An analytical model for photomultiplier tube calibration

The purpose of the present publication is to offer an analytical model that can be used for the calibration of photomultiplier tubes (PMTs). The derivation of the mathematical formulae involved is discussed extensively and we apply this machinery to a real problem; the gain determination of the R7081 Hamamatsu PMT. We hope that our work can provide a third, powerful alternative to the task of gain deconvolution. We also believe that the techniques explained in this article can be applied to other problems in PMT calibration and monitoring

Calibration of the Hamamatsu R7081 photomultiplier tube

The purpose of the present article is to demonstrate the calibration of the Hamamatsu R7081 photomultiplier using a numerical method based on the Discrete Fourier Transform (DFT). Conventional techniques, usually employed in the literature, use approximate models or brute force numerical calculations of the convolution integrals that lead to the charge response function of the photomultiplier, S_R(x). In this publication, we explain how a truncated gaussian model for the single photoelectron amplification can lead to rigorous results if one leans on the DFT approach. The distinct feature of this procedure is that S_R(x) is calculated to all orders in the Poisson mean $\mu$ that characterizes the light intensity and no approximations are needed. The same scheme can be applied to other photomultiplier tubes that share the same properties with R7081

Numerical Implementation of lepton-nucleus interactions and its effect on neutrino oscillation analysis

We discuss the implementation of the nuclear model based on realistic nuclear spectral functions in the GENIE neutrino interaction generator. Besides improving on the Fermi gas description of the nuclear ground state, our scheme involves a new prescription for $Q^2$ selection, meant to efficiently enforce energy momentum conservation. The results of our simulations, validated through comparison to electron scattering data, have been obtained for a variety of target nuclei, ranging from carbon to argon, and cover the kinematical region in which quasi elastic scattering is the dominant reaction mechanism. We also analyse the influence of the adopted nuclear model on the determination of neutrino oscillation parameters.Comment: 19 pages, 35 figures, version accepted by Phys. Rev.

Determining appropriate approaches for using data in feature selection

Feature selection is increasingly important in data analysis and machine learning in big data era. However, how to use the data in feature selection, i.e. using either ALL or PART of a dataset, has become a serious and tricky issue. Whilst the conventional practice of using all the data in feature selection may lead to selection bias, using part of the data may, on the other hand, lead to underestimating the relevant features under some conditions. This paper investigates these two strategies systematically in terms of reliability and effectiveness, and then determines their suitability for datasets with different characteristics. The reliability is measured by the Average Tanimoto Index and the Inter-method Average Tanimoto Index, and the effectiveness is measured by the mean generalisation accuracy of classification. The computational experiments are carried out on ten real-world benchmark datasets and fourteen synthetic datasets. The synthetic datasets are generated with a pre-set number of relevant features and varied numbers of irrelevant features and instances, and added with different levels of noise. The results indicate that the PART approach is more effective in reducing the bias when the size of a dataset is small but starts to lose its advantage as the dataset size increases

Adjusted Measures for Feature Selection Stability for Data Sets with Similar Features

For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features. Existing adjusted stability measures, that is, stability measures that take into account the similarities between features, have major theoretical drawbacks. We introduce new adjusted stability measures that overcome these drawbacks. We compare them to each other and to existing stability measures based on both artificial and real sets of selected features. Based on the results, we suggest using one new stability measure that considers highly similar features as exchangeable

Algebraic Comparison of Partial Lists in Bioinformatics

The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or just within a meta-analysis comparison, instead of one list it is often the case that sets of alternative feature lists (possibly of different lengths) are obtained. Here we introduce a method, based on the algebraic theory of symmetric groups, for studying the variability between lists ("list stability") in the case of lists of unequal length. We provide algorithms evaluating stability for lists embedded in the full feature set or just limited to the features occurring in the partial lists. The method is demonstrated first on synthetic data in a gene filtering task and then for finding gene profiles on a recent prostate cancer dataset

Determination of muon momentum in the MicroBooNE LArTPC using an improved model of multiple Coulomb scattering

We discuss a technique for measuring a charged particle's momentum by means of multiple Coulomb scattering (MCS) in the MicroBooNE liquid argon time projection chamber (LArTPC). This method does not require the full particle ionization track to be contained inside of the detector volume as other track momentum reconstruction methods do (range-based momentum reconstruction and calorimetric momentum reconstruction). We motivate use of this technique, describe a tuning of the underlying phenomenological formula, quantify its performance on fully contained beam-neutrino-induced muon tracks both in simulation and in data, and quantify its performance on exiting muon tracks in simulation. Using simulation, we have shown that the standard Highland formula should be re-tuned specifically for scattering in liquid argon, which significantly improves the bias and resolution of the momentum measurement. With the tuned formula, we find agreement between data and simulation for contained tracks, with a small bias in the momentum reconstruction and with resolutions that vary as a function of track length, improving from about 10% for the shortest (one meter long) tracks to 5% for longer (several meter) tracks. For simulated exiting muons with at least one meter of track contained, we find a similarly small bias, and a resolution which is less than 15% for muons with momentum below 2 GeV/c. Above 2 GeV/c, results are given as a first estimate of the MCS momentum measurement capabilities of MicroBooNE for high momentum exiting tracks

Measurement of cosmic-ray reconstruction efficiencies in the MicroBooNE LArTPC using a small external cosmic-ray counter

The MicroBooNE detector is a liquid argon time projection chamber at Fermilab designed to study short-baseline neutrino oscillations and neutrino-argon interaction cross-section. Due to its location near the surface, a good understanding of cosmic muons as a source of backgrounds is of fundamental importance for the experiment. We present a method of using an external 0.5 m (L) x 0.5 m (W) muon counter stack, installed above the main detector, to determine the cosmic-ray reconstruction efficiency in MicroBooNE. Data are acquired with this external muon counter stack placed in three different positions, corresponding to cosmic rays intersecting different parts of the detector. The data reconstruction efficiency of tracks in the detector is found to be $\epsilon_{\mathrm{data}}=(97.1\pm0.1~(\mathrm{stat}) \pm 1.4~(\mathrm{sys}))\%$, in good agreement with the Monte Carlo reconstruction efficiency $\epsilon_{\mathrm{MC}} = (97.4\pm0.1)\%$. This analysis represents a small-scale demonstration of the method that can be used with future data coming from a recently installed cosmic-ray tagger system, which will be able to tag $\approx80\%$ of the cosmic rays passing through the MicroBooNE detector.Comment: 19 pages, 12 figure