Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy

Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the $1s$ levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the [100] direction.Comment: Published version. Corrected b and B values from previous versio

Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.Comment: 13 pages, 6 figure

The six functors for Zariski-constructible sheaves in rigid geometry

We prove a generic smoothness result in rigid analytic geometry over a characteristic zero nonarchimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well-adapted to "spreading out" arguments, in analogy with the use of generic points in scheme theory. As an application, we develop a six functor formalism for Zariski-constructible \'etale sheaves on characteristic zero rigid spaces. Among other things, this implies that characteristic zero rigid spaces support a well-behaved theory of perverse sheaves

A UPLC-MS/MS METHOD DEVELOPMENT AND VALIDATION FOR THE ESTIMATION OF SOFOSBUVIR FROM HUMAN PLASMA

Objective: The present work aimed to develop a simple, rapid, specific and precise ultra-performance liquid chromatography-tandem mass spectrophotometric (LC–MS/MS) validated method for quantification of sofosbuvir and internal standard (ISTD) Sofosbuvir-d3 in human plasma.Methods: Samples prepared by employing liquid-liquid extraction (LLE) using 2.5 ml of ethyl acetate. Chromatographic separation was achieved on Gemini 5µ C18, 50 x 4.6 mm column using a mixture of 0.1% (v/v) formic acid in water to methanol at a ratio of 30:70 v/v as the mobile phase. The flow rate was 0.50 ml/min. The LC eluent was split, and approximately 0.1 ml/min was introduced into Tandem mass spectrometer using turbo Ion Spray interface at 325 °C. Quantitation was performed by transitions of 428.35/279.26 (m/z) for sofosbuvir and 431.38/282.37 (m/z) for sofosbuvir-d3.Results: The concentrations of ten working standards showed linearity between 4.063 to 8000.010ng/ml (r2 ≥ 0.9985). Chromatographic separation was achieved within 2 min. The average extraction recoveries of three quality control concentrations were 75.36% for sofosbuvir and were within the acceptance limits. The coefficient of variation was ≤15% for intra-and inter-batch assays. The %CV of ruggedness ranges 0.35% and 3.09%. The % stability of short term and long term stock solution stability studies was found to be 97.25% and 98.81% respectively.Conclusion: The results obtained for specificity, linearity, accuracy, precision, ruggedness and stability studies were within the acceptance limits. Thus the validated economical method was applied for pharmacokinetic studies of sofosbuvir

A VALIDATED LC-MS/MS METHOD FOR PHARMACOKINETIC STUDY OF CANAGLIFLOZIN IN HEALTHY RABBITS

Objective: A liquid chromatography-tandem mass spectrophotometric (LC-MS/MS) method was developed for quantification of canagliflozin in rabbit plasma employing Liquid-Liquid extraction technique.Methods: Chromatographic separation was achieved on Inertsil ODS 5 µm C18, 50×4.60 mm with 30:70 v/v of 0.01M ammonium acetate: methanol as an isocratic mobile phase with a flow rate of 0.8 ml/min. The developed LC-MS method was applied to assess Cmax, t1/2, AUC0-t, and AUC0-inf of canagliflozin tablet after oral administration in healthy rabbits.Results: The developed method was linear over working range of 5ng/ml to 600ng/ml with a coefficient of correction (r2) = 0.999. The % recovery of the method was found to be 102.05%. The mean intraday and inter-day precision of the method was found to be 0.77 to 3.72%. The Canagliflozin showed Tmax of 1.58±0.2 and mean Cmax, AUC0®t andAUC0®a for Test formulation is 272±13.24, 2571.20±251and 2777.43±276 respectively.Conclusion: The developed method can be applied for routine analysis for quality control and the established LLOQ is sufficiently low to conduct a pharmacokinetic study with any marketing formulation of Canagliflozin in healthy rabbits

Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings

A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighbouring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. An adiabatic SWAP operation within each donor/dot pair solves the scalability issues intrinsic to exchange-based two-qubit gates, as it does not rely on sub-nanometer precision in donor placement and is robust against noise in the control fields. We use this SWAP together with well established global microwave Rabi pulses and parallel electron shuttling to construct a surface code that needs minimal, feasible local control.Comment: Published version - more detailed discussions, robustness to dephasing pointed out additionall

A framework for assessing product innovation strategies in a competitive context

The development of new products capable of satisfying customer demands on a timely basis has become a priority for firms seeking to improve their competitive advantage in a global context. However, this challenge has become highly complex due to a growing diversity of both products and processes, higher costs, and unprecedented considerations for quality and service. Despite knowing a great deal about both the characteristics of successful firms and new product development processes, little is known regarding requisite guidelines for successful strategies in product development