Irregular Partition Research Articles

A Partition Spatial Filtering Method for Acoustic Array Configuration

Acoustic array is a ubiquitous tool for locating and quantifying sound sources. However, its effectiveness depends greatly on the array configuration. This paper presents an array configuration method to enhance array performance, especially on the spatial resolution and the Doppler effect correction. The problem of array configuration is formulated into a position matrix determined by introducing partition spatial filtering. Irregular coaxial ring grid spacings and partition filtering conditions are suggested to control array spatial resolution. Geometrical parameters and performance indicators are constructed to quantify the relationships between the array configuration and performance. Based on these quantitative relations, the spatial variation of the array beam pattern and the Doppler effect has got adaptive adjustment. In particular, an adaptive partition algorithm is proposed to reduce computation time. The performance of the method is examined numerically and experimentally, which is compared with the other methods. The results provide the method to guide the design of a 64‐microphone optimized array with high performance (1.8° spatial angle resolution and 40% Doppler frequency correction over the bandwidth from 800 Hz to 3000 Hz) and fast computing speed (18 s array generated time for 2000 arrays). Furthermore, an unusual feature of the method is that it can be utilized in the case when the source moves at a nonconstant velocity.

A Thinned Irregular Array Synthesis Approach Based on Benders Decomposition

A thinned irregular tiled array synthesis approach is proposed for 5G base station array design. To fit the needs of multiusers, different sizes of vertical tiles with thinned elements ae considered. The tiling configuration and excitations are optimized to achieve high gain, low sidelobes, and wide-angle scanning simultaneously. A mixed integer second-order cone programming (MISOCP) model is obtained from convexity analysis and transformation. Besides, a generalized Benders decomposition algorithm is built to decouple the complex original problem into mixed integer linear programming (MILP) master problems and convex second-order cone programming (SOCP) subproblems, which is used to solve the large-scale problems efficiently. Irregular partition optimization is based on full-wave simulations of regular finite arrays. The joint effects of active VSWR and radiation patterns are considered to reduce the mismatch between element simulations and final performances. Numerical results show that the 5G array synthesized by the proposed approach is superior to those reported by the state-of-the-art methods in terms of both E- and H-plane scans and the number of T/R modules.

Sparsely Excited Tightly Coupled Dipole Arrays Based on Irregular Array Techniques

An innovative architecture for sparsely excited tightly coupled dipole arrays is proposed, based on the irregular array techniques. In such a framework, an improved maximumentropy model considering the difference of embedded element patterns is applied to optimize the irregular partition to suppress the grating lobes. Meanwhile, guidelines for the entire design procedure including antenna elements, power dividers, and optimization design of irregular feeding networks are presented. In order to achieve large elevation angle scanning, the differential evolution (DE) algorithm is used to synthesize active pattern and active reflection coefficient simultaneously. Finally, a 192-port prototype operating at 8-12 GHz has been fabricated and measured, where the port spacing is 0.576λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> is the free-space wavelength at the highest frequency). Numerical and experimental results show that the prototype array is able to achieve the reduction of gain <; 1 dB for scanning to near broadside and about 2.7 dB for scanning up to 60°, in comparison with that of conventional Taylor arrays.

Analysis of delay time and layout using Heuristics algorithms

ALB is commonly known as combinatorial optimization problem in manufacturing industries and operation management circumstances. Because of the NP-hard characteristics of ALB problem, lot of tries have been done to solve the problem professionally. The critical concern in analysing ALB is how to generate a possible task order which does not disrupt the priority restrictions. This job arranging is a vigorous work to be answered prior to passing on jobs to workstation. Balance delay time (total idle time) is the total of idle time on fabrication assembly lines triggered by the irregular partition of work among operators or stations. In this thesis, SALBP-1 analysed using the three heuristic techniques. Kilbridge and Westers Method (KWM), Ranked Positional weight (RPW) and biologically inspired evolutionary computing tool which is heuristic treated Genetic Algorithm (GA) was applied to solve the ALB problem with the main aim of reducing the balance delay time in the workstation and the best method was selected. The selection criterion was based on the minimum balance delay for the sample problem. The result obtained by heuristic treated GA with 4.545% of balance delay for the sample problem taken was the best when compared to other two methods.

Parallel viewshed analysis on a PC cluster system using triple-based irregular partition scheme

Using digital elevation models (DEMs), viewshed analysis algorithms determine the visibility of each point on the terrain at a given location in space. As a data-parallel algorithm, real-time viewshed analysis from grid DEM poses a practical challenge to personal computer (PC) users, particularly when dealing with higher resolution and accuracy of large terrain data. Therefore, this paper presents a universal domain decomposition algorithm based on an equal-area strategy for the parallel viewshed analysis on a PC cluster system. The approach uses a scan-line filling method for data partitioning of the irregular bounding polygon of the terrain. The terrain data are divided into sectors of the same area that are connected by the viewpoint and the region vertices, ignoring the null value (or NODATA) points. Furthermore, each sector is assigned to one processor and is organized in the form of triples composed of location and elevation at one point. An index of triples is built to store all of the locations of terminal vertices row-by-row and thus the random access of any point is achieved by using the offsets in each row. Two commonly applied viewshed algorithms, namely, “reference plane” and “Xdraw” algorithms are employed to verify the performance. In addition, two experiments focus on evaluating the efficiency performance and comparing traditional implementation, respectively. Experimental results demonstrate a significant performance improvement compared with the sequential computing method. The memory usage gradually decreases as the number of processors increases. Based on the equal-area decomposition, partitions in terms of sectors can guarantee a suitable load balance. Additional benefits of the proposed solution also include high storage efficiency and program portability.

Classical Virasoro irregular conformal block II

We present a new systematic way to evaluate the classical limit of the Virasoro irregular conformal block for arbitrary rank n based on the irregular partition function. In addition, we prove that the classical irregular conformal block has the exponential form as suggested by A. Zamolodchikov and Al. Zamolodchikov for the regular case. We provide an explicit calculation for the rank 2 case in detail.

A global optimization algorithm for simulation-based problems via the extended DIRECT scheme

This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.

Importance of the Voronoi domain partition for position-jump reaction-diffusion processes on nonuniform rectilinear lattices

Position-jump processes are used for the mathematical modeling of spatially extended chemical and biological systems with increasing frequency. A large subset of the literature concerning such processes is concerned with modeling the effect of stochasticity on reaction-diffusion systems. Traditionally, computational domains have been divided into regular voxels. Molecules are assumed well mixed within each of these voxels and are allowed to react with other molecules within the same voxel or to jump to neighboring voxels with predefined transition rates. For a variety of reasons implementing position-jump processes on irregular grids is becoming increasingly important. However, it is not immediately clear what form an appropriate irregular partition of the domain should take if it is to allow the derivation of mean molecular concentrations that agree with a given partial differential equation for molecular concentrations. It has been demonstrated, in one dimension, that the Voronoi domain partition is the appropriate method with which to divide the computational domain. In this Brief Report, we investigate theoretically the propriety of the Voronoi domain partition as an appropriate method to partition domains for position-jump models in higher dimensions. We also provide simulations of diffusion processes in two dimensions in order to corroborate our results.

Analysis for Floor Slabs of Wall-Slab System

The structure of Wall-slab is composed of slab and shear wall, and only in the outer wall part are the shear wall connected by a coupling beam. The floor and shear wall can bear vertical force and horizontal lateral force together. While under the situation of irregular bearing form shear wall and irregular partition loads, tablet computing becomes an urgent problem. Aiming at this problem, the model which is one layer of floor of Wall system has been used for analysis through the Safe software. In the condition of different thickness of slabs, exploratory results can get about the slab deformations, stresses and reinforcement ratios. The paragraph provides the basis to determine the optimal thickness of plate.

Content-based irregularly shaped macroblock partition for inter frame prediction in video coding

Although rate–distortion adaptive, variable block-size motion compensation has significantly contributed to the performance improvement in compression efficiency of H.264/AVC over the other existing video coding standards, the shape of the block for motion compensation prediction (MCP) in H.264/AVC is still limited to the regular rectangle. To further improve the accuracy of MCP, a novel content-adaptive macroblock partition method for inter frame prediction is proposed in this paper, where irregularly shaped partitions are introduced to MCP. The proposed method irregularly segments the current coding macroblock (MB) by referring to the matching reference region (MRR) in the reference frames, which is obtained relying on the inherent structural similarity of the video contents among successive frames and can be traced with the relative displacement vector between the current MB and the MRR. Consequently, the irregular partition of the current MB is content adaptive and the partition information is implicitly indicated by the MRR, without resorting to an explicit description of the shape information of the irregular segmentation. Experimental results demonstrate that the proposed method outperforms the MCP based on the regular rectangle blocks in terms of coding efficiency, by providing more precise motion estimation for macroblocks at little cost of extra side information.

In-package P/G planes analysis and optimization based on transmission matrix method

Power integrity (PI) has become a limiting factor for the chip’s overall performance, and how to place in-package decoupling capacitors to improve a chip’s PI performance has become a hot issue. In this paper, we propose an improved transmission matrix method (TMM) for fast decoupling capacitance allocation. An irregular grid partition mechanism is proposed, which helps speed up the impedance computation and complies better with the irregular power/ground (P/G) plane or planes with many vias and decoupling capacitors. Furthermore, we also ameliorate the computation procedure of the impedance matrix whenever decoupling capacitors are inserted or removed at specific ports. With the fast computation of impedance change, in-package decoupling capacitor allocation is done with an efficient change based method in the frequency domain. Experimental results show that our approach can gain about 5× speedup compared with a general TMM, and is efficient in restraining the noise on the P/G plane.

Stepwise pH-gradient elution for the preparative separation of natural anthraquinones by multiple liquid-liquid partition.

Preparative-scale separation of substituted anthraquinones by multiple liquid-liquid partition was studied using isopropylmethyl ketone (IMK)/aqueous phosphate buffer (aq.) as the solvent system and the Hietala apparatus with 100 partition units as the partition equipment. The lower (aq.) phase was chosen as mobile, while the upper (IMK) phase remained stationary. Hence, the principle of stepwise pH-gradient elution could be utilized to separate the components in two complex mixtures of hydroxyanthraquinones and hydroxyanthraquinone carboxylic acids, isolated from the fungus Dermocybe sanguinea. In spite of the nonlinearity of the partition isotherms for these anthraquinones, implying deviations from the Nernst partition law, remarkable separations were achieved for the components in each mixture. Every anthraquinone carboxylic acid showed markedly irregular partition behavior, appearing in the effluent as two more or less resolved concentration zones. Such splitting was attributed to the formation of relatively stable sandwich-dimers, which were in a slow equilibrium with the monomers in the more nonpolar organic phase. At lower pH-values, only the polar monomers were distributed into the mobile aqueous phase and moved forward, whereas the nonpolar sandwich-dimers remained almost entirely in the stationary organic phase and lagged behind. When the pH of the mobile aqueous phase was raised high enough, the firmly linked dimers were monomerized and emerged from the apparatus as a second concentration profile. Intermolecular hydrogen bonding and pi-pi interaction between the pi-systems of two anthraquinone molecules in a parallel orientation were considered responsible for the nonlinear and markedly irregular partition behavior of the natural anthraquinones studied. The nonlinearity of the partition behavior of the hydroxyanthraquinones lacking the carboxyl group, appeared merely as excessive broadening of the experimental concentration profile, which impaired the resolution between the components only insignificantly. Thus, e.g. the main components, dermocybin and emodin, could both be obtained from Separation 1 in a purity of at least 99%.

Spline interpolation techniques for variational methods

AbstractInterpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm.Among global interpolation techniques, bicubic splines and spline‐blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper‐elements, while high precision finite elements become convenient for very fine or irregular partition.