Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive

We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, Z say, is in the domain of attraction of a stable law with index alpha is an element of (1,2]. In particular, we are able to prove a quenched version of the result that the spectral dimension of the random walk is 2 alpha/(2 alpha-1). Furthermore, we demonstrate that when alpha is an element of (1,2) there are logarithmic fluctuations in the quenched transition density of the simple random walk, which contrasts with the log-logarithmic fluctuations seen when alpha=2. In the course of our arguments, we obtain tail bounds for the distribution of the nth generation size of a Galton-Watson branching process with offspring distribution Z conditioned to survive, as well as tail bounds for the distribution of the total number of individuals born up to the nth generation, that are uniform in n

Biased random walk on critical Galton-Watson trees conditioned to survive

We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs

Drf1-dependent Kinase Interacts with Claspin through a Conserved Protein Motif

The Dbf4/Drf1-dependent kinase (DDK) is required for the initiation of DNA replication in eukaryotes. Another protein, Claspin, mediates the activation of a cellular checkpoint response to stalled replication forks and is also a regulator of replication. In this study, we found that DDK phosphorylates Claspin in vitro and forms a nuclear complex containing Cdc7, Drf1, and Claspin in Xenopus egg extracts. In addition, purified Claspin and DDK are capable of a direct in vitro interaction. We identified a conserved binding site on Claspin required for its interaction with DDK. This site corresponds to the first of two sequence repeats in the Chk1-binding domain of Claspin. Furthermore, we have established that two amino acids in this motif, Asp^(861) and Gln^(866), are essential for the interaction between Claspin and DDK. We found that mutant forms of Claspin incapable of interacting with DDK are still able to associate with and activate Chk1 in response to DNA replication blockages. However, Claspin-depleted egg extracts that have been reconstituted with these mutants of Claspin undergo DNA replication more slowly. These findings suggest that the interaction of DDK with Claspin mediates a checkpoint-independent function of Claspin related to DNA replication

Evolution of Paramagnetic Quasiparticle Excitations Emerged in the High-Field Superconducting Phase of CeCoIn5

We present In NMR measurements in a novel thermodynamic phase of CeCoIn5 in high magnetic field, where exotic superconductivity coexists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly-emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

Tunneling splitting of magnetic levels in Fe8 detected by 1H NMR cross relaxation

Measurements of proton NMR and the spin lattice relaxation rate 1/T1 in the octanuclear iron (III) cluster [Fe8(N3C6H15)6O2(OH)12][Br8 9H2O], in short Fe8, have been performed at 1.5 K in a powder sample aligned along the main anisotropy z axis, as a function of a transverse magnetic field (i.e., perpendicular to the main easy axis z). A big enhancement of 1/T1 is observed over a wide range of fields (2.5-5 T), which can be attributed to the tunneling dynamics; in fact, when the tunneling splitting of the pairwise degenerate m=+-10 states of the Fe8 molecule becomes equal to the proton Larmor frequency a very effective spin lattice relaxation channel for the nuclei is opened. The experimental results are explained satisfactorily by considering the distribution of tunneling splitting resulting from the distribution of the angles in the hard xy plane for the aligned powder, and the results of the direct diagonalization of the model Hamiltonian.Comment: J. Appl. Phys., in pres

Electronic phase diagram of La1.875_{1.875}Ba0.125−x_{0.125-x}Srx_xCuO4_4

We performed systematic measurements of magnetic susceptibility on single crystals of La$_{1.875}$Ba$_{0.125-x}$Sr$_x$CuO$_4$. The dependence of the superconducting transition temperature on Sr-concentration demonstrates a step-like pattern upon doping at {\it x}$\sim$0.08 as the crystal structure changes from low-temperature tetragonal (LTT) to low-temperature orthorhombic (LTO) phase at low temperature. Upon cooling, an anomalous upturn in the susceptibility was observed at the structural phase transition between the LTT-LTO phases under the magnetic field parallel to {\it c}-axis.Comment: 6 pages, 4 figures, Proceeding paper of the Stripes2000 conference in Roma, Ital

Hydroacoustic evaluation of spawning red hind (Epinephelus guttatus) aggregations along the coast of Puerto Rico in 2002 and 2003

Red hind (Epinephelus guttatus) have been overfished in the Caribbean and were included with seven other regional grouper species deemed vulnerable to risk of extinction. The Puerto Rico Department of Natural and Environmental Resources desired to map spawning red hind aggregations within commonwealth waters as part of their resource management program for the species. Mobile hydroacoustic surveys were conducted over 3-day periods in 2002 and 2003, indexed to the full moon phase in February or March when red hind were known to aggregate. Four vessels concurrently sampled the southwest, south, and southeast coasts of Puerto Rico in 2002. In 2003, three vessels conducted complementary surveys of the northwest, north, and northeast coasts of the island, completing a circuit of the coastal shelf-spawning habitat. These surveys indicated that red hind spawning aggregations were prevalent along the south and west coasts, and sparse along the north coast during the survey periods. Highest spawning red hind concentrations were observed in three areas offshore of the west coast of Puerto Rico, around Mona and Desecheo islands (20,443 and 10,559 fish/km2, respectively) and in the Bajo de Cico seasonal closed area (4,544 fish/km2). Following both 2002 and 2003 surveys, a series of controlled acoustic measurements of known local fish species in net pens were conducted to assess the mean target strength (acoustic backscatter) of each group. Ten species of fish were measured, including red hind (E. guttatus), coney (E. fulvus), white grunt (Haemulon plumieri), pluma (Calamus pennatula), blue tang (Acanthurus coeruleus), squirrel fish (Holocentrus spp.), black durgeon (Melichtyhs niger), ocean file fish (Canthidermis sufflamen), ocean surgeon fish (Acanthurus bahianus), and butter grouper (Mycteroperca spp.). In general, the mean target strength results from the caged fish experiments were in agreement with published target strength length relationships, with the exception of white grunt and pluma