On reliability of the folded hypercubes

In this paper, we explore the 2-extra connectivity and 2-extra-edge-connectivity of the folded hypercube FQ_n. We show that κ₂(FQ_n) = 3n − 2 for n ⩾ 8; and λ₂(FQ_n) = 3n − 1 for n ⩾ 5. That is, for n ⩾ 8 (resp. n ⩾ 5), at least 3n − 2 vertices (resp. 3n − 1 edges) of FQ_n are removed to get a disconnected graph that contains no isolated vertices (resp. edges). When the folded hypercube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.     

Highly fault-tolerant cycle embeddings of hypercubes

The hypercube Q_n is one of the most popular networks. In this paper, we first prove that the n-dimensional hypercube is 2n − 5 conditional fault-bipancyclic. That is, an injured hypercube with up to 2n − 5 faulty links has a cycle of length l for every even 4 ⩽ l ⩽ 2ⁿ when each node of the hypercube is incident with at least two healthy links. In addition, if a certain node is incident with less than two healthy links, we show that an injured hypercube contains cycles of all even lengths except hamiltonian cycles with up to 2n − 3 faulty links. Furthermore, the above two results are optimal. In conclusion, we find cycles of all possible lengths in injured hypercubes with up to 2n − 5 faulty links under all possible fault distributions.     

A fast fault-identification algorithm for bijective connection graphs using the PMC model

Diagnosis of reliability is an important topic for interconnection networks. Under the classical PMC model, Dahura and Masson [5] proposed a polynomial time algorithm with time complexity O(N^2.5) to identify all faulty nodes in an N-node network. This paper addresses the fault diagnosis of so called bijective connection (BC) graphs including hypercubes, twisted cubes, locally twisted cubes, crossed cubes, and Möbius cubes. Utilizing a helpful structure proposed by Hsu and Tan [20] that was called the extending star by Lin et al. [24], and noting the existence of a structured Hamiltonian path within any BC graph, we present a fast diagnostic algorithm to identify all faulty nodes in O(N) time, where N = 2ⁿ, n ? 4, stands for the total number of nodes in the n-dimensional BC graph. As a result, this algorithm is significantly superior to Dahura–Masson’s algorithm when applied to BC graphs.     

Broadcast in the rendezvous model

In many large, distributed or mobile networks, broadcast algorithms are used to update information stored at the nodes. In this paper, we propose a new model of communication based on rendezvous and analyze a multi-hop distributed algorithm to broadcast a message in a synchronous setting. In the rendezvous model, two neighbors u and v can communicate if and only if u calls v and v calls u simultaneously. Thus nodes u and v obtain a rendezvous at a meeting point. If m is the number of meeting points, the network can be modeled by a graph of n vertices and m edges. At each round, every vertex chooses a random neighbor and there is a rendezvous if an edge has been chosen by its two extremities. Rendezvous enable an exchange of information between the two entities. We get sharp lower and upper bounds on the time complexity in terms of number of rounds to broadcast: we show that, for any graph, the expected number of rounds is between ln n and O (n²). For these two bounds, we prove that there exist some graphs for which the expected number of rounds is either O (ln (n)) or Ω (n²). For specific topologies, additional bounds are given.     

Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults

The star graph is viewed as an attractive alternative to the hypercube. In this paper, we investigate the Hamiltonicity of an n-dimensional star graph. We show that for any n-dimensional star graph (n≥4) with at most 3n−10 faulty edges in which each node is incident with at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves on the previously best known result for the case where the number of tolerable faulty edges is bounded by 2n−7. We also demonstrate that our result is optimal with respect to the worst case scenario, where every other node of a cycle of length 6 is incident with exactly n−3 faulty noncycle edges.     

Petri net based decision system modeling in real-time scheduling and control of flexible automotive manufacturing systems

This paper presents the design and the implementation of a Petri net (PN) model for the control of a flexible manufacturing system (FMS). A flexible automotive manufacturing system used in this environment enables quick cell configuration, and the efficient operation of cells. In this paper, we attempt to propose a flexible automotive manufacturing approach for modeling and analysis of shop floor scheduling problem of FMSs using high-level PNs. Since PNs have emerged as the principal performance modeling tools for FMS, this paper provides an object-oriented Petri nets (OOPNs) approach to performance modeling and to implement efficient production control. In this study, we modeled the system as a timed marked graph (TMG), a well-known subclass of PNs, and we showed that the problem of performance evaluation can be reduced to a simple linear programming (LP) problem with m − n + 1 variables and n constraints, where m and n represent the number of places and transitions in the marked graph, respectively. The presented PN based method is illustrated by modeling a real-time scheduling and control for flexible automotive manufacturing system (FAMS) in Valeo Turkey.     

Generalized Strong Pseudoprime Tests and Applications

We describe probabilistic primality tests applicable to integers whose prime factors are all congruent to 1 mod r where r is a positive integer;r =  2 is the Miller–Rabin test. We show that if ν rounds of our test do not find n ≠  =  (r +  1)²composite, then n is prime with probability of error less than (2 r) ^− ν. Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.     

Development of an optical fibre reflectance sensor for copper (II) detection based on immobilised salicylic acid

Immobilized salicylic acid onto XAD-2 (styrene–divinylbenzene cross-linked copolymer) has been attempted in this study as a reagent phase for the development of an optical fibre copper (II) sensor. The measurements were carried out at a given wavelength of 690.27 nm since it yielded the largest divergence different in reflectance spectra before and after reaction with the analyte element. The optimum response was obtained at pH 5.0. The linear dynamic range of Cu(II) was found within the concentration range of 1.0–2.0 mmol L⁻¹ with its LOD of 0.5 mmol L⁻¹. The sensor response from different probes (n = 9) gave an R.S.D. of 8.4% at 0.55 mmol L⁻¹ Cu(II). The effect of interfered ions at 1:1 molar ratio of Cu(II):foreign ion was also studied in this work.     

Energy-efficient topology control algorithm for maximizing network lifetime in wireless sensor networks with mobile sink

Uneven energy consumption is an inherent problem in wireless sensor networks characterized by multi-hop routing and many-to-one traffic pattern. Such unbalanced energy dissipation can significantly reduce network lifetime. In this paper, we study the problem of prolonging network lifetime in large-scale wireless sensor networks where a mobile sink gathers data periodically along the predefined path and each sensor node uploads its data to the mobile sink over a multi-hop communication path. By using greedy policy and dynamic programming, we propose a heuristic topology control algorithm with time complexity O(n(m + n log n)), where n and m are the number of nodes and edges in the network, respectively, and further discuss how to refine our algorithm to satisfy practical requirements such as distributed computing and transmission timeliness. Theoretical analysis and experimental results show that our algorithm is superior to several earlier algorithms for extending network lifetime.     

On identifying codes that are robust against edge changes

Assume that G = (V, E) is an undirected graph, and C ⊆ V. For every v ∈ V, denote I_r(G; v) = {u ∈ C: d(u,v) ≤ r}, where d(u,v) denotes the number of edges on any shortest path from u to v in G. If all the sets I_r(G; v) for v ∈ V are pairwise different, and none of them is the empty set, the code C is called r-identifying. The motivation for identifying codes comes, for instance, from finding faulty processors in multiprocessor systems or from location detection in emergency sensor networks. The underlying architecture is modelled by a graph. We study various types of identifying codes that are robust against six natural changes in the graph; known or unknown edge deletions, additions or both. Our focus is on the radius r = 1. We show that in the infinite square grid the optimal density of a 1-identifying code that is robust against one unknown edge deletion is 1/2 and the optimal density of a 1-identifying code that is robust against one unknown edge addition equals 3/4 in the infinite hexagonal mesh. Moreover, although it is shown that all six problems are in general different, we prove that in the binary hypercube there are cases where five of the six problems coincide.     

Primary Decomposition of Lattice Basis Ideals

We study the primary decomposition of lattice basis ideals. These ideals are binomial ideals with generators given by the elements of a basis of a saturated integer lattice. We show that the minimal primes of such an ideal are completely determined by the sign pattern of the basis elements, while the embedded primes are not. As a special case we examine the ideal generated by the 2  ×  2 adjacent minors of a generic m × n matrix. In particular, we determine all minimal primes in the 3  × n case. We also present faster ways of computing a generating set for the associated toric ideal from a lattice basis ideal.     

A relation context oriented approach to identify strong ties in social networks

Strong ties play a crucial role in transmitting sensitive information in social networks, especially in the criminal justice domain. However, large social networks containing many entities and relations may also contain a large amount of noisy data. Thus, identifying strong ties accurately and efficiently within such a network poses a major challenge. This paper presents a novel approach to address the noise problem. We transform the original social network graph into a relation context-oriented edge-dual graph by adding new nodes to the original graph based on abstracting the relation contexts from the original edges (relations). Then we compute the local k-connectivity between two given nodes. This produces a measure of the robustness of the relations. To evaluate the correctness and the efficiency of this measure, we conducted an implementation of a system which integrated a total of 450 GB of data from several different data sources. The discovered social network contains 4,906,460 nodes (individuals) and 211,403,212 edges. Our experiments are based on 700 co-offenders involved in robbery crimes. The experimental results show that most strong ties are formed with k ? 2.     

Curves of Genus 2 with (N,N) Decomposable Jacobians

Let C be a curve of genus 2 and ψ₁: C  −  → E ₁  a map of degree n, from C to an elliptic curveE₁ , both curves defined over C. This map induces a degree n map φ₁:P¹  −  → P ¹  which we call a Frey–Kani covering. We determine all possible ramifications for φ₁. If ψ₁:C  −  → E ₁  is maximal then there exists a maximal map ψ₂: C  −  → E ₂  , of degree n, to some elliptic curveE₂ such that there is an isogeny of degree n²from the JacobianJ_C to E₁ × E₂. We say thatJ_C is (n, n)-decomposable. If the degree n is odd the pair (ψ₂, E₂) is canonically determined. For n =  3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable.     

The possibility of using C20 fullerene and graphene as semiconductor segments for detection,and destruction of cyanogen-chloride chemical agent

Detection of hazardous chemical species by changing the electrical conductivity of a semiconductor matter is a proposed and applied way for decreasing their subsequent unpleasant effects. Recently, many examples of using inorganic or organic materials, polymeric, and also nano-sized species as sensors were reported in which, in some cases, those matters were strongly affective and suitable.In this project, we have made an assessment on whether the graphene segment or C₂₀ fullerene, able to sense the existence of cyanogen chloride NCCl? In order to gain trustable results, the possible reaction pathways along with the adsorption kinetics were investigated. Moreover, the electronic density of states DOS showed that C₂₀ fullerene senses the existence of cyanogen chloride agent with a clearer signal (ΔE_g = 0.0110 eV) compared to the graphene segment (ΔE_g = 0.0001 eV). Also the adsorption energy calculations showed that cyanogen chloride could be adsorbed by the fullerene in a multi-step process (E_ads1 = −0.852 kcal mol⁻¹; E_ads2 = −0.446 kcal mol⁻¹; E_ads3 = −2.330 kcal mol⁻¹).     

Bounds for the Roots of Lacunary Polynomials

A polynomial P(X)  = X^d + a_d − 1X^d − 1 + ⋯ is called lacunary when a_d − 1 =  0. We give bounds for the roots of such polynomials with complex coefficients. These bounds are much smaller than for general polynomials.     

A distributed model of water balance in the Motueka catchment,New Zealand

A distributed water balance model is used to simulate the soil moisture regime of the Motueka catchment. The model is a major simplification of the Distributed Hydrology–Vegetation–Soil Model (DHVSM) with modifications suitable for the study area. The model was applied at 25-m resolution with a 1-day time-step for 10 years. The simulated hydrograph showed good correspondence with the observed hydrograph and there was good agreement of simulated and measured mean annual discharges (57.3 m³ s⁻¹ as compared with 58.7 m³ s⁻¹). Five different land cover scenarios were used to predict the effects of vegetation change on the hydrological regime: (1) current land cover; (2) prehistoric land cover; (3) maximum pine planting; (4) pine trees on easy slopes; and (5) pine trees on steep slopes. The pine scenarios all reduced the mean annual flow by about 2 m³ s⁻¹, while the prehistoric scenario reduced the mean annual flow by about 6 m³ s⁻¹. The pine scenarios (3, 4, and 5) reduced the 7-day 5-year low flow from 7.4 m³ s⁻¹ to between 6.5 m³ s⁻¹ and 6.8 m³ s⁻¹, respectively; and the prehistoric scenario reduced the 7-day 5-year low flow to 5.3 m³ s⁻¹.     

Bi-enzymatic amperometric biosensor for oxalate

The development of a new amperometric biosensor for oxalate utilising two enzymes, oxalate oxidase (OXO) and horseradish peroxidase (HRP), incorporated into carbon paste electrode modified with silica gel coated with titanium oxide containing toluidine blue is described. OXO has been immobilised on silica gel modified with titanium oxide surface using glutaraldehyde for crosslinking. HRP has been immobilised with covalent binding with carbodiimide on graphite powder. The biosensor showed a good performance with a linear response range between 0.1 and 2.0 mmol l⁻¹ of oxalate, fit by the equation i=0.33(±0.04)+2.29(±0.04) [oxalate], where i is the current in μA and [oxalate] is the oxalate concentration in mmol l⁻¹ with a correlation coefficient of 0.998 for n=20. The biosensor could be used for 80 determinations when stored in a succinate buffer at pH 3.8 in a refrigerator. The response time was about 0.5 s. The detection limit, considering three times the noise, was 0.09 mmol l⁻¹ for oxalate. The time for oxalate determination in spinach samples decreased by 3 days when this biosensor was used, compared to the AOAC method.     

Hybrid real-coded genetic algorithm for data partitioning in multi-round load distribution and scheduling in heterogeneous systems

Data partitioning and scheduling is one the important issues in minimizing the processing time for parallel and distributed computing system. We consider a single-level tree architecture of the system and the case of affine communication model, for a general m processor system with n rounds of load distribution. For this case, there exists an optimal activation order, optimal number of processors m* (m * ≤ m), and optimal rounds of load distribution n* (n * ≤ n), such that the processing time of the entire processing load is a minimum. This is a difficult optimization problem because for a given activation order, we have to first identify the processors that are participating (in the computation process) in every round of load distribution and then obtain the load fractions assigned to them, and the processing time. Hence, in this paper, we propose a real-coded genetic algorithm (RCGA) to solve the optimal activation order, optimal number of processors m* (m * ≤ m), and optimal rounds of load distribution n* (n * ≤ n), such that the processing time of the entire processing load is a minimum. RCGA employs a modified crossover and mutation operators such that the operators always produce a valid solution. Also, we propose different population initialization schemes to improve the convergence. Finally, we present a comparative study with simple real-coded genetic algorithm and particle swarm optimization to highlight the advantage of the proposed algorithm. The results clearly indicate the effectiveness of the proposed real-coded genetic algorithm.     

DFT study on X−·(H2O)n=1-10 (X = OH,NO2, NO3, CO3) anionic water cluster

A theoretical study to understand the interaction between anion and the water molecules through the hydration (X⁻·(H₂O)_n (X = OH, NO₂, NO₃, CO₃), where n = 1–10), using the density functional theory method with B3LYP functional and 6-311++G(d,p) basis set has been carried out systematically. In these hydrated clusters we notice three different cases of bond arrangements, namely, symmetrical double hydrogen bond, single hydrogen bond and inter-water hydrogen bond. All the complexes are dominated by the OH⋯O hydrogen bond, in which the anion act as a proton acceptor, while the water molecule act as a proton donor. A linear correlation is obtained between the solvent stabilization energy and the size (n) of the hydrated cluster for all the anions. The weighted average interaction energy values, shows that the water molecules strongly bind with the OH⁻ anion. Besides, the solvation of the OH⁻ anion requires less number of water molecules when compared with the other anions. Energy decomposition analysis (EDA) shows the strong dominance of the electrostatic energy component within the interaction energy. The total NPA charges on the anions indicate an increase in the solvation due to hydration. From AIM analysis, excellent linear inverse correlation is observed for both the electron density and Laplacian of the electron density with respect to the hydrogen bond length. Natural bonding orbital analysis (NBO) predicts large charge transfer between the OH⁻ anion and the water molecules.     

Simultaneous determination of epinephrine and ascorbic acid at the electrochemical sensor of triazole SAM modified gold electrode

The electrochemical sensor of triazole (TA) self-assembled monolayer (SAM) modified gold electrode (TA SAM/Au) was fabricated. The electrochemical behaviors of epinephrine (EP) at TA SAM/Au have been studied. The TA SAM/Au shows an excellent electrocatalytic activity for the oxidation of EP and accelerates electron transfer rate. The diffusion coefficient is 1.135 × 10⁻⁶ cm² s⁻¹. Under the optimum experiment conditions (i.e. 0.1 mol L⁻¹, pH 4.4, sodium borate buffer, accumulation time: 180 s, accumulation potential: 0.6 V, scan rate: 0.1 Vs⁻¹), the cathodic peak current of EP versus its concentration has a good linear relation in the ranges of 1.0 × 10⁻⁷ to 1.0 × 10⁻⁵ mol L⁻¹ and 1.0 × 10⁻⁵ to 6.0 × 10⁻⁴ mol L⁻¹ by square wave adsorptive stripping voltammetry (SWASV), with the correlation coefficient of 0.9985 and 0.9996, respectively. Detection limit is down to 1.0 × 10⁻⁸ mol L⁻¹. The TA SAM/Au can be used for the determination of EP in practical injection. Meantime, the oxidative peak potentials of EP and ascorbic acid (AA) are well separated about 200 ± 10 mV at TA SAM/Au, the oxidation peak current increases approximately linearly with increasing concentration of both EP and AA in the concentration range of 2.0 × 10⁻⁵ to 1.6 × 10⁻⁴ mol L⁻¹. It can be used for simultaneous determination of EP and AA.