Search

The fragmentation cross sections of carbon ion beams with kinetic energies of $115 - 353~\text{MeV/u}$ impinging on thin targets of graphite (C), polyvinyl-toluene (C$_9$H$_{10}$) and PMMA (C$_2$O$_5$H$_8$) have been measured at 90$^{\text{o}}$ and 60$^{\text{o}}$ at the CNAO particle therapy center (Pavia, Italy). The presented measurements are a complete reanalysis by the FOOT collaboration of already published elemental cross section on composite targets, in order to refine the analysis, improve the systematic uncertainties and show the comparison with the FLUKA Monte Carlo code calculations. In this work, the kinetic energy at production of measured fragments has been completely redefined, together with the efficiencies computation. The new analysis strategy has been successfully validated against the Monte Carlo cross sections. Two detection arms were positioned at two different angles to perform the measurement at 90$^{\text{o}}$ and 60$^{\text{o}}$. The fragment species have been identified in charge (Z$_{id}$ = H) and mass (M$_{id}$ = $^1$H, $^2$H, $^3$H) combining the information of the deposited energy in thin plastic scintillators, of the deposited energy in a thick LYSO crystal and of the fragments Time of Flight (ToF) measurement. The ToF was also used to compute the fragments measured kinetic energy. The cross sections are presented as a function of the fragments kinetic energy at production thanks to an unfolding technique applied to the data., Comment: Corresponding Author: Marco Toppi, marco.toppi@uniroma1.it

This paper presents the measurements of the angular differential cross sections for the forward production of He, Li, Be, B, C and N nuclei in the fragmentation process of a 400$\text{MeV/nucleon}$ $^{16}\text{O}$ beam interacting with a graphite target. Due to the limited data available in this energy regime, these measurements of nuclear fragmentation cross sections are relevant to improve nuclear interaction models for Particle Therapy and space radioprotection applications. The data analyzed in this paper were collected during a measurement campaign carried out at the GSI Helmholtz Center for Heavy Ion Research facility in Darmstadt (Germany) in 2021 by the FOOT collaboration. The results are compared with similar results found in the literature and with a previous FOOT measurement of the same process, using the same setup, from a previous pilot run performed at GSI in 2019. The pilot run data, however, had limited statistics and only allowed for the measurement of elemental fragmentation cross sections integrated in the setup acceptance. The 2021 data set, with statistics more than 100 times larger compared to the data collected in 2019, enabled the measurement of angular differential cross sections, fully exploiting the granularity of the FOOT $\Delta \text{E}$-TOF system. Furthermore, a better comprehension of the FOOT apparatus allowed to improve the analysis techniques, leading to a reduction in the final systematic uncertainties.

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Specifically, we consider the cases when the underlying random variables satisfy the proportional hazard rate model and the proportional reversed hazard rate model. A setting based on random variables having the 'new better than used' property is also analyzed., Comment: 11 pages

We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the Richards growth curve through a given constant boundary. The relevant features of the modified growth model are studied and compared with those of the original one. A sensitivity analysis on the switching time is also performed. Then, we define two different stochastic processes, i.e. a non-homogeneous linear birth-death process and a lognormal diffusion process, such that their means identify to the growth curve under investigation. For the diffusion process, we address the problem of parameters estimation through the maximum likelihood method. The estimates are obtained via meta-heuristic algorithms (namely, Simulated Annealing and Ant Lion Optimizer). A simulation study to validate the estimation procedure is also presented, together with a real application to oil production in France. Special attention is devoted to the approximation of switching time density, viewed as the first-passage-time density for the lognormal process., Comment: 24 pages, 18 figures

This paper analyzes the dynamics of a level-dependent quasi-birth-death process ${\cal X}=\{(I(t),J(t)): t\geq 0\}$, i.e., a bi-variate Markov chain defined on the countable state space $\cup_{i=0}^{\infty} l(i)$ with $l(i)=\{(i,j) : j\in\{0,...,M_i\}\}$, for integers $M_i\in\mathbb{N}_0$ and $i\in\mathbb{N}_0$, which has the special property that its $q$-matrix has a block-tridiagonal form. Under the assumption that the first passage to the subset $l(0)$ occurs in a finite time with certainty, we characterize the probability law of $(\tau_{\max},I_{\max},J(\tau_{\max}))$, where $I_{\max}$ is the running maximum level attained by process ${\cal X}$ before its first visit to states in $l(0)$, $\tau_{\max}$ is the first time that the level process $\{I(t): t\geq 0\}$ reaches the running maximum $I_{\max}$, and $J(\tau_{\max})$ is the phase at time $\tau_{\max}$. Our methods rely on the use of restricted Laplace-Stieltjes transforms of $\tau_{\max}$ on the set of sample paths $\{I_{\max}=i,J(\tau_{\max})=j\}$, and related processes under taboo of certain subsets of states. The utility of the resulting computational algorithms is demonstrated in two epidemic models: the SIS model for horizontally and vertically transmitted diseases; and the SIR model with constant population size., Comment: 28 pages, 5 figures

We consider a two-dimensional time-inhomogeneous birth-death process to model the time-evolution of fake news in a population. The two components of the process represent, respectively, (i) the number of individuals (say spreaders) who know the rumor and intend to spread it, and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function-based approach to obtain the moments and the covariance of the two-dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modelling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.\, Comment: 41 pages, 12 figures, 7 tables, accepted for publication on "Mathematical Methods in the Applied Sciences"

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary., Comment: 37 pages, 36 figures

We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main properties of the curve, such as the limit behavior, the inflection points and the threshold-crossing-time through a fixed boundary. We also present an application in population dynamics of plants based on real data. Then, we define two different birth-death processes, one with linear birth and death rates and the other with quadratic rates, and we analyze their main features. The conditions under which the processes have a mean of multi-sigmoidal logistic type and the first-passage-time problem are also discussed. Finally, with the aim of obtaining a more manageable stochastic description of the growth, we perform a scaling procedure leading to a lognormal diffusion process with mean of multi-sigmoidal logistic type. We finally conduct a detailed probabilistic analysis of this process, Comment: 28 pages, 30 figures

We investigate the effects of the resetting mechanism to the origin for a random motion on the real line characterized by two alternating velocities $v_1$ and $v_2$. We assume that the sequences of random times concerning the motions along each velocity follow two independent geometric counting processes of intensity $\lambda$, and that the resetting times are Poissonian with rate $\xi >0$. Under these assumptions we obtain the probability laws of the modified telegraph process describing the position and the velocity of the running particle. Our approach is based on the Markov property of the resetting times and on the knowledge of the distribution of the intertimes between consecutive velocity changes. We obtain also the asymptotic distribution of the particle position when (i) $\lambda$ tends to infinity, and (ii) the time goes to infinity. In the latter case the asymptotic distribution arises properly as an effect of the resetting mechanism. A quite different behavior is observed in the two cases when $v_2<0

In this paper, we introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered $\alpha$-stable subordinator. We study its distributional properties and its connection to differential equations. The L\'{e}vy measure for the BTSFPP is also derived. A bivariate competing risks and shock model based on the BTSFPP for predicting the failure times of the items that undergo two random shocks is also explored. The system is supposed to break when the sum of two types of shocks reaches a certain random threshold. Various results related to reliability such as reliability function, hazard rates, failure density, and the probability that the failure occurs due to a certain type of shock are studied. We show that for a general L\'{e}vy subordinator, the failure time of the system is exponentially distributed with mean depending on the Laplace exponent of the L\'{e}vy subordinator when the threshold has geometric distribution. Some special cases and several typical examples are also demonstrated., Comment: 16 pages, 6 figures

Given a random variable $X$ and considered a family of its possible distortions, we define two new measures of distance between $X$ and each its distortion. For these distance measures, which are extensions of the Gini's mean difference, conditions are determined for the existence of a minimum, or a maximum, within specific families of distortions, generalizing some results presented in the recent literature., Comment: 14 pages, 3 figures, previous version submitted for publication on March 20, 2023

We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of $k$-out-of-$n$ systems and with stress-strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions., Comment: 25 pages, 1 figure, revision submitted on September 19, 2023

We present a study of a directional search for Dark Matter boosted forward when scattered by cosmic-ray nuclei, using a module of the NEWSdm experiment. The boosted Dark Matter flux at the edge of the Earth's atmosphere is expected to be pointing to the Galactic Center, with a flux 15 to 20 times larger than in the transverse direction. The module of the NEWSdm experiment consists of a 10 kg stack of Nano Imaging Trackers, i.e.~newly developed nuclear emulsions with AgBr crystal sizes down to a few tens of nanometers. The module is installed on an equatorial telescope. The relatively long recoil tracks induced by boosted Dark Matter, combined with the nanometric granularity of the emulsion, result in an extremely low background. This makes an installation at the INFN Gran Sasso laboratory, both on the surface and underground, viable. A comparison between the two locations is made. The angular distribution of nuclear recoils induced by boosted Dark Matter in the emulsion films at the surface laboratory is expected to show an excess with a factor of 3.5 in the direction of the Galactic Center. This excess allows for a Dark Matter search with directional sensitivity. The surface laboratory configuration prevents the deterioration of the signal in the rock overburden and it emerges as the most powerful approach for a directional observation of boosted Dark Matter with high sensitivity. We show that, with this approach, a 10 kg module of the NEWSdm experiment exposed for one year at the Gran Sasso surface laboratory can probe Dark Matter masses between 1 keV/c$^2$ and 1 GeV/c$^2$ and cross-section values down to $10^{-30}$~cm$^2$ with a directional sensitive search., Comment: 15 pages, 14 figures, updated references, clarified discussion in intro section. Accepted in JCAP

This paper describes a new $\nu_e$ identification method specifically designed to improve the low-energy ($< 30\,\mathrm{GeV}$) $\nu_e$ identification efficiency attained by enlarging the emulsion film scanning volume with the next generation emulsion readout system. A relative increase of 25-70% in the $\nu_e$ low-energy region is expected, leading to improvements in the OPERA sensitivity to neutrino oscillations in the framework of the 3 + 1 model. The method is applied to a subset of data where the detection efficiency increase is expected to be more relevant, and one additional $\nu_e$ candidate is found. The analysis combined with the $\nu_\tau$ appearance results improves the upper limit on $\sin^2 2\theta_{\mu e}$ to 0.016 at 90% C.L. in the MiniBooNE allowed region $\Delta m^2_{41} \sim 0.3\,\mathrm{eV}^2$., Comment: 13 pages, 6 figures

This paper provides an overview of experiments and facilities for accelerator-based dark matter searches as part of the US Community Study on the Future of Particle Physics (Snowmass 2021). Companion white papers to this paper present the physics drivers: thermal dark matter, visible dark portals, and new flavors and rich dark sectors., Comment: contribution to Snowmass 2021

Tau neutrinos are the least studied particle in the Standard Model. This whitepaper discusses the current and expected upcoming status of tau neutrino physics with attention to the broad experimental and theoretical landscape spanning long-baseline, beam-dump, collider, and astrophysical experiments. This whitepaper was prepared as a part of the NuTau2021 Workshop., Comment: 155 pages, 63 figures, 10 tables, 69 endorsers, comments welcome, Contribution to Snowmass 2021. v2: published version

High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe Standard Model (SM) processes and search for physics beyond the Standard Model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential., Comment: 429 pages, contribution to Snowmass 2021

We deal with a continuous-time Ehrenfest model defined over an extended star graph, defined as a lattice formed by the integers of $d$ semiaxis joined at the origin. The dynamics on each ray are regulated by linear transition rates, whereas the switching among rays at the origin occurs according to a general stochastic matrix. We perform a detailed investigation of the transient and asymptotic behavior of this process. We also obtain a diffusive approximation of the considered model, which leads to an Ornstein-Uhlenbeck diffusion process over a domain formed by semiaxis joined at the origin, named spider. We show that the approximating process possesses a truncated Gaussian stationary density. Finally, the goodness of the approximation is discussed through comparison of stationary distributions, means and variances., Comment: 30 pages, 9 figures, 3 tables, to be published in "Mathematical Methods in the Applied Sciences"

The aim of this research is to identify an efficient model to describe the fluctuations around the trend of the soil temperatures monitored in the volcanic caldera of the Campi Flegrei area in Naples (Italy). The study focuses on the data concerning the temperatures in the mentioned area through a seven-year period. The research is initially finalized to identify the deterministic component of the model, given by the seasonal trend of the temperatures, which is obtained through an adapted regression method on the time series. Subsequently, the stochastic component from the time series is tested to represent a fractional Brownian motion (fBm). An estimation based on the periodogram of the data is used to estabilish that the data series follows a fBm motion, rather then a fractional Gaussian noise. An estimation of the Hurst exponent $H$ of the process is also obtained. Finally, an inference test based on the detrended moving average of the data is adopted in order to assess the hypothesis that the time series follows a suitably estimated fBm.

During the upcoming High Luminosity phase of the Large Hadron Collider (HL-LHC), the integrated luminosity of the accelerator will increase to 3000 fb$^{-1}$. The expected experimental conditions in that period in terms of background rates, event pileup, and the probable aging of the current detectors present a challenge for all the existing experiments at the LHC, including the Compact Muon Solenoid (CMS) experiment. To ensure a highly performing muon system for this period, several upgrades of the Resistive Plate Chamber (RPC) system of the CMS are currently being implemented. These include the replacement of the readout system for the present system, and the installation of two new RPC stations with improved chamber and front-end electronics designs. The current overall status of this CMS RPC upgrade project is presented.

Different strategies of reliability theory for the analysis of coherent systems have been studied by various researchers. Here, the Gini-type index is utilized as an applicable tool for the study and comparison of the ageing properties of complex systems. A new stochastic order in terms of Gini-type index is introduced to compare the speed of ageing of components and systems. The parallel-series and series-parallel systems with shared components are studied by their corresponding Gini-type indexes. Also, the generalization of Gini-type index for the multidimensional case is discussed, and is used to compare components lifetimes properties in the presence of other dependent components. It is shown that the ageing properties of a component lifetime can differ when the other components are working or have already failed. Numerous illustrative examples are given for better intuition of Gini-type and generalized Gini-type indexes throughout the paper., Comment: 29 pages, 16 figures

Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy., Comment: 15 pages, accepted for publication in Metrika

To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables., Comment: 19 pages, 3 figures

We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both the transient and steady-state probabilities of the above model. Further, the first passage time through state 0 is discussed. We perform a jump-diffusion approximation of the above model, which leads to the Ornstein-Uhlenbeck process with catastrophes. The underlying jump-diffusion process is finally studied, with special attention to the symmetric case arising when the Ehrenfest model has equal upward and downward transition rates., Comment: 21 pages, 10 figures

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments. For the approximating process we determine the steady-state distribution, the transient distribution and a first-passage-time density., Comment: 31 pages, 18 figures

We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability $\alpha$, or reflected upwards, with probability $1-\alpha$. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.