Universal Behavior in Large-scale Aggregation of Independent Noisy Observations

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a protypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.Comment: 10 pages, 3 figure

Minimizing Unsatisfaction in Colourful Neighbourhoods

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional explanatio

Measurement of Cosmic-ray Muons and Muon-induced Neutrons in the Aberdeen Tunnel Underground Laboratory

We have measured the muon flux and production rate of muon-induced neutrons at a depth of 611 m water equivalent. Our apparatus comprises three layers of crossed plastic scintillator hodoscopes for tracking the incident cosmic-ray muons and 760 L of gadolinium-doped liquid scintillator for producing and detecting neutrons. The vertical muon intensity was measured to be $I_{\mu} = (5.7 \pm 0.6) \times 10^{-6}$ cm$^{-2}$s$^{-1}$sr$^{-1}$. The yield of muon-induced neutrons in the liquid scintillator was determined to be $Y_{n} = (1.19 \pm 0.08 (stat) \pm 0.21 (syst)) \times 10^{-4}$ neutrons/($\mu\cdot$g$\cdot$cm$^{-2}$). A fit to the recently measured neutron yields at different depths gave a mean muon energy dependence of $\left\langle E_{\mu} \right\rangle^{0.76 \pm 0.03}$ for liquid-scintillator targets.Comment: 14 pages, 17 figures, 3 table

Lithium-ion drifting: Application to the study of point defects in floating-zone silicon

The use of lithium-ion (Li(+)) drifting to study the properties of point defects in p-type Floating-Zone (FZ) silicon crystals is reported. The Li(+) drift technique is used to detect the presence of vacancy-related defects (D defects) in certain p-type FZ silicon crystals. SUPREM-IV modeling suggests that the silicon point defect diffusivities are considerably higher than those commonly accepted, but are in reasonable agreement with values recently proposed. These results demonstrate the utility of Li(+) drifting in the study of silicon point defect properties in p-type FZ crystals. Finally, a straightforward measurement of the Li(+) compensation depth is shown to yield estimates of the vacancy-related defect concentration in p-type FZ crystals

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

Thoracoscopic repair of congenital diaphragmatic hernia: two centres’ experience with 60 patients

© 2014, Springer-Verlag Berlin Heidelberg. Methods: All patients who underwent thoracoscopic repair of congenital diaphragmatic hernia between 2010 and 2013 at the two tertiary referral centres were identified. Medical records were retrospectively reviewed. Data including patients’ demographics, peri-operative outcomes, length of hospitalisation and post-operative complications were extracted and analysed. Introduction: Congenital diaphragmatic hernia is a potentially life-threatening neonatal condition which required surgical intervention. With the advances in endosurgical instruments and techniques, thoracoscopic approach is gaining popularity as a standard procedure in the treatment of this condition. In this study, we reviewed our two centres’ experience with thoracoscopic repair of congenital diaphragmatic hernia in recent years. Conclusion: Thoracoscopic repair of congenital diaphragmatic hernia can be performed safely in specialised centres. The post-operative recovery and cosmesis are excellent. Diaphragmatic hernia with large defect remains a challenge for surgeons. Results: 60 patients were identified over the study period, with 46 males and 14 females. 48 patients received operation within the first 7 days of life. There were seven patients with delayed presentation and were operated after 1 month old. The average body weight was 3.03 kg. Left-sided hernia was more prevalent (n = 50). The mean operative time was 88.5 min (range 31–194 min). No conversion to open thoracotomy or laparotomy was required in any of the patients. All patients except one were intubated and paralysed in neonatal intensive care units for at least 3 days after operation. Average hospital stay was 14.6 days. There was no mortality in this series. There were five recurrences, one being the patient without post-operative paralysis, and the others with deficient posterior muscle rim. No musculoskeletal deformity was noted on follow-up examination.postprin