Freeze-in, glaciation, and UV sensitivity from light mediators

Dark matter (DM) freeze-in through a light mediator is an appealing model with excellent detection prospects at current and future experiments. Light mediator freeze-in is UV-insensitive insofar as most DM is produced at late times, and thus the DM abundance does not depend on the unknown early evolution of our universe. However the final DM yield retains a dependence on the initial DM population, which is usually assumed to be exactly zero. We point out that in models with light mediators, the final DM yield will also depend on the initial conditions assumed for the light mediator population. We describe a class of scenarios we call "glaciation" where DM freezing in from the SM encounters a pre-existing thermal bath of mediators, and study the dependence of the final DM yield on the initial temperature of this dark radiation bath. To compute DM scattering rates in this cosmology, we derive for the first time an exact integral expression for the Boltzmann collision term describing interactions between two species at different temperatures. We quantify the dependence of the DM yield on the initial dark temperature and find that it can be sizeable in regions near the traditional (zero initial abundance) freeze-in curve. We generalize the freeze-in curve to a glaciation band, which can extend as much as an order of magnitude below the traditional freeze-in direct detection target, and point out that the DM phase space distribution as well as the yield can be strongly dependent on initial conditions.Comment: 31 pages, 5 figure

Gradient waveform design for variable density sampling in Magnetic Resonance Imaging

Fast coverage of k-space is a major concern to speed up data acquisition in Magnetic Resonance Imaging (MRI) and limit image distortions due to long echo train durations. The hardware gradient constraints (magnitude, slew rate) must be taken into account to collect a sufficient amount of samples in a minimal amount of time. However, sampling strategies (e.g., Compressed Sensing) and optimal gradient waveform design have been developed separately so far. The major flaw of existing methods is that they do not take the sampling density into account, the latter being central in sampling theory. In particular, methods using optimal control tend to agglutinate samples in high curvature areas. In this paper, we develop an iterative algorithm to project any parameterization of k-space trajectories onto the set of feasible curves that fulfills the gradient constraints. We show that our projection algorithm provides a more efficient alternative than existinf approaches and that it can be a way of reducing acquisition time while maintaining sampling density for piece-wise linear trajectories

A projection algorithm for gradient waveforms design in Magnetic Resonance Imaging

International audienceCollecting the maximal amount of information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, ...), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g. spiral, radial lines, ...) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time

A projection method on measures sets

We consider the problem of projecting a probability measure π on a set MN of Radon measures. The projection is defined as a solution of the following variational problem: inf µ∈M N h (µ − π) 2 2 , where h ∈ L 2 (Ω) is a kernel, Ω ⊂ R d and denotes the convolution operator. To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with N dots) or continuous line drawing (representing an image with a continuous line). We provide a necessary and sufficient condition on the sequence (MN) N ∈N that ensures weak convergence of the projections (µ * N) N ∈N to π. We then provide a numerical algorithm to solve a discretized version of the problem and show several illustrations related to computer-assisted synthesis of artistic paintings/drawings

A projection algorithm on measures sets

We consider the problem of projecting a probability measure $\pi$ on a set $\mathcal{M}_N$ of Radon measures. The projection is defined as a solution of the following variational problem:\begin{equation*}\inf_{\mu\in \mathcal{M}_N} \|h\star (\mu - \pi)\|_2^2,\end{equation*}where $h\in L^2(\Omega)$ is a kernel, $\Omega\subset \R^d$ and $\star$ denotes the convolution operator.To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with $N$ dots) or continuous line drawing (representing an image with a continuous line).We provide a necessary and sufficient condition on the sequence $(\mathcal{M}_N)_{N\in \N}$ that ensures weak convergence of the projections $(\mu^*_N)_{N\in \N}$ to $\pi$.We then provide a numerical algorithm to solve a discretized version of the problem and show several illustrations related to computer-assisted synthesis of artistic paintings/drawings

Comment représenter une image avec un spaghetti ?

International audienceWe study the problem of projecting a given measure on a set of pushforward measures associated with some classes of parameterizedfunctions. We propose an original numerical algorithm to solve the problem based on an analogy with an attraction-repulsion problem. Thiswork is an extension of some recent stippling results that enables us to represent images with continuous curves.Nous étudions ici le problème de projection d'une mesure sur un ensemble de mesures discrètes (une somme de Diracs). Des contraintes cinématiques sur la position des points nous permettent d'étendre ce problème de projection à des courbes discrètes. Nous proposons une analogie physique de ce problème avec la répartition de charges ponctuelles dans un potentiel. Ceci nous permet de proposer un algorithme pour déterminer une configuration de Diracs visuellement satisfaisante. Notre problème de projection généralise les résultats de stippling existants qui permettent la représentation d'images à partir de points isolés. Abstract – We study the problem of projecting a given measure on a set of pushforward measures associated with some classes of parameterized functions. We propose an original numerical algorithm to solve the problem based on an analogy with an attraction-repulsion problem. This work is an extension of some recent stippling results that enables us to represent images with continuous curves

Sur la génération de schémas d'échantillonnage compressé en IRM

International audienceThis article contains two contributions. First, we describe the state-of-the-art theories in compressed sensing for Magnetic ResonanceImaging (MRI). This allows us to bring out important principles that should guide the generation of sampling patterns. Second, wedescribe an original methodology to design efficient sampling schemes. It consists of projecting a sampling density on the space of feasiblemeasures for MRI. We end up by proposing comparisons to current sampling strategies on simulated data. This illustrates the well-foundednessof our approach.Cet article a deux finalités. Premièrement, nous proposons un état de l'art des théories d'échantillonnage compressé pour l'Imagerie par résonance magnétique (IRM). Ceci nous permet de dégager quelques grands principes à suivre pour générer des schémas performants en termes de temps d'acquisition et de qualité de reconstruction. Dans une deuxième partie, nous proposons une méthodologie originale de conception de schémas qui repose sur des algorithmes de projection de densités sur des espaces de mesures. Nous proposons finalement des comparaisons avec des stratégies actuelles d'échantillonnage sur des simulations et montrons ainsi le bien-fondé de notre approche. Abstract – This article contains two contributions. First, we describe the state-of-the-art theories in compressed sensing for Magnetic Resonance Imaging (MRI). This allows us to bring out important principles that should guide the generation of sampling patterns. Second, we describe an original methodology to design efficient sampling schemes. It consists of projecting a sampling density on the space of feasible measures for MRI. We end up by proposing comparisons to current sampling strategies on simulated data. This illustrates the well-foundedness of our approach

Unravelling the Dodecahedral Spaces

The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincar\'e homology sphere).Comment: 15 pages + 6 pages appendix, 7 figures, 4 table

The therapy of idiopathic pulmonary fibrosis: what is next?

Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive, fibrosing interstitial lung disease, characterised by progressive scarring of the lung and associated with a high burden of disease and early death. The pathophysiological understanding, clinical diagnostics and therapy of IPF have significantly evolved in recent years. While the recent introduction of the two antifibrotic drugs pirfenidone and nintedanib led to a significant reduction in lung function decline, there is still no cure for IPF; thus, new therapeutic approaches are needed. Currently, several clinical phase I–III trials are focusing on novel therapeutic targets. Furthermore, new approaches in nonpharmacological treatments in palliative care, pulmonary rehabilitation, lung transplantation, management of comorbidities and acute exacerbations aim to improve symptom control and quality of life. Here we summarise new therapeutic attempts and potential future approaches to treat this devastating disease