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Lactate is crucial in the brain, as it is involved in neuronal activity and memory formation. This is thought to be related to the astrocyte-neuron lactate shuttle hypothesis (ANLS), which has been debated for 30 years, not least because it is difficult to measure lactate compartmentation and exchange in vivo. In particular, while ANLS requires transfer of lactate via the extracellular space, intracellular/extracellular exchange rate remains unknown. In this work, we propose to use time-dependent diffusion MRS to assess lactate exchange and lactate compartmentation in mouse brain gray matter in vivo. First, by comparing lactate time-dependent diffusivity and kurtosis with those of water and purely intracellular metabolites (which exhibit "fast" and "no" exchange signatures, respectively), we estimate that lactate exchange is slow (i.e. on the order of hundreds of milliseconds). Then, using biophysical models neglecting exchange, we estimate extracellular, neuronal and astrocytic lactate fractions compatible with the ANLS hypothesis.

We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is sufficiently close to the identity, must be $\mathscr{C}^\infty$ definably diffeomorphic to $M$. The definable diffeomorphism between $N$ and $M$ is then provided by a tubular neighborhood of $M$., Comment: Final version

Given a bounded subanalytic submanifold of $\mathbb{R}^n$, possibly admitting singularities within its closure, we study the cohomology of $L^p$ differential forms having an $L^p$ exterior differential (in the sense of currents) and satisfying Dirichlet or Neumann condition. We show an $L^p$ Hodge decomposition theorem, an $L^p$ de Rham theorem, as well as a Lefschetz duality theorem between $L^p$ and $L^{p'}$ forms (with $\frac{1}{p}+\frac{1}{p'}=1$) in the case where $p$ is large or close to $1$. This is achieved by proving that de Rham's pairing between complementary $L^p$ differential forms induces a pairing between cohomology classes which is nondegenerate (for such $p$). The main difficulty to carry it out is to show the density (in Sobolev spaces of differential forms) of forms that vanish near some singularities and are smooth up to the closure of the underlying manifold in the case $p$ large (Theorem 4.1). This result, which is of independent interest, also makes it possible to give a trace theorem that leads us to some explicit characterizations of Dirichlet and Neumann conditions in terms of traces and residues.

Let $K$ be a locally compact field of characteristic 0. Let $G$ be a linear algebraic group defined over $K$, acting algebraically on an algebraic variety $V$. We prove that the action of $G(K)$ (the group of $K$-rational points of $G$) on $V(K)$ is topologically amenable, if and only if all points stabilizers in $G(K)$ are solvable-by-compact. This follows by combining a result by Borel-Serre \cite{BoSe} with the following fact: let $G$ be a second countable locally compact group acting continuously on a second countable locally compact space $Y$. If the action $G\curvearrowright Y$ is smooth (i.e. the Borel structure on $G\backslash Y$ is countably separated), then topological amenability of $G\curvearrowright Y$ is equivalent to amenability of all point stabilizers in $G$.

We will present a first step in design of a broadband physical model for microphones. Within the proposed model, classical directivity patterns (omnidirectional, bidirectional and cardioids family) are refound as limit cases: monochromatic excitation, low frequency and far-field approximation. Monophonic pieces of music are used as sources for the model so we can listen the simulation of the associated recorded sound field in realtime thanks to a Max/MSP application. Listening and subbands analysis show that the directivity is a function of frequential subband and source location. This model also exhibits an interesting proximity effect. Audio demonstrations will be given.Paper 6638 presented at the 120th Convention of the Audio Engineering Society, Paris, 2006

The unique irreducible representation of $\SL_2(\R)$ on $\R^n$ induces an action, called the \textit{linear action}, of $\SL_2(\Z)$ on the torus $\T^n$ for every $n\geq 2$. For $n$ odd, it factors through $\PSL_2(\Z)$, so we denote by $G_n$ the group $\SL_2(\Z)$ for $n$ even, and $\PSL_2(\Z)$ for $n$ odd. We prove that the action is free and ergodic for every $n\geq 2$, that if $h\in \SL_2(\Z)$ is a hyperbolic element and if $n$ is even, then the action of the subgroup generated by $h$ is still ergodic, but also that, for $n$ odd, no amenable subgroup of $\PSL_2(\Z)$ acts ergodically on $\T^n$. We deduce also that every ergodic sub-equivalence relation $\Rr$ of the orbital equivalence relation $\mathcal{S}_n$ of $G_n$ on $\T^n$ is either amenable or rigid, extending a result by Ioana for $n=2$. This result has the following corollaries: firstly, for $n\geq 2$ even, if $H$ is a maximal amenable subgroup of $\SL_2(\Z)$ containing an hyperbolic matrix, then the associated crossed product II$_1$ factor $L^\infty(\T^n)\rtimes H$ is a maximal Haagerup subalgebra of $L^\infty(\T^n)\rtimes \SL_2(\Z)$; secondly , for every $n$, the fundamental group of $L^\infty(\T^n)\rtimes G_n$ is trivial., Comment: Section 3.2 fully re-written due to gap detected in the original version. Revised version to appear in Journal of Operator Theory

We introduce the French Land cover from Aerospace ImageRy (FLAIR), an extensive dataset from the French National Institute of Geographical and Forest Information (IGN) that provides a unique and rich resource for large-scale geospatial analysis. FLAIR contains high-resolution aerial imagery with a ground sample distance of 20 cm and over 20 billion individually labeled pixels for precise land-cover classification. The dataset also integrates temporal and spectral data from optical satellite time series. FLAIR thus combines data with varying spatial, spectral, and temporal resolutions across over 817 km2 of acquisitions representing the full landscape diversity of France. This diversity makes FLAIR a valuable resource for the development and evaluation of novel methods for large-scale land-cover semantic segmentation and raises significant challenges in terms of computer vision, data fusion, and geospatial analysis. We also provide powerful uni- and multi-sensor baseline models that can be employed to assess algorithm's performance and for downstream applications. Through its extent and the quality of its annotation, FLAIR aims to spur improvements in monitoring and understanding key anthropogenic development indicators such as urban growth, deforestation, and soil artificialization. Dataset and codes can be accessed at https://ignf.github.io/FLAIR/, Comment: NeurIPS 2023 - Datasets & Benchmarks Track

We analyse the signature and origin of transient structures embedded in the slow solar wind, and observed by the Wide-Field Imager for Parker Solar Probe (WISPR) during its first ten passages close to the Sun. WISPR provides a new in-depth vision on these structures, which have long been speculated to be a remnant of the pinch-off magnetic reconnection occurring at the tip of helmet streamers. We pursued the previous modelling works of Reville (2020b, 2022) that simulate the dynamic release of quasi-periodic density structures into the slow wind through a tearing-induced magnetic reconnection at the tip of helmet streamers. Synthetic WISPR white-light (WL) images are produced using a newly developed advanced forward modelling algorithm that includes an adaptive grid refinement to resolve the smallest transient structures in the simulations. We analysed the aspect and properties of the simulated WL signatures in several case studies that are typical of solar minimum and near-maximum configurations. Quasi-periodic density structures associated with small-scale magnetic flux ropes are formed by tearing-induced magnetic reconnection at the heliospheric current sheet and within 3-7Rs. Their appearance in WL images is greatly affected by the shape of the streamer belt and the presence of pseudo-streamers. The simulations show periodicities on ~90-180min, ~7-10hr and ~25-50hr timescales, which are compatible with WISPR and past observations. This work shows strong evidence for a tearing-induced magnetic reconnection contributing to the long-observed high variability of the slow solar wind., Comment: 23 pages, 14 figures, to appear in Astronomy & Astrophysics, associated movies available at https://doi.org/10.5281/zenodo.8135595

Water diffusion MRI is a very powerful tool for probing tissue microstructure, but disentangling the contribution of compartment-specific structural disorder from cellular restriction and inter-compartment exchange remains an open challenge. Here, we use diffusion MR spectroscopy (dMRS) of water and metabolites as a function of diffusion time in vivo in mouse Gray Matter (GM) to shed light on: which of these concomitant mechanisms dominates the MR measurements and with which specific signature. We report the diffusion time-dependence of water with excellent SNR conditions up to 500 ms. Water kurtosis decreases with increasing diffusion time, showing the concomitant influence of both structural disorder and exchange. Despite the excellent SNR, we were not able to identify clearly the nature of the structural disorder (i.e. 1D versus 2D/3D short-range disorder). Measurements of intracellular metabolites diffusion time-dependence (up to 500 ms) show opposite behavior to water, with metabolites kurtosis increasing as a function of diffusion time. We show that this is a signature of diffusion restricted in the intracellular space from which cellular microstructural features can be estimated. Finally, by comparing water and metabolites diffusion time-dependencies, we attempt to disentangle the effect of intra/extracellular exchange and structural disorder of the extracellular space (both impacting water diffusion only). Our results suggest a relatively short intra/extracellular exchange time (1-50 ms) and short-range disorder (still unclear if 1D or 2D/3D) most likely coming from the extracellular compartment. This work provides novel insights to interpret water diffusion time-dependent measurements in terms of the underlying GM microstructure and suggests that diffusion time-dependent measurements of intracellular metabolites may offer a new way to quantify microstructural restrictions in GM.

The FLAIR #2 dataset hereby presented includes two very distinct types of data, which are exploited for a semantic segmentation task aimed at mapping land cover. The data fusion workflow proposes the exploitation of the fine spatial and textural information of very high spatial resolution (VHR) mono-temporal aerial imagery and the temporal and spectral richness of high spatial resolution (HR) time series of Copernicus Sentinel-2 satellite images. The French National Institute of Geographical and Forest Information (IGN), in response to the growing availability of high-quality Earth Observation (EO) data, is actively exploring innovative strategies to integrate these data with heterogeneous characteristics. IGN is therefore offering this dataset to promote innovation and improve our knowledge of our territories.

Brain cell structure and function reflect neurodevelopment, plasticity and ageing, and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to non-invasively disentangle cellular structural features are needed and are a substantial focus of brain research. Diffusion-weighted MR spectroscopy (dMRS) gives access to diffusion properties of endogenous intracellular brain metabolites that are preferentially located inside specific brain cell populations. Despite its great potential, dMRS remains a challenging technique on all levels: from the data acquisition to the analysis, quantification, modelling and interpretation of results. These challenges were the motivation behind the organisation of the Lorentz Workshop on 'Best Practices and Tools for Diffusion MR Spectroscopy' held in Leiden in September 2021. During the workshop, the dMRS community established a set of recommendations to execute robust dMRS studies. This paper provides a description of the steps needed for acquiring, processing, fitting and modelling dMRS data and provides links to useful resources., Comment: 49 pages, 5 figures, 5 tables, supplementary material

Facial expression generation is one of the most challenging and long-sought aspects of character animation, with many interesting applications. The challenging task, traditionally having relied heavily on digital craftspersons, remains yet to be explored. In this paper, we introduce a generative framework for generating 3D facial expression sequences (i.e. 4D faces) that can be conditioned on different inputs to animate an arbitrary 3D face mesh. It is composed of two tasks: (1) Learning the generative model that is trained over a set of 3D landmark sequences, and (2) Generating 3D mesh sequences of an input facial mesh driven by the generated landmark sequences. The generative model is based on a Denoising Diffusion Probabilistic Model (DDPM), which has achieved remarkable success in generative tasks of other domains. While it can be trained unconditionally, its reverse process can still be conditioned by various condition signals. This allows us to efficiently develop several downstream tasks involving various conditional generation, by using expression labels, text, partial sequences, or simply a facial geometry. To obtain the full mesh deformation, we then develop a landmark-guided encoder-decoder to apply the geometrical deformation embedded in landmarks on a given facial mesh. Experiments show that our model has learned to generate realistic, quality expressions solely from the dataset of relatively small size, improving over the state-of-the-art methods. Videos and qualitative comparisons with other methods can be found at \url{https://github.com/ZOUKaifeng/4DFM}.

For $n\geq 1$, let $\rho_n$ denote the standard action of $GL_2(\Z)$ on the space $P_n(\Z)\simeq\Z^{n+1}$ of homogeneous polynomials of degree $n$ in two variables, with integer coefficients. For $G$ a non-amenable subgroup of $GL_2(\Z)$, we describe the maximal Haagerup subgroups of the semi-direct product $\Z^{n+1}\rtimes_{\rho_n} G$, extending the classification of Jiang-Skalski \cite{JiSk} of the maximal Haagerup subgroups in $\Z^2\rtimes SL_2(\Z)$. We prove that, for $n$ odd, the group $P_n(\Z)\rtimes SL_2(\Z)$ admits infinitely many pairwise non-conjugate maximal Haagerup subgroups which are free groups; and that, for $n$ even, the group $P_n(\Z)\rtimes GL_2(\Z)$ admits infinitely many pairwise non-conjugate maximal Haagerup subgroups which are isomorphic to $SL_2(\Z)$., Comment: Third version, with classification of maximal amenable subgroups of $SL_2(\mathbb{Z})$

We consider the semi-direct products $G=\mathbb Z^2\rtimes GL_2(\mathbb Z), \mathbb Z^2\rtimes SL_2(\mathbb Z)$ and $\mathbb Z^2\rtimes\Gamma(2)$ (where $\Gamma(2)$ is the congruence subgroup of level 2). For each of them, we compute both sides of the Baum-Connes conjecture, namely the equivariant $K$-homology of the classifying space $\underline{E}G$ for proper actions on the left-hand side, and the analytical K-theory of the reduced group $C^*$-algebra on the right-hand side. The computation of the LHS is made possible by the existence of a 3-dimensional model for $\underline{E}G$, which allows to replace equivariant K-homology by Bredon homology. We pay due attention to the presence of torsion in $G$, leading to an extensive study of the wallpaper groups associated with finite subgroups. For the second and third groups, the computations in $K_0$ provide explicit generators that are matched by the Baum-Connes assembly map.

This is a semi-survey paper, where we start by advertising Tits' synthetic construction from \cite{Tits}, of the hyperbolic plane $H^2(Cay)$ over the Cayley numbers $Cay$, and of its automorphism group which is the exceptional simple Lie group $G=F_{4(-20)}$. Let $G=KAN$ be the Iwasawa decomposition. Our contributions are: a) Writing down explicitly the action of $N$ on $H^2(Cay)$ in Tits'model, facing the lack of associativity of $Cay$. b) If $MAN$ denotes the minimal parabolic subgroup of $G$, characterizing $M$ geometrically.

Aggregation and disaggregation of clusters of attractive particles under flow are studied from numerical and theoretical points of view. Two-dimensional molecular dynamics simulations of both Couette and Poiseuille flows highlight the growth of the average steady-state cluster size as a power law of the adhesion number, a dimensionless number that quantifies the ratio of attractive forces to shear stress. Such a power-law scaling results from the competition between aggregation and disaggregation processes, as already reported in the literature. Here, we rationalize this behavior through a model based on an energy function, which minimization yields the power-law exponent in terms of the cluster fractal dimension, in good agreement with the present simulations and with previous works., Comment: 13 pages, 6 figures

We prove a trace formula for integration by parts on subanalytic bounded submanifolds of $\mathbb{R}^n$, possibly non closed. We also establish density results for $\mathbf{W}^{1,p}_\nabla (M)$, $M$ bounded subanalytic manifold, which is the space of the $L^p$ tangent vector fields $v$ on $M$ for which $\nabla v$ is $L^p$, where $\nabla$ is the divergence operator. We derive from these results some theorems of existence and uniqueness of solutions of the Laplace equation with Dirichlet and Neumann boundary type conditions. We then study the $p$-Laplace equation, for $p\in [1,\infty)$ large., Comment: Minor changes in the last section

We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally show, given a definable family of domains $(\Omega_t)_{t\in \mathbb{R}^k}$, that the constant of this inequality remains bounded, if so does the volume of $\Omega_t$.

Colloidal suspensions and the relation between their rheology and their microstructure is investigated. The literature showed great evidence of the relation between rheological quantities and particle volume fraction, ignoring the influence of the cluster. We propose to extend previous models using a new double fractal structure which allows, first, to recover the well-known models on the case of percolated system and, second, to capture the influence of the cluster size. This new model emphasises the necessity of such structure to account for recent experimental results. Then, the model is compared with data coming from the literature and shows close agreement., Comment: 5 pages, 3 figures, 1 table, letter

We prove that if $M\subset \mathbb{R}^n$ is a bounded subanalytic submanifold of $\mathbb{R}^n$ such that $B(x_0,\epsilon)\cap M$ is connected for every $x_0\in\overline{M}$ and $\epsilon>0$ small, then, for $p\in [1,\infty)$ sufficiently large, the space $C^\infty(\overline{M})$ is dense in the Sobolev space $W^{1,p}(M)$. We also show that for $p$ large, if $A\subset \overline{M}\setminus M$ is subanalytic then the restriction mapping $ C^\infty(\overline{M})\ni u\mapsto u_{|A}\in L^p(A)$ is continuous (if $A$ is endowed with the Hausdorff measure), which makes it possible to define a trace operator, and then prove that compactly supported functions are dense in the kernel of this operator. We finally generalize these results to the case where our assumption of connectedness at singular points of $\overline{M}$ is dropped.

Let $\Omega$ be a subanalytic bounded open subset of $\mathbb{R}^n$, with possibly singular boundary. We show that given $p\in [1,\infty)$, there is a constant $C$ such that for any $u\in W^{1,p}(\Omega)$ we have $||u-u_{\Omega}||_{L^p} \le C||\nabla u||_{L^p},$ where we have set $u_{\Omega}:=\frac{1}{|\Omega|}\int_{\Omega} u.$, Comment: final version

By highlighting the regions of the input image that contribute the most to the decision, saliency maps have become a popular method to make neural networks interpretable. In medical imaging, they are particularly well-suited to explain neural networks in the context of abnormality localization. However, from our experiments, they are less suited to classification problems where the features that allow to distinguish between the different classes are spatially correlated, scattered and definitely non-trivial. In this paper we thus propose a new paradigm for better interpretability. To this end we provide the user with relevant and easily interpretable information so that he can form his own opinion. We use Disentangled Variational Auto-Encoders which latent representation is divided into two components: the non-interpretable part and the disentangled part. The latter accounts for the categorical variables explicitly representing the different classes of interest. In addition to providing the class of a given input sample, such a model offers the possibility to transform the sample from a given class to a sample of another class, by modifying the value of the categorical variables in the latent representation. This paves the way to easier interpretation of class differences. We illustrate the relevance of this approach in the context of automatic sex determination from hip bones in forensic medicine. The features encoded by the model, that distinguish the different classes were found to be consistent with expert knowledge.

Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R^3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces.

These notes focus on the Lipschitz geometry of sets that are definable in o-minimal structures (expanding the real field). We show that every set which is definable in a polynomially bounded o-minimal structure admits a stratification which is locally definably bi-Lipschitz trivial along the strata. This result is obtained as a byproduct of two foregoing results of the author. The first one asserts that, given a family definable in an o-minimal structure, there is a regular vector, up to a definable family of bi-Lipschitz homeomorphisms. The second one is a bi-Lipschitz version of the famous Hardt's theorem. We give proofs of these two theorems that avoid the use of the real spectrum. The article recalls the basic facts and the results about Lipschitz geometry that are needed to understand the proofs, providing references.

We study the Wasserstein (or earthmover) metric on the space $P(X)$ of probability measures on a metric space $X$. We show that, if a finite metric space $X$ embeds stochastically with distortion $D$ in a family of finite metric trees, then $P(X)$ embeds bi-Lipschitz into $\ell^1$ with distortion $D$. Next, we re-visit the closed formula for the Wasserstein metric on finite metric trees due to Evans-Matsen \cite{EvMat}. We advocate that the right framework for this formula is real trees, and we give two proofs of extensions of this formula: one making the link with Lipschitz-free spaces from Banach space theory, the other one algorithmic (after reduction to finite metric trees)., Comment: 17 pages

Efroymson's approximation theorem asserts that if $f$ is a $\mathcal{C}^0$ semialgebraic mapping on a $\mathcal{C}^\infty$ semialgebraic submanifold $M$ of $\mathbb{R}^n$ and if $\varepsilon:M\to \mathbb{R}$ is a positive continuous semialgebraic function then there is a $\mathcal{C}^\infty$ semialgebraic function $g:M\to \mathbb{R}$ such that $|f-g|<\varepsilon$. We prove a generalization of this result to the globally subanalytic category. Our theorem actually holds in a larger framework since it applies to every function which is definable in a polynomially bounded o-minimal structure (expanding the real field) that admits $\mathcal{C}^\infty$ cell decomposition. We also establish approximation theorems for Lipschitz and $\mathcal{C}^1$ definable functions.

In this work, we extend the analyses devoted to Newtonian viscous fluids previously reported by Ribe [Physical Review E 68, 036305 (2003)], by investigating shear thickening (dilatant) and shear thinning (pseudoplastic) effects on the development of folding instabilities in non-Newtonian viscous sheets of which viscosity is given by a power-law constitutive equation. Such instabilities are trigged by compression stresses acting on viscous sheets that leave a channel at a very small initial velocity, fall, and then hit a solid surface or a fluid substrate. Our study is conducted through a mixed approach combining direct numerical simulations, energy budget analyses, scaling laws, and experiments. The numerical results are based on an adaptive variational multi-scale method for multiphase flows, while Carpobol gel sheets are considered for the conducted experiments. Two folding regimes are observed: (1) the viscous regime; and (2) the gravitational one. Interestingly, only the latter is affected by shear thinning/thickening manifestations within the material. In short, when gravity is balanced by viscous forces along the non-Newtonian viscous sheet, both the folding amplitude and the folding frequency are given by a power-law function of the sheet slenderness, the Galileo number (the ratio of the gravitational stress to the viscous one), and the flow behaviour index. Highly shear thickening materials develop large amplitude (and low frequency) instabilities, which, in contrast, tend to be suppressed by shear thinning effects, and eventually cease. Lastly, nonNewtonian effects on folding onset/cessation are also carefully explored. As a result, non-Newtonian folding onset and cessation criteria are presented.

We address the problem of multimodal liver segmentation in paired but unregistered T1 and T2-weighted MR images. We compare several strategies described in the literature, with or without multi-task training, with or without pre-registration. We also compare different loss functions (cross-entropy, Dice loss, and three adversarial losses). All methods achieved comparable performances with the exception of a multi-task setting that performs both segmentations at once, which performed poorly., Comment: 4 pages, 3 figures and 3 tables. Conference paper

For $0<\alpha\le 1$, we say that a sequence $(X_k)_{k>0}$ of $d$-regular graphs has property $D_\alpha$ if there exists a constant $C>0$ such that $\mathrm{diam}(X_k)\ge C\cdot|X_k|^\alpha$. We investigate property $D_\alpha$ for arithmetic box spaces of the solvable Baumslag-Solitar groups $BS(1,m)$ (with $m\geq 2$): those are box spaces obtained by embedding $BS(1,m)$ into the upper triangular matrices in $GL_2(\mathbb{Z}[1/m])$ and intersecting with a family $M_{N_k}$ of congruence subgroups of $GL_2(\mathbb{Z}[1/m])$, where the levels $N_k$ are coprime with $m$ and $N_k|N_{k+1}$. We prove: - if an arithmetic box space has $D_\alpha$, then $\alpha\le\frac{1}{2}$~; - if the family $(N_k)_k$ of levels is supported on finitely many primes, the corresponding arithmetic box space has $D_{1/2}$~; - if the family $(N_k)_k$ of levels is supported on a family of primes with positive analytic primitive density, then the corresponding arithmetic box space does not have $D_\alpha$, for every $\alpha>0$. Moreover, we prove that if we embed $BS(1,m)$ in the group of invertible upper-triangular matrices $T_n(\mathbb{Z}[1/m])$, then every finite index subgroup of the embedding contains a congruence subgroup. This is a version of the congruence subgroup property (CSP)., Comment: 16 pages

Inflammation of brain tissue is a complex response of the immune system to the presence of toxic compounds or to cell injury, leading to a cascade of pathological processes that include glial cell activation. Noninvasive magnetic resonance imaging markers of glial reactivity would be very useful for in vivo detection and monitoring of inflammation processes in the brain, as well as for evaluating the efficacy of personalized treatments. Due to their specific location in glial cells, myo-inositol (mIns) and choline compounds (tCho) seem the best candidates for probing glial-specific intra-cellular compartments. However, their concentrations quantified using conventional proton magnetic resonance spectroscopy (MRS) are not specific for inflammation. In contrast, it has been recently suggested that mIns intra-cellular diffusion, measured using diffusion-weighted MRS (DW-MRS) in a mouse model of reactive astrocytes, could be a specific marker of astrocytic hypertrophy. In order to evaluate the specificity of both mIns and tCho diffusion to inflammation-driven glial alterations, we performed DW-MRS in the corpus callosum of cuprizone-fed mice after 6 weeks of intoxication and evaluated the extent of astrocytic and microglial alterations using immunohistochemistry. Both mIns and tCho apparent diffusion coefficients were significantly elevated in cuprizone-fed mice compared to control mice, while histologic evaluation confirmed the presence of severe inflammation. Additionally, mIns and tCho diffusion showed, respectively, strong and moderate correlations with histological measures of astrocytic and microglial area fractions, confirming DW-MRS as a promising tool for specific detection of glial changes under pathological conditions., Comment: 31 pages, 9 figures

An energy of $362\:\text{MJ}$ is stored in each of the two LHC proton beams for nominal beam parameters. This will be further increased to about $700\:\text{MJ}$ in the future High Luminosity LHC (HL-LHC) and uncontrolled beam losses represent a significant hazard for the integrity and safe operation of the machine. In this paper, a number of failure mechanisms that can lead to a fast increase of beam losses are analyzed. Most critical are failures in the magnet protection system, namely the quench heaters and a novel protection system called Coupling-Loss Induced Quench (CLIQ). An important outcome is that magnet protection has to be evaluated for its impact on the beam and designed accordingly. In particular, CLIQ, which is to protect the new HL-LHC triplet magnets, constitutes the fastest known failure in the LHC if triggered spuriously. A schematic change of CLIQ to mitigate the hazard is presented. A loss of the Beam-Beam Kick due to the extraction of one beam is another source of beam losses with a fast onset. A significantly stronger impact is expected in the upcoming LHC Run III and HL-LHC as compared to the current LHC, mainly due to the increased bunch intensity. Its criticality and mitigation methods are discussed. It is shown that symmetric quenches in the superconducting magnets for the final focusing triplet can have a significant impact on the beam on short timescales. The impact on the beam due to failures of the Beam-Beam Compensating Wires as well as coherent excitations by the transverse beam damper are also discussed., Comment: 28 pages, 23 figures. To be published in Physical Review Accelerators and Beams

We investigate the existence and properties of a double asymptotic expansion in $1/N^{2}$ and $1/\sqrt{D}$ in $\mathrm{U}(N)\times\mathrm{O}(D)$ invariant Hermitian multi-matrix models, where the $N\times N$ matrices transform in the vector representation of $\mathrm{O}(D)$. The crucial point is to prove the existence of an upper bound $\eta(h)$ on the maximum power $D^{1+\eta(h)}$ of $D$ that can appear for the contribution at a given order $N^{2-2h}$ in the large $N$ expansion. We conjecture that $\eta(h)=h$ in a large class of models. In the case of traceless Hermitian matrices with the quartic tetrahedral interaction, we are able to prove that $\eta(h)\leq 2h$; the sharper bound $\eta(h)=h$ is proven for a complex bipartite version of the model, with no need to impose a tracelessness condition. We also prove that $\eta(h)=h$ for the Hermitian model with the sextic wheel interaction, again with no need to impose a tracelessness condition., Comment: 28 pages, 20 figures; v2: refs added, matches published version

We study the double- and triple-scaling limits of a complex multi-matrix model, with $\mathrm{U}(N)^2\times \mathrm{O}(D)$ symmetry. The double-scaling limit amounts to taking simultaneously the large-$N$ (matrix size) and large-$D$ (number of matrices) limits while keeping the ratio $N/\sqrt{D}=M$ fixed. The triple-scaling limit consists in taking the large-$M$ limit while tuning the coupling constant $\lambda$ to its critical value $\lambda_c$ and keeping fixed the product $M(\lambda_c-\lambda)^\alpha$, for some value of $\alpha$ that depends on the particular combinatorial restrictions imposed on the model. Our first main result is the complete recursive characterization of the Feynman graphs of arbitrary genus which survive in the double-scaling limit. Next, we classify all the dominant graphs in the triple-scaling limit, which we find to have a plane binary tree structure with decorations. Their critical behavior belongs to the universality class of branched polymers. Lastly, we classify all the dominant graphs in the triple-scaling limit under the restriction to three-edge connected (or two-particle irreducible) graphs. Their critical behavior falls in the universality class of Liouville quantum gravity (or, in other words, the Brownian sphere)., Comment: 55 pages, 33 figures; v2: minor corrections; v3: matches journal version, to appear in Ann. Inst. Henri Poincar\'e D

We investigate the problem of Poincar\'e duality for $L^p$ differential forms on bounded subanalytic submanifolds of $\mathbb{R}^n$ (not necessarily compact). We show that, when $p$ is sufficiently close to $1$ then the $L^p$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where $p$ is large, we show that $L^p$ cohomology is dual to intersection homology. As a consequence, we can deduce that the $L^p$ cohomology is Poincar\'e dual to $L^q$ cohomology, if $p$ and $q$ are H\"older conjugate to each other and $p$ is sufficiently large.

The Wide-field Imager for Solar PRobe (WISPR) obtained the first high-resolution images of coronal rays at heights below 15 R$_\odot$ when the Parker Solar Probe (PSP) was located inside 0.25 au during the first encounter. We exploit these remarkable images to reveal the structure of coronal rays at scales that are not easily discernible in images taken from near 1 au. To analyze and interpret WISPR observations, which evolve rapidly both radially and longitudinally, we construct a latitude versus time map using the full WISPR dataset from the first encounter. From the exploitation of this map and also from sequential WISPR images, we show the presence of multiple substructures inside streamers and pseudostreamers. WISPR unveils the fine-scale structure of the densest part of streamer rays that we identify as the solar origin of the heliospheric plasma sheet typically measured in situ in the solar wind. We exploit 3D magnetohydrodynamic models, and we construct synthetic white-light images to study the origin of the coronal structures observed by WISPR. Overall, including the effect of the spacecraft relative motion toward the individual coronal structures, we can interpret several observed features by WISPR. Moreover, we relate some coronal rays to folds in the heliospheric current sheet that are unresolved from 1 au. Other rays appear to form as a result of the inherently inhomogeneous distribution of open magnetic flux tubes., Comment: for associated mpeg file see https://nuage.irap.omp.eu/index.php/s/x2tHzaBM9fyL1bt, 21 pages, 16 figures, published in ApJS: "Early Results from Parker Solar Probe: Ushering a New Frontier in Space Exploration"