Mean square approximation I

Robust least mean logarithmic square adaptive filtering algorithms

The logarithmic transformation can be utilized to equilibrate variances of traits of different size when these variances scale proportionally to the square of the trait means. Otherwise variances will not be equilibrated by log transformation. A simple model of ontogenetic growth is utilized to show that trait variances increase with the square of the mean during ontogeny when individual growth increments are perfectly correlated. Alternatively, if these individual growth increments are uncorrelated, trait variance accumulates only in direct proportion to the mean itself. For most actual ontogenies, the incremental growths would not be perfectly correlated, so log-transformed variances would be expected to decrease during ontogeny. The model was extended to address the comparison of variances between two traits differing in size. When two traits are highly correlated, the ratio of variances of the traits will be proportional to the square of the mean ratio. When two traits are uncorrelated, the ratio of variances scales directly to the ratio of means. Biological traits are usually characterized by varying degrees of intercorrelation (i.e., they exhibit multivariate structure). Since the appropriate transformation to accommodate scale depends upon the intercorrelation among a set of traits, it is unlikely that a single transformation would equilibrate variances (and covariances) among all traits. A similar caution applies to genetic variances and covariances in quantitative genetics. However, narrow-sense heritabilities and additive genetic correlations are both approximately invariant under a change of scale and can be compared across traits and/or populations with less concern about scale effect.

To explore protein adaptation to extremely high temperatures, two parameters related to macromolecular dynamics, the mean square atomic fluctuation and structural resilience, expressed as a mean force constant, were measured by neutron scattering for hyperthermophilic malate dehydrogenase from Methanococcus jannaschii and a mesophilic homologue, lactate dehydrogenase from Oryctolagus cunniculus (rabbit) muscle. The root mean square fluctuations, defining flexibility, were found to be similar for both enzymes (1.5 A) at their optimal activity temperature. Resilience values, defining structural rigidity, are higher by an order of magnitude for the high temperature-adapted protein (0.15 Newtons/meter for O. cunniculus lactate dehydrogenase and 1.5 Newtons/meter for M. jannaschii malate dehydrogenase). Thermoadaptation appears to have been achieved by evolution through selection of appropriate structural rigidity in order to preserve specific protein structure while allowing the conformational flexibility required for activity.

Robust incremental growing multi-experts network

POS0307 A PHASE 2 TRIAL OF PERESOLIMAB FOR ADULTS WITH RHEUMATOID ARTHRITIS

Acoustic-to-articulatory inversion has potential application in number of fields. For decades, average root mean square error and Pearson correlation coefficient are the most prevalent quantities adopted to evaluate the performance of acoustic-to-articulatory inversion. Various inversion methods have been developed to less the average root mean square error, but very few studies explored whether the average root mean square error is appropriate for evaluating and comparing the performance of different inversion methods. In this study, we attempt to tackle this issue by comparing not only the average root mean square error but also channel root mean square error of each articulatory channel, and the root mean square error of the critical and non-critical portions of each articulatory channel for methods within and between different groups. It is found that: i) the root mean square error of each articulatory channel, and the root mean square error of the critical and non-critical portions of each articulatory channel decrease while the average root mean square error decrease if the AAI methods belong to the same group; ii) exceptions are found if the inversion methods belong to different categories; iii) the average root mean square error is dominated by that of non-critical portions of articulatory channels. This suggests that new methods, which pay more attention to the performance of acoustic-to-articulatory inversion on critical articulators and facilitate the comparison of performance of methods belonging to different categories, should be developed in the future.

Comment

Summary This paper describes a generalization of probability plotting to supplement general analysis of variance procedures. The mean squares in a general orthogonal analysis of variance are ordered and plotted against the corresponding expected values of standardized ordered mean squares. Since the mean squares may have differing degrees of freedom, alternate conceptions are possible with respect to association of the ordered mean squares with their parent distributions. In considering the statistical distribution of the ith standardized ordered mean square, the view adopted here is that of complete conditioning, that is, repeated sampling so constrained that the order relationships of the sample mean squares is such that the ith ordered mean square comes from a χ2(vi)/vi distribution, for i = 1, …, K, where K denotes the total number of mean squares in the collection and v1, v2, …, vK are the respective degrees of freedom of the ordered mean squares as observed. Using this completely conditioned distribution, methods are described for computing the required plotting positions, viz. the expected values of the standardized ordered mean squares. Some illustrative examples of use of the proposed procedure are given.

Given a collection of analysis of variance mean squares, not all of which necessarily have the same degrees of freedom, the present paper describes a method of "mapping" them so as to facilitate the statistical structuring of the mean squares. Even under a null model of no real effects, the mean squares do not have the same distribution because their degrees of freedom may differ, and the ordered mean squares cannot be regarded as the usual order statistics of a sample from a single common distribution. If the ordered mean squares in a general orthogonal analysis of variance are $0 < S_1 \leqq S_2 \leqq \cdots \leqq S_K$ with corresponding degrees of freedom, $\nu_1,\nu_2, \cdots, \nu_K$, then the inferential reference set in the present approach is one obtained by so-called complete conditioning, i.e., repeated sampling from a set of $K$ populations such that the $i$th ordered mean square will be considered to have come from the population associated with $v_i$ degrees of freedom, for $i = 1,2, \cdots, K$. The approach consists of obtaining from each of the ordered mean squares, in turn, a maximum likelihood estimate of a presumed common error variance based on an order statistics formulation which employs complete conditioning of the mean squares. Methods of obtaining the sequence of maximum likelihood estimates as well as two graphical modes of displaying them are described. Illustrative examples are included.

A family of robust adaptive filtering algorithms based on sigmoid cost

The variable step size least mean square algorithm has been suggested since a number of years as a potential solution for improving the performance of least mean square algorithm. In this article, the variable step size least mean square algorithm is classified by the techniques which are used to update step size. Unfortunately, for variable step size least mean square algorithms with forgetting factor, a constant forgetting factor may slow down its convergence speed. For this reason, a variable forgetting factor method for variable step size least mean square is proposed in this article. First, the convergence analysis of a new variable step size least mean square algorithm with the variable forgetting factor is provided. Then, simulations expose the characteristics of this variable forgetting factor method. Last, a micro-vibration control experimental system is established. Four typical variable step size least mean square algorithms and their variable forgetting factor modified version are verified through experiments. The results show that the proposed variable forgetting factor method can effectively improve convergence speed while maintaining the steady-state performance of the variable step size least mean square algorithm with the constant forgetting factor.

Noise reduction is an important process in a communication system, one of which is radio communication. In the process of broadcasting radio Frequency Modulation (FM) often encountered noise so that listeners find it difficult to understand the information provided. In the past, noise reduction used traditional filters that were only able to filter certain frequencies. However, for future technologies an adaptive filter is needed that can dynamically reduce noise effectively. Register Level-Software Defined Radio (RTL-SDR) can capture signals with a very wide frequency range but has a less clear sound quality. So it needs to be done noise reduction. In this study, two methods are used, namely Least Mean Square (LMS) and Recursive Least Square (RLS). The data used five radio stations in Malang. The results showed that the LMS algorithm is stable but has a slow convergence speed, whereas the RLS algorithm has poor stability but has a high convergence speed. From the test, it can be concluded that the performance of RLS is better than LMS for noise reduction in RTL-SDR. The best performance is the reduction of White Noise using RLS on the Oryza radio station with an Normalized Weight Differences (NWD) value of -13.93 dB.

The Least Mean Square (LMS) algorithm has a slow convergence rate as it is dependent on the eigenvalue spread of the input correlation matrix. In this research, we solved this problem by introducing a novel adaptive filtering algorithm for complex domain signal processing based on q-derivative. The proposed algorithm is based on Wirtinger calculus and is called as q- Complex Least Mean Square (q-CLMS) algorithm. The proposed algorithm could be considered as an extension of the q-LMS algorithm for the complex domain. Transient and steady-state analyses of the proposed q-CLMS algorithm are performed and exact analytical expressions for mean analysis, mean square error (MSE), excess mean square error (EMSE), mean square deviation (MSD) and misadjustment are presented. Extensive experiments have been conducted and a good match between the simulation results and theoretical findings is reported. The proposed q-CLMS algorithm is also explored for whitening applications with satisfactory performance. A modification of the proposed q-CLMS algorithm called Enhanced q-CLMS (Eq-CLMS) is also proposed. The Eq-CLMS algorithm eliminates the need for a pre-coded value of the q-parameter thereby automatically adapting to the best value. Extensive experiments are performed on system identification and channel equalization tasks and the proposed algorithm is shown to outperform several benchmark and state-of-the-art approaches namely Complex Least Mean Square (CLMS), Normalized Complex Least Mean Square (NCLMS), Variable Step Size Complex Least Mean Square (VSS-CLMS), Complex FLMS (CFLMS) and Fractional-ordered-CLMS (FoCLMS) algorithms.

The structure and intrinsic activities of conserved STAS domains of the ubiquitous SulP/SLC26 anion transporter superfamily have until recently remained unknown. Here we report the heteronuclear, multidimensional NMR spectroscopy solution structure of the STAS domain from the SulP/SLC26 putative anion transporter Rv1739c of Mycobacterium tuberculosis. The 0.87-Å root mean square deviation structure revealed a four-stranded β-sheet with five interspersed α-helices, resembling the anti-σ factor antagonist fold. Rv1739c STAS was shown to be a guanine nucleotide-binding protein, as revealed by nucleotide-dependent quench of intrinsic STAS fluorescence and photoaffinity labeling. NMR chemical shift perturbation analysis partnered with in silico docking calculations identified solvent-exposed STAS residues involved in nucleotide binding. Rv1739c STAS was not an in vitro substrate of mycobacterial kinases or anti-σ factors. These results demonstrate that Rv1739c STAS binds guanine nucleotides at physiological concentrations and undergoes a ligand-induced conformational change but, unlike anti-σ factor antagonists, may not mediate signals via phosphorylation.

Analysis of Variance Through Examples