Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

A variable delay integrated receiver for differential phase-shift keying optical transmission systems

An integrated variable delay receiver for DPSK optical transmission systems is presented. The device is realized in silicon-on-insulator technology and can be used to detect DPSK signals at any bit-rates between 10 and 15 Gbit/s

Retrospective Database Analysis Evaluating the Clinical Outcomes of Changing Treatment of People with Type 2 Diabetes Mellitus (T2DM) from Other DPP-4 Inhibitor Therapy to Alogliptin in a Primary Care Setting

This is the final version. Available on open access from Springer via the DOI in this recordIntroduction: Although some differences between individual dipeptidyl peptidase-4 (DPP-4) inhibitors may exist, the National Institute for Health and Clinical Excellence (NICE) have recommended that ‘prescribers should be encouraged to select the individual DPP-4 inhibitor with the lowest acquisition cost available to them, where all other factors are equal’. We aimed to determine whether or not ‘within class’ switching to alogliptin, the DPP-4 inhibitor with lowest acquisition cost, is a clinically appropriate strategy. Methods: This study evaluated people with type 2 diabetes taking DPP-4 inhibitor therapy in addition to at least one other diabetes therapy. Primary care records were reviewed from six clinical commissioning groups (CCGs). For people who had been switched from other DPP-4 inhibitors to alogliptin, an assessment of the impact of switch on both absolute haemoglobin A1c (HbA1c) levels and on HbA1c trajectory was undertaken. Persistence on alogliptin and the need for therapy intensification was also assessed. Results: Overall, 865 people with diabetes met the eligibility criteria for the study. There was no significant difference between pre- and post-switch mean HbA1c level [8.44% (SD 1.52%) vs 8.42% (1.62%), p = 0.6]. Similarly, for patients where there was sufficient data to assess the impact of switching on HbA1c trajectory (n = 319) minimal impact was identified (actual HbA1c at 3 months 8.33% vs projected 8.31%). The majority of people with diabetes (80.76%) remained on alogliptin treatment at 6 months and only 4.54% required additional diabetes therapies. Switching to alogliptin resulted in a median saving of £7.24 per patient-month. Conclusion: Switching United Kingdom (UK) primary care patients from other DPP-4 inhibitors to alogliptin did not result in a statistically significant or clinically meaningful change in HbA1c level and few required the addition of further diabetes therapies, suggesting that therapy change or intensification was not considered necessary in most patients who were switched to alogliptin. Trial Registration: ENCePP clinical trial registration number EUPAS29153. Funding: Takeda UK Ltd.National Institute for Health Research (NIHR

Optimal time-domain combination of the two calibrated output quadratures of GEO 600

GEO 600 is an interferometric gravitational wave detector with a 600 m arm-length and which uses a dual-recycled optical configuration to give enhanced sensitivity over certain frequencies in the detection band. Due to the dual-recycling, GEO 600 has two main output signals, both of which potentially contain gravitational wave signals. These two outputs are calibrated to strain using a time-domain method. In order to simplify the analysis of the GEO 600 data set, it is desirable to combine these two calibrated outputs to form a single strain signal that has optimal signal-to-noise ratio across the detection band. This paper describes a time-domain method for doing this combination. The method presented is similar to one developed for optimally combining the outputs of two colocated gravitational wave detectors. In the scheme presented in this paper, some simplifications are made to allow its implementation using time-domain methods

Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon \in(0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.Comment: 35 page

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L^\infty_\ell$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.Comment: 64 page

Deep three-dimensional solid-state qubit arrays with long-lived spin coherence

Nitrogen-vacancy centers (NVCs) in diamond show promise for quantum computing, communication, and sensing. However, the best current method for entangling two NVCs requires that each one is in a separate cryostat, which is not scalable. We show that single NVCs can be laser written 6–15-µm deep inside of a diamond with spin coherence times that are an order of magnitude longer than previous laser-written NVCs and at least as long as naturally occurring NVCs. This depth is suitable for integration with solid immersion lenses or optical cavities and we present depth-dependent T2 measurements. 200 000 of these NVCs would fit into one diamond

Robust vetoes for gravitational-wave burst triggers using known instrumental couplings

The search for signatures of transient, unmodelled gravitational-wave (GW) bursts in the data of ground-based interferometric detectors typically uses `excess-power' search methods. One of the most challenging problems in the burst-data-analysis is to distinguish between actual GW bursts and spurious noise transients that trigger the detection algorithms. In this paper, we present a unique and robust strategy to `veto' the instrumental glitches. This method makes use of the phenomenological understanding of the coupling of different detector sub-systems to the main detector output. The main idea behind this method is that the noise at the detector output (channel H) can be projected into two orthogonal directions in the Fourier space -- along, and orthogonal to, the direction in which the noise in an instrumental channel X would couple into H. If a noise transient in the detector output originates from channel X, it leaves the statistics of the noise-component of H orthogonal to X unchanged, which can be verified by a statistical hypothesis testing. This strategy is demonstrated by doing software injections in simulated Gaussian noise. We also formulate a less-rigorous, but computationally inexpensive alternative to the above method. Here, the parameters of the triggers in channel X are compared to the parameters of the triggers in channel H to see whether a trigger in channel H can be `explained' by a trigger in channel X and the measured transfer function.Comment: 14 Pages, 8 Figures, To appear in Class. Quantum Gra

Huddle test measurement of a near Johnson noise limited geophone

In this paper, the sensor noise of two geophone configurations (L-22D and L-4C geophones from Sercel with custom built amplifiers) was measured by performing two huddle tests. It is shown that the accuracy of the results can be significantly improved by performing the huddle test in a seismically quiet environment and by using a large number of reference sensors to remove the seismic foreground signal from the data. Using these two techniques, the measured sensor noise of the two geophone configurations matched the calculated predictions remarkably well in the bandwidth of interest (0.01 Hz–100 Hz). Low noise operational amplifiers OPA188 were utilized to amplify the L-4C geophone to give a sensor that was characterized to be near Johnson noise limited in the bandwidth of interest with a noise value of 10−11 m/Hz⎯⎯⎯⎯⎯√10−11 m/Hz at 1 Hz

Low-Background gamma counting at the Kimballton Underground Research Facility

The next generation of low-background physics experiments will require the use of materials with unprecedented radio-purity. A gamma-counting facility at the Kimballton Underground Research Facility (KURF) has been commissioned to perform initial screening of materials for radioactivity primarily from nuclides in the 238U and 232Th decay chains, 40K and cosmic-ray induced isotopes. The facility consists of two commercial low-background high purity germanium (HPGe) detectors. A continuum background reduction better than a factor of 10 was achieved by going underground. This paper describes the facility, detector systems, analysis techniques and selected assay results.Comment: 7 pages, 7 figures. Submitted to NIM