Nonlinear Measurement Function in the Ensemble Kalman Filter

ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

Functional outcomes after home-based rehabilitation for heroin-induced spongiform leukoencephalopathy

A 22-year-old man with a 2-year history of heroin vapor inhalation developed spongiform leukoencephalopathy and underwent clinical and home-based rehabilitative treatments. Activities of daily living were measured using the Functional Independence Measure at discharge and at 6, 12, and 24 months after discharge. His neurological symptoms gradually disappeared with rehabilitative treatment, and the functional scale scores increased from 55 on admission to 105 at 24 months after discharge. These results suggest that home-based rehabilitation was effective in ameliorating the pathology and improving activities of daily living in this patient with heroin-induced spongiform leukoencephalopathy.

A Basic Topological Approach to the Continuity of the Size Function

We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.

ON THE MEASURABILITY FOR FUNCTIONAL OF EMPIRICAL PROCESSES

In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.

Risk assessment model of tunnel water inrush based on improved attribute mathematical theory

Tunnel water inrush is one of the common geological disasters in the underground engineering construction.In order to effectively evaluate and control the occurrence of water inrush,the risk assessment model of tunnel water inrush was proposed based on improved attribute mathematical theory.The trigonometric functions were adopted to optimize the attribute mathematical theory,avoiding the influence of mutation points and linear variation zones in traditional linear measurement functions on the accuracy of the model.Based on comprehensive analysis of various factors,five parameters were selected as the evaluation indicators for the model,including tunnel head pressure,permeability coefficient of surrounding rock,crushing degree of surrounding rock,relative angle of joint plane and tunnel section size,under the principle of dimension rationality,independence,directness and quantification.The indicator classifications were determined.The links among measured data were analyzed in detail,and the objective weight of each indicator was determined by using similar weight method.Thereby the tunnel water inrush risk assessment model is established and applied in four target segments of two different tunnels in engineering.The evaluation results and the actual excavation data agree well,which indicates that the model is of high credibility and feasibility.

THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET

First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.

The Need and Its Influence Factors for Community-based Rehabilitation Services for Disabled Persons in One District in Beijing

Purpose To explore the needs for basic community-based rehabilitation services for disabled persons in Xuanwu District, Beijing, China, and to identify factors which influence disabled persons to accept rehabilitation services. Method One hundred and eight disabled persons were selected by systematic sampling and simple random sampling to assess their needs for community-based rehabilitation services. Results Of the interviewees, 57A% needed the community-based rehabilitation services, but only 13.9% took advantage of it. The main factors influencing the interviewees to accept these services were cost （P〈0.05）, knowledge about rehabilitation medicine （P〈0.05）; and the belief in the therapeutic benefit of the community-based rehabilitation service （P〈0.05）. Conclusion A considerable gap exists between the supply of community-based rehabilitation services in Beijing and the needs for these services by disabled residents underscoring the need for improved availability, and for additional research.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

Fire risk evaluation research on fully mechanized coalface based on the uncertainty measure theory

A relatively perfect coalmine fire risk-evaluating and order-arranging model that includes sixteen influential factors was established according to the statistical information of the fully mechanized coalface ground on the uncertainty measure theory. Then the single-index measure function of sixteen influential factors and the calculation method of computing the index weight ground on entropy theory were respectively established. The value assignment of sixteen influential factors was carried out by the qualitative analysis and observational data, respectively, in succession. The sequence of fire danger class of four experimental coalfaces could be obtained by the computational aids of Matlab according to the confidence level criterion. Some conclusions that the fire danger class of the No.l, No.2 and No.3 coalface belongs to high criticality can be obtained. But the fire danger class of the No.4 coalface belongs to higher criticality. The fire danger class of the No.4 coalface is more than that of the No.2 coalface. The fire danger class of the No.2 coalface is more than that of the No.1 coalface. Finally, the fire danger class of the No.1 coalface is more than that of the No.3 coalface.

Investigate Targeted Factors to Achieve Prediction Goal in Stroke Convalescence in Terms of Causal Relationships of Prediction Error

Background and Purpose: To investigate target functional independence measure (FIM) items to achieve the prediction goal in terms of the causal relationships between prognostic prediction error and FIM among stroke patients in the convalescent phase using the structural equation modeling (SEM) analysis. Methods: A total of 2992 stroke patients registered in the Japanese Rehabilitation Database were analyzed retrospectively. The prediction error was calculated based on a prognostic prediction formula proposed in a previous study. An exploratory factor analysis (EFA) then the factor was determined using confirmatory factorial analysis (CFA). Finally, multivariate analyses were performed using SEM analysis. Results: The fitted indices of the hypothesized model estimated based on EFA were confirmed by CFA. The factors estimated by EFA were applied, and interpreted as follows: “Transferring (T-factor),” “Dressing (D-factor),” and “Cognitive function (C-factor).” The fit of the structural model based on the three factors and prediction errors was supported by the SEM analysis. The effects of the D- and C-factors yielded similar causal relationships on prediction error. Meanwhile, the effects between the prediction error and the T-factor were low. Observed FIM items were related to their domains in the structural model, except for the dressing of the upper body and memory (p < 0.01). Conclusions: Transfer, which was not heavily considered in the previous prediction formula, was found in causal relationships with prediction error. It is suggested to intervene to transfer together with positive factors to recovery for achieving the prediction goal.

（Dis）Economies of Scale in Business Software Systems Development and Enhancement Projects

In the software engineering literature, it is commonly believed that economies of scale do not occur in case of software Development and Enhancement Projects （D＆EP）. Their per-unit cost does not decrease but increase with the growth of such projects product size. Thus this is diseconomies of scale that occur in them. The significance of this phenomenon results from the fact that it is commonly considered to be one of the fundamental objective causes of their low effectiveness. This is of particular significance with regard to Business Software Systems （BSS） D＆EP characterized by exceptionally low effectiveness comparing to other software D＆EP. Thus the paper aims at answering the following two questions： （1） Do economies of scale really not occur in BSS D＆EP？ （2） If economies of scale may occur in BSS D＆EP, what factors are then promoting them？ These issues classify into economics problems of software engineering research and practice.

An experimental study on the conversion between IFPUG and UCP functional size measurement units

The use of functional size measurement(FSM) methods in software development organizations is growing during the years. Also, object oriented(OO) techniques have become quite a standard to design the software and, in particular, Use Cases is one of the most used techniques to specify functional requirements. Main FSM methods do not include specific rules to measure the software functionality from its Use Cases analysis. To deal with this issue some other methods like Kramer's functional measurement method have been developed. Therefore, one of the main issues for those organizations willing to use OO functional measurement method in order to facilitate the use cases count procedure is how to convert their portfolio functional size from the previously adopted FSM method towards the new method. The objective of this research is to find a statistical relationship for converting the software functional size units measured by the International Function Point Users Group(IFPUG) function point analysis(FPA) method into Kramer-Smith's use cases points(UCP) method and vice versa. Methodologies for a correct data gathering are proposed and results obtained are analyzed to draw the linear and non-linear equations for this correlation. Finally, a conversion factor and corresponding conversion intervals are given to establish the statistical relationship.

Mercer Kernel Based Fuzzy Clustering Self-Adaptive Algorithm

A novel mercer kernel based fuzzy clustering self-adaptive algorithm is presented. The mercer kernel method is introduced to the fuzzy c-means clustering. It may map implicitly the input data into the high-dimensional feature space through the nonlinear transformation. Among other fuzzy c-means and its variants, the number of clusters is first determined. A self-adaptive algorithm is proposed. The number of clusters, which is not given in advance, can be gotten automatically by a validity measure function. Finally, experiments are given to show better performance with the method of kernel based fuzzy c-means self-adaptive algorithm.

The Advances of the Research for Random Recursive Sets(Ⅰ)

We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;

The Conjugate Gradient Method in Random Variables

We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.

Measurement and estimation of free field to eardrumtransfer function for virtual acoustic space research

Free field to Eardrum Thansfer Function (FETF) is one of the major factors influencing the identification of the sound source direction. FETF can be employed to generate a Virtual Acoustic Space (VAS) by computer and other equlpment. In this paper the methods to improve the measurement and estimation of FETF are approached. Least-mean-squares (LMS)method is much better than empirical FFT method. This paper also gives a sample description of excitation signals for measuring the impulse response of FETF.

Application and measurement of underwater acoustic reciprocity transfer functions in reverberant sound field

The reciprocity measurement theory in anomalous reverberant sound fields was investigated.An improved method Was proposed due to the interrelated errors.The source volume velocity Was corrected by spatial average of measurement results and evaluation of the reverberant sound field influence on acoustic energy density.The result was validated in underwater experiment,corrected reciprocity measurement results were almost the same as direct measurement results.It indicates that reverberant sound field does not affect the validitv of the principle,but influences the obtainment of source volume velocity,then influences the measurement of transfer functions with the principle.The proposed method is simple and effective in anomalous reverberant sound fields.The study mav be valuable for the applications which are based on the principle.

Using the system function to analyze the performance of transducer's impedance measurement method

Prom investigation of the advantages and disadvantages of conventional tri-voltage method,a method for the measurement of the transmitting transducer＇s impedance was presented to solve the difficult problem of examining the consistency of the transmitting phased array on the single-mode excitation sea spot.In the method based on the system function, the circuit structure of tri-voltage method was used but new parameters were measured.The principle of the method was given first.Then when resistors with different nominal values were used in the circuit,the measured results for the impedance of transducers were reported.The results were compared with the higher precision impedance analyzer.Finally,the error analysis was performed according to the impedance formula and the equivalent circuit parameters were fitted.Under the condition of guaranteeing the sampling precision,by performance analyzing, the resistor value in series was chosen relatively smaller than the impedance of transducer,the measurement of impedance could achieve the same precision as the higher precision impedance analyzer.Finally,the least squares curve-fitting of measured curves indicated that the transducer equivalent electrical parameters could be extracted accurately and used to design the matching network.

Phase Retrieval of Real-valued Functions in Sobolev Space

The Sobolev space HS（Rd） with s 〉 d/2 contains many important functions such as the bandlimited or rational ones. In this paper we propose a sequence of measurement functions { φj^r,k}∈C H^-S（R^d） to the phase retrieval problem for the real-valued functions in H^s（R^d）. We prove that any real-valued function f ∈ H^s （Rd） can be determined, up to a global sign, by the phaseless measurements {｜（ f, φj^r,k}｜}. It is known that phase retrieval is unstable in infinite dimensional spaces with respect to perturbations of the measurement functions. We examine a special type of perturbations that ensures the stability for the phase-retrieval problem for all the real-valued functions in Hs（Rd） ∩ C1（Rd）, and prove that our iterated reconstruction procedure guarantees uniform convergence for any function f ∈ Hs （Rd）∩ C1 （Rd） whose Fourier transform f is L1-integrable. Moreover, numerical simulations are conducted to test the efficiency of the reconstruction algorithm.