A fast algorithm for constructing nearly optimal prefix codes

Huffman algorithm allows for constructing optimal prefix‐codes with O(n·logn) complexity. As the number of symbols ngrows, so does the complexity of building the code‐words. In this paper, a new algorithm and implementation are proposed that achieve nearly optimal coding without sorting the probabilities or building a tree of codes. The complexity is proportional to the maximum code length, making the algorithm especially attractive for large alphabets. The focus is put on achieving almost optimal coding with a fast implementation, suitable for real‐time compression of large volumes of data. A practical case example about checkpoint files compression is presented, providing encouraging results. Copyright © 2015 John Wiley & Sons, Ltd.     

A combinatorial property of codes having finite synchronization delay

Necessary and sufficient conditions are given under which a code has finitesynchronization delay. The proof of the theorem makes use of three lemmas involving combinatorial properties of the free monoid related with the synchronization delay. A corollary of these lemmas (Property 3) gives also an upper bound on the synchronization delay of a code A, which linearly depends on the number of states of the minimal automaton recognizing A^p*.     

A reduction architecture for the optimal scheduling of binary trees

This paper addresses the problem of designing a parallel reduction architecture for applicative languages. An interconnection network that allows for scheduling of binary trees of arbitrary depth is presented. It is shown that using a static scheduling strategy the architecture achieves optimal performance while scheduling complete binary trees. Some issues related to the design of a machine based on this network are also discussed.     

A class of 1-generator quasi-cyclic codes over finite chain rings

Using another method, which is different with the one given by Cao [1-generator quasi-cyclic (QC) codes over finite chain rings, Appl. Algebra Eng. Commun. Comput. 24 (2013), pp. 53–72], we investigate the structural properties of a class of 1-generator QC codes over finite chain rings. We give the structure of the annihilator of 1-generator QC codes, the conditions for 1-generator QC codes to be free and the minimum distance bounds on 1-generator QC codes. Under some conditions, we also discuss the enumeration of 1-generator QC codes and describe how to obtain the one and only one generator for each 1-generator QC code.     

On the costs of optimal and near-optimal binary search trees

Summary We show that the cost of an optimal binary search tree can vary substantially, depending only on the left-to-right order imposed on the probabilities. We also prove that the costs of some common classes of near-optimal trees cannot be bounded above by the cost of an optimal tree plus a constant. This work was supported by the National Research Council of Canada, while the author was at the University of Waterloo     

Validation and analysis of aerosol optical thickness retrieval over land

Aerosol optical thickness (AOT) retrieval from Moderate Resolution Imaging Spectroradiometer (MODIS) data has been well established over oceans, but this is not the case over land. In this article, the AOT data sets retrieved by exploiting the synergy of TERRA and AQUA MODIS data (SYNTAM) over land are validated with ground-based measurements from Aerosol Robotic Network (AERONET) data, as well as from the National Aeronautics and Space Administration (NASA) AOT products, amended with a DeepBlue algorithm in Asian (15–60° N and 35–150° E) and American areas (30–40° N and 100–120° W). Overall, AOT retrieval errors of around 10–20% against AERONET data are found at both 1 and 10 km resolutions. The spectral and spatial sensitivities of the AOT correlation are explicitly addressed at both 1 and 10 km resolutions. Three window sizes, 1?×?1, 3?×?3 and 5?×?5, are tested for SYNTAM to evaluate the effect of window size on parameter statistics, and it is found that the accuracy of the SYNTAM method decreases with increasing window size. The validations at three spectral bands of 0.47, 0.55 and 0.66 μm show that the accuracies of different bands are 80–90% similar, and that the band at 0.47 μm has the highest accuracy most of the time. Comparisons between AOT data sets derived from the SYNTAM and AOT products from the NASA Dark Dense Vegetation (DDV) and the DeepBlue algorithms are also conducted using data from the USA. More pixels with AOT values for the area could be retrieved using the SYNTAM method with the NASA DeepBlue algorithm. The AOT values of more than 90% of pixels derived by both methods are very close. This clearly shows that AOT data from SYNTAM are very close to the AOT data set from the NASA DeepBlue algorithm in cloud-free areas. The synergic use of both the SYNTAM and DeepBlue algorithms could produce AOT values over much greater land areas.     

A model of optimal control over a nonlinear multidimensional innovation diffusion process

A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is proved for the problem of diffusion of two competitive innovations, and sufficient conditions of existence of optimum control are obtained for the system. A numerical algorithm is constructed for solving optimum control problems, and numerical results for a model example are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 120–133, July–August 2008.     

Brother trees: A family of optimal 1p-hamiltonian and 1-edge hamiltonian graphs

In this paper we propose a family of cubic bipartite planar graphs, brother trees, denoted by BT(n) with n?2. Any BT(n) is hamiltonian. It remains hamiltonian if any edge is deleted. Moreover, it remains hamiltonian when a pair of nodes (one from each partite set) is deleted. These properties are optimal. Furthermore, the number of nodes in BT(n) is 6·2ⁿ−4 and the diameter is 2n+1.     

Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica

We investigated the single scattering optical properties of snow for different ice particle shapes and degrees of microscopic scale roughness. These optical properties were implemented and tested in a coupled atmosphere-snow radiative transfer model. The modeled surface spectral albedo and radiance distribution were compared with surface measurements. The results show that the reflected radiance and irradiance over snow are sensitive to the snow grain size and its vertical profile. When inhomogeneity of the particle size distribution in the vertical is taken into account, the measured spectral albedo can be matched, regardless of the particle shapes. But this is not true for the modeled radiance distribution, which depends a lot on the particle shape. The usual “equivalent spheres” assumption significantly overestimates forward reflected radiances, and underestimates backscattering radiances, around the principal plane. On average, the aggregate shape assumption has the best agreement with the measured radiances to a mean bias within 2%.The snow optical properties with the aggregate assumption were applied to the retrieval of snow grain size over the Antarctic plateau. The retrieved grain sizes of the top layer showed similar and large seasonal variation in all years, but only small year to year variation. Using the retrieved snow grain sizes, the modeled spectral and broadband radiances showed good agreements with MODIS and CERES measurements over the Antarctic plateau. Except for the MODIS 2.13 μm channel, the mean relative model-observation differences are within few percent. The modeled MODIS radiances using measured surface reflectance at Dome C also showed good agreement in visible channels, where radiation is not sensitive to snow grain size and the measured surface bidirectional reflectance is applicable over the Antarctic plateau. But modeled radiances using local, surface-measured reflectance in the near infrared yielded large errors because of the high sensitivity to the snow grain size, which varies spatially and temporally. The CERES broadband shortwave radiance is moderately sensitive to the snow grain size, comparable to the MODIS 0.86 μm channel. The variation of broadband snow reflectance due to the seasonal variation in snow grain size is about 5% in a year over the Antarctic plateau. CERES broadband radiances simulated with grain sizes retrieved using MODIS are about 2% larger than those observed.     

On the number of Dejean words over alphabets of 5, 6, 7, 8, 9 and 10 letters

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for 5≤k≤10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0.005. As a consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for 5≤k≤10.     

Construction of punctured and extended quantum codes over GF(2)

On the basis of elementary transformation,we propose a new method for constructing a class of pure quantum codes [[n-i,2k-n+i,d-i]]2 and [[n+1,2k-n-1,d+1]]2 from a class of classical linear codes [n,k,d]2 that contain their dual codes.The construction process was based on the elementary algebra;the error-correcting performance of the quantum codes was analyzed according to the relationship between the parity-check matrix and the minimum distance of the classical linear codes;the encoding and decoding networks were constructed based on the stabilizer.The proposed method is simple,straightforward and easy to implement using a computer and other hardware system.The theoretical results showed that the method is practical for the construction of a class of quantum codes.     

A comparative study of 2-3 trees and AVL trees

This paper presents an analysis, a survey, and compares the pertinent characteristics of AVL and 2-3 trees. In an attempt to optimize the space complexity of 2-3 trees, it introduces a new space saving and efficient top-down insertion and construction algorithm. The analysis shows that neither data structure totally dominates the other. The decision as to which is cost-wise efficient is a function of the application.     

Encoding and decoding the knowledge of association rules over SVM classification trees

This paper presents a constructive method for association rule extraction, where the knowledge of data is encoded into an SVM classification tree (SVMT), and linguistic association rule is extracted by decoding of the trained SVMT. The method of rule extraction over the SVMT (SVMT-rule), in the spirit of decision-tree rule extraction, achieves rule extraction not only from SVM, but also over the decision-tree structure of SVMT. Thus, the obtained rules from SVMT-rule have the better comprehensibility of decision-tree rule, meanwhile retains the good classification accuracy of SVM. Moreover, profiting from the super generalization ability of SVMT owing to the aggregation of a group of SVMs, the SVMT-rule is capable of performing a very robust classification on such datasets that have seriously, even overwhelmingly, class-imbalanced data distribution. Experiments with a Gaussian synthetic data, seven benchmark cancers diagnosis, and one application of cell-phone fraud detection have highlighted the utility of SVMT and SVMT-rule on comprehensible and effective knowledge discovery, as well as the superior properties of SVMT-rule as compared to a purely support-vector based rule extraction. (A version of SVMT Matlab software is available online at )

Development of discharge-stage curves affected by hysteresis using time varying models,model trees and neural networks

Flow data forms the base on which much of the edifice of water management is raised. However, flow measurements are expensive and difficult to conduct. Therefore, the more accessible stage measurements are employed in combination with stage–discharge relationships. Setting up such relationships is often infeasible using traditional regression techniques. Two case studies are examined that show hystereses using various approaches, namely (1) single rating curves, (2) rating curves with dynamic correction, (3) artificial neural networks (ANN) and (4) M5′ model trees. All methods outperform the traditional rating curve. The presented approach that uses a dynamically corrected rating curve delivers accurate results and allows for physical interpretation. The ANNs mimic the calibration data precisely, but suffer from overfitting when a small amount of data is applied for training. The rarely used M5′ model tree's architecture is easier to interpret than that of neural networks and delivers more accurate results.     

Transference and retrieval of voice message over low signal strength in satellite communication

This paper presents a method of transferring voice using short messaging service in satellite communication system. The method is especially applicable in a situation where signal strength is low and voice call is not possible. In a tunnel, basement or environment with bad climate conditions, signal strength usually gets weak which make voice call difficult but SMS works in such situation. An application has been developed using J2ME language in order to test the proposed method. For experimentation, Thuraya SG-2520 satellite phone has been used.     

Investigating the effect of varying block size on power and energy consumption of GPU kernels

The Journal of Supercomputing - Power consumption is likely to remain a significant concern for exascale performance in the foreseeable future. In addition, graphics processing units (GPUs) have...     

二元域上三次和四次剩余码的幂等生成元

有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了二元域[F2]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解该幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。