A Fractional Hawkes Process

We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $\beta + 1 \in (1, 2 ]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities

31P nuclear magnetic resonance and X-ray diffraction study of Na-Sr-phosphate glass-ceramics

A set of Na-Sr-phosphate glass and glass-ceramic samples, with general formula xSrO:(0.55-x)Na2O:0.45P2O5, were prepared and analysed by solid state 31P nuclear magnetic resonance spectroscopy and X-ray powder diffraction. The results show the presence of Q1 and Q2 phosphate species in all samples. At low concentrations of Sr2+ (x £ 0.20) the strontium is preferentially incorporated in Sr2+-Q1 crystalline phases, and only at higher Sr2+ concentrations are crystalline phases present which Sr2+ is associated with Q2 phosphate units

In situ wavelength calibration of the edge CXS spectrometers on JET

A method for obtaining an accurate wavelength calibration over the entire focal plane of the JET edge CXS spectrometers is presented that uses a combination of the fringe pattern created with a Fabry-Pérot etalon and a neon lamp for cross calibration. The accuracy achieved is 0.03 Å, which is the same range of uncertainty as when neglecting population effects on the rest wavelength of the CX line. For the edge CXS diagnostic, this corresponds to a flow velocity of 4.5 km/s in the toroidal direction or 1.9 km/s in the poloidal direction

Performance of information criteria for selection of Hawkes process models of financial data

We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling. The information criteria are Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn criterion (HQ). Since we work with simulated data, we are able to measure the performance of model selection by the success rate of the IC in selecting the model that was used to generate the data. In particular, we are interested in the relation between correct model selection and underlying sample size. The analysis includes realistic sample sizes and parameter sets from recent literature where parameters were estimated using empirical financial intra-day data. We compare our results to theoretical predictions and similar empirical findings on the asymptotic distribution of model selection for consistent and inconsistent IC

Fitness benefits of prolonged post-reproductive lifespan in women

Most animals reproduce until they die, but in humans, females can survive long after ceasing reproduction. In theory, a prolonged post-reproductive lifespan will evolve when females can gain greater fitness by increasing the success of their offspring than by continuing to breed themselves. Although reproductive success is known to decline in old age, it is unknown whether women gain fitness by prolonging lifespan post-reproduction. Using complete multi-generational demographic records, we show that women with a prolonged post-reproductive lifespan have more grandchildren, and hence greater fitness, in pre-modern populations of both Finns and Canadians. This fitness benefit arises because post-reproductive mothers enhance the lifetime reproductive success of their offspring by allowing them to breed earlier, more frequently and more successfully. Finally, the fitness benefits of prolonged lifespan diminish as the reproductive output of offspring declines. This suggests that in female humans, selection for deferred ageing should wane when one's own offspring become post-reproductive and, correspondingly, we show that rates of female mortality accelerate as their offspring terminate reproduction

Poisson transition rates from time-domain measurements with finite bandwidth

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus is ten times faster than the process under study. We derive here a quantitative form for this correction using a straightforward state-transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.Comment: 4 pages, 5 figure

Searches for New Quarks and Leptons Produced in Z-Boson Decay

We have searched for events with new-particle topologies in 390 hadronic Z decays with the Mark II detector at the SLAC Linear Collider. We place 95%-confidence-level lower limits of 40.7 GeV/c^2 for the top-quark mass, 42.0 GeV/c^2 for the mass of a fourth-generation charge - 1/3 quark, and 41.3 GeV/c^2 for the mass of an unstable Dirac neutral lepton

Measurement of Z Decays into Lepton Pairs

We present measurements by the Mark II experiment of the ratios of the leptonic partial widths of the Z boson to the hadronic partial width. The results are Γ_(ee)/Γ_(had)=0.037_(-0.012^()+0.016),Γ_(µµ)/Γ_(had)=0.053-_(0.015)^(+0.020), and Γ_(ττ)/Γ_(had)=0.066_(-0.017)^(+0.021), in good agreement with the standard-model prediction of 0.048. From the average leptonic width result, Γ_(ll)/Γ_(had)=0.053_(-0.009)^(+0.010), we derive Γ_(had)=1.56_(-0.24)^(+0.28) GeV. We find for the vector coupling constants of the tau and muon v_τ^2=0.31±0.31_(-0.30)^(+0.43) and v_μ^2=0.05±0.30_(-0.23)^(+0.34)

Feasibility of nanofluid-based optical filters

In this article we report recent modeling and design work indicating that mixtures of nanoparticles in liquids can be used as an alternative to conventional optical filters. The major motivation for creating liquid optical filters is that they can be pumped in and out of a system to meet transient needs in an application. To demonstrate the versatility of this new class of filters, we present the design of nanofluids for use as long-pass, short-pass, and bandpass optical filters using a simple Monte Carlo optimization procedure. With relatively simple mixtures, we achieve filters with <15% mean-squared deviation in transmittance from conventional filters. We also discuss the current commercial feasibility of nanofluid-based optical filters by including an estimation of today's off-the-shelf cost of the materials. While the limited availability of quality commercial nanoparticles makes it hard to compete with conventional filters, new synthesis methods and economies of scale could enable nanofluid-based optical filters in the near future. As such, this study lays the groundwork for creating a new class of selective optical filters for a wide range of applications, namely communications, electronics, optical sensors, lighting, photography, medicine, and many more