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.

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.     

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.     

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.

(<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.     

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.     

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.     

Proving Arrow’s theorem by <Emphasis Type="SmallCaps">PROLOG</Emphasis>

This paper presented a simple PROLOG implementation for Arrow’s Social welfare function (SWF). Arrow (Social choice and individual values, Yale University Press, 1963) proved that any SWF which satisfies a set of conditions IIA, Pareto, and unrestricted domain should be dictatorial. The PROLOG program can prove the theorem for 3-alternative 2-agent case. With a minor modification it proves a version of the theorem without the Pareto condition by Wilson (Journal of Economic Theory, 5, 478–486, 1972).     

Difficult Configurations—On the Complexity of <Emphasis Type="Italic">LTrL</Emphasis>

The complexity of LTrL, a global linear time temporal logic over traces is investigated. The logic is global because the truth of a formula is evaluated in a global state, also called configuration. The logic is shown to be non-elementary with the main reason for this complexity being the nesting of until operators in formulas. The fragment of the logic without the until operator is shown to be EXPSPACE-hard.Supported by Polish KBN grant No. 8 T11C 002 11.     

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.     

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.     

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.     

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

A discipline for a stage? A Shakespearean reflection on the research <Emphasis Type="Italic">plot</Emphasis> and <Emphasis Type="Italic">performance</Emphasis> of the Information Systems field

The different traditions of European and North American Information Systems research are highlighted and traditional means of measuring research quality (including citation patterns and journal impact factors) are questioned. Shakespearean metaphors are used to highlight these distinctions. The article concludes with a call for greater diversity and appreciation of alternative research traditions and cultures, and of the journals that publish such research.     

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).     

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.     

ℚ-bounds consistency for the <Emphasis Type="SmallCaps">spread</Emphasis> constraint with variable mean

The spread constraint enforces a relationship amongst a set of variables, their mean, and their standard deviation. The ?-bounds consistency (BC) algorithms that have been formally published and the implementations of which we are aware all assume a fixed mean value. A sketch of the BC algorithm with variable mean was proposed, which relies on the continuity property of a key function used in the fixed mean case. We show that this function may be piecewise discontinuous, meaning that the extension of the algorithm to the variable mean case that is suggested in the literature is unsound. We propose a simple modification of the algorithm that achieves ?-BC with variable mean.     

The <Emphasis Type="Italic">λ</Emphasis>-Calculus and the Unity of Structural Proof Theory

In the context of intuitionistic implicational logic, we achieve a perfect correspondence (technically an isomorphism) between sequent calculus and natural deduction, based on perfect correspondences between left-introduction and elimination, cut and substitution, and cut-elimination and normalisation. This requires an enlarged system of natural deduction that refines von Plato’s calculus. It is a calculus with modus ponens and primitive substitution; it is also a “coercion calculus”, in the sense of Cervesato and Pfenning. Both sequent calculus and natural deduction are presented as typing systems for appropriate extensions of the λ-calculus. The whole difference between the two calculi is reduced to the associativity of applicative terms (sequent calculus = right associative, natural deduction = left associative), and in fact the achieved isomorphism may be described as the mere inversion of that associativity. The novel natural deduction system is a “multiary” calculus, because “applicative terms” may exhibit a list of several arguments. But the combination of “multiarity” and left-associativity seems simply wrong, leading necessarily to non-local reduction rules (reason: normalisation, like cut-elimination, acts at the head of applicative terms, but natural deduction focuses at the tail of such terms). A solution is to extend natural deduction even further to a calculus that unifies sequent calculus and natural deduction, based on the unification of cut and substitution. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for a class of nonlinear networked control systems

In this paper, the mixed H ₂/H _∞ control problem is investigated for a class of nonlinear discrete-time networked control systems with random network-induced delays, stochastic packet dropouts and probabilistic sensor faults. The packet dropouts process is modeled as a homogeneous Markov chains taking values in a finite state space. Network-induced delays occur in a random way with known upper bound. A set of stochastic variables are exploited to describe sensor faults with different probabilistic density functions. By using a delay-dependent Lyapunov functional, a mode-dependent mixed H ₂/H _∞ controller is designed to guarantee both stochastic stability of the closed-loop system and the prescribed H2, H¥ control performances. Sufficient conditions for the existence of the mixed H ₂/H _∞ controller are presented in terms of a series of LMIs. If these LMIs are feasible, then the modedependent mixed H ₂/H _∞ controller can be obtained. A numerical example is given to demonstrate the effectiveness of the developed method.