A priori bounds for superlinear problems involving the N-Laplacian

In this paper we establish a priori bounds for positive solution of the N-Laplace equation in a bounded smooth domain in R^N, and with a nonlinearity having at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis-Merle to the N-Laplacian, in combination with the Trudinger-Moser inequality,the Moving Planes method and a Comparison Principle for the N-Laplacian

Surgical treatment of pressure injuries in children: A multicentre experience

Pressure injuries (PI) are infrequent in paediatric patients, prevalence estimates ranging from 1.4% to 8.2%, and reaching values as high as 43.1% in critical care areas. They can be associated with congenital neurological or metabolic disorders that cause reduced mobility or require the need for medical devices. In children, most pressure injuries heal spontaneously. However, a small percentage of ulcers that is refractory to conservative management or is too severe at presentation (Stage 3 or 4) will be candidates for surgery. We retrospectively reviewed the clinical history of paediatric patients affected by pressure injuries from four European Plastic Surgery Centres. Information was collected from clinical and radiology records, and laboratory reports. An accurate search of the literature revealed only two articles reporting on the surgical treatment of pressure injuries in children. After debridement, we performed surgical coverage of the pressure injuries. We report here our experience with 18 children aged 1-17 years, affected by pressure injury Stages 3 and 4. They were successfully treated with pedicled (17 patients) or free flaps (1 patient). The injuries involved the sacrum (6/18 patients), lower limb (3/18 patients), thoracic spine (2/18 patients), ischium (3/18 patients, bilateral in one patient), temporal area (3/18 patients), hypogastrium (1/18 patients) and were associated to medical devices in three cases. Flaps were followed for a minimum of 19 months and up to 13 years. Only two patients developed true recurrences that were treated again surgically. Pressure injuries are infrequent in children and rarely need surgical treatment. Pedicled flaps have a high success rate. Recurrences, contrary to what is reported in the literature, were rare

Migration induced epidemics: Dynamics of flux-based multipatch models

Classical disease models use a mass action term as the interaction between infected and susceptible people in separate patches. We derive the equations when this interaction is a migration of people between patches. The results model what happens when a new population is moved into a region with endemic disease.Comment: 25 page

Damage to Broca's area does not contribute to long-term speech production outcome after stroke

Broca’s area in the posterior half of the left inferior frontal gyrus has long been thought to be critical for speech production. The current view is that long-term speech production outcome in patients with Broca’s area damage is best explained by the combination of damage to Broca’s area and neighbouring regions including the underlying white matter, which was also damaged in Paul Broca’s two historic cases. Here, we dissociate the effect of damage to Broca’s area from the effect of damage to surrounding areas by studying long-term speech production outcome in 134 stroke survivors with relatively circumscribed left frontal lobe lesions that spared posterior speech production areas in lateral inferior parietal and superior temporal association cortices. Collectively, these patients had varying degrees of damage to one or more of nine atlas-based grey or white matter regions: Brodmann areas 44 and 45 (together known as Broca’s area), ventral premotor cortex, primary motor cortex, insula, putamen, the anterior segment of the arcuate fasciculus, uncinate fasciculus and frontal aslant tract. Spoken picture description scores from the Comprehensive Aphasia Test were used as the outcome measure. Multiple regression analyses allowed us to tease apart the contribution of other variables influencing speech production abilities such as total lesion volume and time post-stroke. We found that, in our sample of patients with left frontal damage, long-term speech production impairments (lasting beyond 3 months post-stroke) were solely predicted by the degree of damage to white matter, directly above the insula, in the vicinity of the anterior part of the arcuate fasciculus, with no contribution from the degree of damage to Broca’s area (as confirmed with Bayesian statistics). The effect of white matter damage cannot be explained by a disconnection of Broca’s area, because speech production scores were worse after damage to the anterior arcuate fasciculus with relative sparing of Broca’s area than after damage to Broca’s area with relative sparing of the anterior arcuate fasciculus. Our findings provide evidence for three novel conclusions: (i) Broca’s area damage does not contribute to long-term speech production outcome after left frontal lobe strokes; (ii) persistent speech production impairments after damage to the anterior arcuate fasciculus cannot be explained by a disconnection of Broca’s area; and (iii) the prior association between persistent speech production impairments and Broca’s area damage can be explained by co-occurring white matter damage, above the insula, in the vicinity of the anterior part of the arcuate fasciculus

Calibration of the charge and energy loss per unit length of the MicroBooNE liquid argon time projection chamber using muons and protons

We describe a method used to calibrate the position- and time-dependent response of the MicroBooNE liquid argon time projection chamber anode wires to ionization particle energy loss. The method makes use of crossing cosmic-ray muons to partially correct anode wire signals for multiple effects as a function of time and position, including cross-connected TPC wires, space charge effects, electron attachment to impurities, diffusion, and recombination. The overall energy scale is then determined using fully-contained beam-induced muons originating and stopping in the active region of the detector. Using this method, we obtain an absolute energy scale uncertainty of 2% in data. We use stopping protons to further refine the relation between the measured charge and the energy loss for highly-ionizing particles. This data-driven detector calibration improves both the measurement of total deposited energy and particle identification based on energy loss per unit length as a function of residual range. As an example, the proton selection efficiency is increased by 2% after detector calibration

Reconstruction and measurement of (100) MeV energy electromagnetic activity from π0 arrow γγ decays in the MicroBooNE LArTPC

We present results on the reconstruction of electromagnetic (EM) activity from photons produced in charged current νμ interactions with final state π0s. We employ a fully-automated reconstruction chain capable of identifying EM showers of (100) MeV energy, relying on a combination of traditional reconstruction techniques together with novel machine-learning approaches. These studies demonstrate good energy resolution, and good agreement between data and simulation, relying on the reconstructed invariant π0 mass and other photon distributions for validation. The reconstruction techniques developed are applied to a selection of νμ + Ar → μ + π0 + X candidate events to demonstrate the potential for calorimetric separation of photons from electrons and reconstruction of π0 kinematics

Noise Characterization and Filtering in the MicroBooNE Liquid Argon TPC

The low-noise operation of readout electronics in a liquid argon time projection chamber (LArTPC) is critical to properly extract the distribution of ionization charge deposited on the wire planes of the TPC, especially for the induction planes. This paper describes the characteristics and mitigation of the observed noise in the MicroBooNE detector. The MicroBooNE's single-phase LArTPC comprises two induction planes and one collection sense wire plane with a total of 8256 wires. Current induced on each TPC wire is amplified and shaped by custom low-power, low-noise ASICs immersed in the liquid argon. The digitization of the signal waveform occurs outside the cryostat. Using data from the first year of MicroBooNE operations, several excess noise sources in the TPC were identified and mitigated. The residual equivalent noise charge (ENC) after noise filtering varies with wire length and is found to be below 400 electrons for the longest wires (4.7 m). The response is consistent with the cold electronics design expectations and is found to be stable with time and uniform over the functioning channels. This noise level is significantly lower than previous experiments utilizing warm front-end electronics.Comment: 36 pages, 20 figure

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

Convolutional Neural Networks Applied to Neutrino Events in a Liquid Argon Time Projection Chamber

We present several studies of convolutional neural networks applied to data coming from the MicroBooNE detector, a liquid argon time projection chamber (LArTPC). The algorithms studied include the classification of single particle images, the localization of single particle and neutrino interactions in an image, and the detection of a simulated neutrino event overlaid with cosmic ray backgrounds taken from real detector data. These studies demonstrate the potential of convolutional neural networks for particle identification or event detection on simulated neutrino interactions. We also address technical issues that arise when applying this technique to data from a large LArTPC at or near ground level

The Pandora multi-algorithm approach to automated pattern recognition of cosmic-ray muon and neutrino events in the MicroBooNE detector

The development and operation of Liquid-Argon Time-Projection Chambers for neutrino physics has created a need for new approaches to pattern recognition in order to fully exploit the imaging capabilities offered by this technology. Whereas the human brain can excel at identifying features in the recorded events, it is a significant challenge to develop an automated, algorithmic solution. The Pandora Software Development Kit provides functionality to aid the design and implementation of pattern-recognition algorithms. It promotes the use of a multi-algorithm approach to pattern recognition, in which individual algorithms each address a specific task in a particular topology. Many tens of algorithms then carefully build up a picture of the event and, together, provide a robust automated pattern-recognition solution. This paper describes details of the chain of over one hundred Pandora algorithms and tools used to reconstruct cosmic-ray muon and neutrino events in the MicroBooNE detector. Metrics that assess the current pattern-recognition performance are presented for simulated MicroBooNE events, using a selection of final-state event topologies.Comment: Preprint to be submitted to The European Physical Journal