New high-dimensional networks based on polyoxometalate and crown ether building blocks

Three novel supramolecular assemblies constructed from polyoxometalate and crown ether building blocks, [(DB18C6)Na(H2O)(1.5)](2)Mo6O19.CH3CN, 1, and [{Na(DB18C6)(H2O)(2)}(3)(H2O)(2)]XMo12O40.6DMF.CH3CN (X = P, 2, and As, 3; DB18C6 = dibenzo-18-crown-6; DMF = N,N-dimethylfomamide), have been synthesized and characterized by elemental analyses, IR, UV-vis, EPR, TG, and single crystal X-ray diffraction. Compound 1 crystallizes in the tetragonal space group P4/mbm with a = 16.9701(6) Angstrom, c = 14.2676(4) Angstrom, and Z = 2. Compound 2 crystallizes in the hexagonal space group P6(3)/m with a = 15,7435(17) Angstrom, c = 30.042(7) Angstrom, gamma = 120degrees, and Z = 2. Compound 3 crystallizes in the hexagonal space group P6(3)/m with a = 15.6882(5) Angstrom, c = 29.9778(18) Angstrom, gamma = 120degrees, and Z = 2. Compound 1 exhibits an unusual three-dimensional network with one-dimensional sandglasslike channels based on the extensive weak forces between the oxygen atoms on the [Mo6O19](2-) polyoxoanions and the CH2 groups of crown ether molecules, Compounds 2 and 3 are isostructural, and both contain a novel semiopen cagelike trimeric cation [{Na(DB18C6)(H2O)(2)}(3)(H2O)(2)](3+). In their packing arrangement, an interesting 2-D "honeycomblike" "host" network is formed, in which the [XMo12O40](3-) (X = As and P) polyoxoanion "guests" resided.

Integration of a photonic crystal polarization beam splitter and waveguide bend

In this work, we present the design of an integrated photonic-crystal polarization beam splitter (PC-PBS) and a low-loss photonic-crystal 60 waveguide bend. Firstly, the modal properties of the PC-PBS and the mechanism of the low-loss waveguide bend are investigated by the two-dimensional finite-difference time-domain (FDTD) method, and then the integration of the two devices is studied. It shows that, although the individual devices perform well separately, the performance of the integrated circuit is poor due to the multi-mode property of the PC-PBS. By introducing deformed airhole structures, a single-mode PC-PBS is proposed, which significantly enhance the performance of the circuit with the extinction ratios remaining above 20dB for both transverse-electric (TE) and transverse-magnetic (TM) polarizations. Both the specific result and the general idea of integration design are promising in the photonic crystal integrated circuits in the future. (C) 2009 Optical Society of America

An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.

Pattern Recognition With Weighted Complex Networks

In this paper we introduce a weighted complex networks model to investigate and recognize structures of patterns. The regular treating in pattern recognition models is to describe each pattern as a high-dimensional vector which however is insufficient to express the structural information. Thus, a number of methods are developed to extract the structural information, such as different feature extraction algorithms used in pre-processing steps, or the local receptive fields in convolutional networks. In our model, each pattern is attributed to a weighted complex network, whose topology represents the structure of that pattern. Based upon the training samples, we get several prototypal complex networks which could stand for the general structural characteristics of patterns in different categories. We use these prototypal networks to recognize the unknown patterns. It is an attempt to use complex networks in pattern recognition, and our result shows the potential for real-world pattern recognition. A spatial parameter is introduced to get the optimal recognition accuracy, and it remains constant insensitive to the amount of training samples. We have discussed the interesting properties of the prototypal networks. An approximate linear relation is found between the strength and color of vertexes, in which we could compare the structural difference between each category. We have visualized these prototypal networks to show that their topology indeed represents the common characteristics of patterns. We have also shown that the asymmetric strength distribution in these prototypal networks brings high robustness for recognition. Our study may cast a light on understanding the mechanism of the biologic neuronal systems in object recognition as well.

An Extension of Self-Organizing Maps to Categorical Data

Self-organizing maps (SOM) have been recognized as a powerful tool in data exploratoration, especially for the tasks of clustering on high dimensional data. However, clustering on categorical data is still a challenge for SOM. This paper aims to extend standard SOM to handle feature values of categorical type. A batch SOM algorithm (NCSOM) is presented concerning the dissimilarity measure and update method of map evolution for both numeric and categorical features simultaneously.

Triangle Evolution-A Hybrid Heuristic for Global Optimization

Abstract This paper presents a hybrid heuristic{triangle evolution (TE) for global optimization. It is a real coded evolutionary algorithm. As in di®erential evolution (DE), TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is di®erent. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and e±cient for global optimization problems with continuous variables. Moreover, it requires only one (explicit) control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.

大行程高分辨率微定位机构的设计分析

压电驱动器的位移输出能力有限，因此通常借助于柔性机构对其位移量进行放大。对常用的柔性放大机构的性能进行了分析。提出一种柔性八杆放大机构，并对其进行有限元分析和理论计算。为了提高放大率，提出两级串连式机构。机构整体具有结构紧凑、放大效率较高的优点。

大行程高分辨率微定位机构的设计分析

压电驱动器的位移输出能力有限，通常借助于柔性机构对其位移量进行放大。提出一种柔性八杆放大机构，并对其进行有限元分析和理论计算。为了提高放大率，提出两级串连式机构。机构整体具有结构紧凑、放大效率较高的优点。

The multi-weight neuron with geometry algorithm and its application

A novel approach for multi-dimension signals processing, that is multi-weight neural network based on high dimensional geometry theory, is proposed. With this theory, the geometry algorithm for building the multi-weight neuron is mentioned. To illustrate the advantage of the novel approach, a Chinese speech emotion recognition experiment has been done. From this experiment, the human emotions are classified into 6 archetypal classes: fear, anger, happiness, sadness, surprise and disgust. And the amplitude, pitch frequency and formant are used as the feature parameters for speech emotion recognition. Compared with traditional GSVM model, the new method has its superiority. It is noted that this method has significant values for researches and applications henceforth.

Study on Closed-set Speaker Identification Based on Biomimetic Pattern Recognition

In this paper, a new classifier of speaker identification has been proposed, which is based on Biomimetic pattern recognition (BPR). Distinguished from traditional speaker recognition methods, such as DWT, HMM, GMM, SVM and so on, the proposed classifier is constructed by some finite sub-space which is reasonable covering of the points in high dimensional space according to distributing characteristic of speech feature points. It has been used in the system of speaker identification. Experiment results show that better effect could be obtained especially with lesser samples. Furthermore, the proposed classifier employs a much simpler modeling structure as compared to the GMM. In addition, the basic idea "cognition" of Biomimetic pattern recognition (BPR) results in no requirement of retraining the old system for enrolling new speakers.

The application of DBF neural networks for object recognition

On the basis of DBF nets proposed by Wang Shoujue, the model and properties of DBF neural network were discussed in this paper. When applied in pattern recognition, the algorithm and implement on hardware were presented respectively. We did experiments on recognition of omnidirectionally oriented rigid objects on the same level, using direction basis function neural networks, which acts by the method of covering the high dimensional geometrical distribution of the sample set in the feature space. Many animal and vehicle models (even with rather similar shapes) were recognized omnidirectionally thousands of times. For total 8800 tests, the correct recognition rate is 98.75%, the error rate and the rejection rate are 0.5% and 1.25% respectively. (C) 2003 Elsevier Inc. All rights reserved.

Double synaptic weight neuron theory and its application

In this paper, a novel mathematical model of neuron-Double Synaptic Weight Neuron (DSWN)(l) is presented. The DSWN can simulate many kinds of neuron architectures, including Radial-Basis-Function (RBF), Hyper Sausage and Hyper Ellipsoid models, etc. Moreover, this new model has been implemented in the new CASSANN-II neurocomputer that can be used to form various types of neural networks with multiple mathematical models of neurons. The flexibility of the DSWN has also been described in constructing neural networks. Based on the theory of Biomimetic Pattern Recognition (BPR) and high-dimensional space covering, a recognition system of omni directionally oriented rigid objects on the horizontal surface and a face recognition system had been implemented on CASSANN-II neurocomputer. In these two special cases, the result showed DSWN neural network had great potential in pattern recognition.

Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Differences and commonalities between connectionism and symbolicism

The differences between connectionism and symbolicism in artificial intelligence (AI) are illustrated on several aspects in details firstly; then after conceptually decision factors of connectionism are proposed, the commonalities between connectionism and symbolicism are tested to make sure, by some quite typical logic mathematics operation examples such as "parity"; At last, neuron structures are expanded by modifying neuron weights and thresholds in artificial neural networks through adopting high dimensional space geometry cognition, which give more overall development space, and embodied further both commonalities.

A criterion for local interconvertibility between all-tripartite Gaussian states

We arrive at a necessary and sufficient criterion that can be readily used for interconvertibility between general, all-tripartite Gaussian states under local quantum operation. The derivation involves a systematic reduction that converts the original complex conditions in high-dimensional, 6n x 6n matrix space eventually into 2 x 2 matrix problems.