Recurrence and Polya number of general one-dimensional random walks

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities $l$ and $r$, or remain at the same position with probability $o$ ($l+r+o=1$). We calculate P\'{o}lya number $P$ of this model and find a simple expression for $P$ as, $P=1-\Delta$, where $\Delta$ is the absolute difference of $l$ and $r$ ($\Delta=|l-r|$). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability $l$ equals to the right-moving probability $r$.Comment: 3 page short pape

Keeping calm in the face of change: towards optimisation of FRP by reasoning about change

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals (time-varying values). FRP is based on the synchronous data-flow paradigm and supports both (an approximation to) continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of structurally dynamic networks of n-ary signal functions operating on mixed continuous-time and discrete-time signals. We first define an ideal denotational semantics (time is truly continuous) for this kind of FRP, along with temporal properties, expressed in temporal logic, of signals and signal functions pertaining to change and change propagation. Using this framework, we then show how to reason about change; specifically, we identify and justify a number of possible optimisations, such as avoiding recomputation of unchanging values. Note that due to structural dynamism, and the fact that the output of a signal function may change because time is passing even if the input is unchanging, the problem is significantly more complex than standard change propagation in networks with static structure

Measurement of the mass difference between top quark and antiquark in pp collisions at root s=8 TeV

Peer reviewe

Curvature-bias corrections using a pseudomass method

Momentum measurements for very high momentum charged particles, such as muons from electroweak vector boson decays, are particularly susceptible to charge-dependent curvature biases that arise from misalignments of tracking detectors. Low momentum charged particles used in alignment procedures have limited sensitivity to coherent displacements of such detectors, and therefore are unable to fully constrain these misalignments to the precision necessary for studies of electroweak physics. Additional approaches are therefore required to understand and correct for these effects. In this paper the curvature biases present at the LHCb detector are studied using the pseudomass method in proton-proton collision data recorded at centre of mass energy √s = 13 TeV during 2016, 2017 and 2018. The biases are determined using Z → μ+μ- decays in intervals defined by the data-taking period, magnet polarity and muon direction. Correcting for these biases, which are typically at the 10-4 GeV-1 level, improves the Z → μ+μ- mass resolution by roughly 18% and eliminates several pathological trends in the kinematic-dependence of the mean dimuon invariant mass

Investigating strangeness enhancement with multiplicity in pp collisions using angular correlations

A study of strange hadron production associated with hard scattering processes and with the underlying event is conducted to investigate the origin of the enhanced production of strange hadrons in small collision systems characterised by large charged-particle multiplicities. For this purpose, the production of the single-strange meson KS0 and the double-strange baryon Ξ± is measured, in each event, in the azimuthal direction of the highest-pT particle (“trigger” particle), related to hard scattering processes, and in the direction transverse to it in azimuth, associated with the underlying event, in pp collisions at s = 5.02 TeV and s = 13 TeV using the ALICE detector at the LHC. The per-trigger yields of KS0 and Ξ± are dominated by the transverse-to-leading production (i.e., in the direction transverse to the trigger particle), whose contribution relative to the toward-leading production is observed to increase with the event charged-particle multiplicity. The transverse-to-leading and the toward-leading Ξ±/KS0 yield ratios increase with the multiplicity of charged particles, suggesting that strangeness enhancement with multiplicity is associated with both hard scattering processes and the underlying event. The relative production of Ξ± with respect to KS0 is higher in transverse-to-leading processes over the whole multiplicity interval covered by the measurement. The KS0 and Ξ± per-trigger yields and yield ratios are compared with predictions of three different phenomenological models, namely Pythia8.2 with the Monash tune, Pythia8.2 with ropes and EPOS LHC. The comparison shows that none of them can quantitatively describe either the transverse-to-leading or the toward-leading yields of KS0 and Ξ±.publishedVersio