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The studies of intracloud (IC) discharges might shed light on the microphysical structure of thunderclouds. As both the magnitude and the sign of charge separation due to graupel collides with ice crystals within the strong updrafts are influenced by the surrounding environment. Here, a compact all-fiber coherent Doppler wind lidar (CDWL) working at the 1.5 µm wavelength is applied for probing the dynamics and microphysics structure of thunderstorms. Thanks to the precise spectrum measurement, multi-component spectra signals of thunderstorms can be analyzed by the CDWL. The spectrum width, skewness, and Doppler velocity of CDWL is used to separate and identify the particle composition and polarity. In experiment, the thundercloud properties are detected by the CDWL, 10.6 cm Doppler weather radar (DWR), and Advanced Geosynchronous Radiation Imager (AGRI) onboard Fengyun-4 satellites. In particular, the spectrum width and skewness of the thundercloud below the 0 ℃ isotherm are increased, and when a cloud-ground lightning occurs, there has additional graupel with a velocity greater than 5 m/s. It indicates that this region is a melting layer, and lightning activity changes the motion characteristics of graupel, affecting the charge structure of the whole thundercloud. In general, our findings provide details on the velocity, phase, and composition of particles in the outside updraft region of the thunderstorm. The identification and analysis of graupel is particularly important. It is proved that the precise spectrum of CDWL is a promising indicator to study the charge structure of thunderstorms.

Bioaerosols are usually defined as aerosols arising from biological systems such as bacteria, fungi, and viruses. They play an important role in atmospheric physical and chemical processes including ice nucleation and cloud condensation. As such, their dispersion affects not only public health but also regional climate. Lidar is an effective technique for aerosol detection and pollution monitoring. It is also used to profile the vertical distribution of wind vectors. In this paper, a coherent Doppler wind lidar (CDWL) is deployed for aerosol and wind detection in Hefei, China, from 11 to 20 March in 2020. A wideband integrated bioaerosol sensor (WIBS) is used to monitor variations in local fluorescent bioaerosols. Three aerosol transport events are captured. The WIBS data show that, during these transport events, several types of fluorescent aerosol particles exhibit abnormal increases in their concentration, number fractions to total particles, and number fractions to whole fluorescent aerosols. These increases are attributed to external fluorescent bioaerosols instead of local bioaerosols. Based on the HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) backward trajectory model and the characteristics of external aerosols in WIBS, their possible sources, transport paths, and components are discussed. The results prove the influence of external aerosol transport on local high particulate matter (PM) pollution and fluorescent aerosol particle composition. The combination of WIBS and CDWL expands the aerosol monitoring parameters and provides a potential method for real-time monitoring of fluorescent biological aerosol transport events. In addition, it also helps to understand the relationships between atmospheric phenomena at high altitudes like virga and the variation of surface bioaerosol. It contributes to the further understanding of long-range bioaerosol transport, the roles of bioaerosols in atmospheric processes, and in aerosol–cloud–precipitation interactions.

Myocardial fibrosis, a common pathological manifestation of cardiac remodeling (CR), often leads to heart failure (HF) and even death. The underlying molecular mechanism of the role of TRIM33 in Ang II-induced myocardial fibrosis is not fully understood. We found that TRIM33 was specifically upregulated in CFs and myocardial tissue after Ang II stimulation. Adult mice induced by Ang II were used as

Although coherent Doppler wind lidar (CDWL) is promising in detecting boundary layer height (BLH), differences between BLH results are observed when different CDWL measurements are used as tracers. Here, a robust solution for BLH detections with CDWL is proposed and demonstrated: mixed layer height (MLH) is retrieved best from turbulent kinetic energy dissipation rate (TKEDR), while stable boundary layer height (SBLH) and residual layer height (RLH) can be retrieved from carrier-to-noise ratio (CNR). To study the cause of the BLH differences, an intercomparison experiment is designed with two identical CDWLs, where only one is equipped with a stability control subsystem. During the experiment, it is found that the CNR could be distorted by instrument instability because the coupling efficiency from free-space to the polarization-maintaining fiber of the telescope is sensitive to the surrounding environment. In the ML, a bias up to 2.13 km of the MLH from CNR is found, which is caused by the CNR deviation. In contrast, the MLH from TKEDR is robust as long as the accuracy of wind is guaranteed. In the SBL (RL), the CNR is found capable to retrieve SBLH and RLH simultaneously and robustly. This solution is tested during an observation period over one month. Statistical analysis shows that the root-mean-square errors (RMSE) in the MLH, SBLH, and RLH are 0.28 km, 0.23 km, and 0.24 km, respectively.

Bioaerosols are usually defined as aerosols derived from biological systems such as bacteria, fungi, and viruses. They play an important role in atmospheric physical and chemical processes including ice nucleation and cloud condensation. As such, their dispersion affects not only public health but regional climate as well. Lidar is an effective technique for aerosol detection and pollution monitoring. It is also used to profile the vertical distribution of wind vectors. In this paper, a coherent Doppler wind lidar (CDWL) was deployed for wind and aerosol detection in Hefei, China, from 11 to 20 March in 2020. A wideband integrated bioaerosol sensor (WIBS) was deployed to monitor variations in local fluorescent bioaerosol levels. During observation, three aerosol transport events were captured. The WIBS data show that during these transport events, several types of fluorescent aerosol particles exhibit abnormal increases in either their concentration, number fractions to total particles, or number fractions to whole fluorescent aerosols. These increases are attributed to transported external fluorescent bioaerosols instead of local bioaerosols. Based on the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) backward trajectory model and the characteristics of external aerosols in WIBS, their possible sources, transport paths, and components are discussed. This work proves the influence of external aerosol transport on local high particulate matter (PM) pollution and fluorescent aerosol particle composition. The combination of WIBS and CDWL expands the aerosol monitoring parameters and proves to be a potential method for the real-time monitoring of fluorescent biological aerosol transport events. It contributes to the further understanding of bioaerosol transport.

P16ink4a can accumulate in senescent cells and can be induced by different oncogenic stimulations. These functions make p16ink4a a biomarker of senescence and cancer. However, the exact role of p16ink4a remains unclear in cardiovascular disease. This study was aimed to investigate the role of p16ink4a in cardiac remodeling after myocardial infarction (MI).In vivo, gain and loss of function experiments using p16ink4a overexpression and knockdown adenovirus were induced to determine the effect of p16ink4a on cardiac structure and function after MI. The in vitro effects of p16ink4a were evaluated by overexpression and knockdown adenovirus of p16ink4a on isolated neonatal mouse cardiac myocytes (NMCMs) and neonatal mouse cardiac fibroblasts (NMCFs).Expression level of p16ink4a was increased after MI and enriched in the infarction area. In vivo, overexpression of p16ink4a protected, while knockdown of p16ink4a worsened cardiac function. In vitro, p16ink4a did not influence the hypertrophy of NMCMs. Overexpression of p16ink4a inhibited the proliferation and migration of NMCFs and reduced the level of collagen I and α-SMA. Consistently, knockdown of p16ink4a in vitro displayed the opposite effects. Further mechanism studies revealed that p16ink4a affected the expression level of cyclin-dependent kinase 4 (CDK4) and phosphorylation of retinoblastoma (pRb), which could be a potential pathway in regulating cardiac remodeling after MI.Overexpression of 16ink4a in cardiac fibroblasts can ameliorate cardiac dysfunction and attenuate pathological cardiac remodeling in mice after MI by regulating the p16ink4a/CDK4/pRb pathway.

Spectroscopy is a well-established nonintrusive tool that has played an important role in identifying and quantifying substances, from quantum descriptions to chemical and biomedical diagnostics. Challenges exist in accurate spectrum analysis in free space, which hinders us from understanding the composition of multiple gases and the chemical processes in the atmosphere. A photon-counting distributed free-space spectroscopy is proposed and demonstrated using lidar technique, incorporating a comb-referenced frequency-scanning laser and a superconducting nanowire single-photon detector. It is suitable for remote spectrum analysis with a range resolution over a wide band. As an example, a continuous field experiment is carried out over 72 h to obtain the spectra of carbon dioxide (CO2) and semi-heavy water (HDO, isotopic water vapor) in 6 km, with a range resolution of 60 m and a time resolution of 10 min. Compared to the methods that obtain only column-integrated spectra over kilometer-scale, the range resolution is improved by 2–3 orders of magnitude in this work. The CO2 and HDO concentrations are retrieved from the spectra acquired with uncertainties as low as ±1.2% and ±14.3%, respectively. This method holds much promise for increasing knowledge of atmospheric environment and chemistry researches, especially in terms of the evolution of complex molecular spectra in open areas., A photon-counting distributed free-space spectroscopy is proposed and demonstrated using lidar technique. It is suitable for remote spectrum analysis with range resolution over wide band.

The coherent Doppler wind lidar (CDL) shows capability in precipitation detection. Retrieval of the raindrop size distribution (DSD) using CDL is still challenging work, as both accurate backscattering cross section at the working wavelength and reflectivity spectrum of raindrop are required. Firstly, the Mie theory and the vectorial complex ray model (VCRM) are applied to calculate backscattering cross section for small spheric raindrops and large oblate raindrops, respectively. Secondly, an iterative deconvolution method is proposed to separate the reflectivity spectrum of raindrop from the lidar power spectrum, which is a superposition of rain and aerosol components. An accompanying aerosol signal model considering the effect of temporal window, from the same height and time, is used to improve the accuracy and robustness of the iteration. In experiment, a co-located micro rain radar (MRR) is used for comparison. Good agreements are obtained despite tremendous differences in wavelength and scattering characteristics. As an example, at 600 m height, the R2 of linear fitting to the mean rain velocity and mean raindrop diameter between CDL and MRR are 0.96 and 0.93, respectively.

The atmospheric boundary layer height (BLH) is a key parameter in weather forecasting and air quality prediction. To investigate the relationship between BLH and air pollution under different conditions, a compact micro-pulse lidar integrating both direct-detection lidar (DDL) and coherent Doppler wind lidar (CDWL) has been built. This hybrid lidar is operated at 1.5 µm, which is eye-safe and made of all-fibre components. The BLH can be determined from aerosol density and vertical wind independently. During a 45 h continuous observation in June 2018, the stable boundary layer, residual layer and convective boundary layer are identified. The fine structure of the aerosol layers, drizzles and vertical wind near the cloud base are also detected. In comparison, the standard deviation between BLH values derived from DDL and CDWL is 0.06 km, indicating the accuracy of this work. The retrieved convective BLH is a little higher than that from ERA5 reanalysis due to different retrieval methods. Correlation between different BLH and PM2.5 is strongly negative before a precipitation event and becomes much weaker after the precipitation. Different relationships between PM2.5 and BLH may result from different BLH retrieval methods, pollutant sources and meteorological conditions.

Conditional Random Field (CRF) based neural models are among the most performant methods for solving sequence labeling problems. Despite its great success, CRF has the shortcoming of occasionally generating illegal sequences of tags, e.g. sequences containing an "I-" tag immediately after an "O" tag, which is forbidden by the underlying BIO tagging scheme. In this work, we propose Masked Conditional Random Field (MCRF), an easy to implement variant of CRF that impose restrictions on candidate paths during both training and decoding phases. We show that the proposed method thoroughly resolves this issue and brings consistent improvement over existing CRF-based models with near zero additional cost., accepted by NAACL 2021

In this demonstration, we present an efficient BERT-based multi-task (MT) framework that is particularly suitable for iterative and incremental development of the tasks. The proposed framework is based on the idea of partial fine-tuning, i.e. only fine-tune some top layers of BERT while keep the other layers frozen. For each task, we train independently a single-task (ST) model using partial fine-tuning. Then we compress the task-specific layers in each ST model using knowledge distillation. Those compressed ST models are finally merged into one MT model so that the frozen layers of the former are shared across the tasks. We exemplify our approach on eight GLUE tasks, demonstrating that it is able to achieve both strong performance and efficiency. We have implemented our method in the utterance understanding system of XiaoAI, a commercial AI assistant developed by Xiaomi. We estimate that our model reduces the overall serving cost by 86%., Comment: To appear in ACL2022

Accurate power spectrum analysis of weak backscattered signals are the primary constraint in long-distance coherent Doppler wind lidar (CDWL) applications. To study the atmospheric boundary layer, an all-fiber CDWL with 300µJ pulse energy is developed. In principle, the coherent detection method can approach the quantum limit sensitivity if the noise in the photodetector output is dominated by the shot noise of the local oscillator. In practice, however, abnormal power spectra occur randomly, resulting in error estimation and low inversion probability. This phenomenon is theoretically analyzed and shown to be due to the leakage of a time-varying DC noise of the balanced detector. Thus, a correction algorithm with accurate noise modeling is proposed and demonstrated. The accuracy of radial velocity, carrier-to-noise ratio (CNR), and spectral width are improved. In wind profiling process, a robust sine-wave fitting algorithm with data quality control is adopted in the velocity-azimuth display (VAD) scanning detection. Finally, in 5-day continuous wind detection, the inversion probability is tremendously enhanced. As an example, it is increased from 8.6% to 52.1% at the height of 4 km.

Observation of a melting layer using a 1.55 µm coherent Doppler lidar (CDL) is first presented during a stratiform precipitation event. Simultaneous radar measurements are also performed by co-located 1.24 cm micro rain radar (MRR) and 10.6 cm Doppler weather radar (DWR). As a well-known bright band in radar reflectivity appears during precipitation, an interesting dark band about 160 m below that in lidar backscattering is observed. Due to the absorption effect, the backscattering from raindrops at 1.55 µm is found much weaker than that at short wavelengths usually used in direct detection lidars. However, the CDL provides additional Doppler information which is helpful for melting layer identification. For example, a spectrum bright band with broadened width and sign conversion of skewness is detected in this case. After a deep analysis of the power spectra, the aerosol and precipitation components are separated. The fall speed of hydrometeors given by CDL is found smaller than that of MRR, with the differences of approximately 0.5 m/s and 1.5 m/s for the snow and rainfall, respectively. To illustrate the influence of absorption effect, simulations of the backscatter coefficient and extinction coefficient of aerosol and rainfall are also performed at the wavelength range of 0.3 ∼ 2.2 µm using the Mie theory.

Evaluation of the cloud seeding effect is a challenge due to lack of directly physical observational evidence. In this study, an approach for directly observing the cloud seeding effect is proposed using a 1548 nm coherent Doppler wind lidar (CDWL). Normalized skewness was employed to identify the components of the reflectivity spectrum. The spectrum detection capability of a CDWL was verified by a 24.23-GHz Micro Rain Radar (MRR) in Hefei, China (117°15′ E, 31°50′ N), and different types of lidar spectra were detected and separated, including aerosol, turbulence, cloud droplet, and precipitation. Spectrum analysis was applied as a field experiment performed in Inner Mongolia, China (112°39′ E, 42°21′ N ) to support the cloud seeding operation for the 70th anniversary of China’s national day. The CDWL can monitor the cloud motion and provide windshear and turbulence information ensuring operation safety. The cloud-precipitation process is detected by the CDWL, microwave radiometer (MWR) and Advanced Geosynchronous Radiation Imager (AGRI) in FY4A satellites. In particular, the spectrum width and skewness of seeded cloud show a two-layer structure, which reflects cloud component changes, and it is possibly related to cloud seeding effects. Multi-component spectra are separated into four clusters, which are well distinguished by spectrum width and vertical velocity. In general, our findings provide new evidence that the reflectivity spectrum of CDWL has potential for assessing cloud seeding effects.

Doppler wind lidar is an effective tool for wind detection with high temporal and spatial resolution. However, precise wind profile measurement under rainy conditions is a challenge, due to the interfering signals from raindrop reflections. In this work, a compact all-fiber coherent Doppler lidar (CDL) at working wavelength of 1.5 µm is applied for simultaneous wind and precipitation detection. The performance of the lidar is validated by comparison with the weather balloons. Thanks to the ability of precise spectrum measurement, both aerosol and rainfall signals can be detected by the CDL under rainy conditions. The spectrum width is used to identify the precipitation events, during which the two-peak Doppler spectrum is observed. The spectrum is fitted by a two-component Gaussian model and two velocities are obtained. By using the velocity-azimuth display (VAD) scanning technique, wind speed and rainfall speed are simultaneously retrieved. The false detection probability of wind speed in the rainy conditions is thus reduced.

A long-live gravity wave (GW) in atmospheric boundary layer (ABL) during a field experiment in Anqing, China (116°58′ E, 30°37′ N) is analysed. Persistent GWs over 10 hours with periods ranging from 10 to 30 min in the ABL within 2 km height are detected by a coherent Doppler lidar from 4 to 5 in September 2018. The amplitudes of the vertical wind due to these GWs are about 0.15~0.2 m s−1. The lifetime of the GWs is more than 20 wave cycles. There is no apparent phase progression with altitude. The vertical and zonal perturbations of the GWs are apparent quadrature with vertical perturbations generally leading ahead of zonal ones. Based on experiments and simplified 2-Dimensional Computational Fluid Dynamics (CFD) numerical simulations, a reasonable generation mechanism of this persistent wave is proposed. A westerly low-level jet of ~ 5 m s−1 exists at the altitude of 1~2 km in the ABL. The wind shear around the low-level jet lead to the wave generation in the condition of light horizontal wind. Furthermore, a combination of thermal and Doppler ducts occurs in the ABL. Thus, the ducted wave motions are trapped in the ABL with long lifetime.

We propose Independent Component Autoencoder (ICAE), a deep neural network-based framework for nonlinear Independent Component Analysis (ICA). The proposed method consists of a penalized autoencoder and a training objective that is to minimize a combination of the reconstruction loss and an ICA contrast. Unlike many previous ICA methods that are usually tailored to separate specific mixture, our method can recover sources from various mixtures, without prior knowledge on the nature of that mixture.

The atmospheric boundary layer height (BLH) is a key parameter in weather forecast and air quality prediction. To investigate the relationship between BLH and air pollution under different conditions, a compact micro-pulse lidar integrated both direct detection lidar (DDL) and coherent Doppler wind lidar (CDWL) is built. Then the BLH can be determined from aerosol density or vertical wind independently. During a 45-hour continuous observation in June 2018, stable boundary layer, residual layer and convective boundary layer are identified. Fine structure of aerosol layers, drizzles and vertical wind near cloudbase are also detected. In comparison, the standard deviation between BLH values derived from DDL and CDWL is 60 m, indicating the accuracy of this work. The retrieved convective BLH is a little higher than that from ERA5 reanalysis due to different retrieval methods. Negative correlation between BLH and PM2.5 is analyzed before and after a precipitation. A criterion is proposed to classify the residual layer and convective boundary layer. Different trends show that the relationship between PM2.5 and BLH should be considered in different boundary layer categories.

Generally, the pulse duration of a coherent Doppler wind lidar (CDWL) is shortened to minimize the spatial resolution at the sacrifice of carrier-to-noise ratio, since the peak power of a laser source is limited by the stimulated Brillouin scattering or other nonlinear optical phenomena. To solve this problem, an all-fiber CDWL incorporating Golay coding is proposed and demonstrated. Given the peak power of the laser pulse, the Golay coding method can improve the measuring precision by improving the pulse repetition frequency of the outgoing laser. In the experiment, the Golay coding implementation is optimized by normalizing the intensity of every single pulse of the outgoing laser with a closed-loop feedback, achieving a spatial resolution of 6 m and a temporal resolution of 2 s with a maximum detection range of 552 m. The wind profile in line of sight and the result derived from another noncoding CDWL show good agreement.

Researches on the atmospheric boundary layer (ABL) need accurate measurements with high temporal and spatial resolutions from a series of different instruments. Here, a method for identifying cloud, precipitation, windshear, and turbulence in the ABL using a single coherent Doppler wind lidar (CDWL) is proposed and demonstrated. Based on deep analysis of the power spectrum of the backscattering signal, multiple lidar products, such as carrier-to-noise (CNR), spectrum width, spectrum skewness, turbulent kinetic energy dissipation rate (TKEDR), and shear intensity are derived for weather identification. Firstly, the cloud is extracted by Haar wavelet covariance transform (HWCT) algorithm based on the CNR after range correction. Secondly, since the spectrum broadening may be due to turbulence, windshear or precipitation, the spectrum skewness is introduced to distinguish the precipitation from two other conditions. Whereas wind velocity is obtained by single peak fitting in clear weather condition, the double-peak fitting is used to retrieve wind and rainfall velocities simultaneously in the precipitation condition. Thirdly, judging from shear intensity and TKEDR, turbulence and windshear are classified. As a double check, the temporal continuity is used. Stable wind variances conditions such as low-level jets are identified as windshear, while arbitrary wind variances conditions are categorized as turbulence. In the field experiment, the method is implemented on a micro-pulse CDWL to provide meteorological services for the 70th anniversary of the China’s National Day, in Inner Mongolia, China (43°54′N, 115°58′E). All weather conditions are successfully classified. By comparing lidar results to that of microwave radiometer (MWR), the spectrum skewness is found be more accurate to indicate precipitation than spectrum width or vertical speed. Finally, the parameter relationships and distributions are analyzed statistically in different weather conditions.

International audience; The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex optimization over spaces of tensors is now gaining much interest due to its potential applications in signal processing, statistics and engineering. The goal of this paper is to present an extension of the approach by Lewis [16] for the analysis of the subdifferential of certain convex functions of the spectrum of symmetric tensors. We give a complete characterization of the subdifferential of Schatten-type tensor norms for symmetric tensors. Some partial results in this direction are also given for Orthogonally Decomposable tensors.

The FastICA algorithm is one of the most popular algorithms in the domain of independent component analysis (ICA). Despite its success, it is observed that FastICA occasionally yields outcomes that do not correspond to any true solutions (known as demixing vectors) of the ICA problem. These outcomes are commonly referred to as spurious solutions. Although FastICA is a well-studied ICA algorithm, the occurrence of spurious solutions is not yet completely understood by the ICA community. In this contribution, we aim at addressing this issue. In the first part of this work, we are interested in characterizing the relationship between demixing vectors, local optimizers of the contrast function and (attractive or unattractive) fixed points of FastICA algorithm. We will show that there exists an inclusion relationship between these sets. In the second part, we investigate the possible scenarios where spurious solutions occur. It will be shown that when certain bimodal Gaussian mixture distributions are involved, there may exist spurious solutions that are attractive fixed points of FastICA. In this case, popular nonlinearities such as "Gauss" or "tanh" tend to yield spurious solutions, whereas "kurtosis" gives much more reliable results.

Using an infinite sample, the contrast function and the FastICA algorithm are deterministic. In the practical case, we have only a finite sample. Then the contrast function and the FastICA algorithm become estimators of the deterministic case. This paper provides a unified study of the deflation FastICA algorithm assuming a finite or an infinite sample. We consider four random probability distributions based on the finite sample, and construct four FastICA estimators. We show that under mild conditions, each of these estimators are equal to a local minimizer of the contrast function with respect to the underlying random probability distribution. Making use of the existing results of M-estimators, we give a rigorous analysis of the asymptotic errors of FastICA estimators. We derive five criteria for the optimal choice of the nonlinearity function.

We consider a noisy observed vector y=x+u@?R^n. The unobserved vector x is a solution of a non-invertible linear system Ax=v, where v is a forcing term. A unique solution of the system is obtained by considering additional constraint on the vector x. This constraint is defined by a triple (@b,F,A^-), where @b is a vector, F denotes a matrix whose range is equal to N(A) (the null space of A) and A^- is a generalized inverse of A. Each triple (@b,F,A^-) defines the solution x=F@b+A^-v and the general linear mixed model y=F@b+A^-v+u. Given the covariance matrices of u and v, we will prove that the best linear unbiased predictor of x knowing y depends only on A. If @b is a parameter and (F,A^-) is given, then we will study the asymptotic behavior of the best linear estimator of @b. If the constraint (@b,F,A^-) is not known, then we will estimate it using the data y. Some numerical results will be given.

For two matrices in R n 1 × n 2 , von Neumann's trace inequality says that their scalar product is less than or equal to the scalar product of their singular spectrum. In this short note, we extend this result to real tensors and provide a complete study of the equality case.

This contribution deals with the generalized symmetric FastICA algorithm in the domain of Independent Component Analysis (ICA). The generalized symmetric version of FastICA has been shown to have the potential to achieve the Cram\'er-Rao Bound (CRB) by allowing the usage of different nonlinearity functions in its parallel implementations of one-unit FastICA. In spite of this appealing property, a rigorous study of the asymptotic error of the generalized symmetric FastICA algorithm is still missing in the community. In fact, all the existing results exhibit certain limitations, such as ignoring the impact of data standardization on the asymptotic statistics or being based on a heuristic approach. In this work, we aim at filling this blank. The first result of this contribution is the characterization of the limits of the generalized symmetric FastICA. It is shown that the algorithm optimizes a function that is a sum of the contrast functions used by traditional one-unit FastICA with a correction of the sign. Based on this characterization, we derive a closed-form analytic expression of the asymptotic covariance matrix of the generalized symmetric FastICA estimator using the method of estimating equation and M-estimator., Comment: Final version of the paper