This paper presents a new way to classify different radiation sources by the parameter of directivity, which is a characteristic parameter of electromagnetic radiation sources. The parameter can be determined from measurements of the electric field intensity radiating in all directions in space. We develop three basic antenna models, which are for 3GHz operation, and set 125,000 groups of cube receiving arrays along the main lobe of their radiation patterns to receive the data of far field electric intensity in groups. Then the Back Propagation (BP) neural network and the Support Vector Machine (SVM) method are adopted to analyze training data set, and build and test the classification model. Owing to the powerful nonlinear simulation ability, the SVM method offers higher classification accuracy than the BP neural network in noise environment. At last, the classification model is comprehensively evaluated in three aspects, which are capability of noise immunity, F1 measure and the normalization method.

Secure sets and defensive alliances in graphs are studied. They are sets of vertices that are safe in some senses. In this paper, we first present a fixed-parameter algorithm for finding a small secure set, whose running time is much faster than the previously known one. We then present improved bound on the smallest sizes of defensive alliances and secure sets for hypercubes. These results settle some open problems paused recently.

An n-dimensional folded hypercube, denoted by FQn, is an enhanced n-dimensional hypercube with one extra link between nodes that have the furthest Hamming distance. Let FFv (respectively, FFe) denote the set of faulty nodes (respectively, faulty links) in FQn. Under the assumption that every fault-free node in FQn is incident to at least two fault-free links, Hsieh et al. (Inform. Process. Lett. 110 (2009) pp.41-53) showed that if |FFv|+|FFe| ≤ 2n-4 for n ≥ 3, then FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv|. In this paper, we show that, under the same conditional fault model, FQn with n ≥ 5 can tolerate more faulty elements and provides the same lower bound of the length of a longest fault-free cycle, i.e., FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv| if |FFv|+|FFe| ≤ 2n-3 for n ≥ 5.

Many discrete functions are often compactly represented by Decision Diagrams (DD). The main problem in the construction of decision diagrams is the space and time requirements. While constructing a decision diagram the memory requirement may grow exponentially with the function. Also, large numbers of temporary nodes are created while constructing the decision diagram for a function. Here the problem of reducing the number of temporary nodes is addressed with respect to the PLA specification format of a function, where the function is represented using a set of cubes. Usually a DD is constructed by recursively processing the input cubes in the PLA specification. The DD, representing a sub function, is specified by a single cube. This DD is merged with a master DD, which represents the entire previously processed cubes. Thus the master DD is constructed recursively, until all the cubes in the input cube set are processed. In this paper, an efficient method is proposed, which reorders and also partitions the cube set into unequal number of cubes per subset, in such a way that, the number of temporary nodes created and the number of logical operations done, during the merging of cubes with the master DD are reduced. This results in the reduction of space and time required for the construction of DDs to a remarkable extent.

This paper proposes several improved Side-channel cube attacks (SCCAs) on PRESENT-80/128 under single bit leakage model. Assuming the leakage is in the output of round 3 as in previous work, we discover new results of SCCA on PRESENT. Then an enhanced SCCA is proposed to extract key related non-linear equations. 64-bit key for both PRESENT-80 and 128 can be obtained. To mount more effective attack, we utilize the leakage in round 4 and enhance SCCA in two ways. A partitioning scheme is proposed to handle huge polynomials, and an iterative scheme is proposed to extract more key bits. With these enhanced techniques, the master key search space can be reduced to 28 for PRESENT-80 and to 229 for PRESENT-128.

This paper presents a grid-based, real-time surface modeling algorithm in which the generation of a precise 3D model is possible by considering the user's intention during the course of the spatial input. In order to create the corresponding model according to the user's input data, plausible candidates of wand traversal patterns of grid edges are defined by considering the sequential and directional characteristics of the wand input. The continuity of the connected polygonal surfaces, including the octree space partitioning, is guaranteed without the extra crack-patching algorithm and the pre-defined patterns. Furthermore, the proposed system was shown to be a suitable and effective surface generation tool for the spatial sketching system. It is not possible to implement the unusual input intention of the 3D spatial sketching system using the conventional Marching Cubes algorithm.

Although the Marching Cube (MC) algorithm is very popular for displaying images of voxel-based objects, its slow surface extraction process is usually considered to be one of its major disadvantages. It was pointed out that for the original MC algorithm, we can limit vertex calculations to once per vertex to speed up the surface extraction process, however, it did not mention how this process could be done efficiently. Neither was the reuse of these MC vertices looked into seriously in the literature. In this paper, we propose a “Group Marching Cube” (GMC) algorithm, to reduce the time needed for the vertex identification process, which is part of the surface extraction process. Since most of the triangle-vertices of an iso-surface are shared by many MC triangles, the vertex identification process can avoid the duplication of the vertices in the vertex array of the resultant triangle data. The MC algorithm is usually done through a hash table mechanism proposed in the literature and used by many software systems. Our proposed GMC algorithm considers a group of voxels simultaneously for the application of the MC algorithm to explore interesting features of the original MC algorithm that have not been discussed in the literature. Based on our experiments, for an object with more than 1 million vertices, the GMC algorithm is 3 to more than 10 times faster than the algorithm using a hash table. Another significant advantage of GMC is its compatibility with other algorithms that accelerate the MC algorithm. Together, the overall performance of the original MC algorithm is promoted even further.

The popularity of cloud computing services is driving the boom in building mega-datacenters. This trend is forcing significant increases in the required scale of the intra-datacenter network. To meet this requirement, this paper proposes a photonic network architecture based on a multi-layer hypercube topology. The proposed architecture uses the Cyclic-Frequency Arrayed Waveguide Grating (CF-AWG) device to realize a multi-layer hypercube and properly combines several multiplexing systems that include Time Division Multiplexing (TDM), Wavelength Division Multiplexing (WDM), Wave-Band Division Multiplexing (WBDM) and Space Division Multiplexing (SDM). An estimation of the achievable network scale reveals that the proposed architecture can achieve a Peta-bit to Exa-bit class, large scale hypercube network with existing technologies.

Today, practical semiconductor products are an integral part of our lives and the infrastructure of society, and this trend will continue in the future. New areas of application will expand into medical, environmental, and agriculture (food)-related fields in addition to the conventional information and communication technology (ICT)-related field. Low-cost semiconductor devices with advanced functions have thus far been realized by miniaturization. However, we are now approaching the physical limit of miniaturization, and also, the investment required for new semiconductor manufacturing facilities has become huge. Under such circumstances, we propose an approach based on semiconductor devices called microcube chips and ideas of semiconductor development, i.e., agile integration and "inch-fab." Our approach is expected to contribute to expanding the range of companies that can fabricate semiconductor devices to include small-size companies, exploring new applications of semiconductor devices, and providing a wide variety of semiconductor devices at a low cost from the semiconductor industry.

Hypercube Qn is a well-known graph structure having three different kinds of equivalent definitions that are: 1. binary n bit sequences with the adjacency condition, 2. Q1=K2, Qn=Qn-1 K2, where means the Cartesian product, 3. the Cayley graph on Z2n with the generator set {100, 0100, , 001}. We give a necessary and sufficient condition for a set of binary sequences to be a generator set for the hypercube. Then, we give relations between some generator sets and relational products. These results show the wide variety of representability of hypercubes which would be used for many applications.

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spatial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have the same size and the length must be a power of two, which limits the application of the Hilbert scan greatly. Thus in order to remove these constraints and improve the Hilbert scan for general application, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed in this paper. The merit of the proposed algorithm is that implementation is much easier than the original one while preserving the original characteristics. The experimental results indicate that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points, and it also shows the competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques. We believe that this novel scan technique undoubtedly leads to many new applications in those areas can benefit from reducing the dimensionality of the problem.

This paper addresses a new surface reconstruction scheme for approximating the isosurface from a set of tomographic cross sectional images. Differently from the novel Marching Cubes (MC) algorithm, our method does not extract the iso-density surface (isosurface) directly from the voxel data but calculates the iso-density point (isopoint) first. After building a coarse initial mesh approximating the ideal isosurface by the cell-boundary representation, it metamorphoses the mesh into the final isosurface by a relaxation scheme, called shrink-wrapping process. Compared with the MC algorithm, our method is robust and does not make any cracks on surface. Furthermore, since it is possible to utilize lots of additional isopoints during the surface reconstruction process by extending the adjacency definition, theoretically the resulting surface can be better in quality than the MC algorithm. According to experiments, it is proved to be very robust and efficient for isosurface reconstruction from cross sectional images.

In this paper, we study the feedback vertex set problem for trivalent Cayley graphs, and construct a minimum feedback vertex set in trivalent Cayley graphs using the result on cube-connected cycles and the Cayley graph representation of trivalent Cayley graphs.

In this paper, we study the layout problem of the supercube by embedding-in-book technique. The supercube, a generalization of the hypercube, can be constructed for an arbitrary system size. Moreover, it has the same diameter and connectivity of the corresponding hypercube. Embedding a graph in book is to place nodes along the spine of the book and to draw the edges such that edges residing in a page do not cross. An n-dimensional hypercube is regular because the degree of each node is n. The corresponding supercube with N nodes, where 2n-1 < N 2n and N ≠ 32n-2, is irregular because the degree of each node ranges from 2n - 2 to n - 1. Although Chung et al. have shown that an n-dimensional hypercube can be embedded with n - 1 pages, to lay out the supercube remains a challenging problem owing to its higher degree and irregular structure. In this paper, we show that a supercube of N nodes, where 2n-1 < N 2n, can also be embedded with n - 1 pages and book width N - 2n-2 for 2n-1 < N < 32n-2, and 2n-1 for 32n-2 N 2n.

System-level fault diagnosis deals with the problem of identifying faulty nodes (processors) in a multiprocessor system. Each node is faulty or fault-free, and it can test other nodes in the system, and outputs the test results. The test result from a node is reliable if the node is fault-free, but the result is unreliable if it is faulty. In this paper, we prove that four variants of the hypercube: the crossed cube, the twisted cube, the Mobius cube, and the enhanced cube, are adaptively diagnosed using at most 4 parallel testing rounds, with at most n faulty nodes (for the enhanced cube, with at most n + 1 faulty nodes), where each processor participates in at most one test in each round. Furthermore, we propose another diagnosis algorithm for the n-dimensional enhanced cube with at most n + 1 faulty nodes, and show that it is adaptively diagnosed with at most 5 rounds in the worst case, but with at most 3 rounds if the number of existing faulty nodes is at most n -log(n + 1).

The Mobius cube MQn proposed by Cull et al. is an alternative to the popular hypercube network. Recently, MQn was shown to be pancyclic, i.e., cycles of any lengths at least four can be embedded into it. Due to the importance of the fault tolerance in the parallel processing area, in this paper, we study an injured MQn with mixed node and link faults. We show that it is (n - 2)-fault-tolerant pancyclic for n 3, that is, an injured n-dimensional MQn is still pancyclic with up to (n - 2) faults. Furthermore, our result is optimal.

Cluster computation has been used in the applications that demand performance, reliability, and availability, such as cluster server groups, large-scale scientific computations, distributed databases, distributed media-on-demand servers and search engines etc. In those applications, multicast can play the vital roles for the information dissemination among groups of servers and users. This paper proposes a set of novel efficient fault-tolerant multicast routing algorithms on hypercube interconnection of cluster computers using multicast shared tree approach. We present some new algorithms for selecting an optimal core (root) and constructing the shared tree so as to minimize the average delay for multicast messages. Simulation results indicate that our algorithms are efficient in the senses of short end-to-end average delay, load balance and less resource utilizations over hypercube cluster interconnection networks.

In this work, a novel Multiple Valued Exclusive-Or Sum Of Products (MVESOP) minimization formulation is analyzed and an algorithm is presented that detects minimum MVESOP expressions when the weight of the function is less than eight. A heuristic MVESOP algorithm based on a novel cube transformation operation is then presented. Experimental results on MCNC benchmarks and randomly generated functions indicate that the algorithm matches or outperforms the quality of the state of the art in ESOP minimizers.

In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the distance to each destination over the tree the same as the distance in the original graph. In the following, we first propose an algorithm that grows a multicast tree in a greedy manner, in the sense that for each intermediate vertex of the tree, the outgoing edges of the vertex are selected in a non-increasing order of the number of destinations that can use the edge in a shortest path to the destination. We then evaluate the goodness of the algorithm in terms of the worst case ratio of the size of the generated tree to the size of an optimal tree. It is proved that for any k 5 and n 6, the performnance ratio of the greedy algorithm is c kn - o(n) for some constant 1/12 c 1/2.

An n-dimensional crossed cube, CQn, is a variation of the hypercube. In this paper, we prove that CQn is (n-2)-Hamiltonian and (n-3)-Hamiltonian connected. That is, a ring of length 2n-fv can be embedded in a faulty CQn with fv faulty nodes and fe faulty edges, where fv+fen-2 and n3. In other words, we show that the faulty CQn is still Hamiltonian with n-2 faults. In addition, we also prove that there exists a Hamiltonian path between any pair of vertices in a faulty CQn with n-3 faults. The above results are optimum in the sense that the fault-tolerant Hamiltonicity (fault-tolerant Hamiltonian connectivity respectively) of CQn is at most n-2 (n-3 respectively). A recent result has shown that a ring of length 2n-2fv can be embedded in a faulty hypercube, if fv+fen-1 and n4, with a few additional constraints. Our results, in comparison to the hypercube, show that longer rings can be embedded in CQn without additional constraints.