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.

随机变量的共轭梯度方法

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.

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 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.

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.

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.\;

HAUSDORFF CENTRED MEASURE OF NON-SYMMETRY CANTOR SETS

Let 0<λ_1,λ_2<1 and 1-λ_1-λ_2≥max｛λ_1,λ_2｝.Let ~K(λ_1,λ_2) be the attractor of the iterated function system ｛φ_1,φ_2｝on the line,where φ_1(x)=λ_1x and φ_2(x)=1-λ_2+λ_2x,x∈R.~K(λ_1,λ_2) is called a non-symmetry Cantor set. In this paper,it is proved that the exact Hausdorff centred measure of K(λ_1,λ_2) equals 2s(1-λ)s,where λ=max｛λ_1,λ_2｝ and s is the Hausdorff dimension of K(λ_1,λ_2).

MULTIFRACTAL STRUCTURE AND PRODUCT OF MATRICES

There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attention to the important classes of self-similar measures that have matrix representations. The dimension spectra and the L q -spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifractal structure and they will be discussed in detail.

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.

Nondestructive measurement of thermal contact resistance for the power vertical double-diffused metal-oxide-semiconductor

To obtain thermal contact resistance（TCR） between the vertical double-diffused metal-oxide-semiconductor（VDMOS） and the heat sink, we derived the relationship between the total thermal resistance and the contact force imposed on the VDMOS. The total thermal resistance from the chip to the heat sink is measured under different contact forces, and the TCR can be extracted nondestructively from the derived relationship. Finally, the experimental results are compared with the simulation results.

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.

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.

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.

Thermionic emission as a tool for measuring the work function of anodic titanium dioxide

Titanium dioxide(TiO_2)is being extensively applied in such fields as photocatalysis,sensing,photoelectrolysis,and photovoltaics[1].The work function(WF)of a material is one of the vital factors that determine the performance of this material in electron emission,chemical reaction,surface

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.