Search

We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics of disk-shaped systems and aligning with methodologies from other research, we analyze the influence of the central body. This analysis reveals analytical relationships among black holes, bulges, and the entire stellar disk. Additionally, we incorporate a specific angular momentum distribution (SAMD) that aligns more closely with observational data, showing that for the self-gravitating disk, with the same surface density, a reduction in its spin results in only a slight decrease in its radius, whereas with the same SAMD, an increment in its spin significantly limits its extent. A key feature of our model is its prediction that the surface density profile of an isolated disk will invariably exhibit downbending at a sufficient distance, a hypothesis that future observations can test. Our refined equations provide a notably improved fit for SBPs, particularly in the central regions of stellar disks. While our findings underscore the significance of statistical mechanics in comprehending spiral galaxy structures, they also highlight areas in our approach that warrant further discussion and exploration. [ABSTRACT FROM AUTHOR]

The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It is argued that this contributes to the untrustworthiness problem in several different ways, including [a] statistical misspecification, [b] unwarranted evidential interpretations of frequentist inference results, and [c] questionable modeling strategies that rely on curve-fitting. What is more, the alternative proposals to replace or modify frequentist testing, including [i] replacing p-values with observed confidence intervals and effects sizes, and [ii] redefining statistical significance, will not address the untrustworthiness of evidence problem since they are equally vulnerable to [a]–[c]. The paper calls for distinguishing between unduly data-dependant 'statistical results', such as a point estimate, a p-value, and accept/reject H 0 , from 'evidence for or against inferential claims'. The post-data severity (SEV) evaluation of the accept/reject H 0 results, converts them into evidence for or against germane inferential claims. These claims can be used to address/elucidate several foundational issues, including (i) statistical vs. substantive significance, (ii) the large n problem, and (iii) the replicability of evidence. Also, the SEV perspective sheds light on the impertinence of the proposed alternatives [i]–[iii], and oppugns [iii] the alleged arbitrariness of framing H 0 and H 1 which is often exploited to undermine the credibility of frequentist testing. [ABSTRACT FROM AUTHOR]

In the last decade permutation entropy (PE) has become a popular tool to analyze the degree of randomness within a time series. In typical applications, changes in the dynamics of a source are inferred by observing changes of PE computed on different time series generated by that source. However, most works neglect the crucial question related to the statistical significance of these changes. The main reason probably lies in the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty. In this paper we propose a method to overcome this issue by using generation of surrogate time series. The analysis conducted on both synthetic and experimental time series shows the reliability of the approach, which can be promptly implemented by means of widely available numerical tools. The method is computationally affordable for a broad range of users. [ABSTRACT FROM AUTHOR]

The correlation-based network is a powerful tool to reveal the influential mechanisms and relations in stock markets. However, current methods for developing network models are dominantly based on the pairwise relationship of positive correlations. This work proposes a new approach for developing stock relationship networks by using the linear relationship model with LASSO to explore negative correlations under a systemic framework. The developed model not only preserves positive links with statistical significance but also includes link directions and negative correlations. We also introduce blends cliques with the balance theory to investigate the consistency properties of the developed networks. The ASX 200 stock data with 194 stocks are applied to evaluate the effectiveness of our proposed method. Results suggest that the developed networks not only are highly consistent with the correlation coefficient in terms of positive or negative correlations but also provide influence directions in stock markets. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by Cα-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between Cα-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values. [ABSTRACT FROM AUTHOR]

Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, rL = rG = r) are for FuzzyMEn (in addition to setting nL = 3 and nG = 2) were recommended to yield the fine classification results for the NSR and CHF groups. [ABSTRACT FROM AUTHOR]

Aims: Bubble entropy ( b E n ) is an entropy metric with a limited dependence on parameters. b E n does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of b E n for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and b E n changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of b E n , which considered the cost of ordering two additional samples. We first compared it with the original b E n estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of 10 < m < 20 , where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for b E n , which ensures that b E n   = 1 when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator. [ABSTRACT FROM AUTHOR]

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods. [ABSTRACT FROM AUTHOR]

Multidimensional datapoint clouds representing large datasets are frequently characterized by non-trivial low-dimensional geometry and topology which can be recovered by unsupervised machine learning approaches, in particular, by principal graphs. Principal graphs approximate the multivariate data by a graph injected into the data space with some constraints imposed on the node mapping. Here we present ElPiGraph, a scalable and robust method for constructing principal graphs. ElPiGraph exploits and further develops the concept of elastic energy, the topological graph grammar approach, and a gradient descent-like optimization of the graph topology. The method is able to withstand high levels of noise and is capable of approximating data point clouds via principal graph ensembles. This strategy can be used to estimate the statistical significance of complex data features and to summarize them into a single consensus principal graph. ElPiGraph deals efficiently with large datasets in various fields such as biology, where it can be used for example with single-cell transcriptomic or epigenomic datasets to infer gene expression dynamics and recover differentiation landscapes. [ABSTRACT FROM AUTHOR]