Non-circular motion evidences in the circumnuclear region of M100 (NGC 4321)

We analyse new integral field spectroscopy of the inner region (central 2.5 kpc) of the spiral galaxy NGC 4321 to study the peculiar kinematics of this region. Fourier analysis of the velocity residuals obtained by subtracting an axisymmetric rotation model from the $\rm H\alpha$ velocity field, indicates that the distortions are {\em global} features generated by an $m=2$ perturbation of the gravitational potential which can be explained by the nuclear bar. This bar has been previously observed in the near-infrared but not in the optical continuum dominated by star formation. We detect the optical counterpart of this bar in the 2D distribution of the old stellar population (inferred from the equivalent width map of the stellar absorption lines). We apply the Tremaine--Weinberg method to the stellar velocity field to calculate the pattern speed of the inner bar, obtaining a value of $\Omega_b$=160$\pm70\rm km s^{-1} kpc^{-1}$. This value is considerably la rger than the one obtained when a simple bar model is considered. However the uncertainties in the pattern speed determination prevent us to give support to alternative scenarios.Comment: 11 pages, 11 figures, accepted for publication in MNRA

Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin

Neural Network DPD for Aggrandizing SM-VCSEL-SSMF-Based Radio over Fiber Link Performance

This paper demonstrates an unprecedented novel neural network (NN)-based digital predistortion (DPD) solution to overcome the signal impairments and nonlinearities in Analog Optical fronthauls using radio over fiber (RoF) systems. DPD is realized with Volterra-based procedures that utilize indirect learning architecture (ILA) and direct learning architecture (DLA) that becomes quite complex. The proposed method using NNs evades issues associated with ILA and utilizes an NN to first model the RoF link and then trains an NN-based predistorter by backpropagating through the RoF NN model. Furthermore, the experimental evaluation is carried out for Long Term Evolution 20 MHz 256 quadraturre amplitude modulation (QAM) modulation signal using an 850 nm Single Mode VCSEL and Standard Single Mode Fiber to establish a comparison between the NN-based RoF link and Volterra-based Memory Polynomial and Generalized Memory Polynomial using ILA. The efficacy of the DPD is examined by reporting the Adjacent Channel Power Ratio and Error Vector Magnitude. The experimental findings imply that NN-DPD convincingly learns the RoF nonlinearities which may not suit a Volterra-based model, and hence may offer a favorable trade-off in terms of computational overhead and DPD performance

Bayesian polynomial neural networks and polynomial neural ordinary differential equations

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs

Radial Profiles of Surface Density in Debris Discs

Resolved observations of debris discs can be used to derive radial profiles of Azimuthally-averaged Surface Density (ASD), which carries important information about the disc structure even in presence of non-axisymmetric features and has improved signal-to-noise characteristics. We develop a (semi-)analytical formalism allowing one to relate ASD to the underlying semi-major axis and eccentricity distributions of the debris particles in a straightforward manner. This approach does not involve the distribution of particle apsidal angles, thus simplifying calculations. It is a much faster, more flexible and effective way of calculating ASD than the Monte Carlo sampling of orbital parameters of debris particles. We present explicit analytical results based on this technique for a number of particle eccentricity distributions, including two cases of particular practical importance: a prescribed radial profile of eccentricity, and the Rayleigh distribution of eccentricities. We then show how our framework can be applied to observations of debris discs and rings for retrieving either the semi-major axis distribution or (in some cases) the eccentricity distribution of debris, thus providing direct information about the architecture and dynamical processes operating in debris discs. Our approach also provides a fast and efficient way of forward modeling observations. Applications of this technique to other astrophysical systems, e.g. the nuclear stellar disc in M31 or tenuous planetary rings, are also discussed.Comment: 16 pages, 13 figures, submitted to MNRAS, comments welcom