Incomplete Yamabe flows and removable singularities

We study the Yamabe flow on a Riemannian manifold of dimension $m\geq3$ minus a closed submanifold of dimension $n$ and prove that there exists an instantaneously complete solution if and only if $n>\frac{m-2}{2}$. In the remaining cases $0\leq n\leq\frac{m-2}{2}$ including the borderline case, we show that the removability of the $n$-dimensional singularity is necessarily preserved along the Yamabe flow. In particular, the flow must remain geodesically incomplete as long as it exists. This is contrasted with the two-dimensional case, where instantaneously complete solutions always exist

Minimal hypertori in the four-dimensional sphere

We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric, immersed ones. Our analysis also yields infinitely many, pairwise non-isometric, minimally embedded hyperspheres and thus provides a self-contained solution to Chern's spherical Bernstein conjecture in dimensions four and six.Comment: Published version with the journal's style file. 33 pages, 7 figure

Topological control for min-max free boundary minimal surfaces

We establish general bounds on the topology of free boundary minimal surfaces obtained via min-max methods in compact, three-dimensional ambient manifolds with mean convex boundary. We prove that the first Betti number is lower semicontinuous along min-max sequences converging in the sense of varifolds to free boundary minimal surfaces. In the orientable case, we obtain an even stronger result which implies that if the number of boundary components increases in the varifold limit, then the genus decreases at least as much. We also present several compelling applications, such as the variational construction of a free boundary minimal trinoid in the Euclidean unit ball.Comment: 35 pages, 5 figures; minor expository changes in section

Disc stackings and their Morse index

We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our work implies for any positive integer $k$ the existence of $k$-tuples of distinct, pairwise non-congruent, embedded free boundary minimal surfaces all having the same topological type. In addition, since we prove that the equivariant Morse index of any such free boundary minimal stacking, with respect to its maximal symmetry group, is bounded from below by (the integer part of) half the number of layers and from above strictly by twice the same number, it follows that any possible realization of such surfaces via an equivariant min-max method would need to employ sweepouts with an arbitrarily large number of parameters. This also shows that it is only for $N=2$ and $N=3$ layers that free boundary minimal disc stackings are achievable by means of one-dimensional mountain pass schemes.Comment: 55 pages, 8 figure

Free boundary minimal surfaces with connected boundary and arbitrary genus

We employ min-max techniques to show that the unit ball in $\mathbb{R}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus

Targeted Ablation of Oligodendrocytes Triggers Axonal Damage

Glial dysfunction has been implicated in a number of neurodegenerative diseases. In this study we investigated the consequences of glial and oligodendrocyte ablation on neuronal integrity and survival in Drosophila and adult mice, respectively. Targeted genetic ablation of glia was achieved in the adult Drosophila nervous system using the GAL80-GAL4 system. In mice, oligodendrocytes were depleted by the injection of diphtheria toxin in MOGi-Cre/iDTR double transgenic animals. Acute depletion of oligodendrocytes induced axonal injury, but did not cause neuronal cell death in mice. Ablation of glia in adult flies triggered neuronal apoptosis and resulted in a marked reduction in motor performance and lifespan. Our study shows that the targeted depletion of glia triggers secondary neurotoxicity and underscores the central contribution of glia to neuronal homeostasis. The models used in this study provide valuable systems for the investigation of therapeutic strategies to prevent axonal or neuronal damage

When is giving an impulse? An ERP investigation of intuitive prosocial behavior

Human prosociality is often assumed to emerge from exerting reflective control over initial, selfish impulses. However, recent findings suggest that prosocial actions can also stem from processes that are fast, automatic and intuitive. Here, we attempt to clarify when prosocial behavior may be intuitive by examining prosociality as a form of reward seeking. Using event-related potentials (ERPs), we explored whether a neural signature that rapidly encodes the motivational salience of an event\u2014the P300\u2014can predict intuitive prosocial motivation. Participants allocated varying amounts of money between themselves and charities they initially labelled as high- or low-empathy targets under conditions that promoted intuitive or reflective decision making. Consistent with our predictions, P300 amplitude over centroparietal regions was greater when giving involved high-empathy targets than low-empathy targets, but only when deciding under intuitive conditions. Reflective conditions, alternatively, elicited an earlier frontocentral positivity related to response inhibition, regardless of target. Our findings suggest that during prosocial decision making, larger P300 amplitude could (i) signal intuitive prosocial motivation and (ii) predict subsequent engagement in prosocial behavior. This work offers novel insight into when prosociality may be driven by intuitive processes and the roots of such behaviors

Ram pressure feeding super-massive black holes

When supermassive black holes at the center of galaxies accrete matter (usually gas), they give rise to highly energetic phenomena named Active Galactic Nuclei (AGN). A number of physical processes have been proposed to account for the funneling of gas towards the galaxy centers to feed the AGN. There are also several physical processes that can strip gas from a galaxy, and one of them is ram pressure stripping in galaxy clusters due to the hot and dense gas filling the space between galaxies. We report the discovery of a strong connection between severe ram pressure stripping and the presence of AGN activity. Searching in galaxy clusters at low redshift, we have selected the most extreme examples of jellyfish galaxies, which are galaxies with long tentacles of material extending for dozens of kpc beyond the galaxy disk. Using the MUSE spectrograph on the ESO Very Large Telescope, we find that 6 out of the 7 galaxies of this sample host a central AGN, and two of them also have galactic-scale AGN ionization cones. The high incidence of AGN among the most striking jellyfishes may be due to ram pressure causing gas to flow towards the center and triggering the AGN activity, or to an enhancement of the stripping caused by AGN energy injection, or both. Our analysis of the galaxy position and velocity relative to the cluster strongly supports the first hypothesis, and puts forward ram pressure as another, yet unforeseen, possible mechanism for feeding the central supermassive black hole with gas.Comment: published in Nature, Vol.548, Number 7667, pag.30

Longitudinal changes of SARA scale in Friedreich ataxia: Strong influence of baseline score and age at onset

BACKGROUND: The Scale for Assessment and Rating of Ataxia (SARA) is widely used in different types of ataxias and has been chosen as the primary outcome measure in the European natural history study for Friedreich ataxia (FA). METHODS: To assess distribution and longitudinal changes of SARA scores and its single items, we analyzed SARA scores of 502 patients with typical-onset FA (<25 years) participating in the 4-year prospective European FA Consortium for Translational Studies (EFACTS). Pattern of disease progression was determined using linear mixed-effects regression models. The chosen statistical model was re-fitted in order to estimate parameters and predict disease progression. Median time-to-change and rate of score progression were estimated using the Kaplan-Meier method and weighted linear regression models, respectively. RESULTS: SARA score at study enrollment and age at onset were the major predictive factors of total score progression during the 4-year follow-up. To a less extent, age at evaluation also influenced the speed of SARA progression, while disease duration did not improve the prediction of the statistical model. Temporal dynamics of total SARA and items showed a great variability in the speed of score increase during disease progression. Gait item had the highest annual progression rate, with median time for one-point score increase of 1 to 2 years. INTERPRETATION: Analyses of statistical properties of SARA suggest a variable sensitivity of the scale at different disease stages, and provide important information for population selection and result interpretation in future clinical trials