Invariance properties of the multidimensional matching distance in Persistent Topology and Homology

Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the ranks of persistent homology groups. Initially introduced by considering real-valued filtering functions, Persistent Topology has been subsequently generalized to a multidimensional setting, i.e. to the case of $\R^n$-valued filtering functions, leading to studying the ranks of multidimensional homology groups. In particular, a multidimensional matching distance has been defined, in order to compare these ranks. The definition of the multidimensional matching distance is based on foliating the domain of the ranks of multidimensional homology groups by a collection of half-planes, and hence it formally depends on a subset of $\R^n\times\R^n$ inducing a parameterization of these half-planes. It happens that it is possible to choose this subset in an infinite number of different ways. In this paper we show that the multidimensional matching distance is actually invariant with respect to such a choice.Comment: 14 pages, 2 figure

Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia

Understanding the nature of the turbulent fluctuations below the ion gyroradius in solar-wind turbulence is a great challenge. Recent studies have been mostly in favor of kinetic Alfv\'en wave (KAW) type of fluctuations, but other kinds of fluctuations with characteristics typical of magnetosonic, whistler and ion Bernstein modes, could also play a role depending on the plasma parameters. Here we investigate the properties of the sub-proton-scale cascade with high-resolution hybrid-kinetic simulations of freely-decaying turbulence in 3D3V phase space, including electron inertia effects. Two proton plasma beta are explored: the "intermediate" $\beta_p=1$ and "low" $\beta_p=0.2$ regimes, both typically observed in solar wind and corona. The magnetic energy spectum exhibits $k_\perp^{-8/3}$ and $k_\|^{-7/2}$ power laws at $\beta_p=1$, while they are slightly steeper at $\beta_p=0.2$. Nevertheless, both regimes develop a spectral anisotropy consistent with $k_\|\sim k_\perp^{2/3}$ at $k_\perp\rho_p>1$, and pronounced small-scale intermittency. In this context, we find that the kinetic-scale cascade is dominated by KAW-like fluctuations at $\beta_p=1$, whereas the low-$\beta$ case presents a more complex scenario suggesting the simultaneous presence of different types of fluctuations. In both regimes, however, a non-negligible role of ion Bernstein type of fluctuations at the smallest scales seems to emerge.Comment: 6 pages, 5 figures, final version published in The Astrophysical Journal Letters: Cerri, Servidio & Califano, ApJL 846, L18 (2017

OPTIMAL HOMEOMORPHISMS BETWEEN CLOSED CURVES

The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance

About the rapidity and helicity distributions of the W bosons produced at LHC

$W$ bosons are produced at LHC from a forward-backward symmetric initial state. Their decay to a charged lepton and a neutrino has a strong spin analysing power. The combination of these effects results in characteristic distributions of the pseudorapidity of the leptons decaying from $W^+$ and $W^-$ of different helicity. This observation may open the possibility to measure precisely the $W^+$ and $W^-$ rapidity distributions for the two transverse polarisation states of $W$ bosons produced at small transverse momentum.Comment: 8 pages, 5 figure

Influence of notillage on carbon sequestration and erosion in Brazil

Les sols constituent le plus gros réservoir superficiel de C (hors les roches carbonatées), environ 1500 Gt C, ce qui équivaut à presque trois fois la quantité stockée dans la biomasse terrestre, et deux fois celle de l'atmosphère. Toute modification de l'usage des terres et, même pour les systèmes agricoles à l'équilibre, toute modification de l'itinéraire technique, peut induire des variations du stockage du carbone dans les sols. Les pratiques de labour favorisent souvent une aération du sol, qui est propice à l'activité microbienne et conduisent à une dégradation de la structure. Il en résulte sur le moyen et long terme une minéralisation accrue de la matière organique du sol. Du fait de l'absence (ou limitation) des travaux du sol (No-tillage, NT) et d'un maintien d'une couverture végétale permanente (DMC), les systèmes de semis direct favoriseraient la séquestration du carbone et limiteraient l'érosion. Au Brésil, l'apparition du semi-direct dans la Région Sud, au Paraná date du début des années 1970. Un des objectifs majeurs de l'époque était la lutte contre l'érosion, puis les recherches se sont développées vers la gestion des résidus de récolte et leur effet sur la fertilité, que ce soit pour la gestion du phosphore, le contrôle de l'acidité ou la localisation des engrais. Cette pratique, qui a pris une grande extension et continue de s'accroître dans le centre et le nord du pays, occupe actuellement entre environ 18 millions d'hectares avec une très grande diversité de milieux, d'agrosystèmes et d'itinéraires techniques. Au Brésil, la plus part des auteurs donnent des vitesses de stockage du carbone dans des sols sous semis-direct allant de 0,4 à 1,7 t C/ha/yr pour la couche 0-40 cm, avec les taux les plus élevés pour la région centrale du Cerrado. Mais certaines précautions sont nécessaires lors de la comparaison, en terme de séquestration du carbone, des systèmes de semis direct avec les systèmes labourés. Les comparaisons ne doivent pas se limiter au seul stockage de carbone dans le sol, mais doivent prendre compte les changements dans les émissions de méthane et d'oxyde nitreux qui sont des gaz à effet de serres importants. L'adoption des techniques de semis-direct s'accompagne d'une diminution des pertes en sol par érosion de l'ordre de 90% et du ruissellement superficiel de l'ordre de 70%. Ce qui évite ainsi la perte de nutriments qui sont souvent en quantité limite dans les sols du Brésil. Le succès des techniques de semis-direct au Brésil est dû historiquement au contrôle de la fertilité des sols qui est assuré surtout par la préservation de la ressource sol. Plus récemment, ce succès est amplifié par la préservation de la ressource carbone. (Résumé d'auteur

Pressure anisotropy generation in a magnetized plasma configuration with a shear flow velocity

The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth's magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this complex nonlinear dynamics.Comment: 11 pages, 7 figures, submitted to Plasma Phys. Control. Fusio

Multidimensional persistent homology is stable

Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove that multidimensional rank invariants are stable with respect to function perturbations. More precisely, we construct a distance between rank invariants such that small changes of the function imply only small changes of the rank invariant. This result can be obtained by assuming the function to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence.Comment: 14 pages, 3 figure

Variational Autoencoders for New Physics Mining at the Large Hadron Collider

Using variational autoencoders trained on known physics processes, we develop a one-sided threshold test to isolate previously unseen processes as outlier events. Since the autoencoder training does not depend on any specific new physics signature, the proposed procedure doesn't make specific assumptions on the nature of new physics. An event selection based on this algorithm would be complementary to classic LHC searches, typically based on model-dependent hypothesis testing. Such an algorithm would deliver a list of anomalous events, that the experimental collaborations could further scrutinize and even release as a catalog, similarly to what is typically done in other scientific domains. Event topologies repeating in this dataset could inspire new-physics model building and new experimental searches. Running in the trigger system of the LHC experiments, such an application could identify anomalous events that would be otherwise lost, extending the scientific reach of the LHC.Comment: 29 pages, 12 figures, 5 table