This study proposes a method to decompose a signal into a set of periodic signals. The proposed decomposition method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of decomposition and avoid the overestimation of periods. This penalty is defined as the weighted sum of the l2 norms of the resultant periodic subsignals. This decomposition is approximated by an unconstrained minimization problem. In order to solve this problem, a relaxation algorithm is applied. In the experiments, decomposition results are presented to demonstrate the simultaneous detection of periods and waveforms hidden in signal mixtures.

The fixed charge transportation problem (FCTP) is a classic challenge for combinatorial optimization; it is based on the well-known transportation problem (TP), and is one of the prime examples of an NP-complete variant of the TP, of general importance in a wide range of transportation network design problems. Many techniques have been applied to this problem, and the most effective so far (in terms of near-optimal results in reasonable time on large instances) are evolutionary algorithm based approaches. In particular, an EA proposed by Eckert and Gottlieb has produced the best performance so far on a set of specific benchmark instances. We introduce a new scheme, which has more general applicability, but which we test here on the FCTP. The proposed scheme applies an adaptive mutation process immediately following the evaluation of a phenotype. It thereby adapts automatically to learned information encoded in the chromosome. The underlying encoding approach is to encode an ordering of elements for interpretation by a constructive algorithm (such as with the Link and Node Biased encoding for spanning trees, and the Random Keys encoding which has been applied to both scheduling and graph problems), however the main adaptive process rewards links in such a way that genes effectively encode a measure of the number of times their associated link has appeared in selected solutions. Tests are done which compare our approach with Eckert and Gottlieb's results on benchmark FCTP instances, and other approaches.

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 propose a new scheme to represent three-dimensional (3-D) dynamic scenes using a hierarchical decomposition of depth maps. In the hierarchical decomposition, we split a depth map into four types of images: regular mesh, boundary, feature point and number-of-layer (NOL) images. A regular mesh image is obtained by down-sampling a depth map. A boundary image is generated by gathering pixels of the depth map on the region of edges. For generating feature point images, we select pixels of the depth map on the region of no edges according to their influence on the shape of a 3-D surface, and convert the selected pixels into images. A NOL image includes structural information to manage the other three images. In order to render a frame of 3-D dynamic scenes, we first generate an initial surface utilizing the information of regular mesh, boundary and NOL images. Then, we enhance the initial surface by adding the depth information of feature point images. With the proposed scheme, we can represent consecutive 3-D scenes successfully within the framework of a multi-layer structure. Furthermore, we can compress the data of 3-D dynamic scenes represented by a mesh structure by a 2-D video coder.

This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.

This letter extends the existent MPL (Max-Plus Linear) state-space representation and proposes a new form that can account for both capacity and order constraints. It is often essential to consider these factors when applying the MPL approach to scheduling problems for production or transportation systems. The derived form is a type of augmented state-representation and can contribute to obtaining the earliest start and completion times for processes in installed facilities.

This paper discusses a new structure of M-channel IIR perfect reconstruction filter banks. A novel building block defined as a cascade connection of some IIR building blocks and FIR building blocks is presented. An IIR building block is written by state space representation, where we easily obtain a stable filter bank by setting eigenvalues of the state transition matrix into the unit circle. Due to cascade connection of building blocks, we are able to design a system with a larger number of free parameters while keeping the stability. We introduce the condition which obtains the new building block without increasing of the filter order in spite of cascade connection. Additionally, by showing the simulation results, we show that this implementation has a better stopband attenuation than conventional methods.

A hierarchical representation formed by an octree for a volume ray casting is a well-known data structure to skip over transparent regions requiring little preprocessing and storage. However, it accompanies unnecessary comparison and level shift between octants. We propose a new data structure named half-skewed octree, which is an auxiliary octree to support the conventional octree. In preprocessing step, a half-skewed octree selects eight different child octants in each generation step compared with the conventional octree. During rendering, after comparing an octant of the conventional octree with corresponding octant of the half-skewed octree simultaneously at the same level, a ray chooses one of two octants to jump over transparent regions farther away. By this method, we can reduce unnecessary comparison and level shift between octants. Another problem of a conventional octree structure is that it is difficult to determine a distance from the boundary of a transparent octant to opposite boundary. Although we exploit the previously proposed distance template, we cannot expect the acceleration when a ray direction is almost parallel to the octant's boundary. However, our method can solve it without additional operations because a ray selects one octant to leap farther away. As a result, our approach is much faster than the method using conventional octree while preserving image quality and requiring minimal storage.

This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of µ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2n-5 (n ≤ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.

A floorplan is a subdivision of a rectangle into rectangular faces with horizontal and vertical line segments. Heuristic search algorithms are used to find desired floorplans in applications, including sheet-cutting, scheduling, and VLSI layout design. Representation of floorplan is critical in floorplan algorithms, because it determines the solution space searched by floorplan algorithms. In this paper, we show a surjective mapping from permutations to room-to-room floorplans. This mapping gives us a simple representation of room-to-room floorplans.

This paper presents the Physical Optics field calculation in terms of only line integrations by using the Modified Edge Representation technique (MER), the alternative way of the surface integration. Not only the diffracted fields as in the conventional method of equivalent edge currents (EEC) but also the scattering geometrical optics fields are expressed in terms of the MER line integrals. The far field patterns of parabolic reflector antennas with the defocused dipole feed are discussed and the satisfactory agreement with those obtained by the Physical Optics surface integration is demonstrated.

In this letter, a combined method based on the fractional linear and the fractional bilinear time-frequency representations (TFRs) is proposed. The method combines the windowed fractional short-time Fourier transform with the fractional Wigner distribution (WD) to estimate the instantaneous frequency (IF) of signals in the appropriate fractional time-frequency domain. For a multi-component signal, the method can significantly eliminate the cross terms and improve the time-frequency resolution of the auto-terms. It is applied to the detection and parameter estimation of linear frequency modulated (LFM) signals. The computer simulations clearly demonstrate that the method is effective.

A hardware algorithm for integer division is proposed. It is based on the radix-2 non-restoring division algorithm. Fast computation is achieved by the use of the radix-2 signed-digit (SD2) representation. The algorithm does not require normalization of the divisor, and hence, does not require an area-consuming leading-one (or zero) detection nor shifts of variable-amount. Combinational (unfolded) implementation of the algorithm yields a regularly structured array divider, and sequential implementation yields compact dividers.

Let A(n, d, w) denote the maximum possible number of code words in binary (n,d,w) constant weight codes. For smaller instances of (n, d, w)s, many improvements have occurred over the decades. However, unknown instances still remain for larger (n, d, w)s (for example, those of n > 30 and d > 10). In this paper, we propose a new class of binary constant weight codes that fill in the remaining blank instances of (n, d, w)s. Specifically, we establish several new non-trivial lower bounds such as 336 for A(64, 12, 8), etc. (listed in Table 2). To obtain these results, we have developed a new systematic technique for construction by means of groups acting on some sets. The new technique is performed by considering a triad (G, Ω, f) := ("Group G," "Set Ω," "Action f on Ω") simultaneously. Our results described in Sect. 3 are obtained by using permutations of the elements of a set that include ∞ homogeneously like the other elements, which play a role to improve their randomness. Specifically, in our examples, we adopt the following model such as (PGL2(Fq), P1(Fq), "linear fractional action of subgroups of PGL2(Fq) on P1(Fq)") as a typical construction model. Moreover, as an application, the essential examples in [7] constructed by using an alternating group are again reconstructed with our new technique of a triad model, after which they are all systematically understood in the context of finite subgroups that act fractionally on a projective space over a finite field.

Recent IDEs have become more extensible tool platforms but do not concern themselves with how other tools running on them collaborate with each other. They compel developers to use proprietary representations or the classical abstract syntax tree (AST) to build source code tools. Although these representations contain sufficient information, they are neither portable nor extensible. This paper proposes a tool platform that manages commonly used, fined-grained, information about Java source code by using an XML representation. Our representation is suitable for developing tools which browse and manipulate actual source code, since the original code is annotated with tags based on its structure and retained within the tags. Additionally, it exposes information resulting from global semantic analysis, which is never provided by the typical AST. Our proposed platform allows the developers to extend the representation for the purpose of sharing or exchanging various kinds of information about the source code, and also enables them to build new tools by using existing XML utilities.

We propose a new analysis technique against a class of countermeasure using randomized binary signed digit (BSD) representations. We also introduce some invariant properties between BSD representations. The proposed analysis technique can directly recover the secret key from power measurements without information for algorithm because of the invariant properties of BSD representation. Thus the proposed attack is applicable to all countermeasures using BSD representations. Finally, we give the simulation results against some countermeasures using BSD representation such as Ha-Moon method, Ebeid-Hasan method, and the method of Agagliate et al. The results show that the proposed attack is practical analysis method.

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.

Recently, the radix-3 representation of integers is used for the efficient implementation of pairing based cryptosystems. In this paper, we propose non-adjacent form of radix-r representation (rNAF) and efficient algorithms for generating rNAF. The number of non-trivial digits is (r-2)(r+1)/2 and its average density of non-zero digit is asymptotically (r-1)/(2r-1). For r=3, the non-trivial digits are {2, 4} and the non-zero density is 0.4. We then investigate the width-w version of rNAF for the general radix-r representation, which is a natural extension of the width-w NAF. Finally we compare the proposed algorithms with the generalized NAF (gNAF) discussed by Joye and Yen. The proposed scheme requires a larger table but its non-zero density is smaller even for large radix. We explain that gNAF is a simple degeneration of rNAF--we can consider that rNAF is a canonical form for the radix-r representation. Therefore, rNAF is a good alternative to gNAF.

Sinusoidal representation has been widely applied to speech modification, low bit rate speech and audio coding. Usually, speech signal is analyzed and synthesized using the overlap-add algorithm or the peak-picking algorithm. But the overlap-add algorithm is well known for high computational complexity and the peak-picking algorithm cannot track the transient and syllabic variation well. In this letter, both algorithms are applied to speech analysis/synthesis. Peaks are picked in the curve of power spectral density for speech signal; the frequencies corresponding to these peaks are arranged according to the descending orders of their corresponding power spectral densities. These frequencies are regarded as the candidate frequencies to determine the corresponding amplitudes and initial phases according to the least mean square error criterion. The summation of the extracted sinusoidal components is used to successively approach the original speech signal. The results show that the proposed algorithm can track the transient and syllabic variation and can attain the good synthesized speech signal with low computational complexity.

Incremental modification and optimization in VLSI physical design is of fundamental importance. Based on the O-tree (ordered tree) representation which has more prominent advantages in comparison with other topological representations of non-slicing floorplans, in this paper, we present an incremental placement algorithm for BBL (Building Block Layout) design in VLSI physical design. The good performance of experimental results in dealing with some instances proves the effectiveness of our algorithm.