Unsupervised feature-learning for galaxy SEDs with denoising autoencoders

With the increasing number of deep multi-wavelength galaxy surveys, the spectral energy distribution (SED) of galaxies has become an invaluable tool for studying the formation of their structures and their evolution. In this context, standard analysis relies on simple spectro-photometric selection criteria based on a few SED colors. If this fully supervised classification already yielded clear achievements, it is not optimal to extract relevant information from the data. In this article, we propose to employ very recent advances in machine learning, and more precisely in feature learning, to derive a data-driven diagram. We show that the proposed approach based on denoising autoencoders recovers the bi-modality in the galaxy population in an unsupervised manner, without using any prior knowledge on galaxy SED classification. This technique has been compared to principal component analysis (PCA) and to standard color/color representations. In addition, preliminary results illustrate that this enables the capturing of extra physically meaningful information, such as redshift dependence, galaxy mass evolution and variation over the specific star formation rate. PCA also results in an unsupervised representation with physical properties, such as mass and sSFR, although this representation separates out. less other characteristics (bimodality, redshift evolution) than denoising autoencoders.Comment: 11 pages and 15 figures. To be published in A&

Stellar black holes: cosmic history and feedback at the dawn of the universe

Significant historic cosmic evolution for the formation rate of stellar black holes is inferred from current theoretical models of the evolution of massive stars, the multiple observations of compact stellar remnants in the near and distant universe, and the cosmic chemical evolution. The mean mass of stellar black holes, the fraction of black holes/neutron stars, and the fraction of black hole high mass X-ray binaries (BH-HMXBs)/solitary black holes increase with redshift. The energetic feedback from large populations of BH-HMXBs form in the first generations of star burst galaxies has been overlooked in most cosmological models of the reionization epoch of the universe. The powerful radiation, jets, and winds from BH-HMXBs heat the intergalactic medium over large volumes of space and keep it ionized until AGN take over. It is concluded that stellar black holes constrained the properties of the faintest galaxies at high redshifts. I present here the theoretical and observational grounds for the historic cosmic evolution of stellar black holes. Detailed calculations on their cosmic impact are presented elsewhere (Mirabel, Dijkstra, Laurent, Loeb, Pritchard, 2011).Comment: 9 pages, 1 color figure. Invited talk at the IAU Symp. 275, Jets at all scales. Held in Buenos Aires on 13-17 September 2010. To be published by Cambridge University Press. Eds. G. Romero, R. Sunyaev and T. Bellon

Monitoring of Orientation in Molecular Ensembles by Polarization Sensitive Nonlinear Microscopy

We present high resolution two-photon excitation microscopy studies combining two-photon fluorescence (TPF) and second harmonic generation (SHG) in order to probe orientational distributions of molecular ensembles at room temperature. A detailed polarization analysis of TPF and SHG signals is used in order to unravel the parameters of the molecular orientational statistical distribution, using a technique which can be extended and generalized to a broad variety of molecular arrangements. A polymer film containing molecules active for TPF and/or SHG emission is studied as a model system. Polarized TPF is shown to provide information on specific properties pertaining to incoherent emission in molecular media, such as excitation transfer. SHG, being highly sensitive to a slight departure from centrosymmetry such as induced by an external electric field in the medium, complements TPF. The response of each signal to a variable excitation polarization allows investigation of molecular behavior in complex environments which affect their orientations and interactions.Comment: submitted April 9th, 2003 to J. Phys. Chem.

Notes on the SWIFT method based on Shannon Wavelets for Option Pricing -- Revisited

This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023. In particular, it discusses some possible improvements and exposes some concrete drawbacks of the method

The Quadratic Local Variance Gamma Model: an arbitrage-free interpolation of class C3\mathcal{C}^3 for option prices

This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma models. The quadratic local variance function results in an arbitrage-free interpolation of class $\mathcal{C}^3$. The increased smoothness over the piecewise-constant and piecewise-linear representation allows to reduce the number of knots when interpolating raw market quotes, thus providing an interesting alternative to regularization while reducing the computational cost.Comment: arXiv admin note: text overlap with arXiv:2004.0865

Instabilities of Super-Time-Stepping Methods on the Heston Stochastic Volatility Model

This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model. The stability remarks are relevant beyond the scope of super-time-stepping schemes