Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

Sign-time distribution for a random walker with a drifting boundary

We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.Comment: 5 page

Time efficiency and efficacy of a centralized computer-aided-design/computer-aided-manufacturing workflow for implant crown fabrication: A prospective controlled clinical study

OBJECTIVE To assess time efficiency and the efficacy of the prosthetic manufacturing for implant crown fabrication in a centralized workflow applying computer aided design and computer aided manufacturing (CAD-CAM). MATERIAL AND METHODS Fifty-nine patients with one posterior implant each, were randomly allocated to either a centralized digital workflow (c-DW, test) or a laboratory digital workflow (l-DW, control). Patients were excluded from efficiency and efficacy analyses, if any additional restoration than this single implant crown had to be fabricated. A customized titanium abutment and a monolithic zirconia crown were fabricated in the c-DW. In the l-DW, models were digitalized for CAD-CAM fabrication of a monolithic zirconia crown using a standardized titanium base abutment. Time for impression, laboratory operating and delivery time were recorded. The efficacy of the prosthetic manufacturing was evaluated at try-in and at delivery. Data was analyzed descriptively. Statistical analyses using student's unpaired t- and paired Wilcoxon were performed (p < 0.05). RESULTS At impression taking, 12 patients (c-DW) and 19 patients (l-DW) were included. The impression time was 9.4±3.5 min (c-DW) and 15.1 ± 4.6 min (l-DW) (p < 0.05). The laboratory operating time was 130 ± 31 min (c-DW) and 218.0±8 min (l-DW) (p < 0.05). The delivery time was significantly longer in the c-DW (5.9 ± 3.5 1 days) as compared to the l-DW (0.5±0.05 days). At try-in and at delivery, efficacy of prosthetic manufacturing was similar high in both workflows. CLINICAL RELEVANCE The c-DW was more time efficient compared to the lab-DW and rendered a similar efficacy of prosthetic manufacturing

Interface sharpening in CoFeB magnetic tunnel junctions

We report grazing incidence x-ray scattering evidence for sharpening of the interface between amorphous Co60Fe20B20 and AlOx during in situ annealing below the Co60Fe20B20 crystallization temperature. Enhancement of the interference fringe amplitude in the specular scatter and the absence of changes in the diffuse scatter indicate that the sharpening is not a reduction in topological roughness but a reduction in the width of the chemical composition profile across the interface. The temperature at which the sharpening occurs corresponds to that at which a maximum is found in the tunneling magnetoresistance of magnetic tunnel junctions

Opa1 overexpression ameliorates the phenotype of two mitochondrial disease mouse models

SummaryIncreased levels of the mitochondria-shaping protein Opa1 improve respiratory chain efficiency and protect from tissue damage, suggesting that it could be an attractive target to counteract mitochondrial dysfunction. Here we show that Opa1 overexpression ameliorates two mouse models of defective mitochondrial bioenergetics. The offspring from crosses of a constitutive knockout for the structural complex I component Ndufs4 (Ndufs4−/−), and of a muscle-specific conditional knockout for the complex IV assembly factor Cox15 (Cox15sm/sm), with Opa1 transgenic (Opa1tg) mice showed improved motor skills and respiratory chain activities compared to the naive, non-Opa1-overexpressing, models. While the amelioration was modest in Ndufs4−/−::Opa1tg mice, correction of cristae ultrastructure and mitochondrial respiration, improvement of motor performance and prolongation of lifespan were remarkable in Cox15sm/sm::Opa1tg mice. Mechanistically, respiratory chain supercomplexes were increased in Cox15sm/sm::Opa1tg mice, and residual monomeric complex IV was stabilized. In conclusion, cristae shape amelioration by controlled Opa1 overexpression improves two mouse models of mitochondrial disease

Critical dimensions of the diffusion equation

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the persistence exponents for low dimensions.Comment: 4 pages, 5 figure

BAT AGN Spectroscopic Survey-III. An observed link between AGN Eddington ratio and narrow emission line ratios

We investigate the observed relationship between black hole mass ($M_{\rm BH}$), bolometric luminosity ($L_{\rm bol}$), and Eddington ratio (${\lambda}_{\rm Edd}$) with optical emission line ratios ([NII] {\lambda}6583/H{\alpha}, [SII] {\lambda}{\lambda}6716,6731/H{\alpha}, [OI] {\lambda}6300/H{\alpha}, [OIII] {\lambda}5007/H{\beta}, [NeIII] {\lambda}3869/H{\beta}, and HeII {\lambda}4686/H{\beta}) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the [NII] {\lambda}6583/H{\alpha} ratio exhibits a significant correlation with ${\lambda}_{\rm Edd}$ ($R_{\rm Pear}$ = -0.44, $p$-value=$3\times10^{-13}$, {\sigma} = 0.28 dex), and the correlation is not solely driven by $M_{\rm BH}$ or $L_{\rm bol}$. The observed correlation between [NII] {\lambda}6583/H{\alpha} ratio and $M_{\rm BH}$ is stronger than the correlation with $L_{\rm bol}$, but both are weaker than the ${\lambda}_{\rm Edd}$ correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that the [NII] {\lambda}6583/H{\alpha} is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure ${\lambda}_{\rm Edd}$ and thus $M_{\rm BH}$ from the measured $L_{\rm bol}$, even for high redshift obscured AGN. We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows.Comment: Accepted for publication in MNRAS, 9 pages, 5 figures, 1 tabl

On Kaluza's sign criterion for reciprocal power series

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

Invited Article: Filamentary deposition of laser energy in glasses with Bessel beams

We investigate the nonlinear absorption of laser energy in the bulk of transparent dielectrics for femtosecond and picosecond laser pulses focused by a conical lens. We highlight the influence of the pulse duration, laser pulse energy, and cone angle on laser energy absorption in transparent dielectrics. We provide a semi-analytical model allowing the calculation of maps for the density of nonlinear absorption of energy in BK7 and in SiO2 as a function of the pulse duration and peak fluence in the focal region. The comparison of the density of nonlinear absorption of energy with the available energy density determines optimal pulse durations and Bessel beam cone angles compatible with uniform laser energy deposition in the Bessel zone. The results reproduce quantitatively the transmission measurements for experiments in BK7 with picosecond pulses and suggest that the loss of propagation invariance and uniform laser energy deposition is responsible for a previously reported transition between different types of damage morphology in SiO2 [M. K. Bhuyan et al., Appl. Phys. Lett. 104, 021107 (2014)].We investigate the nonlinear absorption of laser energy in the bulk of transparent dielectrics for femtosecond and picosecond laser pulses focused by a conical lens. We highlight the influence of the pulse duration, laser pulse energy, and cone angle on laser energy absorption in transparent dielectrics. We provide a semi-analytical model allowing the calculation of maps for the density of nonlinear absorption of energy in BK7 and in SiO2 as a function of the pulse duration and peak fluence in the focal region. The comparison of the density of nonlinear absorption of energy with the available energy density determines optimal pulse durations and Bessel beam cone angles compatible with uniform laser energy deposition in the Bessel zone. The results reproduce quantitatively the transmission measurements for experiments in BK7 with picosecond pulses and suggest that the loss of propagation invariance and uniform laser energy deposition is responsible for a previously reported transition between different typ..