How many zeros of a random sparse polynomial are real?

We investigate the number of real zeros of a univariate $k$-sparse polynomial $f$ over the reals, when the coefficients of $f$ come from independent standard normal distributions. Recently B\"urgisser, Erg\"ur and Tonelli-Cueto showed that the expected number of real zeros of $f$ in such cases is bounded by $O(\sqrt{k} \log k)$. In this work, we improve the bound to $O(\sqrt{k})$ and also show that this bound is tight by constructing a family of sparse support whose expected number of real zeros is lower bounded by $\Omega(\sqrt{k})$. Our main technique is an alternative formulation of the Kac integral by Edelman-Kostlan which allows us to bound the expected number of zeros of $f$ in terms of the expected number of zeros of polynomials of lower sparsity. Using our technique, we also recover the $O(\log n)$ bound on the expected number of real zeros of a dense polynomial of degree $n$ with coefficients coming from independent standard normal distributions

Extracting chromatic properties of electron beams from spectral analysis of turn-by-turn beam position data

A method to estimate linear chromaticity, RMS energy spread, and chromatic beta-beating, directly from turn-by-turn beam position data in a circular electron accelerator, is presented. This technique is based on frequency analysis of a transversely excited beam, in the presence of finite chromaticity. Due to the turn-by-turn chromatic modulation of the beam's envelope, betatron sidebands appear around the main frequency of the Fourier spectra. By determining the amplitude of both sidebands, chromatic properties of the beam can be estimated. In this paper, analytical derivations justifying the proposed method are given, along with results from tracking simulations. To this end, results from practical applications of this technique at the KARA electron ring are demonstrated

Baseline Jet Energy Corrections for the CMS Experiment at the CERN LHC

Ο Μεγάλος Επιταχυντής Αδρονίων LHC (Large Hadron Collider) στο Εργαστήριο CERN παρέχει συγκρούσεις πρωτονίου-πρωτονίου στα 13 TeV, η υψηλότερη ενέργεια μέχρι σήμερα, καθιστώντας τα πειράματα ικανά να ελέγξουν και να διερευνήσουν το Καθιερωμένο Πρότυπο (ΚΜ) με μεγάλη ακρίβεια. Οι αδρονικοί πίδακες είναι οι πειραματικές υπογραφές των κουάρκ και γκλουονίων που παράγονται στην τελική κατάσταση υψηλοενεργειακών σκεδάσεων, όπως αυτές που πραγματοποιούνται στο πείραμα CMS (Compact Muon Solenoid) στον LHC. Ένα μεγάλο πλήθος αναλύσεων φυσικής που στοχεύουν όχι μόνο στην μελέτη υπογραφών του Καθιερωμένου Προτύπου, αλλά και στην εύρεση φυσικής πέραν αυτού, χρησιμοποιούν τους αδρονικούς πίδακες, κάνοντας επιτακτική την ανάγκη για μεγάλης ακρίβειας μετρήσεις της ενέργειας τους και των συστηματικών αβεβαιοτήτων. Στην διπλωματική αυτή εργασία θα παρουσιασθούν οι βασικές διορθώσεις ενέργειας που παράγονται χρησιμοποιώντας προσομοιώσεις (Monte Carlo) και αποτελούν το πρώτο και κύριο μέρος της αλυσίδας των διορθώσεων ενέργειας. Οι διορθώσεις αυτές χωρίζονται σε δύο επίπεδα, αυτές που αφαιρούν την επιπρόσθετη ενέργεια που οφείλεται σε δευτερεύουσες αλληλεπιδράσεις πέραν της κύριας, και αυτές που στοχεύουν στην εξίσωση της ενέργειας σε επίπεδο ανακατασκευής με την αντίστοιχη στο επίπεδο του γεννήτορα που δεν λαμβάνει υπ' όψιν τις ατέλειες του ανιχνευτή και της ανακατασκευής του γεγονότος. Πριν συζητηθούν οι διορθώσεις της ενέργειας, θα παρουσιασθούν τα βασικά χαρακτηριστικά της Κβαντικής Χρωμοδυναμικής και του σχηματισμού των αδρονικών πιδάκων. Επιπλέον, θα περιγραφεί η ανιχνευτική διάταξη του πειράματος CMS και θα συζητηθούν οι τρόποι με τους οποίους ανακατασκευάζονται και ομαδοποιούνται οι αδρονικοί πίδακες στο CMS.Jets are the experimental signature of quarks and gluons produced in the final state of high energy scatterings, as the ones that take place in the CMS experiment at the Large Hadron Collider. Numerous physics analyses that not only aim to study Standard Model (SM) Processes, but also to search for physics beyond the SM, use jets, thus creating the need for high accuracy in the estimation of their energy and the associated uncertainties. The factorized Jet Energy Corrections (JEC) that are utilized by the CMS experiment aim to provide exactly that. In this thesis the baseline jet energy corrections that are derived from simulation and constitute the first and main step of the JEC chain, will be presented. These corrections are divided into two levels; the pileup offset corrections (L1) whose goal is to remove the excess jet energy that is caused by additional proton - proton collisions different from the main hard scatter, and the relative and absolute corrections (L2L3) that aim to refer the jet energy at reconstruction level to the respective one at generator level , thus proving an estimation of the true jet energy without the detector resolution and reconstruction effects being considered. Before discussing the jet energy correction estimation and showing the final results, the theoretical aspects of Quantum Chromodynamics and jet formation will be presented. Furthermore, a description of the CMS detector layout will be provided, along with the methods used in order to reconstruct and cluster jets in the CMS experiment

Inequities blocking the path to circular economies:A bio-inspired network-based approach for assessing the sustainability of the global trade of waste metals

Considering the importance of waste metals for the transition to circular economies, this study follows a bio-inspired approach to evaluate their material and monetary global trade patterns for sustainability and equity. Between 2000 and 2022, the global trade grew by 5 % in trading countries, by 37 % in trade links, by 71 % in material flows, and by 569 % in economic flows. Driven by indirect effects, the average circulation of material and monetary flows ranged between 21.8–34.9 % depending on the demand or supply perspective but showed a declining trend. Due to homogenization, high network redundancy, and low network efficiency the trade remained robust yet outside the "window of vitality" characterizing natural ecosystems. A few, mostly high-income countries dominated the market, consolidating imports of high-value metal waste mostly from low- and middle-income exporters. Policies should address circularity and trade inequities, accounting for environmental and social ramifications throughout the lifecycle of products and materials

Measurement of inclusive and differential cross sections for single top quark production in association with a W boson in proton-proton collisions at s \sqrt{s} = 13 TeV

Measurements of the inclusive and normalised differential cross sections are presented for the production of single top quarks in association with a W boson in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used were recorded with the CMS detector at the LHC during 2016-2018, and correspond to an integrated luminosity of 138 fb$^{−1}$. Events containing one electron and one muon in the final state are analysed. For the inclusive measurement, a multivariate discriminant, exploiting the kinematic properties of the events is used to separate the signal from the dominant $t\bar{t}$ background. A cross section of 79.2 ± 0.9 (stat) $^{+7.7}_{−8.0}$ (syst) ± 1.2 (lumi) pb is obtained, consistent with the predictions of the standard model. For the differential measurements, a fiducial region is defined according to the detector acceptance, and the requirement of exactly one jet coming from the fragmentation of a bottom quark. The resulting distributions are unfolded to particle level and agree with the predictions at next-to-leading order in perturbative quantum chromodynamics

Observation of the Rare Decay of the η Meson to Four Muons

A search for the rare η→μ+μ−μ+μ− double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers during 2017 and 2018 and corresponding to an integrated luminosity of 101  fb−1. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the η→μ+μ− decay as normalization, the branching fraction B(η→μ+μ−μ+μ−)=[5.0±0.8(stat)±0.7(syst)±0.7(B2μ)]×10−9 is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over 5 orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions

Search for top squarks in the four-body decay mode with single lepton final states in proton-proton collisions at s \sqrt{s} = 13 TeV

A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark (t∼1), is presented. The search targets the four-body decay of the t∼1, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino (χ∼01), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb−1 of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a high-momentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between m(t∼1) and m(χ∼01). The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for m(t∼1) − m(χ∼01) = 10 and 80 GeV, respectively