Locating the Eigenvalues of Matrix Polynomials

Some known results for locating the roots of polynomials are extended to the case of matrix polynomials. In particular, a theorem by Pellet [Bull. Sci. Math. (2), 5 (1881), pp. 393--395], some results from Bini [Numer. Algorithms, 13 (1996), pp. 179--200] based on the Newton polygon technique, and recent results from Gaubert and Sharify (see, in particular, [Tropical scaling of polynomial matrices, Lecture Notes in Control and Inform. Sci. 389, Springer, Berlin, 2009, pp. 291--303] and [Sharify, Scaling Algorithms and Tropical Methods in Numerical Matrix Analysis: Application to the Optimal Assignment Problem and to the Accurate Computation of Eigenvalues, Ph.D. thesis, École Polytechnique, Paris, 2011]). These extensions are applied to determine effective initial approximations for the numerical computation of the eigenvalues of matrix polynomials by means of simultaneous iterations, like the Ehrlich--Aberth method. Numerical experiments that show the computational advantage of these results are presented

A simulation tool for MRPC telescopes of the EEE project

The Extreme Energy Events (EEE) Project is mainly devoted to the study of the secondary cosmic ray radiation by using muon tracker telescopes made of three Multigap Resistive Plate Chambers (MRPC) each. The experiment consists of a telescope network mainly distributed across Italy, hosted in different building structures pertaining to high schools, universities and research centers. Therefore, the possibility to take into account the effects of these structures on collected data is important for the large physics programme of the project. A simulation tool, based on GEANT4 and using GEMC framework, has been implemented to take into account the muon interaction with EEE telescopes and to estimate the effects on data of the structures surrounding the experimental apparata.A dedicated event generator producing realistic muon distributions, detailed geometry and microscopic behavior of MRPCs have been included to produce experimental-like data. The comparison between simulated and experimental data, and the estimation of detector resolutions is here presented and discussed

New Eco-gas mixtures for the Extreme Energy Events MRPCs: results and plans

The Extreme Energy Events observatory is an extended muon telescope array, covering more than 10 degrees both in latitude and longitude. Its 59 muon telescopes are equipped with tracking detectors based on Multigap Resistive Plate Chamber technology with time resolution of the order of a few hundred picoseconds. The recent restrictions on greenhouse gases demand studies for new gas mixtures in compliance with the relative requirements. Tetrafluoropropene is one of the candidates for tetrafluoroethane substitution, since it is characterized by a Global Warming Power around 300 times lower than the gas mixtures used up to now. Several mixtures have been tested, measuring efficiency curves, charge distributions, streamer fractions and time resolutions. Results are presented for the whole set of mixtures and operating conditions, %. A set of tests on a real EEE telescope, with cosmic muons, are being performed at the CERN-01 EEE telescope. The tests are focusing on identifying a mixture with good performance at the low rates typical of an EEE telescope.Comment: 8 pages, 6 figures, proceedings for the "XIV Workshop on Resistive Plate Chambers and Related Detectors" (19-23 February 2018), Puerto Vallarta, Jalisco State, Mexic

A multi-channel trigger and acquisition board for TDC-based readout: Application to the cosmic rays detector of the PolarQuEEEst 2018 project

In the summer of 2018, the PolarQuEEEst experiment accomplished a measurement of cosmic rays flux in the Arctic. The detector, installed on a sailboat, was based on scintillation tiles read by a total of 16 SiPM. A multi-channel board (called TRB) has been designed to process the discriminated SiPM signals providing both self-trigger capability and time-to-digital conversion; it was based on a Cyclone-V Intel FPGA. Time-to-digital conversion has been implemented both into FPGA and with the HPTDC chip (as a backup). In this document the board will be described, enlightening the main features and the achieved performance. Lastly, the PolarQuEEEst measurement campaigns will be briefly described, showing how the TRB board has proved to be effective for experiments which require low power consumption, integration with position and environmental sensors and great portability as well. Final thoughts on future improvements will be also discussed

The Extreme Energy Events HECR array: status and perspectives

The Extreme Energy Events Project is a synchronous sparse array of 52 tracking detectors for studying High Energy Cosmic Rays (HECR) and Cosmic Rays-related phenomena. The observatory is also meant to address Long Distance Correlation (LDC) phenomena: the network is deployed over a broad area covering 10 degrees in latitude and 11 in longitude. An overview of a set of preliminary results is given, extending from the study of local muon flux dependance on solar activity to the investigation of the upward-going component of muon flux traversing the EEE stations; from the search for anisotropies at the sub-TeV scale to the hints for observations of km-scale Extensive Air Shower (EAS).Comment: XXV ECRS 2016 Proceedings - eConf C16-09-04.

A class of quasi-sparse companion pencils

In this paper, we introduce a general class of quasi-sparse potential companion pencils for arbitrary square matrix polynomials over an arbitrary field, which extends the class introduced in [B. Eastman, I.-J. Kim, B. L. Shader, K.N. Vander Meulen, Companion matrix patterns. Linear Algebra Appl. 436 (2014) 255-272] for monic scalar polynomials. We provide a canonical form, up to permutation, for companion pencils in this class. We also relate these companion pencils with other relevant families of companion linearizations known so far. Finally, we determine the number of different sparse companion pencils in the class, up to permutation.This work has been partially supported by theMinisterio de Economía y Competitividad of Spain through grants MTM2015-68805-REDT and MTM2015-65798-P

INFN What Next: Ultra-relativistic Heavy-Ion Collisions

This document was prepared by the community that is active in Italy, within INFN (Istituto Nazionale di Fisica Nucleare), in the field of ultra-relativistic heavy-ion collisions. The experimental study of the phase diagram of strongly-interacting matter and of the Quark-Gluon Plasma (QGP) deconfined state will proceed, in the next 10-15 years, along two directions: the high-energy regime at RHIC and at the LHC, and the low-energy regime at FAIR, NICA, SPS and RHIC. The Italian community is strongly involved in the present and future programme of the ALICE experiment, the upgrade of which will open, in the 2020s, a new phase of high-precision characterisation of the QGP properties at the LHC. As a complement of this main activity, there is a growing interest in a possible future experiment at the SPS, which would target the search for the onset of deconfinement using dimuon measurements. On a longer timescale, the community looks with interest at the ongoing studies and discussions on a possible fixed-target programme using the LHC ion beams and on the Future Circular Collider.Comment: 99 pages, 56 figure

Multiplicity Studies and Effective Energy in ALICE at the LHC

In this work we explore the possibility to perform ``effective energy'' studies in very high energy collisions at the CERN Large Hadron Collider (LHC). In particular, we focus on the possibility to measure in $pp$ collisions the average charged multiplicity as a function of the effective energy with the ALICE experiment, using its capability to measure the energy of the leading baryons with the Zero Degree Calorimeters. Analyses of this kind have been done at lower centre--of--mass energies and have shown that, once the appropriate kinematic variables are chosen, particle production is characterized by universal properties: no matter the nature of the interacting particles, the final states have identical features. Assuming that this universality picture can be extended to {\it ion--ion} collisions, as suggested by recent results from RHIC experiments, a novel approach based on the scaling hypothesis for limiting fragmentation has been used to derive the expected charged event multiplicity in $AA$ interactions at LHC. This leads to scenarios where the multiplicity is significantly lower compared to most of the predictions from the models currently used to describe high energy $AA$ collisions. A mean charged multiplicity of about 1000-2000 per rapidity unit (at $\eta \sim 0$) is expected for the most central $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 5.5 TeV$.Comment: 12 pages, 19 figures. In memory of A. Smirnitski

Non-Backtracking Alternating Walks

The combinatorics of walks on a graph is a key topic in network science. Here we study a special class of walks on directed graphs. We combine two features that have previously been considered in isolation. We consider alternating walks, which form the basis of algorithms for hub/authority detection and for discovering directed bipartite substructure. Within this class, we restrict to non-backtracking walks, since this constraint has been seen to offer advantages in related contexts. We derive a recursive formula for counting the total number of non-backtracking alternating walks of a given length, leading to an expression for any associated power series expansion. We discuss computational issues for the widely used cases of resolvent and exponential series, showing that non-backtracking can be incorporated at very little extra cost. We also derive an appropriate asymptotic limit which gives a parameter-free, spectral analogue. We perform tests on an artificial data set in order to quantify the advantages of the new methodology. We also show that the removal of backtracking allows us to identify larger bipartite subgraphs within an anatomical connectivity network from neuroscience