Singular Distribution Research Articles

Research on spatial feature differentiation of basin river network geomorphology based on multifractal algorithm

Using multi-fractal algorithm to scientifically quantify watershed morphology is one of the hot spots of geomorphology research. In this paper, based on the DEM data of the Northwest China Basin (Daxiahe), the remote sensing images of the Daxia River Basin were processed. The multi-fractal model was used to extract and analyze the multi-fractal characteristics and quantified characteristic parameters of the Daxia River and 7 sub-basins of the river system, and discussed the geomorphic significance of the spatial characteristics of the watershed. The results showed that the multi-fractal spectrum of the watershed was in the shape of a right hook (Δf < 0). The span of the singular index Δa was between 0.860 and 1.160, and the value was relatively small. This indicated that the Daxia River watershed was evenly distributed in most areas, and the water system was not fully developed. The average values of the multi-fractal spectral height difference (Δf) and the singular index distribution range (Δa) from downstream to upstream were increasing (1.184∼1.570) and decreasing (1.160∼0.933) in sequence, which indicated that the proportion of the geomorphic unit with the smallest slope in the watershed increased sequentially from downstream to upstream, and the change of geomorphic shape from upstream to downstream tended to be complicated. This study is of great significance to effectively solve the complex problems in geomorphology and to master the characteristics and laws of various geomorphological phenomena.

Reliability Analysis of Distribution Transformer with Bayesian Mixture and Cox Regression Approach

The reliability of a transformer has become an important factor to measure considering that the damaged transformer may cause a local power outage that can lead to the profit loss for both the public and the PLN (State Electric Company) itself. The reliability data thought patterns observed during a certain period time might not be a singular distribution pattern, but a mixture distribution such as the Weibull mixture. Each period that generates different reliability patterns will be shown as a specific sub-population in the mixture. Therefore, if during the observation two reliability shifts occur, then the reliability would be a mixture with the sub-populations system. In this research, various sub-population possibilities will be used, starting from 3 sub-population up until 7 sub-population. The parameter estimation in the Weibull mixture is done by using Markov Chain Monte Carlo (MCMC). Then, the best mixture model is chosen by the Bayes Factor. Other than that, the Cox regression in this research is used to understand the factors that impact the transformer lifespan. The best model chosen by the Bayes Factor resulted that the mixture model with 3,4,5,6, and 7 sub-population is considered the same.

Discrimination of Life-Threatening Arrhythmias Using Singular Value, Harmonic Phase Distribution, and Dynamic Time Warping of ECG Signals

The automated analysis of electrocardiogram (ECG) signal is crucial for early recognition of life-threatening arrhythmias. This work presents an efficient ECG feature description model for diagnosis of ventricular arrhythmias (VAs); ventricular fibrillation (VF) and ventricular tachycardia (VT). The concept of a new feature set by applying singular value decomposition (SVD) and harmonic phase distribution is introduced to capture the morphological variation of the ECG signal. The phase characterization and singular value features are extracted from discrete Fourier transform and Empirical mode decomposition of ECG signal, respectively. In addition to that, dynamic time warping (DTW) procedure is applied to measure the similarity/dissimilarity pattern of ECG signals for classifying VAs. The firstfold classification involves the discrimination of VAs and non-VA patterns. Following this, secondfold classification discriminates VF versus VT and normal rhythms from other arrhythmic conditions. Experimental results are validated using the benchmark Physionet ECG database. The proposed method achieved the best performances using 5-s ECG segment with tenfold cross validation strategy. A comparative study with existing methods also shows superior performances of the proposed feature extraction scheme.

The G\u03b1i protein subclass selectivity to the dopamine D2 receptor is also decided by their location at the cell membrane

BackgroundG protein-coupled receptor (GPCR) signaling via heterotrimeric G proteins plays an important role in the cellular regulation of responses to external stimuli. Despite intensive structural research, the mechanism underlying the receptor–G protein coupling of closely related subtypes of Gαi remains unclear. In addition to the structural changes of interacting proteins, the interactions between lipids and proteins seem to be crucial in GPCR-dependent cell signaling due to their functional organization in specific membrane domains. In previous works, we found that Gαs and Gαi3 subunits prefer distinct types of membrane-anchor lipid domains that also modulate the G protein trimer localization. In the present study, we investigated the functional selectivity of dopamine D2 long receptor isoform (D2R) toward the Gαi1, Gαi2, and Gαi3 subunits, and analyzed whether the organization of Gαi heterotrimers at the plasma membrane affects the signal transduction.MethodsWe characterized the lateral diffusion and the receptor–G protein spatial distribution in living cells using two assays: fluorescence recovery after photobleaching microscopy and fluorescence resonance energy transfer detected by fluorescence-lifetime imaging microscopy. Depending on distribution of data differences between Gα subunits were investigated using parametric approach–unpaired T-test or nonparametric–Mann–Whitney U test.ResultsDespite the similarities between the examined subunits, the experiments conducted in the study revealed a significantly faster lateral diffusion of the Gαi2 subunit and the singular distribution of the Gαi1 subunit in the plasma membrane. The cell membrane partitioning of distinct Gαi heterotrimers with dopamine receptor correlated very well with the efficiency of D2R-mediated inhibition the formation of cAMP.ConclusionsThis study showed that even closely related subunits of Gαi differ in their membrane-trafficking properties that impact on their signaling. The interactions between lipids and proteins seem to be crucial in GPCR-dependent cell signaling due to their functional organization in specific membrane domains, and should therefore be taken into account as one of the selectivity determinants of G protein coupling.14xS76kHhGtNWWoUJ8Q-BLVideo abstract

Using geostatistics and maximum entropy model to identify geochemical anomalies: A case study in Mila Mountain region, southern Tibet

Separating geochemical anomalies from background values is crucial for the processing of geochemical data. In the present study, a workflow for identifying geochemical anomalies was constructed by using the direct sampling algorithm of multi-point geostatistics, the maximum entropy model, and local singularity analysis. The smoothing effect and the uncertainty of the unsampled point value in the traditional interpolation method were taken into consideration in this workflow. Based on the statistic of singular exponential distribution of each element with equal probability, the geochemical anomaly probability distribution of each element was obtained (Ag、Cd、Cu、Pb、Zn). Based on the five anomaly probability distributions, the maximum entropy model was used to establish a comprehensive perspective of geochemical anomaly uncertainty evaluation. The validity of the method was verified by analyzing geochemical data of stream sediment samples from the Mila Mountain region in Tibet. The results showed that the prospectivity map of copper deposits generated by the maximum entropy model can effectively link the probability of multivariate geochemical anomalies with the known positions of copper deposits and greatly increase the precision of the potential exploration areas for copper deposits.

Transverse-energy-energy correlations in deep inelastic scattering

Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present the most accurate calculation of the transverse-energy-energy correlation event shape variable in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section is factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. We report the resummed transverse-energy-energy correlation distributions up to N3LL accuracy matched with the NLO cross section for the production of a lepton and two jets. Our work provides a new way to precisely study TMD physics at the future Electron-Ion Collider.

On Singular Distributions With Statistical Structure

In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenböck type curvature operator on tensors, prove the Bochner–Weitzenböck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution.

A distributionally robust analysis of the program evaluation and review technique

Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have been voiced and much research has been devoted to analyzing them. The effect of the beta distribution and corresponding variance PERT assumes is investigated in numerous studies, through analyzing the results for a variety of other distributions. In this paper, we propose a more general method of analyzing PERT’s sensitivity to its assumptions regarding the beta distribution. In particular, we do not assume a singular distribution for the activity duration, but instead assume this distribution to only be partially specified by its support, mean and possibly its mean absolute deviation. The exact worst- and best-case expected project durations over this set of distributions can be calculated through results from distributionally robust optimization on the worst- and best-case distributions themselves. A numerical study of project planning instances from PSPLIB shows that the effect of PERT’s assumption regarding an underlying beta distribution is limited. Furthermore, we find that the added value of knowing the exact mean absolute deviation is also modest.

On an Absolute Autoregressive Model and Skew Symmetric Distributions

By exploiting the connection between a popular construction of a well-known skew-normal distribution and an absolute autoregressive process, we show how the stochastic process approach can lead to other skew symmetric distributions, including a skew-Cauchy distribution and some singular distributions. In so doing, we also correct an erroneous skew-Cauchy-distribution in the literature. We discuss the estimation, for dependent data, of the key parameter relating to the skewness.

Using singular value distribution of backscattered ultrasound waves for tracking the pulmonary edema caused by COVID-19 in lung: A phantom-based study

A condition caused by COVID-19, pulmonary edema is an abnormal buildup of fluid in lungs. B-lines tracking of ultrasound images is a common way to track lung abnormality, however due to multiple scattering this method tracks the air volume change only on the lung surface. The aim of this phantom-based study is to assess the pulmonary edema in lungs using multiple scattering of ultrasonic waves in MHz range. A 128-element array transducer is used to form an Inter-elements Response Matrix (IRM) by firing a 5.2 MHz broadband pulse, element by element and receiving the backscattered signal by the whole array. The distribution of singular values of IRM in frequency domain is then analyzed for polymer sponges (n = 4) with different Water Volume Content (WVC) ranging from 5 to 25 ml mimicking pulmonary edema. The results of Random Matrix Theory are used to show that the mode of the Probability Density Function of singular values increases as the WVC increases in sponge indicating the change in scattering regime. The B-mode image of sponges with different WVC did not represent neither A nor B lines, however our results shows that there is a correlation between the WVC in sponge and the strongest singular value of IRM (R = 0.89) indicating the potential of using quantitative ultrasound in lung for early diagnosis of COVID-19.

Splitting models for multivariate count data

We investigate the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It will be shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, …) can be written as splitting distributions with separate parameters for both components, thus facilitating their interpretation, inference, the study of their probabilistic characteristics and their extensions to regression models. We highlight many probabilistic properties deriving from the compound aspect of splitting distributions and their underlying algebraic properties. Parameter inference and model selection are thus reduced to two separate problems, preserving time and space complexity of the base models. Based on this principle, we introduce several new distributions. In the case of multinomial splitting distributions, conditional independence and asymptotic normality properties for estimators are obtained. Mixtures of splitting regression models are used on a mango tree dataset in order to analyze the patchiness.

Random non-Abelian G-circulant matrices. Spectrum of random convolution operators on large finite groups

We analyze the limiting behavior of the eigenvalue and singular value distribution for random convolution operators on large (not necessarily Abelian) groups, extending the results by Meckes for the Abelian case. We show that for regular sequences of groups, the limiting distribution of eigenvalues (respectively singular values) is a mixture of eigenvalue (respectively singular value) distributions of Ginibre matrices with the directing measure being related to the limiting behavior of the Plancherel measure of the sequence of groups. In particular, for the sequence of symmetric groups, the limiting distributions are just the circular and quarter circular laws, whereas e.g. for the dihedral groups, the limiting distributions have unbounded supports but are different than in the Abelian case. We also prove that under additional assumptions on the sequence of groups (in particular, for symmetric groups of increasing order) families of stochastically independent random convolution operators converge in moments to free circular elements. Finally, in the Gaussian case, we provide Central Limit Theorems for linear eigenvalue statistics.

Research on anti-AM interference of chaotic composite short-range detection system based on singular spectrum decomposition and reconstruction

The Chaotic Phase-modulated Linear Frequency modulation Short-range Detection System(CPLF-SrDS) is a new type of composite detection system. This composited system makes good use of the short-term randomness and long-term determinism of chaos, it has strong precision determination ability and anti-recognition ability. In order to solved the problem of precise distance determination of this system under the emphasized amplitude modulation(AM) interference, this paper proposed a signal denoising method based on singular spectrum decomposition and reconstruction. The singular value distribution characteristics of CPLF-SrDS echo and AM interference has been studied, and the size of the window length during singular spectral decomposition is also been optimized. The method of the paper realized the denoising of the echo detected by different AM interference, and recovered the echo from the doping interference. From the simulation results, this method can better realize the recovery of the echo signals in the case of lower JSR, and can well realized the anti-interference of the CPLF-SrDS.

State Convertibility in the von Neumann Algebra Framework

We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting of Nielsen's theorem on the convertibility of quantum states under local operations and classical communication (LOCC) schemes. Along the way, we introduce an appropriate generalisation of LOCC operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von Neumann algebras. As an application of our result in the setting of $II_1$-factors, we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of Vidal, thus yielding a new way to quantify entanglement in that context. Building on previous work in the infinite-dimensional setting, we show that trace vectors play the role of maximally entangled states for general $II_1$-factors. Examples are drawn from infinite spin chains, quasi-free representations of the CAR, and discretised versions of the CCR.

Freeness over the diagonal and outliers detection in deformed random matrices with a variance profile

Abstract We study the eigenvalue distribution of a Gaussian unitary ensemble (GUE) matrix with a variance profile that is perturbed by an additive random matrix that may possess spikes. Our approach is guided by Voiculescu’s notion of freeness with amalgamation over the diagonal and by the notion of deterministic equivalent. This allows to derive a fixed point equation to approximate the spectral distribution of certain deformed GUE matrices with a variance profile and to characterize the location of potential outliers in such models in a non-asymptotic setting. We also consider the singular values distribution of a rectangular Gaussian random matrix with a variance profile in a similar setting of additive perturbation. We discuss the application of this approach to the study of low-rank matrix denoising models in the presence of heteroscedastic noise, that is when the amount of variance in the observed data matrix may change from entry to entry. Numerical experiments are used to illustrate our results. Deformed random matrix, Variance profile, Outlier detection, Free probability, Freeness with amalgamation, Operator-valued Stieltjes transform, Gaussian spiked model, Low-rank model. 2000 Math Subject Classification: 62G05, 62H12.

Compressed sensing reconstruction using expectation propagation

Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied, the compressed sensing problem, consists in finding the solution with the smallest number of non-zero components of a given system of linear equations for known measurement vector and sensing matrix . Here, we will address the compressed sensing problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli–Gauss). A solution to the problem is attempted through the computation of marginal distributions via expectation propagation, an iterative computational scheme originally developed in statistical physics. We will show that this strategy is more accurate for statistically correlated measurement matrices. For computational strategies based on the Bayesian framework such as variants of belief propagation, this is to be expected, as they implicitly rely on the hypothesis of statistical independence among the entries of the sensing matrix. Perhaps surprisingly, the method outperforms uniformly all the other state-of-the-art methods in our tests.

Smallest singular value and limit eigenvalue distribution of a class of non-Hermitian random matrices with statistical application

Suppose X is an N×n complex matrix whose entries are centered, independent, and identically distributed random variables with variance 1∕n and whose fourth moment is of order O(n−2). Suppose A is a deterministic matrix whose smallest and largest singular values are bounded below and above respectively, and z≠0 is a complex number. First we consider the matrix XAX∗−z, and obtain asymptotic probability bounds for its smallest singular value when N and n diverge to infinity and N∕n→γ,0<γ<∞. Then we consider the special case where A=J=[1i−j=1modn] is a circulant matrix. Using the above result, we show that the limit spectral distribution of XJX∗ exists when N∕n→γ,0<γ<∞ and describe the limit explicitly. Assuming that X represents a ℂN-valued time series which is observed over a time window of length n, the matrix XJX∗ represents the one-step sample autocovariance matrix of this time series. A whiteness test against an MA correlation model for this time series is introduced based on the above limit result. Numerical simulations show the excellent performance of this test.

The Weitzenböck Type Curvature Operator for Singular Distributions

We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior derivatives and their L 2 adjoint operators on tensors. Then, we introduce the Weitzenböck type curvature operator on tensors, prove the Weitzenböck type decomposition formula, and derive the Bochner–Weitzenböck type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian. The assumptions used in the results are reasonable, as illustrated by examples with f-manifolds, including almost Hermitian and almost contact ones.

On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, in using which the characteristic function of the product and its asymptotic distribution under the double asymptotic regime are established. The application of obtained stochastic representation speeds up the simulation studies where the product of a singular Wishart random matrix and a singular normal random vector is present. We further document a good performance of the derived asymptotic distribution within a numerical illustration. Finally, several important properties of the singular Wishart distribution are provided.

Exploring the RNA-Recognition Mechanism Using Supervised Molecular Dynamics (SuMD) Simulations: Toward a Rational Design for Ribonucleic-Targeting Molecules?

Although proteins have represented the molecular target of choice in the development of new drug candidates, the pharmaceutical importance of ribonucleic acids has gradually been growing. The increasing availability of structural information has brought to light the existence of peculiar three-dimensional RNA arrangements, which can, contrary to initial expectations, be recognized and selectively modulated through small chemical entities or peptides. The application of classical computational methodologies, such as molecular docking, for the rational development of RNA-binding candidates is, however, complicated by the peculiarities characterizing these macromolecules, such as the marked conformational flexibility, the singular charges distribution, and the relevant role of solvent molecules. In this work, we have thus validated and extended the applicability domain of SuMD, an all-atoms molecular dynamics protocol that allows to accelerate the sampling of molecular recognition events on a nanosecond timescale, to ribonucleotide targets of pharmaceutical interest. In particular, we have proven the methodological ability by reproducing the binding mode of viral or prokaryotic ribonucleic complexes, as well as that of artificially engineered aptamers, with an impressive degree of accuracy.