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

Identification of Long-lived Charged Particles using Time-Of-Flight Systems at the Upgraded LHC detectors

We study the impact of picosecond precision timing detection systems on the LHC experiments' long-lived particle search program during the HL-LHC era. We develop algorithms that allow us to reconstruct the mass of such charged particles and perform particle identification using the time-of-flight measurement. We investigate the reach for benchmark scenarios as a function of the timing resolution, and find sensitivity improvement of up to a factor of ten, depending on the new heavy particle mass.Comment: 20 pages, 13 figure

Automated Setup to Accurately Calibrate Electrical DC Voltage Generators

At National Institute of Metrological Research (INRIM), an automated setup to calibrate DC Voltage generators, mainly top-level calibrators from 1 mV to 1 kV has been developed. The heart of the setup is an INRIM-built automated fixed ratios DC Voltage divider. The significant achievement of this setup is the possibility to interconnect the divider, a DMM characterized in linearity, a DC Voltage Standard and a DC Voltage generator under calibration and automatically to manage the calibration process. This calibration method allows to save a lot of time, to improve the reliability and to increase the accuracy of the calibration of generators. The relative uncertainties of the system span from 0.6x10-6 to 1.2x10-4 improving the previous capabilities of the INRIM laboratory for calibration of programmable multifunction instruments. In addition, this system allows to avoid the employment of several Standards (some of them still manually operating) carrying out the entire process without changing the setup configuration and without the presence of operators. The concept of this setup can be transferred to secondary high-level electrical calibration Laboratories that could be consider it useful for their calibration activities.Comment: 6 pages 8 figure

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