Showing 1–50 of 127 results for author: Richard, C

On almost periodicity in crystalline measures

Authors: Jan Mazáč, Christoph Richard, Nicolae Strungaru

Abstract: Meyer defined crystalline measures as tempered distributions $μ$ such that both $μ$ and its Fourier transform $\widehatμ$ are pure-point Radon measures of locally finite support. He conjectured that every crystalline measure is almost periodic as a tempered distribution. Favorov constructed a counterexample and asked whether crystalline measures are at least almost periodic as general distribution… ▽ More Meyer defined crystalline measures as tempered distributions $μ$ such that both $μ$ and its Fourier transform $\widehatμ$ are pure-point Radon measures of locally finite support. He conjectured that every crystalline measure is almost periodic as a tempered distribution. Favorov constructed a counterexample and asked whether crystalline measures are at least almost periodic as general distributions. To resolve Favorov's question, we first show that the almost periodicity of a crystalline measure is characterised in terms of its translation boundedness, in any class of Radon measures, tempered distributions, or general distributions. We then construct a crystalline Fourier eigenmeasure that fails to be translation bounded even as a distribution. We finally construct a crystalline measure that fails to be a~Fourier quasicrystal (in particular, it fails to be slowly increasing), but it is an almost periodic tempered distribution whose Fourier transform is even a norm almost periodic measure. Our examples fully resolve the questions of Meyer and Favorov and sharply delineate the class boundary of translation boundedness. They also demonstrate the unusual behaviour of crystalline measures beyond the class of Fourier quasicrystals. △ Less

Submitted 22 May, 2026; originally announced May 2026.

Comments: 34 pages

MSC Class: 46F12 (Primary) 42A75; 42B10 (Secondary)

Development of EAP-based actuators for high-frequency adaptive optics system

Authors: A. Michel, D. Audigier, C. Richard, J. -F. Capsal

Abstract: The present work aims to enhance the electrostrictive strain of the P(VDF-TrFE-CFE) terpolymer for use in adaptive optics, specifically in deformable mirror actuation. In the context of the FlexSiMirror project, these systems seek to operate under alternating electric fields of up to 50 V/um and within the kilohertz (kHz) frequency range, thereby framing the ranges of characterization considered i… ▽ More The present work aims to enhance the electrostrictive strain of the P(VDF-TrFE-CFE) terpolymer for use in adaptive optics, specifically in deformable mirror actuation. In the context of the FlexSiMirror project, these systems seek to operate under alternating electric fields of up to 50 V/um and within the kilohertz (kHz) frequency range, thereby framing the ranges of characterization considered in this study. To achieve greater strains, the incorporation of a polymeric plasticizer up to 20 vol.% and its impact on the actuation strain performance was studied. Hence, the relevance of this approach lies both in the kHz characterization of the mechanical and dielectric properties of the materials and in the utilization of a polymeric plasticizer, instead of the commonly used phthalates suitable for lower frequency ranges. In the kHz range, polymeric plasticizer addition markedly reduces the elastic modulus while limiting molecular migration, leading to more than a threefold increase of the figure of merit associated with strain (FOMstrain) and yielding 1.50% strain output under 50 V/um, 3.6 times greater than that of the unmodified terpolymer. Therefore, these findings show that modified P(VDF-TrFE-CFE) exhibits enhanced electromechanical performance in the kHz range. This advancement opens new possibilities for developing next-generation actuators intended for adaptive optics applications. △ Less

Submitted 22 May, 2026; originally announced May 2026.

Journal ref: Electroactive Polymer Actuators, Sensors, and Devices (EAPAD) 2026, Mar 2026, Vancouver, France. pp.37

Corrections for systematic errors in slit-profiler transverse phase space measurements

Authors: C. Richard, M. Krasilnikov, N. Aftab, Z. Amirkhanyan, D. Dmytriiev, A. Hoffmann, X. -K. Li, Z. Lotfi, F. Stephan, G. Vashchenko, S. Zeeshan

Abstract: In photo injectors, the transverse emittance is one of the key measures of beam quality as it defines the possible performance of the whole facility. As such it is important to measure the emittance in photo injectors and ensure the accuracy of these measurements. While there are many different methods of measuring the emittance, this paper focuses on quantifying the systematic errors present in t… ▽ More In photo injectors, the transverse emittance is one of the key measures of beam quality as it defines the possible performance of the whole facility. As such it is important to measure the emittance in photo injectors and ensure the accuracy of these measurements. While there are many different methods of measuring the emittance, this paper focuses on quantifying the systematic errors present in transverse phase space measurements taken with slit-profiler methods, i.e. scanning a narrow slit over the beam and continually measuring the passed beamlets' divergence with a downstream profiler. The measurement errors include effects of the slit size, beamlet imaging, and residual space charge. While these effects are generally small, they can have significant impact on the measured emittance when the 2D phase space is strongly coupled. The systematic effects studied and corrections are demonstrated with simulations and measurements from the Photo Injector Test facility at DESY in Zeuthen (PITZ) using a slit-screen emittance scanner. △ Less

Submitted 23 January, 2026; v1 submitted 15 January, 2026; originally announced January 2026.

Distributed Riemannian Optimization in Geodesically Non-convex Environments

Authors: Xiuheng Wang, Ricardo Borsoi, Cédric Richard, Ali H. Sayed

Abstract: This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy called diffusion adaptation to Riemannian manifolds, we show that the resulting algorithm, the Riemannian diffusion adaptation, provably exhibits several desirable b… ▽ More This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy called diffusion adaptation to Riemannian manifolds, we show that the resulting algorithm, the Riemannian diffusion adaptation, provably exhibits several desirable behaviors when minimizing a sum of geodesically smooth non-convex functions over manifolds of bounded curvature. More specifically, we establish that the algorithm can approximately achieve network agreement in the sense that Fréchet variance of the iterates among the agents is small. Moreover, the algorithm is guaranteed to converge to a first-order stationary point for general geodesically non-convex cost functions. When the global cost function additionally satisfies the local Riemannian Polyak-Lojasiewicz (PL) condition, we also show that it converges linearly under a constant step size up to a steady-state error. Finally, we apply this algorithm to a decentralized robust principal component analysis (PCA) problem formulated on the Grassmann manifold and low-rank matrix completion problems and illustrate its convergence and performance through numerical simulations. △ Less

Submitted 25 May, 2026; v1 submitted 4 December, 2025; originally announced December 2025.

The HITRAN2024 methane update

Authors: T. Bertin, I. E. Gordon, R. J. Hargreaves, J. Tennyson, S. N. Yurchenko, K. Kefala, V. Boudon, C. Richard, A. V. Nikitin, V. G. Tyuterev, M. Rey, M. Birk, G. Wagner, K. Sung, B. P. Coy, W. Broussard, G. C. Toon, A. A. Rodina, E. Starikova, A. Campargue, Z. D. Reed, J. T. Hodges, Y. Tan, N. A. Malarich, G. B. Rieker

Abstract: Spectroscopic parameters of methane from many different studies were gathered to improve the HITRAN database towards its 2024 version. After a validation process using high-resolution FTS and CRDS spectra, about 80,000 lines of the four most abundant isotopologues were replaced from the dyad to the triacontad regions. These changes amount to 51,000 transition wavenumbers, 18,000 line intensities,… ▽ More Spectroscopic parameters of methane from many different studies were gathered to improve the HITRAN database towards its 2024 version. After a validation process using high-resolution FTS and CRDS spectra, about 80,000 lines of the four most abundant isotopologues were replaced from the dyad to the triacontad regions. These changes amount to 51,000 transition wavenumbers, 18,000 line intensities, 33,000 pressure-broadening half-widths, and 3300 assignments. 44,000 new lines were added with 16,000 old lines removed, extending the database from 12,000 cm$^{-1}$ up to 14,000 cm$^{-1}$, and covering some gaps. A greater focus was brought on the pentad, octad, and tetradecad regions, targeted by several remote sensing instruments. In these regions, comparisons of spectral fits from multiple line lists were performed, taking only the parameters that provide best fit for each line. In the $ν_3$ band, in addition to replacing the previous values, speed-independent pressure broadening parameters of $^{12}$CH$_4$ were gathered and used to fit Padé-approximant functions. These functions then replaced any outdated experimental data in $ν_3$, missing data in the new lines, as well as the values that were determined to be outside their physical boundaries. The CH$_3$D broadening parameters were replaced in the same manner, for missing and low or high values, using a semi-empirical formula instead. △ Less

Submitted 12 January, 2026; v1 submitted 26 November, 2025; originally announced November 2025.

Comments: Added back a missing reference in the summary table from the accepted version of Journal of Quantitative Spectroscopy and Radiative Transfer (JQSRT), November 2025

Journal ref: Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 349, February 2026, 109736

Sparing of DNA irradiated with Ultra-High Dose-Rates under Physiological Oxygen and Salt conditions

Authors: Marc Benjamin Hahn, Sepideh Aminzadeh-Gohari, Anna Grebinyk, Matthias Gross, Andreas Hoffmann, Xiangkun Li, Anne Oppelt, Chris Richard, Felix Riemer, Frank Stephan, Elif Tarakci, Daniel Villani

Abstract: Cancer treatment with radiotherapy aims to kill tumor cells and spare healthy tissue.Thus,the experimentally observed sparing of healthy tissue by the FLASH effect during irradiations with ultra-high dose rates (UHDR) enables clinicians to extend the therapeutic window.However, the underlying radiobiological and chemical mechanisms are far from being understood.DNA is one of the main molecular tar… ▽ More Cancer treatment with radiotherapy aims to kill tumor cells and spare healthy tissue.Thus,the experimentally observed sparing of healthy tissue by the FLASH effect during irradiations with ultra-high dose rates (UHDR) enables clinicians to extend the therapeutic window.However, the underlying radiobiological and chemical mechanisms are far from being understood.DNA is one of the main molecular targets for radiotherapy.Ionizing radiation damage to DNA in water depends strongly on salt,pH,buffer and oxygen content of the solvent.Here we present a study of plasmid DNA pUC19,irradiated with 18MeV electrons at low dose rates (LDR) and UHDR under tightly controlled ambient and physiological oxygen conditions in PBS at pH 7.4.For the first time a sparing effect of DNA strand-break induction between UHDR(>10MGy/s) and LDR(<0.1Gy/s) irradiated plasmid DNA under physiological oxygen, salt and pH is observed for total doses above 10Gy.Under physiological oxygen (physoxia,5%O2,40mmHg),more single (SSB) and double strand-breaks (DSB) are observed when exposed to LDR, than to UHDR.This behaviour is absent for ambient oxygen (normoxia,21%O2,150-160mmHg).The experiments are accompanied by TOPAS-nBio based particle-scattering and chemical MCS to obtain information about the yields of reactive oxygen species (ROS).Hereby,an extended set of chemical reactions was considered, which improved upon the discrepancy between experiment and simulations of previous works, and allowed to predict DR dependent g-values of hydrogen peroxide (H2O2).To explain the observed DNA sparing effect under FLASH conditions at physoxia,the following model was proposed:The interplay of O2 with OH induced H-abstraction at the phosphate backbone,and the conversion of DNA base-damage to SSB,under consideration of the dose-rate dependent H3O+ yield via beta elimination processes is accounted for, to explain the observed behavior. △ Less

Submitted 17 October, 2025; originally announced October 2025.

Comments: 34 pages, 12 figures

Riemannian Change Point Detection on Manifolds with Robust Centroid Estimation

Authors: Xiuheng Wang, Ricardo Borsoi, Arnaud Breloy, Cédric Richard

Abstract: Non-parametric change-point detection in streaming time series data is a long-standing challenge in signal processing. Recent advancements in statistics and machine learning have increasingly addressed this problem for data residing on Riemannian manifolds. One prominent strategy involves monitoring abrupt changes in the center of mass of the time series. Implemented in a streaming fashion, this s… ▽ More Non-parametric change-point detection in streaming time series data is a long-standing challenge in signal processing. Recent advancements in statistics and machine learning have increasingly addressed this problem for data residing on Riemannian manifolds. One prominent strategy involves monitoring abrupt changes in the center of mass of the time series. Implemented in a streaming fashion, this strategy, however, requires careful step size tuning when computing the updates of the center of mass. In this paper, we propose to leverage robust centroid on manifolds from M-estimation theory to address this issue. Our proposal consists of comparing two centroid estimates: the classical Karcher mean (sensitive to change) versus one defined from Huber's function (robust to change). This comparison leads to the definition of a test statistic whose performance is less sensitive to the underlying estimation method. We propose a stochastic Riemannian optimization algorithm to estimate both robust centroids efficiently. Experiments conducted on both simulated and real-world data across two representative manifolds demonstrate the superior performance of our proposed method. △ Less

Submitted 25 August, 2025; originally announced August 2025.

A cometary Fluorescence Model for the $ν_3$ Vibrational Band of Cyanogen

Authors: P. Hardy, P. Rousselot, C. Richard, V. Boudon, X. Landsheere, A. Voute, L. Manceron, F. Kwabia Tchana

Abstract: Cyanogen ($\mathrm{C_2N_2}$) is suspected for a long time to be present in comets and to contribute to the creation of the CN radical. So far no observations with ground-based facilities have managed to detect this species but the Rosetta mission, thanks to in situ observations with the ROSINA mass spectrometer detected this species in the coma of 67P/Churyumov-Gerasimenko. To investigate its pres… ▽ More Cyanogen ($\mathrm{C_2N_2}$) is suspected for a long time to be present in comets and to contribute to the creation of the CN radical. So far no observations with ground-based facilities have managed to detect this species but the Rosetta mission, thanks to in situ observations with the ROSINA mass spectrometer detected this species in the coma of 67P/Churyumov-Gerasimenko. To investigate its presence from infrared spectra in other comets, we developed a fluorescence model for the $ν_3$ fundamental band. From new laboratory high-resolution infrared spectra of cyanogen, we analyzed the region of the $ν_3$ band of $\mathrm{C_2N_2}$, centered around 4.63 $μm$ (2158 $\mathrm{cm^{-1}}$). In addition to line positions and intensities, molecular parameters for the ground and excited vibrational state were obtained. These parameters allowed us to develop a fluorescence model for cyanogen. Line-by-line excitation rates of the $ν_3$ band of cyanogen in cometary comae are presented. An upper limit of the abundance of cyanogen in a spectrum of comet C/2022 E3 (ZTF) is discussed. △ Less

Submitted 5 July, 2025; v1 submitted 23 March, 2025; originally announced March 2025.

DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing

Authors: ChenTong Wang, Jincheng Gao, Fei Zhu, Abderrahim Halimi, Cédric Richard

Abstract: Transformers have shown significant success in hyperspectral unmixing (HU). However, challenges remain. While multi-scale and long-range spatial correlations are essential in unmixing tasks, current Transformer-based unmixing networks, built on Vision Transformer (ViT) or Swin-Transformer, struggle to capture them effectively. Additionally, current Transformer-based unmixing networks rely on the l… ▽ More Transformers have shown significant success in hyperspectral unmixing (HU). However, challenges remain. While multi-scale and long-range spatial correlations are essential in unmixing tasks, current Transformer-based unmixing networks, built on Vision Transformer (ViT) or Swin-Transformer, struggle to capture them effectively. Additionally, current Transformer-based unmixing networks rely on the linear mixing model, which lacks the flexibility to accommodate scenarios where nonlinear effects are significant. To address these limitations, we propose a multi-scale Dilated Transformer-based unmixing network for nonlinear HU (DTU-Net). The encoder employs two branches. The first one performs multi-scale spatial feature extraction using Multi-Scale Dilated Attention (MSDA) in the Dilated Transformer, which varies dilation rates across attention heads to capture long-range and multi-scale spatial correlations. The second one performs spectral feature extraction utilizing 3D-CNNs with channel attention. The outputs from both branches are then fused to integrate multi-scale spatial and spectral information, which is subsequently transformed to estimate the abundances. The decoder is designed to accommodate both linear and nonlinear mixing scenarios. Its interpretability is enhanced by explicitly modeling the relationships between endmembers, abundances, and nonlinear coefficients in accordance with the polynomial post-nonlinear mixing model (PPNMM). Experiments on synthetic and real datasets validate the effectiveness of the proposed DTU-Net compared to PPNMM-derived methods and several advanced unmixing networks. △ Less

Submitted 5 March, 2025; v1 submitted 5 March, 2025; originally announced March 2025.

Specification for the Siril HEALpixel Catalog Format

Authors: Adrian J. E. Knagg-Baugh, Ian Cass, Cécile Melis, Cyril Richard

Abstract: This document specifies the structure of the Siril Catalog Format, designed to support efficient storage and querying of nested HEALpixel based astronomical catalogs such as Gaia DR3. The format includes a fixed length header, an index for rapid look-up, and structured data records optimized for space and speed. The document also outlines recommended search strategies for utilizing the format effe… ▽ More This document specifies the structure of the Siril Catalog Format, designed to support efficient storage and querying of nested HEALpixel based astronomical catalogs such as Gaia DR3. The format includes a fixed length header, an index for rapid look-up, and structured data records optimized for space and speed. The document also outlines recommended search strategies for utilizing the format effectively. △ Less

Submitted 21 January, 2025; originally announced January 2025.

Twice Fourier transformable measures and diffraction theory

Authors: Hans G. Feichtinger, Christoph Richard, Christoph Schumacher, Nicolae Strungaru

Abstract: Mathematical diffraction theory has been developed since about 1995. Hof's initial approach relied on tempered distributions in euclidean space. Nowadays often the Fourier theory by Argabright and Gil de Lamadrid is used, which applies to appropriate measures on locally compact abelian groups. We review diffraction theory using Wiener amalgams as test function spaces. For translation bounded measu… ▽ More Mathematical diffraction theory has been developed since about 1995. Hof's initial approach relied on tempered distributions in euclidean space. Nowadays often the Fourier theory by Argabright and Gil de Lamadrid is used, which applies to appropriate measures on locally compact abelian groups. We review diffraction theory using Wiener amalgams as test function spaces. For translation bounded measures, this unifies and simplifies the former two approaches. We treat weighted versions of Meyer's model sets as examples. △ Less

Submitted 22 November, 2024; originally announced November 2024.

Comments: 46 pages

MSC Class: 43A07; 52C23; 43A60; 78A45

Which Meyer sets are regular model sets? A characterization via almost periodicity

Authors: Daniel Lenz, Christoph Richard, Nicolae Strungaru

Abstract: In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more general setting. Specifically, we show that a Meyer set in any $σ$-compact locally compact abelian group is a regular model set if and only if it is an almost perio… ▽ More In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more general setting. Specifically, we show that a Meyer set in any $σ$-compact locally compact abelian group is a regular model set if and only if it is an almost periodic pattern. △ Less

Submitted 29 October, 2024; originally announced October 2024.

Comments: 26 pages

The D-Subspace Algorithm for Online Learning over Distributed Networks

Authors: Yitong Chen, Danqi Jin, Jie Chen, Cedric Richard

Abstract: This material introduces the D-Subspace algorithm derived on the basis of the centralized algorithm [1], which originally addresses parameter estimation problems under a subspace constraint. This material introduces the D-Subspace algorithm derived on the basis of the centralized algorithm [1], which originally addresses parameter estimation problems under a subspace constraint. △ Less

Submitted 10 November, 2024; v1 submitted 26 October, 2024; originally announced October 2024.

Siril: An Advanced Tool for Astronomical Image Processing

Authors: Cyril Richard, Vincent Hourdin, Cécile Melis, Adrian Knagg-Baugh

Abstract: Siril is a powerful open-source software package designed for the preprocessing and post-processing of astronomical images. It is particularly well-suited for astrophotography enthusiasts and professional astronomers alike. Siril provides advanced tools for tasks such as image stacking, calibration, registration, and enhancement, enabling users to produce high-quality images of celestial objects.… ▽ More Siril is a powerful open-source software package designed for the preprocessing and post-processing of astronomical images. It is particularly well-suited for astrophotography enthusiasts and professional astronomers alike. Siril provides advanced tools for tasks such as image stacking, calibration, registration, and enhancement, enabling users to produce high-quality images of celestial objects. The version discussed here is the development branch 1.4, which, while not officially released, is available for testing and includes the latest features and improvements. △ Less

Submitted 15 October, 2024; v1 submitted 2 August, 2024; originally announced August 2024.

Comments: 4 pages, 1 figure: short article in the form requested by the JOSS guideline

Journal ref: Journal of Open Source Software, 2024

First high peak and average power single-pass THz FEL based on high brightness photoinjector

Authors: M. Krasilnikov, Z. Aboulbanine, G. Adhikari, N. Aftab, A. Asoyan, P. Boonpornprasert, H. Davtyan, G. Georgiev, J. Good, A. Grebinyk, M. Gross, A. Hoffmann, E. Kongmon, X. -K. Li, A. Lueangaramwong, D. Melkumyan, S. Mohanty, R. Niemczyk, A. Oppelt, H. Qian, C. Richard, F. Stephan, G. Vashchenko, T. Weilbach, X. Zhang , et al. (9 additional authors not shown)

Abstract: Advanced experiments using THz pump and X-ray probe pulses at modern free-electron lasers (FELs) like the European X-ray FEL require a frequency-tunable, high-power, narrow-band THz source maintaining the repetition rate and pulse structure of the X-ray pulses. This paper reports the first results from a THz source, that is based on a single-pass high-gain THz FEL operating with a central waveleng… ▽ More Advanced experiments using THz pump and X-ray probe pulses at modern free-electron lasers (FELs) like the European X-ray FEL require a frequency-tunable, high-power, narrow-band THz source maintaining the repetition rate and pulse structure of the X-ray pulses. This paper reports the first results from a THz source, that is based on a single-pass high-gain THz FEL operating with a central wavelength of 100 micrometers. The THz FEL prototype is currently in operation at the Photo Injector Test facility at DESY in Zeuthen (PITZ) and uses the same type of electron source as the European XFEL photo injector. A self-amplified spontaneous emission (SASE) FEL was envisioned as the main mechanism for generating the THz pulses. Although the THz FEL at PITZ is supposed to use the same mechanism as at X-ray facilities, it cannot be considered as a simple scaling of the radiation wavelength because there is a large difference in the number of electrons per radiation wavelength, which is five orders of magnitude higher for the THz case. The bunching factor arising from the electron beam current profile contributes strongly to the initial spontaneous emission starting the FEL process. Proof-of-principle experiments were done at PITZ using an LCLS-I undulator to generate the first high-power, high-repetition-rate single-pass THz FEL radiation. Electron bunches with a beam energy of ~17 MeV and a bunch charge of up to several nC are used to generate THz pulses with a pulse energy of several tens of microjoules. For example, for an electron beam with a charge of ~2.4 nC, more than 100 microjoules were generated at a central wavelength of 100 micrometers. The narrowband spectrum was also demonstrated by spectral measurements. These proof-of-principle experiments pave the way for a tunable, high-repetition-rate THz source providing pulses with energies in the millijoule range. △ Less

Submitted 29 May, 2024; originally announced May 2024.

Comments: (unpublished) for submission to PRAB

Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications

Authors: Katy L. Chubb, Séverine Robert, Clara Sousa-Silva, Sergei N. Yurchenko, Nicole F. Allard, Vincent Boudon, Jeanna Buldyreva, Benjamin Bultel, Athena Coustenis, Aleksandra Foltynowicz, Iouli E. Gordon, Robert J. Hargreaves, Christiane Helling, Christian Hill, Helgi Rafn Hrodmarsson, Tijs Karman, Helena Lecoq-Molinos, Alessandra Migliorini, Michaël Rey, Cyril Richard, Ibrahim Sadiek, Frédéric Schmidt, Andrei Sokolov, Stefania Stefani, Jonathan Tennyson , et al. (30 additional authors not shown)

Abstract: The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the Ariel space mission, but also for related atmospheric studies of exoplanets and brown dwarfs. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical… ▽ More The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the Ariel space mission, but also for related atmospheric studies of exoplanets and brown dwarfs. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical properties of aerosols and surfaces, atmospheric chemistry, UV photodissociation and photoabsorption cross-sections, and standards in the description and format of such data. These data aspects are discussed by addressing the following questions for each topic, based on the experience of the "data-provider" and "data-user" communities: (1) what are the types and sources of currently available data, (2) what work is currently in progress, and (3) what are the current and anticipated data needs. We present a GitHub platform for Ariel-related data, with the goal to provide a go-to place for both data-users and data-providers, for the users to make requests for their data needs and for the data-providers to link to their available data. Our aim throughout the paper is to provide practical information on existing sources of data whether in databases, theoretical, or literature sources. △ Less

Submitted 4 November, 2025; v1 submitted 2 April, 2024; originally announced April 2024.

Comments: 58 pages, published in RAS Techniques and Instruments (RASTI). The authors welcome feedback: corresponding author emails can be found as footnotes on page 2

Journal ref: RAS Techniques and Instruments, Volume 3, Issue 1, January 2024, Pages 636-690

Distributed pressure matching strategy using diffusion adaptation

Authors: Mengfei Zhang, Junqing Zhang, Jie Chen, Cédric Richard

Abstract: Personal sound zone (PSZ) systems, which aim to create listening (bright) and silent (dark) zones in neighboring regions of space, are often based on time-varying acoustics. Conventional adaptive-based methods for handling PSZ tasks suffer from the collection and processing of acoustic transfer functions~(ATFs) between all the matching microphones and all the loudspeakers in a centralized manner,… ▽ More Personal sound zone (PSZ) systems, which aim to create listening (bright) and silent (dark) zones in neighboring regions of space, are often based on time-varying acoustics. Conventional adaptive-based methods for handling PSZ tasks suffer from the collection and processing of acoustic transfer functions~(ATFs) between all the matching microphones and all the loudspeakers in a centralized manner, resulting in high calculation complexity and costly accuracy requirements. This paper presents a distributed pressure-matching (PM) method relying on diffusion adaptation (DPM-D) to spread the computational load amongst nodes in order to overcome these issues. The global PM problem is defined as a sum of local costs, and the diffusion adaption approach is then used to create a distributed solution that just needs local information exchanges. Simulations over multi-frequency bins and a computational complexity analysis are conducted to evaluate the properties of the algorithm and to compare it with centralized counterparts. △ Less

Submitted 13 November, 2023; originally announced November 2023.

High-resolution far-infrared spectroscopy and analysis of the $ν$3 and $ν$6 bands of chloromethane

Authors: Pierre Hardy, C. Richard, Vincent Boudon, Mohammad Vaseem, Laurent Manceron, Nawel Dridi

Abstract: Ro-vibrational spectra of the $ν_3$ and $ν_6$ bands of chloromethane ($\mathrm{CH_3Cl}$) were recorded in the 650--1130 $\mathrm{cm}^{-1}$ range using a Fourier transform spectrometer at the AILES beamline of the SOLEIL synchrotron facility. Two isotopologues ($\mathrm{CH_3^{35}Cl}$ and $\mathrm{CH_3^{37}Cl}$) have been analyzed with the tensorial formalism developed in Dijon and a total of 6753 l… ▽ More Ro-vibrational spectra of the $ν_3$ and $ν_6$ bands of chloromethane ($\mathrm{CH_3Cl}$) were recorded in the 650--1130 $\mathrm{cm}^{-1}$ range using a Fourier transform spectrometer at the AILES beamline of the SOLEIL synchrotron facility. Two isotopologues ($\mathrm{CH_3^{35}Cl}$ and $\mathrm{CH_3^{37}Cl}$) have been analyzed with the tensorial formalism developed in Dijon and a total of 6753 lines were assigned. We derived 23 tensorial parameters for the lines positions (4 for the ground state, 6 for $ν_3$, and 13 for $ν_6$), and 7 for the lines intensities (4 for $ν_3$, 3 for $ν_6$). From those parameters and self-broadening coefficients found in the literature, we simulated spectra of both isotopologues. The derived parameters were converted in the Watson formalism to be compared with a previous study. Using these results, we set up a new database of calculated chloromethane spectral lines (ChMeCaSDa). △ Less

Submitted 21 September, 2023; originally announced September 2023.

Comments: Journal of Quantitative Spectroscopy & Radiative Transfer, In press

The ro-vibrational $ν_2$ mode spectrum of methane investigated by ultrabroadband coherent Raman spectroscopy

Authors: Francesco Mazza, Ona Thornquist, Leonardo Castellanos, Thomas Butterworth, Cyril Richard, Vincent Boudon, Alexis Bohlin

Abstract: We present the first experimental application of coherent Raman spectroscopy (CRS) on the ro-vibrational $ν_2$ mode spectrum of methane (CH$_4$). Ultrabroadband femtosecond/picosecond (fs/ps) CRS is performed in the molecular fingerprint region from 1100 to 2000 cm$^{-1}$, employing fs laser-induced filamentation as the supercontinuum generation mechanism to provide the ultrabroadband excitation p… ▽ More We present the first experimental application of coherent Raman spectroscopy (CRS) on the ro-vibrational $ν_2$ mode spectrum of methane (CH$_4$). Ultrabroadband femtosecond/picosecond (fs/ps) CRS is performed in the molecular fingerprint region from 1100 to 2000 cm$^{-1}$, employing fs laser-induced filamentation as the supercontinuum generation mechanism to provide the ultrabroadband excitation pulses. We introduce a time-domain model of the CH$_4$ $ν_2$ CRS spectrum, including all five ro-vibrational branches allowed by the selection rules $Δv = 1$, $ΔJ = 0$, $\pm1$, $\pm2$; the model includes collisional linewidths, computed according to a modified exponential gap scaling law and validated experimentally. The use of ultrabroadband CRS for in situ monitoring of the CH$_4$ chemistry is demonstrated in a laboratory CH$_4$/air diffusion flame: CRS measurements in the fingerprint region, performed across the laminar flame front, allow the simultaneous detection of molecular oxygen (O$_2$), carbon dioxide (CO$_2$), and molecular hydrogen (H$_2$), along with CH$_4$. Fundamental physicochemical processes, such as H$_2$ production via CH$_4$ pyrolysis, are observed through the Raman spectra of these chemical species. In addition, we demonstrate ro-vibrational CH$_4ν_2$ CRS thermometry, and we validate it against CO$_2$ CRS measurements. The present technique offers an interesting diagnostics approach to in situ measurement of CH$_4$-rich environments, e.g., in plasma reactors for CH$_4$ pyrolysis and H$_2$ production. △ Less

Submitted 24 July, 2023; originally announced July 2023.

Journal ref: Journal of Chemical Physics, 2023, 158 (9)

Self and N2 collisional broadening of far-infrared methane lines at low-temperature with application to Titan

Authors: C. Richard, V. Boudon, L. Manceron, J. Vander Auwera, S. Vinatier, B. Bézard, M. Houelle

Abstract: We report the measurement of broadening coefficients of pure rotational lines of methane at different pressure and temperature conditions. A total of 27 far-infrared spectra were recorded at the AILES beamline of the SOLEIL synchrotron at room-temperature, 200 K and 120 K, in a range of 10 to 800 mbar. Self and N 2 broadening coefficients and temperature dependence exponents of methane pure rotati… ▽ More We report the measurement of broadening coefficients of pure rotational lines of methane at different pressure and temperature conditions. A total of 27 far-infrared spectra were recorded at the AILES beamline of the SOLEIL synchrotron at room-temperature, 200 K and 120 K, in a range of 10 to 800 mbar. Self and N 2 broadening coefficients and temperature dependence exponents of methane pure rotational lines have been measured in the 73-136 cm --1 spectral range using multi-spectrum non-linear least squares fitting of Voigt profiles. These coefficients were used to model spectra of Titan that were compared to a selection of equatorial Cassini/CIRS spectra, showing a good agreement for a stratospheric methane mole fraction of (1.17 $\pm$ 0.08)%. △ Less

Submitted 3 July, 2023; originally announced July 2023.

Journal ref: Icarus, inPress, pp.115692 (2023)

Spatial Deep Deconvolution U-Net for Traffic Analyses with Distributed Acoustic Sensing

Authors: Siyuan Yuan, Martijn van den Ende, Jingxiao Liu, Hae Young Noh, Robert Clapp, Cédric Richard, Biondo Biondi

Abstract: Distributed Acoustic Sensing (DAS) that transforms city-wide fiber-optic cables into a large-scale strain sensing array has shown the potential to revolutionize urban traffic monitoring by providing a fine-grained, scalable, and low-maintenance monitoring solution. However, the real-world application of DAS is hindered by challenges such as noise contamination and interference among closely travel… ▽ More Distributed Acoustic Sensing (DAS) that transforms city-wide fiber-optic cables into a large-scale strain sensing array has shown the potential to revolutionize urban traffic monitoring by providing a fine-grained, scalable, and low-maintenance monitoring solution. However, the real-world application of DAS is hindered by challenges such as noise contamination and interference among closely traveling cars. In response, we introduce a self-supervised U-Net model that can suppress background noise and compress car-induced DAS signals into high-resolution pulses through spatial deconvolution. Our work extends recent research by introducing three key advancements. Firstly, we perform a comprehensive resolution analysis of DAS-recorded traffic signals, laying a theoretical foundation for our approach. Secondly, we incorporate space-domain vehicle wavelets into our U-Net model, enabling consistent high-resolution outputs regardless of vehicle speed variations. Finally, we employ L-2 norm regularization in the loss function, enhancing our model's sensitivity to weaker signals from vehicles in remote traffic lanes. We evaluate the effectiveness and robustness of our method through field recordings under different traffic conditions and various driving speeds. Our results show that our method can enhance the spatial-temporal resolution and better resolve closely traveling cars. The spatial deconvolution U-Net model also enables the characterization of large-size vehicles to identify axle numbers and estimate the vehicle length. Monitoring large-size vehicles also benefits imaging deep earth by leveraging the surface waves induced by the dynamic vehicle-road interaction. △ Less

Submitted 27 June, 2023; v1 submitted 7 December, 2022; originally announced December 2022.

Comments: This preprint was re-submitted as a revised version to the IEEE Transactions on Intelligent Transportation Systems on June 27, 2023

Tuning-free Plug-and-Play Hyperspectral Image Deconvolution with Deep Priors

Authors: Xiuheng Wang, Jie Chen, Cédric Richard

Abstract: Deconvolution is a widely used strategy to mitigate the blurring and noisy degradation of hyperspectral images~(HSI) generated by the acquisition devices. This issue is usually addressed by solving an ill-posed inverse problem. While investigating proper image priors can enhance the deconvolution performance, it is not trivial to handcraft a powerful regularizer and to set the regularization param… ▽ More Deconvolution is a widely used strategy to mitigate the blurring and noisy degradation of hyperspectral images~(HSI) generated by the acquisition devices. This issue is usually addressed by solving an ill-posed inverse problem. While investigating proper image priors can enhance the deconvolution performance, it is not trivial to handcraft a powerful regularizer and to set the regularization parameters. To address these issues, in this paper we introduce a tuning-free Plug-and-Play (PnP) algorithm for HSI deconvolution. Specifically, we use the alternating direction method of multipliers (ADMM) to decompose the optimization problem into two iterative sub-problems. A flexible blind 3D denoising network (B3DDN) is designed to learn deep priors and to solve the denoising sub-problem with different noise levels. A measure of 3D residual whiteness is then investigated to adjust the penalty parameters when solving the quadratic sub-problems, as well as a stopping criterion. Experimental results on both simulated and real-world data with ground-truth demonstrate the superiority of the proposed method. △ Less

Submitted 6 February, 2023; v1 submitted 28 November, 2022; originally announced November 2022.

Comments: IEEE Trans. Geosci. Remote sens., to be published. Manuscript submitted Jun. 30, 2022; revised Oct. 25, 2022, and Dec. 06, 2022; and accepted Feb. 02, 2023

Inter model sets in $\mathbb R^d$ are model sets

Authors: Christoph Richard, Nicolae Strungaru

Abstract: We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic propertie… ▽ More We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original window. Our results hold in fact for a class beyond inter model sets, which we call almost model sets. △ Less

Submitted 2 November, 2022; originally announced November 2022.

Deep Hyperspectral and Multispectral Image Fusion with Inter-image Variability

Authors: Xiuheng Wang, Ricardo Augusto Borsoi, Cédric Richard, Jie Chen

Abstract: Hyperspectral and multispectral image fusion allows us to overcome the hardware limitations of hyperspectral imaging systems inherent to their lower spatial resolution. Nevertheless, existing algorithms usually fail to consider realistic image acquisition conditions. This paper presents a general imaging model that considers inter-image variability of data from heterogeneous sources and flexible i… ▽ More Hyperspectral and multispectral image fusion allows us to overcome the hardware limitations of hyperspectral imaging systems inherent to their lower spatial resolution. Nevertheless, existing algorithms usually fail to consider realistic image acquisition conditions. This paper presents a general imaging model that considers inter-image variability of data from heterogeneous sources and flexible image priors. The fusion problem is stated as an optimization problem in the maximum a posteriori framework. We introduce an original image fusion method that, on the one hand, solves the optimization problem accounting for inter-image variability with an iteratively reweighted scheme and, on the other hand, that leverages light-weight CNN-based networks to learn realistic image priors from data. In addition, we propose a zero-shot strategy to directly learn the image-specific prior of the latent images in an unsupervised manner. The performance of the algorithm is illustrated with real data subject to inter-image variability. △ Less

Submitted 11 April, 2023; v1 submitted 24 August, 2022; originally announced August 2022.

Comments: IEEE Trans. Geosci. Remote sens., to be published. Manuscript submitted August 23, 2022; revised Dec. 15, 2022, and Mar. 13, 2023; and accepted Apr. 07, 2023

Adaptive Random Fourier Features Kernel LMS

Authors: Wei Gao, Jie Chen, Cédric Richard, Wentao Shi, Qunfei Zhang

Abstract: We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism al… ▽ More We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism allows to alleviate the problem of selecting the kernel bandwidth beforehand for the benefit of an improved tracking in non-stationary circumstances. Simulation results confirm that the proposed algorithm achieves a performance improvement in terms of convergence rate, error at steady-state and tracking ability over other kernel adaptive filters with preset kernel bandwidth. △ Less

Submitted 14 July, 2022; originally announced July 2022.

Comments: 5 pages, 2 figures

Integration of Physics-Based and Data-Driven Models for Hyperspectral Image Unmixing

Authors: Jie Chen, Min Zhao, Xiuheng Wang, Cédric Richard, Susanto Rahardja

Abstract: Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes with unknown complex physical characteristics. Data-driven methods have developed rapidly in recent years, in particular deep learning methods because they poss… ▽ More Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes with unknown complex physical characteristics. Data-driven methods have developed rapidly in recent years, in particular deep learning methods because they possess superior capability in modeling complex and nonlinear systems. Simply transferring these methods as black-boxes to conduct unmixing may lead to low physical interpretability and generalization ability. This article reviews hyperspectral unmixing works that integrate advantages of both physics-based models and data-driven methods by means of deep neural network structures design, prior design and loss design. Most of these methods derive from a common mathematical optimization framework, and combine good interpretability with high accuracy. △ Less

Submitted 27 August, 2022; v1 submitted 11 June, 2022; originally announced June 2022.

Comments: IEEE Signal Process. Mag., to be published. Manuscript submitted March 14, 2022; revised June 25, 2022 and July 27, 2022; accepted August 27, 2022

A methane line list with sub-MHz accuracy in the 1250 to 1380 cm-1 range from optical frequency comb Fourier transform spectroscopy

Authors: Matthias Germann, Adrian Hjältén, Vincent Boudon, Cyril Richard, Karol Krzempek, Arkadiusz Hudzikowski, Aleksander Głuszek, Grzegorz Soboń, Aleksandra Foltynowicz

Abstract: We use a Fourier transform spectrometer based on a difference frequency generation optical frequency comb to measure high-resolution, low-pressure, room-temperature spectra of methane in the 1250 - 1380 cm$^{-1}$ range. From these spectra, we retrieve line positions and intensities of 678 lines of two isotopologues: 157 lines from the $^{12}$CH${_4}$ $ν$${_4}$ fundamental band, 131 lines from the… ▽ More We use a Fourier transform spectrometer based on a difference frequency generation optical frequency comb to measure high-resolution, low-pressure, room-temperature spectra of methane in the 1250 - 1380 cm$^{-1}$ range. From these spectra, we retrieve line positions and intensities of 678 lines of two isotopologues: 157 lines from the $^{12}$CH${_4}$ $ν$${_4}$ fundamental band, 131 lines from the $^{13}$CH${_4}$ $ν$${_4}$ fundamental band, as well as 390 lines from two $^{12}$CH${_4}$ hot bands, $ν$${_2}$ + $ν$${_4}$ - $ν$${_2}$ and 2$ν$${_4}$ - $ν$${_4}$. For another 165 lines from the $^{12}$CH${_4}$ $ν$${_4}$ fundamental band we retrieve line positions only. The uncertainties of the line positions range from 0.19 to 2.3 MHz, and their median value is reduced by a factor of 18 and 59 compared to the previously available data for the $^{12}$CH${_4}$ fundamental and hot bands, respectively, obtained from conventional FTIR absorption measurements. The new line positions are included in the global models of the spectrum of both methane isotopologues, and the fit residuals are reduced by a factor of 8 compared to previous absorption data, and 20 compared to emission data. The experimental line intensities have relative uncertainties in the range of 1.5 - 7.7%, similar to those in the previously available data; 235 new $^{12}$CH${_4}$ line intensities are included in the global model. △ Less

Submitted 13 April, 2022; originally announced April 2022.

Journal ref: J. Quant. Spectr. Radiat. Transf 288, 108252 (2022)

High-resolution far-infrared synchrotron FTIR spectroscopy and analysis of the $ν_7$, $ν_{19}$ and $ν_{20}$ bands of trioxane

Authors: Cyril Richard, Pierre Asselin, Vincent Boudon

Abstract: Rovibrational bands spectra of three $ν_{20}$, $ν_7$ and $ν_{19}$ bands of 1, 3, 5 -- trioxane (H$_2$CO)$_3$ were recorded in the 50--650 cm$^{-1}$ range using a long path absorption cell coupled to a high resolution Fourier transform spectrometer and synchrotron radiation at the AILES beamline of the SOLEIL synchrotron. More than 16000 lines were assigned with a dRMS better than… ▽ More Rovibrational bands spectra of three $ν_{20}$, $ν_7$ and $ν_{19}$ bands of 1, 3, 5 -- trioxane (H$_2$CO)$_3$ were recorded in the 50--650 cm$^{-1}$ range using a long path absorption cell coupled to a high resolution Fourier transform spectrometer and synchrotron radiation at the AILES beamline of the SOLEIL synchrotron. More than 16000 lines were assigned with a dRMS better than $0.17\times10^{-3}$ cm$^{-1}$. Two different formalisms (tensorial and Watson) were used to derive accurate rotational and quartic parameters for the three bands and for the first time, a precise determination of Coriolis parameter and $q_+$ $l-$doubling constant for both $ν_{20}$ and $ν_{19}$ perpendicular bands was obtained. Last, each set of spectroscopic parameters is compared and discussed between both formalisms. △ Less

Submitted 11 March, 2022; v1 submitted 2 February, 2022; originally announced February 2022.

Hyperspectral Image Super-resolution with Deep Priors and Degradation Model Inversion

Authors: Xiuheng Wang, Jie Chen, Cédric Richard

Abstract: To overcome inherent hardware limitations of hyperspectral imaging systems with respect to their spatial resolution, fusion-based hyperspectral image (HSI) super-resolution is attracting increasing attention. This technique aims to fuse a low-resolution (LR) HSI and a conventional high-resolution (HR) RGB image in order to obtain an HR HSI. Recently, deep learning architectures have been used to a… ▽ More To overcome inherent hardware limitations of hyperspectral imaging systems with respect to their spatial resolution, fusion-based hyperspectral image (HSI) super-resolution is attracting increasing attention. This technique aims to fuse a low-resolution (LR) HSI and a conventional high-resolution (HR) RGB image in order to obtain an HR HSI. Recently, deep learning architectures have been used to address the HSI super-resolution problem and have achieved remarkable performance. However, they ignore the degradation model even though this model has a clear physical interpretation and may contribute to improve the performance. We address this problem by proposing a method that, on the one hand, makes use of the linear degradation model in the data-fidelity term of the objective function and, on the other hand, utilizes the output of a convolutional neural network for designing a deep prior regularizer in spectral and spatial gradient domains. Experiments show the performance improvement achieved with this strategy. △ Less

Submitted 24 January, 2022; originally announced January 2022.

Comments: Proc. IEEE Int. Conf. on Acoust, Speech, Signal Process. (ICASSP), to be published. Manuscript submitted October 6th, 2021; revised January 8th, 2022; accepted January 22nd, 2022

Transient Performance Analysis of the $\ell_1$-RLS

Authors: Wei Gao, Jie Chen, Cédric Richard, Wentao Shi, Qunfei Zhang

Abstract: The recursive least-squares algorithm with $\ell_1$-norm regularization ($\ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the $\ell_1$-RLS i… ▽ More The recursive least-squares algorithm with $\ell_1$-norm regularization ($\ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the $\ell_1$-RLS in the mean and mean-square sense. Simulation results illustrate the accuracy of these models. △ Less

Submitted 3 November, 2021; v1 submitted 14 September, 2021; originally announced September 2021.

Comments: 5 pages, 2 figures

Spectrum of weak model sets with Borel windows

Authors: Gerhard Keller, Christoph Richard, Nicolae Strungaru

Abstract: Consider the extended hull of a weak model set together with its natural shift action. Equip the extended hull with the Mirsky measure, which is a certain natural pattern frequency measure. It is known that the extended hull is a measure-theoretic factor of some group rotation, which is called the underlying torus. Among other results, in the article "Periods and factors of weak model sets" we sho… ▽ More Consider the extended hull of a weak model set together with its natural shift action. Equip the extended hull with the Mirsky measure, which is a certain natural pattern frequency measure. It is known that the extended hull is a measure-theoretic factor of some group rotation, which is called the underlying torus. Among other results, in the article "Periods and factors of weak model sets" we showed that the extended hull is isomorphic to a factor group of the torus, where certain periods of the window of the weak model set have been factored out. This was proved for weak model sets having a compact window. In this note, we argue that the same results hold for arbitrary measurable and relatively compact windows. Our arguments crucially rely on Moody's work on uniform distribution in model sets. We also discuss implications for the diffraction of such weak model sets and discuss a new class of examples which are generic for the Mirsky measure. △ Less

Submitted 20 May, 2022; v1 submitted 12 July, 2021; originally announced July 2021.

Comments: 14 pages, v2: title changed, minor adjustments, v3: statements of theorems refined, example class added

Leptin densities in amenable groups

Authors: Felix Pogorzelski, Christoph Richard, Nicolae Strungaru

Abstract: Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density… ▽ More Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density from dynamical systems theory. We use Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window, and for a proof of uniform mean almost periodicity of such model sets. △ Less

Submitted 12 November, 2021; v1 submitted 10 July, 2021; originally announced July 2021.

Comments: 28 pages, introduction rewritten, references added, new Lemma 3.8

On the Garden of Eden theorem for B-free subshifts

Authors: Gerhard Keller, Mariusz Lemanczyk, Christoph Richard, Daniel Sell

Abstract: We prove that on B-free subshifts, with B satisfying the Erdös condition, all cellular automata are determined by monotone sliding block codes. In particular, this implies the validity of the Garden of Eden theorem for such systems. We prove that on B-free subshifts, with B satisfying the Erdös condition, all cellular automata are determined by monotone sliding block codes. In particular, this implies the validity of the Garden of Eden theorem for such systems. △ Less

Submitted 4 September, 2024; v1 submitted 28 June, 2021; originally announced June 2021.

Comments: 23 pages

Torsional-rotational spectrum of doubly-deuterated dimethyl ether (CH$_3$OCHD$_2$) -- First ALMA detection in the interstellar medium

Authors: C. Richard, J. K. Jørgensen, L. Margulès, R. A. Motiyenko, J. -C. Guillemin, P. Groner

Abstract: In 2013, we have published the first rotational analysis and detection of mono-deuterated dimethyl ether in the solar-type protostar IRAS 16293-2422 with the IRAM 30m telescope. Dimethyl ether is one of the most abundant complex organic molecules (COMs) in star-forming regions and their D-to-H (D/H) ratios is important to understand its chemistry and trace the source history. We present the first… ▽ More In 2013, we have published the first rotational analysis and detection of mono-deuterated dimethyl ether in the solar-type protostar IRAS 16293-2422 with the IRAM 30m telescope. Dimethyl ether is one of the most abundant complex organic molecules (COMs) in star-forming regions and their D-to-H (D/H) ratios is important to understand its chemistry and trace the source history. We present the first analysis of doubly-deuterated dimethyl ether (methoxy-d2-methane, 1,1-dideuteromethylether) in its ground-vibrational state, based on an effective Hamiltonian for an asymmetric rotor molecules with internal rotors. The analysis covers the frequency range 0.15-1.5THz. The laboratory rotational spectrum of this species was measured between 150 and 1500 GHz with the Lille's submillimeter spectrometer. For the astronomical detection, we used the Atacama Large Millimeter/submillimeter Array (ALMA) observations from the Protostellar Interferometric Line Survey, PILS. New sets of spectroscopic parameters have been determined by a least squares fit with the ERHAM code for both symmetric and asymmetric conformers. As for the mono-deuterated species, these parameters have permitted the first identification in space of both conformers of a doubly-deuterated dimethyl ether via detection near the B component of the Class 0 protostar IRAS 16293-2422. △ Less

Submitted 15 June, 2021; originally announced June 2021.

Comments: 11 pages, 5 figures and 6 tables, not yet published, just accepted

Journal ref: A&A 651, A120 (2021)

Graph topology inference with derivative-reproducing property in RKHS: algorithm and convergence analysis

Authors: Mircea Moscu, Ricardo A. Borsoi, Cédric Richard, José-Carlos M. Bermudez

Abstract: In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may be based on nonlinear relationships adds further complexity to the topology inference problem. Among the latest methods that respond to this need is a topology i… ▽ More In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may be based on nonlinear relationships adds further complexity to the topology inference problem. Among the latest methods that respond to this need is a topology inference one proposed by the authors, which estimates a possibly directed adjacency matrix in an online manner. Contrasting with previous approaches based on linear models, the considered model is able to explain nonlinear interactions between the agents in a network. The novelty in the considered method is the use of a derivative-reproducing property to enforce network sparsity, while reproducing kernels are used to model the nonlinear interactions. The aim of this paper is to present a thorough convergence analysis of this method. The analysis is proven to be sane both in the mean and mean square sense. In addition, stability conditions are devised to ensure the convergence of the analyzed method. △ Less

Submitted 28 April, 2021; originally announced April 2021.

Comments: 24 pages, 11 of which of which are supplementary material; 4 figures

Reflectivity of VUV-sensitive Silicon Photomultipliers in Liquid Xenon

Authors: M. Wagenpfeil, T. Ziegler, J. Schneider, A. Fieguth, M. Murra, D. Schulte, L. Althueser, C. Huhmann, C. Weinheimer, T. Michel, G. Anton, G. Adhikari, S. Al Kharusi, E. Angelico, I. J. Arnquist, I. Badhrees, J. Bane, D. Beck, V. Belov, T. Bhatta, A. Bolotnikov, P. A. Breur, J. P. Brodsky, E. Brown, T. Brunner , et al. (118 additional authors not shown)

Abstract: Silicon photomultipliers are regarded as a very promising technology for next-generation, cutting-edge detectors for low-background experiments in particle physics. This work presents systematic reflectivity studies of Silicon Photomultipliers (SiPM) and other samples in liquid xenon at vacuum ultraviolet (VUV) wavelengths. A dedicated setup at the University of Münster has been used that allows t… ▽ More Silicon photomultipliers are regarded as a very promising technology for next-generation, cutting-edge detectors for low-background experiments in particle physics. This work presents systematic reflectivity studies of Silicon Photomultipliers (SiPM) and other samples in liquid xenon at vacuum ultraviolet (VUV) wavelengths. A dedicated setup at the University of Münster has been used that allows to acquire angle-resolved reflection measurements of various samples immersed in liquid xenon with 0.45° angular resolution. Four samples are investigated in this work: one Hamamatsu VUV4 SiPM, one FBK VUV-HD SiPM, one FBK wafer sample and one Large-Area Avalanche Photodiode (LA-APD) from EXO-200. The reflectivity is determined to be 25-36% at an angle of incidence of 20° for the four samples and increases to up to 65% at 70° for the LA-APD and the FBK samples. The Hamamatsu VUV4 SiPM shows a decline with increasing angle of incidence. The reflectivity results will be incorporated in upcoming light response simulations of the nEXO detector. △ Less

Submitted 26 May, 2021; v1 submitted 16 April, 2021; originally announced April 2021.

Comments: 18 pages, 11 figures

Expanding Cybersecurity Knowledge Through an Indigenous Lens: A First Look

Authors: Farrah Huntinghawk, Candace Richard, Sarah Plosker, Gautam Srivastava

Abstract: Decolonization and Indigenous education are at the forefront of Canadian content currently in Academia. Over the last few decades, we have seen some major changes in the way in which we share information. In particular, we have moved into an age of electronically-shared content, and there is an increasing expectation in Canada that this content is both culturally significant and relevant. In this… ▽ More Decolonization and Indigenous education are at the forefront of Canadian content currently in Academia. Over the last few decades, we have seen some major changes in the way in which we share information. In particular, we have moved into an age of electronically-shared content, and there is an increasing expectation in Canada that this content is both culturally significant and relevant. In this paper, we discuss an ongoing community engagement initiative with First Nations communities in the Western Manitoba region. The initiative involves knowledge-sharing activities that focus on the topic of cybersecurity, and are aimed at a public audience. This initial look into our educational project focuses on the conceptual analysis and planning stage. We are developing a "Cybersecurity 101" mini-curriculum, to be implemented over several one-hour long workshops aimed at diverse groups (these public workshops may include a wide range of participants, from tech-adverse to tech-savvy). Learning assessment tools have been built in to the workshop program. We have created informational and promotional pamphlets, posters, lesson plans, and feedback questionnaires which we believe instill relevance and personal connection to this topic, helping to bridge gaps in accessibility for Indigenous communities while striving to build positive, reciprocal relationships. Our methodology is to approach the subject from a community needs and priorities perspective. Activities are therefore being tailored to fit each community. △ Less

Submitted 30 March, 2021; originally announced April 2021.

Comments: 9 pages, 0 figures

Journal ref: 2020 IEEE CCECE, London, ON, Canada, 2020, pp. 1-4

Fast Unmixing and Change Detection in Multitemporal Hyperspectral Data

Authors: Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez, Cédric Richard

Abstract: Multitemporal spectral unmixing (SU) is a powerful tool to process hyperspectral image (HI) sequences due to its ability to reveal the evolution of materials over time and space in a scene. However, significant spectral variability is often observed between collection of images due to variations in acquisition or seasonal conditions. This characteristic has to be considered in the design of SU alg… ▽ More Multitemporal spectral unmixing (SU) is a powerful tool to process hyperspectral image (HI) sequences due to its ability to reveal the evolution of materials over time and space in a scene. However, significant spectral variability is often observed between collection of images due to variations in acquisition or seasonal conditions. This characteristic has to be considered in the design of SU algorithms. Because of its good performance, the multiple endmember spectral mixture analysis algorithm (MESMA) has been recently used to perform SU in multitemporal scenarios arising in several practical applications. However, MESMA does not consider the relationship between the different HIs, and its computational complexity is extremely high for large spectral libraries. In this work, we propose an efficient multitemporal SU method that exploits the high temporal correlation between the abundances to provide more accurate results at a lower computational complexity. We propose to solve the complex general multitemporal SU problem by separately addressing the endmember selection and the abundance estimation problems. This leads to a simpler solution without sacrificing the accuracy of the results. We also propose a strategy to detect and address abrupt abundance variations in time. Theoretical results demonstrate how the proposed method compares to MESMA in terms of quality, and how effective it is in detecting abundance changes. This analysis provides valuable insight into the conditions under which the algorithm succeeds. Simulation results show that the proposed method achieves state-of-the-art performance at a smaller computational cost. △ Less

Submitted 9 September, 2021; v1 submitted 6 April, 2021; originally announced April 2021.

Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

Authors: Wei Gao, Jie Chen, Cédric Richard

Abstract: Convergence of the diffusion RLS (DRLS) algorithm to steady-state has been extensively studied in the literature, whereas no analysis of its transient convergence behavior has been reported yet. In this letter, we conduct a theoretical analysis of the transient behavior of the DRLS algorithm for cyclostationary colored inputs, in the mean and mean-square error sense. The resulting analytical model… ▽ More Convergence of the diffusion RLS (DRLS) algorithm to steady-state has been extensively studied in the literature, whereas no analysis of its transient convergence behavior has been reported yet. In this letter, we conduct a theoretical analysis of the transient behavior of the DRLS algorithm for cyclostationary colored inputs, in the mean and mean-square error sense. The resulting analytical models allows us to thoroughly investigate the convergence behavior of the algorithm over adaptive networks in such complex scenarios. Simulation results support the accuracy and correctness of the theoretical findings. △ Less

Submitted 12 January, 2021; originally announced January 2021.

Comments: 5 pages, 2 figures

Hyperspectral Image Super-Resolution via Deep Prior Regularization with Parameter Estimation

Authors: Xiuheng Wang, Jie Chen, Qi Wei, Cédric Richard

Abstract: Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional image of the same scene to obtain an HR HSI. In this work, we propose a method that integrates a physical model and deep prior information. Specifically, a novel,… ▽ More Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional image of the same scene to obtain an HR HSI. In this work, we propose a method that integrates a physical model and deep prior information. Specifically, a novel, yet effective two-stream fusion network is designed to serve as a {regularizer} for the fusion problem. This fusion problem is formulated as an optimization problem whose solution can be obtained by solving a Sylvester equation. Furthermore, the regularization parameter is simultaneously estimated to automatically adjust contribution of the physical model and {the} learned prior to reconstruct the final HR HSI. Experimental results on {both simulated and real data} demonstrate the superiority of the proposed method over other state-of-the-art methods on both quantitative and qualitative comparisons. △ Less

Submitted 24 April, 2021; v1 submitted 9 September, 2020; originally announced September 2020.

Comments: IEEE Trans.Circuits Syst, Video Technol., to be published. Manuscript submitted October 13, 2020; revised December 3, 2020 and April 9, 2021; accepted April 24, 2021

Coupled Tensor Decomposition for Hyperspectral and Multispectral Image Fusion with Inter-Image Variability

Authors: Ricardo Augusto Borsoi, Clémence Prévost, Konstantin Usevich, David Brie, José Carlos Moreira Bermudez, Cédric Richard

Abstract: Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based approaches previously proposed assume that the different observed images are acquired under exactly the same conditions. A recent work proposed to accommodate inter-imag… ▽ More Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based approaches previously proposed assume that the different observed images are acquired under exactly the same conditions. A recent work proposed to accommodate inter-image spectral variability in the image fusion problem using a matrix factorization-based formulation, but did not account for spatially-localized variations. Moreover, it lacks theoretical guarantees and has a high associated computational complexity. In this paper, we consider the image fusion problem while accounting for both spatially and spectrally localized changes in an additive model. We first study how the general identifiability of the model is impacted by the presence of such changes. Then, assuming that the high-resolution image and the variation factors admit a Tucker decomposition, two new algorithms are proposed -- one purely algebraic, and another based on an optimization procedure. Theoretical guarantees for the exact recovery of the high-resolution image are provided for both algorithms. Experimental results show that the proposed method outperforms state-of-the-art methods in the presence of spectral and spatial variations between the images, at a smaller computational cost. △ Less

Submitted 5 December, 2020; v1 submitted 30 June, 2020; originally announced June 2020.

Online Graph-Based Change Point Detection in Multiband Image Sequences

Authors: Ricardo Augusto Borsoi, Cédric Richard, André Ferrari, Jie Chen, José Carlos Moreira Bermudez

Abstract: The automatic detection of changes or anomalies between multispectral and hyperspectral images collected at different time instants is an active and challenging research topic. To effectively perform change-point detection in multitemporal images, it is important to devise techniques that are computationally efficient for processing large datasets, and that do not require knowledge about the natur… ▽ More The automatic detection of changes or anomalies between multispectral and hyperspectral images collected at different time instants is an active and challenging research topic. To effectively perform change-point detection in multitemporal images, it is important to devise techniques that are computationally efficient for processing large datasets, and that do not require knowledge about the nature of the changes. In this paper, we introduce a novel online framework for detecting changes in multitemporal remote sensing images. Acting on neighboring spectra as adjacent vertices in a graph, this algorithm focuses on anomalies concurrently activating groups of vertices corresponding to compact, well-connected and spectrally homogeneous image regions. It fully benefits from recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Moreover, the graph is estimated directly from the images using superpixel decomposition algorithms. The learning algorithm is scalable in the sense that it is efficient and spatially distributed. Experiments illustrate the detection and localization performance of the method. △ Less

Submitted 24 June, 2020; originally announced June 2020.

Diffusion LMS with Communication Delays: Stability and Performance Analysis

Authors: Fei Hua, Roula Nassif, Cédric Richard, Haiyan Wang, Ali H. Sayed

Abstract: We study the problem of distributed estimation over adaptive networks where communication delays exist between nodes. In particular, we investigate the diffusion Least-Mean- Square (LMS) strategy where delayed intermediate estimates (due to the communication channels) are employed during the combination step. One important question is: Do the delays affect the stability condition and performance?… ▽ More We study the problem of distributed estimation over adaptive networks where communication delays exist between nodes. In particular, we investigate the diffusion Least-Mean- Square (LMS) strategy where delayed intermediate estimates (due to the communication channels) are employed during the combination step. One important question is: Do the delays affect the stability condition and performance? To answer this question, we conduct a detailed performance analysis in the mean and in the mean-square-error sense of the diffusion LMS with delayed estimates. Stability conditions, transient and steady-state mean-square-deviation (MSD) expressions are provided. One of the main findings is that diffusion LMS with delays can still converge under the same step-sizes condition of the diffusion LMS without delays. Finally, simulation results illustrate the theoretical findings. △ Less

Submitted 19 April, 2020; originally announced April 2020.

Comments: to appear in IEEE Signal Processing Letters

Affine Combination of Diffusion Strategies over Networks

Authors: Danqi Jin, Jie Chen, Cedric Richard, Jingdong Chen, Ali H. Sayed

Abstract: Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strategies for enhanced performance. By assigning a combination coefficient to each node, and using an adaptation mechanism to minimize the network er… ▽ More Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strategies for enhanced performance. By assigning a combination coefficient to each node, and using an adaptation mechanism to minimize the network error, we obtain a combined diffusion strategy that benefits from the best characteristics of all component strategies simultaneously in terms of excess-mean-square error (EMSE). Analyses of the universality are provided to show the superior performance of affine combination scheme and to characterize its behavior in the mean and mean-square sense. Simulation results are presented to demonstrate the effectiveness of the proposed strategies, as well as the accuracy of theoretical findings. △ Less

Submitted 8 February, 2020; originally announced February 2020.

Comments: 31 pages

Online change-point detection with kernels

Authors: André Ferrari, Cédric Richard, Anthony Bourrier, Ikram Bouchikhi

Abstract: Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds, or intrusions into networks. Recently the authors introduced an online kernel-based change-point detection method built upon direct estimation of the density r… ▽ More Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds, or intrusions into networks. Recently the authors introduced an online kernel-based change-point detection method built upon direct estimation of the density ratio on consecutive time intervals. This paper further investigates this algorithm, making improvements and analyzing its behavior in the mean and mean square sense, in the absence and presence of a change point. These theoretical analyses are validated with Monte Carlo simulations. The detection performance of the algorithm is illustrated through experiments on real-world data and compared to state of the art methodologies. △ Less

Submitted 9 September, 2021; v1 submitted 7 February, 2020; originally announced February 2020.

Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review

Authors: Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez, Cédric Richard, Jocelyn Chanussot, Lucas Drumetz, Jean-Yves Tourneret, Alina Zare, Christian Jutten

Abstract: The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout t… ▽ More The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of its results. Therefore, large efforts have been recently dedicated to mitigate the effects of spectral variability in SU. This resulted in the development of algorithms that incorporate different strategies to allow the EMs to vary within a hyperspectral image, using, for instance, sets of spectral signatures known a priori, Bayesian, parametric, or local EM models. Each of these approaches has different characteristics and underlying motivations. This paper presents a comprehensive literature review contextualizing both classic and recent approaches to solve this problem. We give a detailed evaluation of the sources of spectral variability and their effect in image spectra. Furthermore, we propose a new taxonomy that organizes existing works according to a practitioner's point of view, based on the necessary amount of supervision and on the computational cost they require. We also review methods used to construct spectral libraries (which are required by many SU techniques) based on the observed hyperspectral image, as well as algorithms for library augmentation and reduction. Finally, we conclude the paper with some discussions and an outline of possible future directions for the field. △ Less

Submitted 6 April, 2021; v1 submitted 20 January, 2020; originally announced January 2020.

Comments: Published at the IEEE Geoscience and Remote Sensing Magazine

Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning

Authors: Roula Nassif, Stefan Vlaski, Cedric Richard, Jie Chen, Ali H. Sayed

Abstract: The problem of learning simultaneously several related tasks has received considerable attention in several domains, especially in machine learning with the so-called multitask learning problem or learning to learn problem [1], [2]. Multitask learning is an approach to inductive transfer learning (using what is learned for one problem to assist in another problem) and helps improve generalization… ▽ More The problem of learning simultaneously several related tasks has received considerable attention in several domains, especially in machine learning with the so-called multitask learning problem or learning to learn problem [1], [2]. Multitask learning is an approach to inductive transfer learning (using what is learned for one problem to assist in another problem) and helps improve generalization performance relative to learning each task separately by using the domain information contained in the training signals of related tasks as an inductive bias. Several strategies have been derived within this community under the assumption that all data are available beforehand at a fusion center. However, recent years have witnessed an increasing ability to collect data in a distributed and streaming manner. This requires the design of new strategies for learning jointly multiple tasks from streaming data over distributed (or networked) systems. This article provides an overview of multitask strategies for learning and adaptation over networks. The working hypothesis for these strategies is that agents are allowed to cooperate with each other in order to learn distinct, though related tasks. The article shows how cooperation steers the network limiting point and how different cooperation rules allow to promote different task relatedness models. It also explains how and when cooperation over multitask networks outperforms non-cooperative strategies. △ Less

Submitted 21 September, 2021; v1 submitted 7 January, 2020; originally announced January 2020.

Kalman Filtering and Expectation Maximization for Multitemporal Spectral Unmixing

Authors: Ricardo Augusto Borsoi, Tales Imbiriba, Pau Closas, José Carlos Moreira Bermudez, Cédric Richard

Abstract: The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications presses for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember representations to account for temporal spectral variability. By representing the multitemporal mixing proces… ▽ More The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications presses for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember representations to account for temporal spectral variability. By representing the multitemporal mixing process using a state-space formulation, we are able to exploit the Bayesian filtering machinery to estimate the endmember variability coefficients. Moreover, by assuming that the temporal variability of the abundances is small over short intervals, an efficient implementation of the expectation maximization (EM) algorithm is employed to estimate the abundances and the other model parameters. Simulation results indicate that the proposed strategy outperforms state-of-the-art multitemporal SU algorithms. △ Less

Submitted 12 August, 2020; v1 submitted 2 January, 2020; originally announced January 2020.

Online Distributed Learning over Graphs with Multitask Graph-Filter Models

Authors: Fei Hua, Roula Nassif, Cédric Richard, Haiyan Wang, Ali H. Sayed

Abstract: In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graph-shift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an ill-… ▽ More In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graph-shift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an ill-conditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and mean-square sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results. △ Less

Submitted 12 December, 2019; originally announced December 2019.

Comments: 14 pages, 13 figures

Measurements of a 2.1 MeV H$^-$ beam with an Allison scanner

Authors: C. Richard, J. -P. Carneiro, B. Hanna, L. Prost, A. Saini, V. Scarpine, A. Shemyakin

Abstract: Transverse 2D phase space distribution of a 2.1 MeV, 5 mA H$^-$ beam is measured at the PIPIT test accelerator at Fermilab with an Allison scanner. The paper describes the design, calibration, and performance of the scanner as well as the main results of the beam measurements. Analyses of the recorded phase portraits are performed primarily in action-phase coordinates; the stability of the action… ▽ More Transverse 2D phase space distribution of a 2.1 MeV, 5 mA H$^-$ beam is measured at the PIPIT test accelerator at Fermilab with an Allison scanner. The paper describes the design, calibration, and performance of the scanner as well as the main results of the beam measurements. Analyses of the recorded phase portraits are performed primarily in action-phase coordinates; the stability of the action under linear optics makes it easier to compare measurements taken with different beamline conditions, e.g. in various locations. The intensity of a single measured point (\pixel") is proportional to the phase density in the corresponding portion of the beam. When the Twiss parameters are calculated using only the high-phase density part of the beam, the pixel intensity in the beam core is found to be decreasing exponentially with action and to be phase-independent. Outside of the core, the intensities decrease with action at a significantly slower rate than in the core. This `tail' comprises 10-30% of the beam, with 0.1% of the total measured intensity extending beyond the action 10-20 times larger than the rms emittance. The transition from the core to the tail is accompanied by the appearance of a strong phase dependence, which is characterized in action-phase coordinates by two `branches' extending beyond the core. A set of selected measurements shows, in part, that there is no measurable emittance dilution along the beam line in the main portion of the beam; the beam parameters are practically constant over a 0.5 ms pulse; and scraping in various parts of the beam line is an effective way to decrease the transverse tails by removing the branches. △ Less

Submitted 6 December, 2019; originally announced December 2019.