Exact integrability conditions for cotangent vector fields

In Quantum Hydro-Dynamics the following problem is relevant: let (ρ,Λ)∈W1,2(Rd,Ld,R+)×L2(Rd,Ld,Rd) be a finite energy hydrodynamics state, i.e. Λ = 0 when ρ= 0 and E=∫Rd12|∇ρ|2+12Λ2Ld<∞.The question is under which conditions there exists a wave function ψ∈ W1 , 2(Rd, Ld, C) such that ρ=|ψ|,J=ρΛ=I(ψ ̄∇ψ).The second equation gives for ψ=ρw smooth, | w| = 1 , that iΛ=ρw ̄∇w. Interpreting ρLd as a measure in the metric space Rd, this question can be stated in generality as follows: given metric measure space (X, d, μ) and a cotangent vector field v∈ L2(T∗X) , is there a function w∈ W1 , 2(X, μ, S1) such that dw=iwv.Under some assumptions on the metric measure space (X, d, μ) (conditions which are verified on Riemann manifolds with the measure μ= ρVol or more generally on non-branching MCP (K, N)), we show that the necessary and sufficient conditions for the existence of w is that (in the case of differentiable manifold) ∫v(γ(t))·γ ̇(t)dt∈2πZfor π-a.e. γ, where π is a test plan supported on closed curves. This condition generalizes the condition that the vorticity is quantized. We also give a representation of every possible solution. In particular, we deduce that the wave function ψ=ρw is in W1 , 2(X, μ, C) whenever ρ∈W1,2(X,μ,R+)

Microglial Refinement of A-Fiber Projections in the Postnatal Spinal Cord Dorsal Horn Is Required for Normal Maturation of Dynamic Touch

Sensory systems are shaped in postnatal life by the refinement of synaptic connectivity. In the dorsal horn of the spinal cord, somatosensory circuits undergo postnatal activity-dependent reorganisation, including the refinement of primary afferent A-fibre terminals from superficial to deeper spinal dorsal horn laminae which is accompanied by decreases in cutaneous sensitivity. Here we show in the mouse that microglia, the resident immune cells in the CNS, phagocytose A-fibre terminals in superficial laminae in the first weeks of life. Genetic perturbation of microglial engulfment during the initial postnatal period in either sex prevents the normal process of A-fibre refinement and elimination, resulting in altered sensitivity of dorsal horn cells to dynamic tactile cutaneous stimulation, and behavioural hypersensitivity to dynamic touch. Thus, functional microglia are necessary for the normal postnatal development of dorsal horn sensory circuits. In the absence of microglial engulfment, superfluous A-fibre projections remain in the dorsal horn and the balance of sensory connectivity is disrupted, leading to lifelong hypersensitivity to dynamic touch.Significance statement Dynamic touch is the sensation of movement across the skin, transmitted by mechanosensory A-fibres, the myelinated primary afferents that respond to innocuous mechanical stimulation. The central terminals of these fibres are located in the deep laminae of the sensory spinal cord dorsal horn in the adult. However, in early life they are widespread and retract from the superficial laminae of the dorsal horn during normal postnatal development. The underlying mechanisms remain unknown. We found that microglia phagocytose superfluous A-fibres and furthermore, disruption of this process leads to long-term aberrant dynamic touch processing and behaviour. Microglia mediated refinement of A-fibres during the early postnatal period is therefore critical to both normal dorsal horn development and appropriate spatial encoding of dynamic touch

Euclid preparation: XXXV. Covariance model validation for the two-point correlation function of galaxy clusters

Aims. We validate a semi-analytical model for the covariance of the real-space two-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrated a simple model to accurately describe the clustering covariance. Then, we used this model to quantify the likelihood-analysis response to variations in the covariance, and we investigated the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the two-point correlation function of galaxy clusters. By introducing a few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with an accuracy of 10%, with differences of about 5% on the figure of merit of the cosmological parameters Ωm and σ8. We also find that the covariance contains additional valuable information that is not present in the mean value, and the constraining power of cluster clustering can improve significantly when its cosmology dependence is accounted for. Finally, we find that the cosmological figure of merit can be further improved when mass binning is taken into account. Our results have significant implications for the derivation of cosmological constraints from the two-point clustering statistics of the Euclid survey of galaxy clusters

Euclid preparation: XXXIII. Characterization of convolutional neural networks for the identification of galaxy-galaxy strong-lensing events

Forthcoming imaging surveys will increase the number of known galaxy-scale strong lenses by several orders of magnitude. For this to happen, images of billions of galaxies will have to be inspected to identify potential candidates. In this context, deep-learning techniques are particularly suitable for finding patterns in large data sets, and convolutional neural networks (CNNs) in particular can efficiently process large volumes of images. We assess and compare the performance of three network architectures in the classification of strong-lensing systems on the basis of their morphological characteristics. In particular, we implemented a classical CNN architecture, an inception network, and a residual network. We trained and tested our networks on different subsamples of a data set of 40 000 mock images whose characteristics were similar to those expected in the wide survey planned with the ESA mission Euclid, gradually including larger fractions of faint lenses. We also evaluated the importance of adding information about the color difference between the lens and source galaxies by repeating the same training on single- and multiband images. Our models find samples of clear lenses with ≳90% precision and completeness. Nevertheless, when lenses with fainter arcs are included in the training set, the performance of the three models deteriorates with accuracy values of ~0.87 to ~0.75, depending on the model. Specifically, the classical CNN and the inception network perform similarly in most of our tests, while the residual network generally produces worse results. Our analysis focuses on the application of CNNs to high-resolution space-like images, such as those that the Euclid telescope will deliver. Moreover, we investigated the optimal training strategy for this specific survey to fully exploit the scientific potential of the upcoming observations. We suggest that training the networks separately on lenses with different morphology might be needed to identify the faint arcs. We also tested the relevance of the color information for the detection of these systems, and we find that it does not yield a significant improvement. The accuracy ranges from ~0.89 to ~0.78 for the different models. The reason might be that the resolution of the Euclid telescope in the infrared bands is lower than that of the images in the visual band

Real Time Reduced Order Computational Mechanics Parametric PDEs Worked Out Problems

The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity. This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet

Euclid preparation XXXIV. The effect of linear redshift-space distortions in photometric galaxy clustering and its cross-correlation with cosmic shear

Context. The cosmological surveys that are planned for the current decade will provide us with unparalleled observations of the distribution of galaxies on cosmic scales, by means of which we can probe the underlying large-scale structure (LSS) of the Universe. This will allow us to test the concordance cosmological model and its extensions. However, precision pushes us to high levels of accuracy in the theoretical modelling of the LSS observables, so that no biases are introduced into the estimation of the cosmological parameters. In particular, effects such as redshift-space distortions (RSD) can become relevant in the computation of harmonic-space power spectra even for the clustering of the photometrically selected galaxies, as has previously been shown in literature. Aims. In this work, we investigate the contribution of linear RSD, as formulated in the Limber approximation by a previous work, in forecast cosmological analyses with the photometric galaxy sample of the Euclid survey. We aim to assess their impact and to quantify the bias on the measurement of cosmological parameters that would be caused if this effect were neglected. Methods. We performed this task by producing mock power spectra for photometric galaxy clustering and weak lensing, as is expected to be obtained from the Euclid survey. We then used a Markov chain Monte Carlo approach to obtain the posterior distributions of cosmological parameters from these simulated observations. Results. When the linear RSD is neglected, significant biases are caused when galaxy correlations are used alone and when they are combined with cosmic shear in the so-called 3 × 2 pt approach. These biases can be equivalent to as much as 5σ when an underlying ΛCDM cosmology is assumed. When the cosmological model is extended to include the equation-of-state parameters of dark energy, the extension parameters can be shifted by more than 1σ

Quantum information insights into strongly correlated electrons

Recent theoretical and experimental advances have opened new perspectives on the characterization of strongly correlated phases of matter, adding a new layer of understanding based on concepts and tools borrowed from quantum information theory. We join the effort by investigating, within dynamical mean-field theory (DMFT) and its cluster extension, the local and quasilocal (i.e. short-range) quantum information content of salient landmarks in the phase diagram of the two-dimensional Hubbard model, the cornerstone model for the description of the physics of cuprate materials, and of a closely related model for interacting topological states on the honeycomb lattice. In the first part of the thesis, we focus on the DMFT solution of the Kane-Mele-Hubbard model, at zero temperature. In the thermodynamic limit we find evidence of an interaction-driven discontinuous quantum phase transition between the Z2 quantum spin-Hall insulator and anisotropic antiferromagnetic solutions, with an intermediate regime of coexistence of nontrivial topology and magnetic order. A clear-cut interpretation of these results is given in terms of a rigorous quantification of quantum and classical correlations contained in a single local orbital (which we refer to as intra-orbital mutual information), providing a notion of "statistical distance" from the Hartree-Fock description of the system. The resulting analysis complements the established Green's function based understanding of the relationship between dynamical and static mean-field theories. In particular, we find the magnetic solutions of dynamical mean-field theory to asymptotically approach the corresponding uncorrelated Hartree-Fock states, in the strong coupling limit, in stark contrast with the paramagnetic Mott-Hubbard solution, which in turn reveals a maximally correlated local spin-orbital pair at large interaction strength. Furthermore, these findings cast some light on the relationship between Mott localization and the possible development of nonlocal entanglement. In the second part of the thesis, we provide an alternative view of both the interaction-driven and density-driven paramagnetic Mott transitions in the two-dimensional Hubbard model, in terms of rigorous measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: two traditional upper bounds and two recently introduced lower bounds for its magnitude sharply increase at the metal-insulator transition, in contrast with the moderate variation found at all interaction strengths that are sufficiently far from the transition point. At half-filling, the two-site entanglement beyond nearest neighbors is shown to be quickly damped as the inter-site distance is increased within the cluster, suggesting that Mott-Hubbard insulators may follow an area law. However, the size of the simulated clusters does not allow a quantitative analysis of the decay, so that a precise classification of the spatial entanglement properties of the system is left for future study. In the presence of hole-doping, we show how the pseudogap metal separating the Mott-Hubbard insulator from the hole-dominated Fermi liquid features quasilocal entanglement properties that are strikingly similar to the localized Mott phase, while it is separated from the low-entangled Fermi liquid by a discontinuous jump in all the computed entanglement and correlation measures. All the presented results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased, defeating the purpose of capturing and understanding strong electronic correlations with the aid of quantum information concepts. Both the intra-orbital mutual information and the quasilocal two-site entanglement, on the other hand, recover instead the distinctive character of Mott insulators and pseudogap metals as strongly correlated many-body states, demonstrating its central role in future advancements in the field of quantum materials

Addressing limits of Emx2 therapy of glioblastoma multiforme by transgene insulation and epigenetic pharmacological intervention

Activation of a therapeutic transgene encoding for the transcription factor Emx2 acutely suppressed a variety of glioblastoma tumors in vitro. However, employed in TetOFF configuration, this transgene was not able to eradicate glioblastoma in vivo, in homotopically xenotransplanted, immunocompromised mice, because of its silencing, as assessed by an associated EGFP activity reporter. To fix this issue, we decided to model such silencing in vitro. For this purpose, we took again advantage of an IRES-EGFP reporter, associated to the Emx2 transgene or its control, driven here by TetON machinery. To ease the emergence of silencing, we kept these transgenes inactive for a long time past their lentiviral delivery to tumor cells, and we finally activated them by mild doxycycline supplementation. Moreover, to prevent intricacies originating from unexpected leakage of the transgene prior to its intentional activation, we replaced the Emx2-encoding transgene by a surrogate of it, unable to drive synthesis of Emx2 protein, however still harboring sequences supposed to evoke silencing. Resulting, engineered cultures of tumor cells were profiled by cytofluorometry and, finally, the fraction of them expressing the EGFP reporter below a given threshold was employed as an index of transgene silencing. We detected a generalized and progressive decline in activity of all our lentiviral transgenes (both the Emx2-type one and its control), as well as a supplemental decline, specifically affecting Emx2-type constructs since the very early steps of the analytical procedure. We also found that deposition of H3K27me3 and MeCP2 epigenetic marks could contribute to such phenomena. Next, to mimic two key factors supposed to promote silencing in vivo, low O2 peculiar to the glioblastoma niche and "healthy" glia in contact with tumor, we repeated the assays in a hypoxic environment, in the presence of murine neocortical glia. It turned out that both early, generalized transgene dampening, and supplemental Emx2-specific transgene silencing, were enhanced by coculterd glia and, even more, by combined glia and low oxygen. Finally, to mitigate/prevent transgene silencing, we tested two specific devices. First, we insulated the transgene on its 5' side by means of a Ubiquitous Chromatin Opening element (UCOE). Second, we run our assays in the presence of a dedicated drug mix (M3), supposed to lower levels of silencing epigenetic marks H3K27me3, H3K9me3, and 5meCDNA. Both interventions were fruitful, allowing to counteract specific aspects of generalized and Emx2-transgene-peculiar inactivation. We inferred that their combined use might be enough to restore the ability of the Emx2 transgene to acutely suppress glioblastoma in vivo. Building on these findings, now we plan to employ transgene insulation (as described above or further improved by a supplemental 3' element), as well as the M3 mix, to shield the therapeutic Emx2 transgene, and then assess its hopefully improved ability to eradicate glioblastoma - even in a silencing-prone environement - first in vitro and then in vivo