Residual mean first-passage time for jump processes: theory and applications to L\'evy flights and fractional Brownian motion

We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of L/'evy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behaviour. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.Comment: 13 pages, 8 figure

Warmblood fragile foal syndrome type 1 mutation (PLOD1 c.2032G>A) is not associated with catastrophic breakdown and has a low allele frequency in the Thoroughbred breed.

BackgroundCatastrophic fractures are among the most common cause of fatalities in racehorses. Several factors, including genetics, likely contribute to increased risk for fatal injuries. A variant in the procollagen-lysine, 2-oxoglutarate 5-dioxygenase1 gene (PLOD1 c.2032G>A) was shown to cause Warmblood fragile foal syndrome type 1 (WFFS), a fatal recessive defect of the connective tissue. Screening of multiple horse breeds identified the presence of the WFFS allele in the Thoroughbred. PLOD1 is involved in cross-linking of collagen fibrils and thus could potentially increase the risk of catastrophic breakdown.ObjectivesEstimate the frequency of the WFFS allele (PLOD1 c.2032G>A) and determine if it is a risk factor for catastrophic breakdown in the Thoroughbred.Study designCase-control genetic study.MethodsGenomic DNA from hair and/or tissue samples was genotyped for the WFFS allele. Fisher's Exact tests were performed to compare allele and carrier frequencies between the case cohort (catastrophic breakdown, n = 22) and several cohorts with no record of injury (n = 138 raced/trained at same track and season and n = 185 older than 7 years and raced during same season), nonracers (n = 92), and a random sample without consideration for racing history (n = 279).ResultsThe frequency of the PLOD1 c.2032G>A variant in the Thoroughbred breed is low (1.2%). Seventeen of 716 Thoroughbreds tested were carriers (2.4%) and no WFFS homozygotes were detected. Only one catastrophic breakdown case carried the WFFS allele. No statistically significant difference in allele or carrier frequency was identified between case and control cohorts (P>0.05 in all comparisons performed).Main limitationsThis study evaluated cases from one single track.ConclusionsThis study demonstrated that the PLOD1 c.2032G>A associated with WFFS is present at very low frequency in Thoroughbreds and is not a genetic risk factor for catastrophic breakdown

Genetic distance predicts trait differentiation at the subpopulation but not the individual level in eelgrass, Zostera marina.

Ecological studies often assume that genetically similar individuals will be more similar in phenotypic traits, such that genetic diversity can serve as a proxy for trait diversity. Here, we explicitly test the relationship between genetic relatedness and trait distance using 40 eelgrass (Zostera marina) genotypes from five sites within Bodega Harbor, CA. We measured traits related to nutrient uptake, morphology, biomass and growth, photosynthesis, and chemical deterrents for all genotypes. We used these trait measurements to calculate a multivariate pairwise trait distance for all possible genotype combinations. We then estimated pairwise relatedness from 11 microsatellite markers. We found significant trait variation among genotypes for nearly every measured trait; however, there was no evidence of a significant correlation between pairwise genetic relatedness and multivariate trait distance among individuals. However, at the subpopulation level (sites within a harbor), genetic (FST) and trait differentiation were positively correlated. Our work suggests that pairwise relatedness estimated from neutral marker loci is a poor proxy for trait differentiation between individual genotypes. It remains to be seen whether genomewide measures of genetic differentiation or easily measured "master" traits (like body size) might provide good predictions of overall trait differentiation

Test of CPT and Lorentz invariance from muonium spectroscopy

Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts $\delta\nu_{12}$ and $\delta\nu_{34}$ to $\nu_{12}$ and $\nu_{34}$, the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anti-correlated oscillations in $\nu_{12}$ and $\nu_{34}$ at the earth's sidereal frequency. No time dependence was found in $\nu_{12}$ or $\nu_{34}$ at the level of 20 Hz, limiting the size of some CPT and Lorentz violating parameters at the level of $2\times10^{-23}$ GeV, representing Planck scale sensitivity and an order of magnitude improvement in sensitivity over previous limits for the muon.Comment: 4 pages, 4 figures, uses REVTeX and epsf, submitted to Phys. Rev. Let

Complete two-loop correction to the bound-electron g factor

Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(\alpha/\pi)^2 (Z \alpha)^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.Comment: 11 pages, 1 figur

Spin-polarized tunneling spectroscopic studies of the intrinsic heterogeneity and pseudogap phenomena in colossal magnetoresistive manganite La_{0.7}Ca_{0.3}MnO_{3}

Spatially resolved tunneling spectroscopic studies of colossal magnetoresistive (CMR) manganite $\rm La_{0.7}Ca_{0.3}MnO_3$ (LCMO) epitaxial films on $\rm (LaAlO_3)_{0.3}(Sr_2AlTaO_6)_{0.7}$ substrate are investigated as functions of temperature, magnetic field and spin polarization by means of scanning tunneling spectroscopy. Systematic surveys of the tunneling spectra taken with Pt/Ir tips reveal spatial variations on the length scale of a few hundred nanometers in the ferromagnetic state, which may be attributed to the intrinsic heterogeneity of the manganites due to their tendency towards phase separation. The electronic heterogeneity is found to decrease either with increasing field at low temperatures or at temperatures above all magnetic ordering temperatures. On the other hand, spectra taken with Cr-coated tips are consistent with convoluted electronic properties of both LCMO and Cr. In particular, for temperatures below the magnetic ordering temperatures of both Cr and LCMO, the magnetic-field dependent tunneling spectra may be quantitatively explained by the scenario of spin-polarized tunneling in a spin-valve configuration. Moreover, a low-energy insulating energy gap $\sim 0.6$ eV commonly found in the tunneling conductance spectra of bulk metallic LCMO at $T \to 0$ may be attributed to a surface ferromagnetic insulating (FI) phase, as evidenced by its spin filtering effect at low temperatures and vanishing gap value above the Curie temperature. Additionally, temperature independent pseudogap (PG) phenomena existing primarily along the boundaries of magnetic domains are observed in the zero-field tunneling spectra. The PG becomes strongly suppressed by applied magnetic fields at low temperatures when the tunneling spectra of LCMO become highly homogeneous. These findings suggest that the occurrence PG is associated with the electronic heterogeneity of the manganites.Comment: 15 pages, 15 figures. Published in Physical Review B. Corresponding author: Nai-Chang Yeh (E-mail: [email protected]

Exploring complex networks by walking on them

We carry out a comparative study on the problem for a walker searching on several typical complex networks. The search efficiency is evaluated for various strategies. Having no knowledge of the global properties of the underlying networks and the optimal path between any two given nodes, it is found that the best search strategy is the self-avoid random walk. The preferentially self-avoid random walk does not help in improving the search efficiency further. In return, topological information of the underlying networks may be drawn by comparing the results of the different search strategies.Comment: 5 pages, 5 figure

High Resolution Observations of Cepheus a

New high resolution 6 cm observations have been made on Cepheus A using MERLIN, and combined with new VLA observations at 3.7 cm. Angular resolution with the latter was 200 mas, and with MERLIN was 60 mas, except for isolated unresolved sources where 33 mas was achieved. Unresolved objects at 60 mas were observed in Sources 2, 3, and in particular 9 which also was not resolved at 33 mas. There is no evidence for any other object as small as this with any significant flux density, although Source 8 was quiescent at the time. The upper limit to the size of Source 9 sets a minimum brightness temperature of 4.3 $\times$ 10$^5$K, and adds credence to a previous suggestion that it is a gyrosynchrotron source. The compact objects of Sources 2 and 3 are thought to be produced by mass outflow from stars, which could be of spectral type B0 - B1, but this is uncertain. There is a discussion regarding the powerhouse for the molecular outflow. Sources 8 and 9, which are the highly time dependent objects, appear at the centre of the disruption of the high density gas, and their estimated high temperature of 10$^7$ - 10$^8$K indicates that they could produce high velocity winds. On the other hand, the OH masers surrounding Source 2(ii) show an outward velocity of about 10 km s${-1}$, which is small, but higher velocity winds could tunnel through adjacent spaces, and even be responsible for the 300 km s${-1}$ bullet of Source 7. An extrapolation of the orthogonals to the IR polarization vectors are not accurate enough to pinpoint the source of the IR radiation, but it is estimated that Sources 2(ii) and 3(d)(ii) couldComment: 11 pages + 10 Figures (available by contacting [email protected]), PostScripT file, AST-9402-

Supersymmetry and a Time-Dependent Landau System

A general technique is outlined for investigating supersymmetry properties of a charged spin-\half quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schr\"odinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.Comment: 47 pages, submitted to Phys. Rev. A, LaTeX, IUHET 243 and LA-UR-93-20