Information content of data and variables and types of weighting in least-squares regression methods

Algorithms are given for evaluating the relative amount of useful information related to a particular parameter which is carried by individual data points and intervals of the variables. The algorithms provide an efficient means of using the information contained in a set of data. Applications to the optimization of weighting in regression methods are described. Several informational and combined informational-statistical types of weighting are studied as a means of improving the accuracy and precision of the parameters obtained by non-linear regression.     

Pattern-specific neural network design

We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let genuine Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed notbefore, butduring the learning phase.     

Hexagonal Ferrites from Melts and Aqueous Solutions,Magnetic Recording Materials

Owing to their particular crystallographic properties, ferrimagnetic hexagonal ferrites exhibit a far greater coercive force than the conventional magnetic pigments. They therefore appear to be suitable for use in magnetic information storage procedures, some of which are novel and are at the development stage. Thus, magnetic tapes of high coercive force containing barium ferrite could be used as master tapes for copying magnetic information or for producing forgery-proof magnetic cards, if magnetic heads having high-order write fields were successfully developed. Moreover, platelet-like ferrite pigments in which the preferred direction of magnetic orientation is perpendicular to the plane of the platelet are of great interest for perpendicular magnetic recording. In this progress report, the crystal structures, magnetic characteristics of hexagonal ferrites, and chemical processes for their production are discussed. In particular, reactions in salt melts or under hydrothermal conditions produce finely divided pigments whose particles have a pronounced hexagonal, plate-like habit, a narrow particle size distribution, and advantageous magnetic properties. The magnetic properties of the pigments crystallized from salt melts may be adjusted by cation exchange.     

Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.     

A simple optimization strategy based on Rs-minimum and information theory of chromatography

Summary A simple optimization method based on the well-known Rs-minimum method and on the information theory of FUMI Φ is proposed. Resolution (Rs), peak area and height (or width) are the only parameters necessary for the calculation of the information Φ and information flow ϑ. The most precise analysis can be selected as the chromatogram having maximal ϑ. Mobile phase composition, column length, flow rate, detection wavelength, amount of internal standard, etc. can be optimized by this method.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

Automatic hierarchy classification in venation networks using directional morphological filtering for hierarchical structure traits extraction

The extraction of vein traits from venation networks is of great significance to the development of a variety of research fields, such as evolutionary biology. However, traditional studies normally target to the extraction of reticulate structure traits (ReSTs), which is not sufficient enough to distinguish the difference between vein orders. For hierarchical structure traits (HiSTs), only a few tools have made attempts with human assistance, and obviously are not practical for large-scale traits extraction. Thus, there is a necessity to develop the method of automated vein hierarchy classification, raising a new challenge yet to be addressed. We propose a novel vein hierarchy classification method based on directional morphological filtering to automatically classify vein orders. Different from traditional methods, our method classify vein orders from highly dense venation networks for the extraction of traits with ecological significance. To the best of our knowledge, this is the first attempt to automatically classify vein hierarchy. To evaluate the performance of our method, we prepare a soybean transmission image dataset (STID) composed of 1200 soybean leaf images and the vein orders of these leaves are manually coarsely annotated by experts as ground truth. We apply our method to classify vein orders of each leaf in the dataset. Compared with ground truth, the proposed method achieves great performance, while the average deviation on major vein is less than 5 pixels and the average completeness on second-order veins reaches 54.28%.     

Optimal recovery of integral operators and its applications

In this paper we present the solution to a problem of recovering a rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE’s.     

Preparation and photochromic properties of pyrazolones/polyvinyl alcohol composite films

Novel photochromic composite films have been successfully fabricated by dispersing pyrazolone derivative:1,3-Diphenyl-4-(3-chlorobenzal)-5-hydroxypyrazole 4-phenylsemicarbazone (1a) into hydrosol of polyvinyl alcohol (PVA). The microstructure, photochromic behaviors and thermal bleaching properties were investigated by Raman spectroscopy, X-ray powder diffraction (XRD), field emission scanning electron microscopy (FE-SEM) and ultraviolet-visible absorption spectroscopy (UV-vis). The results showed that 1a was not only blended but also well dispersed in the PVA polymer films with a suitable content of chromophore. Upon UV light irradiation, the composite films gradually changed from colorless to yellow and recovered fully to the initial state upon thermal bleaching. The time constants of photochromic reactions were almost the same as those of 1a observed in their crystalline state, indicating that the photochromic phenomenon is barely disturbed by the polymer matrix.     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.