}{\varepsilon^{2}}n\log m\log|\Sigma|) run time. Then, the L ₂ matching problem (pattern matching with an L ₂ distance) is solved with a simple O(nlog m) time algorithm. Finally, we provide an algorithm that approximates the L _∞ matching up to a factor of 1+ε with a run time of O(\frac1enlogmlog|S|)O(\frac{1}{\varepsilon}n\log m\log|\Sigma|) . We also generalize the problem of String Matching with mismatches to have weighted mismatches and present an O(nlog ⁴ m) algorithm that approximates the results of this problem up to a factor of O(log m) in the case that the weight function is a metric.     

Small deviations for two classes of Gaussian stationary processes and <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-functionals, 0 < <Emphasis Type="Italic">p</Emphasis> ≤ ∞

Let w(t) be a standard Wiener process, w(0) = 0, and let η _a (t) = w(t + a) − w(t), t ≥ 0, be increments of the Wiener process, a > 0. Let Z _a (t), t ∈ [0, 2a], be a zeromean Gaussian stationary a.s. continuous process with a covariance function of the form E Z _a (t)Z _a (s) = 1/2[a − |t − s|], t, s ∈ [0, 2a]. For 0 < p < ∞, we prove results on sharp asymptotics as ɛ → 0 of the probabilities

An efficient (<Emphasis Type="Italic">t</Emphasis>,<Emphasis Type="Italic">n</Emphasis>)–threshold secret image sharing scheme

We propose a novel (t,n)–threshold secret image sharing scheme based on Shamir’s polynomial interpolation paradigm. The proposed scheme is a derivative of Thien and Lin’s (Computers & Graphics 26(5):765–770, [13]) and some of its variants by ensuring less intrusive changes in the secret image. This is achieved by cyclically shifting the bits of the secret image, thus allowing a modification in the least significant bit to have a large effect on the values used in computation of shadow images. Statistical tests and simulations are presented to show the efficiency and robustness of the proposed scheme, in particular good randomness of shadow images, little correlation between adjacent pixels, and high entropy. Competence of the proposed scheme is further demonstrated by means of comparison with existing schemes.     

Cryptanalysis and improvement of verifiable quantum (<Emphasis Type="Italic">k</Emphasis>, <Emphasis Type="Italic">n</Emphasis>) secret sharing

After analyzing Yang’s verifiable quantum secret sharing (VQSS) scheme, we show that in their scheme a participant can prepare a false quantum particle sequence corresponding to a forged share, while other any participant cannot trace it. In addition, an attacker or a participant can forge a new quantum sequence by transforming an intercepted quantum sequence; moreover, the forged sequence can pass the verification of other participants. So we propose a new VQSS scheme to improve the existed one. In the improved scheme, we construct an identity-based quantum signature encryption algorithm, which ensures chosen plaintext attack security of the shares and their signatures transmitted in the quantum tunnel. We employ dual quantum signature and one-way function to trace against forgery and repudiation of the deceivers (dealer or participants). Furthermore, we add the reconstruction process of quantum secret and prove the security property against superposition attack in this process.     

Adaptive Finite Element Simulation of the Time-dependent Simplified <Emphasis Type="Italic">P</Emphasis><Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> Equations

The steady-state simplified P _N approximation to the radiative transfer equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified P _N equations have been derived by an asymptotic analysis similar to the asymptotic derivation of the steady-state SP _N equations (Frank et al. in J. Comput. Phys. 226:2289–2305, 2007). In this paper, we present computational results for the time-dependent SP _N equations in two dimensions, obtained by using an adaptive finite element approach. Several numerical comparisons with other existing models are shown.     

An Entropy Stable <Emphasis Type="Italic">h</Emphasis> / <Emphasis Type="Italic">p</Emphasis> Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre–Gauss–Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between non-conforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h / p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.     

Design of optimal and robust control with <Emphasis Type="Italic">H</Emphasis> <Subscript>∞</Subscript>/<Emphasis Type="Italic">γ</Emphasis> <Subscript>0</Subscript> performance criterion

For a double-input single-output system, this paper defines a disturbance attenuation level (called H_∞/γ₀ norm) as the maximum-value L₂ norm of the output under an unknown disturbance with a bounded L₂ norm supplied to the first input and an impulsive disturbance in the form of the product of an unknown vector and the delta function supplied the second input, where the squared L₂ norm of the former disturbance plus the quadratic form of the impulsive disturbance vector does not exceed 1. Weight matrix choice in the H_∞/γ₀ norm yields a trade-off between the attenuation level of the L₂ disturbance and the attenuation level of the impulsive disturbance in corresponding channels. For the uncertain systems with dynamic or parametric uncertainty in the feedback loop, a robust H_∞/γ₀ norm is introduced that includes the robust H_∞ and γ₀ norms as special cases. All these characteristics or their upper bounds in the uncertain system are expressed via solutions of linear matrix inequalities. This gives a uniform approach for designing optimal and robust control laws with the H_∞/γ₀, H_∞ and γ₀ performance criteria.     

Convex maximization and Schachermayer property <Emphasis Type="Italic">α</Emphasis>

The problem of maximization of a convex functional on a closed ball in a nonreflexive Banach space is analyzed. A linear variational principle is proved for problems stated in a Banach space with the Schachermayer property α. This work was carried out with financial support from the Fundamental Researches State Fund of Ukraine. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 166–169, March–April 2009.