A New Approach for Computing the Bandwidth Statistics of Avalanche Photodiodes

A new approach for characterizing the avalanche-buildup-time-limited bandwidth of avalanche photodiodes (APDs) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD’s finite buildup-limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent

Neutron star magnetospheres: the binary pulsar, Crab and magnetars

A number of disparate observational and theoretical pieces of evidence indicate that, contrary to the conventional wisdom, neutron stars' closed field lines are populated by dense, hot plasma and may be responsible for producing some radio and high energy emission. This conclusion is based on eclipse modeling of the binary pulsar system PSR J0737-3039A/B (Lyutikov & Thompson 2005), a quantitative theory of Crab giant pulses (Lyutikov 2007) and a number of theoretical works related to production of non-thermal spectra in magnetars through resonant scattering. In magnetars, dense pair plasma is produced by twisting magnetic field lines and associated electric fields required to lift the particles from the surface. In long period pulsars, hot particles on closed field lines can be efficiently trapped by magnetic mirroring, so that relatively low supply rate, e.g. due to a drift from open field lines, may result in high density. In short period pulsars, magnetic mirroring does not work; large densities may still be expected at the magnetic equator near the Y-point.Comment: Proceedings, Huangshan meeting "Astrophysics of Compact Objects

Nonequilibrium Kondo Effect in a Multi-level Quantum Dot near singlet-triplet transition

The linear and nonlinear transport through a multi-level lateral quantum dot connected to two leads is investigated using a generalized finite-$U$ slave-boson mean field approach. For a two-level quantum dot, our calculation demonstrates a substantial conductance enhancement near the degeneracy point of the spin singlet and triplet states, a non-monotonic temperature-dependence of conductance and a sharp dip and nonzero bias maximum of the differential conductance. These agree well with recent experiment observations. This two-stage Kondo effect in an out-of-equilibrium situation is attributed to the interference between the two energy levels.Comment: 4 pages, 3 figure

Investigating Coupon Effects on Household Interpurchase Behavior for Cheese

In this study, a market segmentation approach is developed and applied to analyze U.S. household cheese purchases. The segmentation is based on household interpurchase time or the hazard rate of purchases. The hazard rate for a household belonging to a given segment is a function of household demographic and marketing-mix variables, and its baseline is assumed to follow a Weibull distribution. The model is flexible and is able to yield increasing, decreasing, or constant hazard rate functions. Four segments have been discovered in the U.S. household cheese purchase market. Two of the segments contain about 40% of the cheese purchase households, which are frequent buyers with an average interpurchase time of 2 weeks. These frequent cheese purchase households are larger in size, with higher income, less proportion of African Americans, and are insensitive to coupons. They are often referenced in the marketing literatures as loyal customers. In contrast, the other two segments contain about 60% of the households, which are infrequent buyers with an average interpurchase time of 6 weeks. These infrequent cheese purchase households are smaller in size, with lower income, higher proportion of African Americans, and are sensitive coupons. The infrequent purchase households are usually the targets of marketing promotions.Consumer/Household Economics,

Z-graded weak modules and regularity

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.Comment: 9 page

Learning distance to subspace for the nearest subspace methods in high-dimensional data classification

The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets