Proof of a conjecture of N. Konno for the 1D contact process

Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers $n,m$, the upper invariant measure has the following property: Conditioned on the event that $O$ is infected, the events $\{$All sites $-n,...,-1$ are healthy$\}$ and $\{$All sites $1,...,m$ are healthy$\}$ are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in \citeBHK.Comment: Published at http://dx.doi.org/10.1214/074921706000000031 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Radial profiles of temperature and viscosity in the Earth's mantle inferred from the geoid and lateral seismic structure

In the framework of dynamical modelling of the geoid, we have estimated basic features of the radial profile of temperature in the mantle. The applied parameterization of the geotherm directly characterizes thermal boundary layers and values of the thermal gradient in the upper and lower mantle. In the inverse modelling scheme these parameters are related to the observables (geoid and seismic structure of the mantle) through the viscosity profile which is parameterized as an exponential function of pressure and temperature. We have tested 104 model geotherms. For each of them we have found proper rheological parameters by fitting the geoid with the aid of a genetic algorithm. The geotherms which best fit the geoid show a significant increase of temperature (600-800ºC) close to the 660-km discontinuity. The value of the thermal gradient in the mid-mantle is found to be sub-adiabatic. Both a narrow thermal core-mantle boundary layer and a broad region with a superadiabatic regime can produce a satisfactory fit of the geoid. The corresponding viscosity profiles show similarities to previously presented models, in particular in the viscosity maximum occurring in the deep lower mantle. The best-fitting model predicts the values of activation volume V and energy E which are in a good agreement with the data from mineral physics, except for V in the lower mantle which is found somewhat lower than the estimate based on melting temperature analysis. An interesting feature of the viscosity profiles is a local decrease of viscosity somewhere between 500 and 1000 km depth which results from the steep increase of temperature in the vicinity of the 660-km discontinuity

Measurement of the average shape of longitudinal profiles of cosmic-ray air showers at the Pierre Auger Observatory

The profile of the longitudinal development of showers produced by ultra-high energy cosmic rays carries information related to the interaction properties of the primary particles with atmospheric nuclei. In this work, we present the first measurement of the average shower pro file in traversed atmospheric depth at the Pierre Auger Observatory. The shapes of profiles are well reproduced by the Gaisser-Hillas parametrization within the range studied, for E &gt; 10(17.8) eV. A detailed analysis of the systematic uncertainties is performed using ten years of data and a full detector simulation. The average shape is quantified using two variables related to the width and asymmetry of the profile, and the results are compared with predictions of hadronic interaction models for different primary particles.</p

Observation of inclined EeV air showers with the radio detector of the Pierre Auger Observatory

With the Auger Engineering Radio Array (AERA) of the Pierre Auger Observatory, we have observed the radio emission from 561 extensive air showers with zenith angles between 60 degrees and 84 degrees. In contrast to air showers with more vertical incidence, these inclined air showers illuminate large ground areas of several km(2) with radio signals detectable in the 30 to 80 MHz band. A comparison of the measured radio-signal amplitudes with Monte Carlo simulations of a subset of 50 events for which we reconstruct the energy using the Auger surface detector shows agreement within the uncertainties of the current analysis. As expected for forward-beamed radio emission undergoing no significant absorption or scattering in the atmosphere, the area illuminated by radio signals grows with the zenith angle of the air shower. Inclined air showers with EeV energies are thus measurable with sparse radio-antenna arrays with grid sizes of a km or more. This is particularly attractive as radio detection provides direct access to the energy in the electromagnetic cascade of an air shower, which in case of inclined air showers is not accessible by arrays of particle detectors on the ground.</p

On the nature of Bose-Einstein condensation enhanced by localization

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied

Some conditional correlation inequalities for percolation and related processes

Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive) result that, conditioned on the event that there is no open path from s to t, the two events ``there is an open path from s to a' and ``there is an open path from s to b' are positively correlated. In the present paper we further investigate and generalize the theorem of which this result was a consequence. This leads to results saying, informally, that, with the above conditioning, the open cluster of s is conditionally positively (self-)associated and that it is conditionally negatively correlated with the open cluster of t. We also present analogues of some of our results for (a) random-cluster measures, and (b) directed percolation and contact processes, and observe that the latter lead to improvements of some of the results in a paper of Belitsky, Ferrari, Konno and Liggett (1997

Breaks in the 45S rDNA Lead to Recombination-Mediated Loss of Repeats

rDNA repeats constitute the most heavily transcribed region in the human genome. Tumors frequently display elevated levels of recombination in rDNA, indicating that the repeats are a liability to the genomic integrity of a cell. However, little is known about how cells deal with DNA double-stranded breaks in rDNA. Using selective endonucleases, we show that human cells are highly sensitive to breaks in 45S but not the 5S rDNA repeats. We find that homologous recombination inhibits repair of breaks in 45S rDNA, and this results in repeat loss. We identify the structural maintenance of chromosomes protein 5 (SMC5) as contributing to recombination-mediated repair of rDNA breaks. Together, our data demonstrate that SMC5-mediated recombination can lead to error-prone repair of 45S rDNA repeats, resulting in their loss and thereby reducing cellular viability