Representation of Finite Abelian Group Elements by Subsequence Sums

Let $G\cong C_{n_1}\oplus ... \oplus C_{n_r}$ be a finite and nontrivial abelian group with $n_1|n_2|...|n_r$. A conjecture of Hamidoune says that if $W=w_1... w_n$ is a sequence of integers, all but at most one relatively prime to $|G|$, and $S$ is a sequence over $G$ with $|S|\geq |W|+|G|-1\geq |G|+1$, the maximum multiplicity of $S$ at most $|W|$, and $\sigma(W)\equiv 0\mod |G|$, then there exists a nontrivial subgroup $H$ such that every element $g\in H$ can be represented as a weighted subsequence sum of the form $g=\sum_{i=1}^{n}w_is_i$, with $s_1... s_n$ a subsequence of $S$. We give two examples showing this does not hold in general, and characterize the counterexamples for large $|W|\geq {1/2}|G|$. A theorem of Gao, generalizing an older result of Olson, says that if $G$ is a finite abelian group, and $S$ is a sequence over $G$ with $|S|\geq |G|+D(G)-1$, then either every element of $G$ can be represented as a $|G|$-term subsequence sum from $S$, or there exists a coset $g+H$ such that all but at most $|G/H|-2$ terms of $S$ are from $g+H$. We establish some very special cases in a weighted analog of this theorem conjectured by Ordaz and Quiroz, and some partial conclusions in the remaining cases, which imply a recent result of Ordaz and Quiroz. This is done, in part, by extending a weighted setpartition theorem of Grynkiewicz, which we then use to also improve the previously mentioned result of Gao by showing that the hypothesis $|S|\geq |G|+D(G)-1$ can be relaxed to $|S|\geq |G|+d^*(G)$, where d^*(G)=\Sum_{i=1}^{r}(n_i-1). We also use this method to derive a variation on Hamidoune's conjecture valid when at least $d^*(G)$ of the $w_i$ are relatively prime to $|G|$

Some results on the space of bounded second κ-variation functions

In this paper, we prove that if a globally Lipschitz non-autonomous superposition operator maps the space of functions of bounded second $\kappa$-variation into itself then its generator function satisfies a Matkowski condition. We also provide conditions for the existence and uniqueness of solutions of the Hammerstein and Volterra equations in this space

Mechanism of RPE Cell Death in α-Crystallin Deficient Mice: A Novel and Critical Role for MRP1-Mediated GSH Efflux

Absence of α-crystallins (αA and αB) in retinal pigment epithelial (RPE) cells renders them susceptible to oxidant-induced cell death. We tested the hypothesis that the protective effect of α-crystallin is mediated by changes in cellular glutathione (GSH) and elucidated the mechanism of GSH efflux. In α-crystallin overexpressing cells resistant to cell death, cellular GSH was >2 fold higher than vector control cells and this increase was seen particularly in mitochondria. The high GSH levels associated with α-crystallin overexpression were due to increased GSH biosynthesis. On the other hand, cellular GSH was decreased by 50% in murine retina lacking αA or αB crystallin. Multiple multidrug resistance protein (MRP) family isoforms were expressed in RPE, among which MRP1 was the most abundant. MRP1 was localized to the plasma membrane and inhibition of MRP1 markedly decreased GSH efflux. MRP1-suppressed cells were resistant to cell death and contained elevated intracellular GSH and GSSG. Increased GSH in MRP1-supressed cells resulted from a higher conversion of GSSG to GSH by glutathione reductase. In contrast, GSH efflux was significantly higher in MRP1 overexpressing RPE cells which also contained lower levels of cellular GSH and GSSG. Oxidative stress further increased GSH efflux with a decrease in cellular GSH and rendered cells apoptosis-prone. In conclusion, our data reveal for the first time that 1) MRP1 mediates GSH and GSSG efflux in RPE cells; 2) MRP1 inhibition renders RPE cells resistant to oxidative stress-induced cell death while MRP1 overexpression makes them susceptible and 3) the antiapoptotic function of α-crystallin in oxidatively stressed cells is mediated in part by GSH and MRP1. Our findings suggest that MRP1 and α crystallin are potential therapeutic targets in pathological retinal degenerative disorders linked to oxidative stress

Low exposure long-baseline neutrino oscillation sensitivity of the DUNE experiment

The Deep Underground Neutrino Experiment (DUNE) will produce world-leading neutrino oscillation measurements over the lifetime of the experiment. In this work, we explore DUNE's sensitivity to observe charge-parity violation (CPV) in the neutrino sector, and to resolve the mass ordering, for exposures of up to 100 kiloton-megawatt-years (kt-MW-yr). The analysis includes detailed uncertainties on the flux prediction, the neutrino interaction model, and detector effects. We demonstrate that DUNE will be able to unambiguously resolve the neutrino mass ordering at a 3$\sigma$ (5$\sigma$) level, with a 66 (100) kt-MW-yr far detector exposure, and has the ability to make strong statements at significantly shorter exposures depending on the true value of other oscillation parameters. We also show that DUNE has the potential to make a robust measurement of CPV at a 3$\sigma$ level with a 100 kt-MW-yr exposure for the maximally CP-violating values \delta_{\rm CP}} = \pm\pi/2. Additionally, the dependence of DUNE's sensitivity on the exposure taken in neutrino-enhanced and antineutrino-enhanced running is discussed. An equal fraction of exposure taken in each beam mode is found to be close to optimal when considered over the entire space of interest

A Gaseous Argon-Based Near Detector to Enhance the Physics Capabilities of DUNE

This document presents the concept and physics case for a magnetized gaseous argon-based detector system (ND-GAr) for the Deep Underground Neutrino Experiment (DUNE) Near Detector. This detector system is required in order for DUNE to reach its full physics potential in the measurement of CP violation and in delivering precision measurements of oscillation parameters. In addition to its critical role in the long-baseline oscillation program, ND-GAr will extend the overall physics program of DUNE. The LBNF high-intensity proton beam will provide a large flux of neutrinos that is sampled by ND-GAr, enabling DUNE to discover new particles and search for new interactions and symmetries beyond those predicted in the Standard Model

Snowmass Neutrino Frontier: DUNE Physics Summary

The Deep Underground Neutrino Experiment (DUNE) is a next-generation long-baseline neutrino oscillation experiment with a primary physics goal of observing neutrino and antineutrino oscillation patterns to precisely measure the parameters governing long-baseline neutrino oscillation in a single experiment, and to test the three-flavor paradigm. DUNE's design has been developed by a large, international collaboration of scientists and engineers to have unique capability to measure neutrino oscillation as a function of energy in a broadband beam, to resolve degeneracy among oscillation parameters, and to control systematic uncertainty using the exquisite imaging capability of massive LArTPC far detector modules and an argon-based near detector. DUNE's neutrino oscillation measurements will unambiguously resolve the neutrino mass ordering and provide the sensitivity to discover CP violation in neutrinos for a wide range of possible values of δCP. DUNE is also uniquely sensitive to electron neutrinos from a galactic supernova burst, and to a broad range of physics beyond the Standard Model (BSM), including nucleon decays. DUNE is anticipated to begin collecting physics data with Phase I, an initial experiment configuration consisting of two far detector modules and a minimal suite of near detector components, with a 1.2 MW proton beam. To realize its extensive, world-leading physics potential requires the full scope of DUNE be completed in Phase II. The three Phase II upgrades are all necessary to achieve DUNE's physics goals: (1) addition of far detector modules three and four for a total FD fiducial mass of at least 40 kt, (2) upgrade of the proton beam power from 1.2 MW to 2.4 MW, and (3) replacement of the near detector's temporary muon spectrometer with a magnetized, high-pressure gaseous argon TPC and calorimeter

Scintillation light detection in the 6-m drift-length ProtoDUNE Dual Phase liquid argon TPC

DUNE is a dual-site experiment for long-baseline neutrino oscillation studies, neutrino astrophysics and nucleon decay searches. ProtoDUNE Dual Phase (DP) is a 6  ×  6  ×  6 m 3 liquid argon time-projection-chamber (LArTPC) that recorded cosmic-muon data at the CERN Neutrino Platform in 2019-2020 as a prototype of the DUNE Far Detector. Charged particles propagating through the LArTPC produce ionization and scintillation light. The scintillation light signal in these detectors can provide the trigger for non-beam events. In addition, it adds precise timing capabilities and improves the calorimetry measurements. In ProtoDUNE-DP, scintillation and electroluminescence light produced by cosmic muons in the LArTPC is collected by photomultiplier tubes placed up to 7 m away from the ionizing track. In this paper, the ProtoDUNE-DP photon detection system performance is evaluated with a particular focus on the different wavelength shifters, such as PEN and TPB, and the use of Xe-doped LAr, considering its future use in giant LArTPCs. The scintillation light production and propagation processes are analyzed and a comparison of simulation to data is performed, improving understanding of the liquid argon properties

Snowmass Neutrino Frontier: DUNE Physics Summary

The Deep Underground Neutrino Experiment (DUNE) is a next-generation long-baseline neutrino oscillation experiment with a primary physics goal of observing neutrino and antineutrino oscillation patterns to precisely measure the parameters governing long-baseline neutrino oscillation in a single experiment, and to test the three-flavor paradigm. DUNE's design has been developed by a large, international collaboration of scientists and engineers to have unique capability to measure neutrino oscillation as a function of energy in a broadband beam, to resolve degeneracy among oscillation parameters, and to control systematic uncertainty using the exquisite imaging capability of massive LArTPC far detector modules and an argon-based near detector. DUNE's neutrino oscillation measurements will unambiguously resolve the neutrino mass ordering and provide the sensitivity to discover CP violation in neutrinos for a wide range of possible values of $\delta_{CP}$. DUNE is also uniquely sensitive to electron neutrinos from a galactic supernova burst, and to a broad range of physics beyond the Standard Model (BSM), including nucleon decays. DUNE is anticipated to begin collecting physics data with Phase I, an initial experiment configuration consisting of two far detector modules and a minimal suite of near detector components, with a 1.2 MW proton beam. To realize its extensive, world-leading physics potential requires the full scope of DUNE be completed in Phase II. The three Phase II upgrades are all necessary to achieve DUNE's physics goals: (1) addition of far detector modules three and four for a total FD fiducial mass of at least 40 kt, (2) upgrade of the proton beam power from 1.2 MW to 2.4 MW, and (3) replacement of the near detector's temporary muon spectrometer with a magnetized, high-pressure gaseous argon TPC and calorimeter.Comment: Contribution to Snowmass 202

Reconstruction of interactions in the ProtoDUNE-SP detector with Pandora

The Pandora Software Development Kit and algorithm libraries provide pattern-recognition logic essential to the reconstruction of particle interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at ProtoDUNE-SP, a prototype for the Deep Underground Neutrino Experiment far detector. ProtoDUNE-SP, located at CERN, is exposed to a charged-particle test beam. This paper gives an overview of the Pandora reconstruction algorithms and how they have been tailored for use at ProtoDUNE-SP. In complex events with numerous cosmic-ray and beam background particles, the simulated reconstruction and identification efficiency for triggered test-beam particles is above 80% for the majority of particle type and beam momentum combinations. Specifically, simulated 1 GeV/$c$ charged pions and protons are correctly reconstructed and identified with efficiencies of 86.1$\pm0.6$% and 84.1$\pm0.6$%, respectively. The efficiencies measured for test-beam data are shown to be within 5% of those predicted by the simulation.Comment: 39 pages, 19 figure

Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector

Measurements of electrons from $\nu_e$ interactions are crucial for the Deep Underground Neutrino Experiment (DUNE) neutrino oscillation program, as well as searches for physics beyond the standard model, supernova neutrino detection, and solar neutrino measurements. This article describes the selection and reconstruction of low-energy (Michel) electrons in the ProtoDUNE-SP detector. ProtoDUNE-SP is one of the prototypes for the DUNE far detector, built and operated at CERN as a charged particle test beam experiment. A sample of low-energy electrons produced by the decay of cosmic muons is selected with a purity of 95%. This sample is used to calibrate the low-energy electron energy scale with two techniques. An electron energy calibration based on a cosmic ray muon sample uses calibration constants derived from measured and simulated cosmic ray muon events. Another calibration technique makes use of the theoretically well-understood Michel electron energy spectrum to convert reconstructed charge to electron energy. In addition, the effects of detector response to low-energy electron energy scale and its resolution including readout electronics threshold effects are quantified. Finally, the relation between the theoretical and reconstructed low-energy electron energy spectrum is derived and the energy resolution is characterized. The low-energy electron selection presented here accounts for about 75% of the total electron deposited energy. After the addition of lost energy using a Monte Carlo simulation, the energy resolution improves from about 40% to 25% at 50~MeV. These results are used to validate the expected capabilities of the DUNE far detector to reconstruct low-energy electrons.Comment: 19 pages, 10 figure