How to Guard a Graph?

We initiate the study of the algorithmic foundations of games in which a set of cops has to guard a region in a graph (or digraph) against a robber. The robber and the cops are placed on vertices of the graph; they take turns in moving to adjacent vertices (or staying). The goal of the robber is to enter the guarded region at a vertex with no cop on it. The problem is to find the minimum number of cops needed to prevent the robber from entering the guarded region. The problem is highly non-trivial even if the robber’s or the cops’ regions are restricted to very simple graphs. The computational complexity of the problem depends heavily on the chosen restriction. In particular, if the robber’s region is only a path, then the problem can be solved in polynomial time. When the robber moves in a tree (or even in a star), then the decision version of the problem is NP-complete. Furthermore, if the robber is moving in a directed acyclic graph, the problem becomes PSPACE-complete.     

On continued fraction expansion of real roots of polynomial systems, complexity and condition numbers

We elaborate on a correspondence between the coefficients of a multivariate polynomial represented in the Bernstein basis and in a tensor-monomial basis, which leads to homography representations of polynomial functions that use only integer arithmetic (in contrast to the Bernstein basis) and are feasible over unbounded regions. Then, we study an algorithm to split this representation and obtain a subdivision scheme for the domain of multivariate polynomial functions. This implies a new algorithm for real root isolation, MCF, that generalizes the Continued Fraction (CF) algorithm of univariate polynomials.A partial extension of Vincent’s Theorem for multivariate polynomials is presented, which allows us to prove the termination of the algorithm. Bounding functions, projection and preconditioning are employed to speed up the scheme. The resulting isolation boxes have optimized rational coordinates, corresponding to the first terms of the continued fraction expansion of the real roots. Finally, we present new complexity bounds for a simplified version of the algorithm in the bit complexity model, and also bounds in the real RAM model for a family of subdivision algorithms in terms of the real condition number of the system. Examples computed with our C++ implementation illustrate the practical aspects of our method.     

An efficient approach for solving the Riccati equation with fractional orders

The present study introduces a novel and simple analytical method for the solution of fractional order Riccati differential equation. In this approach, the solution considered as a Taylor series expansion converges rapidly to the nonlinear problem. New homotopy perturbation method (NHPM) depends only on two components of the homotopy series. The method is illustrated by applications and the results obtained are compared with those of the exact solution. Moreover, comparing the methodology with some known techniques shows that the present approach is relatively easy and efficient.     

Characterizing and approximating eigenvalue sets of symmetric interval matrices

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries are perturbed, with perturbations belonging to some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guarantee exactness. We illustrate our approach by several examples and numerical experiments.     

High-accuracy differential measurement of ultrasonic velocity in liquids

An improved technique for measuring very accurately the difference in sound velocity between two liquids is described. The technique, which can be used over a frequency range from 1 to 100 MHz, uses a differential cell that is completely submerged in a thermostatically controlled fluid and a phase-sensitive detection scheme accurate to 2x10(-4) signal periods. Measurements of the velocity difference between water and dilute NaCl solutions (3x10(-5) to 6.6x10(-4) M), accurate to +/-0.02 cm s(-1) (relative accuracy 1 part in 10(7)), are presented.     

Properties of ZrO2–Al2O3 composite as a function of isothermal holding time

Zirconia and alumina based ceramics present interesting properties for their application as implants, such as biocompatibility, good fracture resistance, as well as high fracture toughness and hardness. In this work the influence of sintering time on the properties of a ZrO₂–Al₂O₃ composite material, containing 20 wt% of Al₂O₃, has been investigated. The ceramic composites were obtained by sintering, in air, at 1600 °C for sintering times between 0 and 1440 min. Sintered samples were characterized by microstructure and crystalline phases, as well as by mechanical properties. The grain growth exponents, n, for the ZrO₂ and Al₂O₃ were 2.8 and 4.1, respectively, indicating that different mechanisms are responsible for grain growth of each phase. After sintering at 1600 °C, the material exhibited a dependency of hardness as function of sintering time, with hardness values between 1500 HV (120 min) and 1310 HV (1440 min) and a fracture toughness of 8 MPa m^1/2, which makes it suitable for bioapplications, such as dental implants.     

Cooperative energy efficient D2D clustering in LTE-A with enhanced QoS

Device-to-device (D2D) communications in the long term evolution (LTE) Advanced (LTE-A) cellular system are investigated. The objective is to form collaborative D2D groups for transmitting/receiving data in the uplink (UL) and downlink (DL) in an energy efficient manner. The energy minimization problem using multihop D2D is formulated as a binary integer linear program. A low complexity suboptimal solution method is proposed, and shown to lead to good performance, especially in the low complexity 1-hop D2D scenario. The investigated framework is applicable to both public safety (PS) and non-PS scenarios. In addition to significant energy savings, the proposed method is shown to lead to reduced delays and enhanced quality of service (QoS), especially when real-time video transmission is considered.     

Ozone Disinfection Efficiency for Indicator Microorganisms at Different pH Values and Temperatures

Disinfection efficiency of ozone was determined in various types of water at different pH (6, 7 and 8) values and temperatures (15, 25 and 35 ^°C) for E. coli and Salmonella. Three different applied ozone concentrations (1.5, 1.7, and 2 mg/L) in the gas phase were applied, and samples were taken at different time intervals to determine microbial survival using spread plate count (SPC) and ozone residual. Highest microbial inactivation was observed in distilled water with applied ozone concentration of 2 mg/L in the gas phase. Survival of E. coli was higher at pH 8 and 15 ^°C as compared to lower pH values and temperatures as depicted by the inactivation kinetics of the test microbes used in the study. Salmonella showed 5 and 6 log removal after contact time of 45 and 60 sec, respectively, at 2 mg/L. Disinfection of mixed culture showed relatively more survival of E. coli; as 3 and 4 log removal of E. coli and 4 and 5 log removal of Salmonella was observed after 45 and 60 sec.     

A contextual-based segmentation of compact PolSAR images using Markov Random Field (MRF) model

As the first major step in each object-oriented feature extraction approach, segmentation plays an essential role as a preliminary step towards further and higher levels of image processing. The primary objective of this paper is to illustrate the potential of Polarimetric Synthetic Aperture Radar (PolSAR) features extracted from Compact Polarimetry (CP) SAR data for image segmentation using Markov Random Field (MRF). The proposed method takes advantage of both spectral and spatial information to segment the CP SAR data. In the first step of the proposed method, k-means clustering was applied to over-segment the image using the appropriate features optimally selected using Genetic Algorithm (GA). As a similarity criterion in each cluster, a probabilistic distance was used for an agglomerative hierarchical merging of small clusters into an appropriate number of larger clusters. In the agglomerative clustering approach, the estimation of the appropriate number of clusters using the data log-likelihood algorithm differs depending on the distance criterion used in the algorithm. In particular, the Wishart Chernoff distance which is independent of samples (pixels) tends to provide a higher appropriate number of clusters compared to the Wishart test statistic distance. This is because the Wishart Chernoff distance preserves detailed data information corresponding to small clusters. The probabilistic distance used in this study is Wishart Chernoff distance which evaluates the similarity of clusters by measuring the distance between their complex Wishart probability density functions. The output of this step, as the initial segmentation of the image, is applied to a Markov Random Field model to improve the final segmentation using vicinity information. The method combines Wishart clustering and enhanced initial clusters in order to access the posterior MRF energy function. The contextual image classifier adopts the Iterated Conditional Mode (ICM) approach to converge to a local minimum and represent a good trade-off between segmentation accuracy and computation burden. The results showed that the PolSAR features extracted from CP mode can provide an acceptable overall accuracy in segmentation when compared to the full polarimetry (FP) and Dual Polarimetry (DP) data. Moreover, the results indicated that the proposed algorithm is superior to the existing image segmentation techniques in terms of segmentation accuracy.     

A survey and comparison on overlay‐underlay mapping techniques in peer‐to‐peer overlay networks

Peer‐to‐peer (P2P) overlay networks were developed initially for file sharing such as Napster and Gnutella; but later, they have become popular for content sharing, media streaming, telephony applications, etc. Underlay‐unawareness in P2P systems can result in suboptimal peer selection for overlay routing and hence poor performance. In this paper, we present a comprehensive survey of the research work carried out to solve the overlay‐underlay mapping problems up till now. The majority of underlay‐aware proposals for peer selection focus on finding the shortest overlay routes by selecting nearest nodes according to proximity information. Another class of approaches is based on passive or active probing for provision of underlay information to P2P applications. Some other optimizations propose use of P2P middleware to extract, process, and refine underlay information and provide it to P2P overlay applications. Another class of approaches strive to use ISPs or third parties to provide underlay information to P2P overlay applications according to their requirements. We have made a state‐of‐the‐art review and comparison for addressing the overlay‐underlay mismatch in terms of their operation, merits, limitations, and future directions.