A state-space search approach for optimizing reliability and cost of execution in distributed sensor networks

Sensor networks are increasingly being used for applications which require fast processing of data, such as multimedia processing and collaboration among sensors to relay observed data to a base station (BS). Distributed computing can be used on a sensor network to reduce the completion time of a task (an application) and distribute the energy consumption equitably across all sensors, so that certain sensors do not die out faster than the others. The distribution of task modules to sensors should consider not only the time and energy savings, but must also improve reliability of the entire task execution. We formulate the above as an optimization problem, and use the A^∗$A^{\ast }$ algorithm with improvements to determine an optimal static allocation of modules among a set of sensors. We also suggest a faster algorithm, called the greedy A^∗$A^{\ast }$ algorithm, if a sub-optimal solution is sufficient. Both algorithms have been simulated, and the results have been compared in terms of energy savings, decrease in completion time of the task, and the deviation of the sub-optimal solution from the optimal one. The sub-optimal solution required 8%–35% less computation, at the cost of 2.5%–15% deviation from the optimal solution in terms of average energy spent per sensor node. Both the A^∗$A^{\ast }$ and greedy A^∗$A^{\ast }$ algorithms have been shown to distribute energy consumption more uniformly across sensors than centralized execution. The greedy A^∗$A^{\ast }$ algorithm is found to be scalable, as the number of evaluations in determining the allocation increases linearly with the number of sensors.     

Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates

In this paper, two delayed SEIR epidemic models with continuous and impulsive vaccination and saturating incidence are investigated. The dynamical behaviors of the disease are analyzed. For continuous vaccination, we obtain a basic reproductive number _R1$R_1$ and prove that if _R1≤1$R_1\le 1$ then the disease-free equilibrium is globally attractive and if _R1>1$R_1>1$ then the disease is permanent by using the Lyapunov functional method. For impulsive vaccination, we obtain two thresholds R^∗$R^{\ast }$ and _R∗$R_{\ast }$ and prove that if R^∗<1$R^{\ast }<1$ then the disease-free periodic solution is globally attractive and if _R∗>1$R_{\ast }>1$ then the disease is permanent by using the comparison theorem of impulsive differential equation and the Lyapunov functional method. Lastly, we compared the effects of two vaccination strategies.     

Accelerating atomistic calculations of quantum energy eigenstates on graphic cards

Electronic properties of nanoscale materials require the calculation of eigenvalues and eigenvectors of large matrices. This bottleneck can be overcome by parallel computing techniques or the introduction of faster algorithms. In this paper we report a custom implementation of the Lanczos algorithm with simple restart, optimized for graphical processing units (GPUs). The whole algorithm has been developed using CUDA and runs entirely on the GPU, with a specialized implementation that spares memory and reduces at most machine-to-device data transfers. Furthermore parallel distribution over several GPUs has been attained using the standard message passing interface (MPI). Benchmark calculations performed on a GaN/AlGaN wurtzite quantum dot with up to 600,000 atoms are presented. The empirical tight-binding (ETB) model with an sp³d⁵s^∗$s{p}^3{d}^5{s}^{\ast }$+spin–orbit parametrization has been used to build the system Hamiltonian (H).     

State-complexity hierarchies of uniform languages of alphabet-size length

We study the state complexity of certain simple languages. If A$A$ is an alphabet of k$k$ letters, then a k$k$-language   is a nonempty set of words of length k$k$, that is, a uniform language of length k$k$. We show that the minimal state complexity of a k$k$-language is k+2$k+2$, and the maximal, (k^k−1−1)/(k−1)+2^k+1$(k^{k-1}-1)/(k-1)+2^k+1$. We prove constructively that, for every i$i$ between the minimal and maximal bounds, there is a language of state complexity i$i$. We introduce a class of automata accepting sets of words that are permutations of A$A$; these languages define a complete hierarchy of complexities between k²−k+3$k^2-k+3$ and 2^k+1$2^k+1$. The languages of another class of automata, based on k$k$-ary trees, define a complete hierarchy of complexities between 2^k+1$2^k+1$ and (k^k−1−1)/(k−1)+2^k+1$(k^{k-1}-1)/(k-1)+2^k+1$. This provides new examples of uniform languages of maximal complexity.     

On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field

We derive an explicit count for the number of singular n×n$n\times n$ Hankel (Toeplitz) matrices whose entries range over a finite field with q$q$ elements by observing the execution of the Berlekamp/Massey algorithm on its elements. Our method yields explicit counts also when some entries above or on the anti-diagonal (diagonal) are fixed. For example, the number of singular n×n$n\times n$ Toeplitz matrices with 0’s on the diagonal is q²ⁿ⁻³+qⁿ⁻¹−qⁿ⁻²$q^{2n-3}+q^{n-1}-q^{n-2}$.     

Some properties of the induced continuous ordered weighted geometric operators in group decision making

In Computers and Industrial Engineering 56 (2009) 1545–1552, an induced continuous ordered weighted geometric (ICOWG) operator is presented to deal with group decision making (GDM) problems with interval multiplicative preference relations. But, we still do not know whether the ICOWG operator can improve the consensus among a group of decision makers. The aim of this paper is to study some desired properties of the ICOWG operator in GDM problems. Firstly, the concept of Compatibility Degree and Compatibility Index (CI) is defined. We then present the Compatibility Index induced COWG (CI-ICOWG) operator to aggregate interval multiplicative preference relations, which induces the order of argument values based on the Compatibility Index of decision makers (DMs). The main novelty of the CI-ICOWG operator is that it aggregates individual preference relation in such a way that more importance is placed on the most compatibility one. Thus, the CI-ICOWG operator can guarantee that the Compatibility Degree is at least as good as the arithmetic mean of all the individual Compatibility Degrees. Additionally, if the leading decision maker’s interval multiplicative preference relation P   and each of interval multiplicative preference relations R⁽¹⁾,R⁽²⁾,…,R^(m)$R^{(1)}\text{,}{R}^{(2)}\text{,}\dots \text{,}{R}^{(m)}$ are of acceptable compatibility, then P   and the collective judgement matrix (CJM) of R⁽¹⁾,R⁽²⁾,…,R^(m)$R^{(1)}\text{,}{R}^{(2)}\text{,}\dots \text{,}{R}^{(m)}$ are of acceptable compatibility. Finally, an illustrative numerical example is used to verify the developed approaches.     

On a compact encoding of the swap automaton

Given a string P of length m over an alphabet Σ of size σ, a swapped version of P is a string derived from P   by a series of local swaps, i.e., swaps of adjacent symbols, such that each symbol can participate in at most one swap. We present a theoretical analysis of the nondeterministic finite automaton for the language _?P′∈ΠPΣ^?P^′${?}_{P^{\prime }\in {\Pi }_P}{\Sigma }^{?}{P}^{\prime }$ (swap automaton, for short), where _ΠP${\Pi }_P$ is the set of swapped versions of P  . Our study is based on the bit-parallel simulation of the same automaton due to Fredriksson, and reveals an interesting combinatorial property that links the automaton to the one for the language Σ^?P${\Sigma }^{?}P$. By exploiting this property and the method presented by Cantone et al. (2012), we obtain a bit-parallel encoding of the swap automaton which takes O(σ²⌈k/w⌉)$O({\sigma }^2\lceil k/w\rceil )$ space and allows one to simulate the automaton on a string of length n   in time O(n⌈k/w⌉)$O(n\lceil k/w\rceil )$, where ⌈m/σ⌉?k?m$\lceil m/\sigma \rceil ?k?m$ is the size of a specific factorization of P defined by Cantone et al. (2012) and w is the word size in bits.     

The weight distributions of cyclic codes with two zeros and zeta functions

We consider the weight distribution of the binary cyclic code of length 2ⁿ−1$2^n-1$ with two zeros α^a,α^b${\alpha }^a,{\alpha }^b$. Our proof gives information in terms of the zeta function of an associated variety. We carry out an explicit determination of the weight distribution in two cases, for the cyclic codes with zeros α³,α⁵${\alpha }^3,{\alpha }^5$ and α,α¹¹$\alpha ,{\alpha }^{11}$. These are the smallest cases of two infinite families where finding the weight distribution is an open problem. Finally, an interesting application of our methods is that we can prove that these two codes have the same weight distribution for all odd n$n$.     

OptQC: An optimized parallel quantum compiler

The software package Qcompiler (Chen and Wang 2013) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software OptQC  , which finds permutation matrices P$P$ and Q$Q$ for a given unitary matrix U$U$ such that the number of gates in the quantum circuit of U=Q^TP^TU^′PQ$U=Q^T{P}^T{U}^{\prime }PQ$ is significantly reduced, where U^′$U^{\prime }$ is equivalent to U$U$ up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.