Transient Random Walks in Random Environment on a Galton-Watson Tree

We consider a transient random walk $(X_n)$ in random environment on a Galton--Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that $X_n$ is of order of magnitude $n^{\Lambda}$, with $\Lambda \in (0,1)$. We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, which improves a recent result of Collevecchio \cite{Col06}

Classification of n-qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene

Upgrades of beam diagnostics in support of emittance-exchange experiments at the Fermilab A0 photoinjector

The possibility of using electron beam phase space manipulations to support a free-electron laser accelerator design optimization has motivated our research. An on-going program demonstrating the exchange of transverse horizontal and longitudinal emittances at the Fermilab A0 photoinjector has benefited recently from the upgrade of several of the key diagnostics stations. Accurate measurements of these properties upstream and downstream of the exchanger beamline are needed. Improvements in the screen resolution term and reduced impact of the optical system's depth-of-focus by using YAG:Ce single crystals normal to the beam direction will be described. The requirement to measure small energy spreads (<10 keV) in the spectrometer and the exchange process which resulted in bunch lengths less than 500 fs led to other diagnostics performance adjustments and upgrades as well. A longitudinal to transverse exchange example is also reported.Comment: 16 p

Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II

The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence under weaker assumptions on the domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of Terry Lyons", Springer Proceedings in Mathematics and Statistic

Understanding the dynamics of cellular responsiveness to modifications of metabolic substrates in perifusion

A novel microperifusion system with capabilities for continuous, real-time, potentiometric monitoring of extracellular hydrogen ion concentration has been used to define the response of HeLa cells to abrupt changes in extracellular energy sources or introduction of an inhibitor of glycolysis. Glycolytic inhibition, induced by removal of glucose or introduction of iodoacetate, each led to a rapid, continuous decrease in acid release. The response to iodoacetate took longer than removal of glucose, perhaps due to the time required for binding and activation. Once inhibition began, however, the rate of change was greater than following glucose removal. Conversely, recovery time following iodoacetate inhibition was much slower than with glucose removal. Unlike the response to short-term glucose depletion, a second pulse of iodoacetate resulted in a faster response followed by an even longer recovery time. The response to switching between glucose and glutamine began almost without evident delay. The response patterns revealed that HeLa cells prefer glutamine to glucose, but, in the presence of both energy sources, some glucose continues to be used. In summary, these results indicate that continuous, real-time monitoring of the kinetics of hydrogen-ion release can be used to gain new insights into the dynamics of cellular response to perturbations of extracellular energy sources. © 1994 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49889/1/1041600103_ftp.pd

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio

Slow movement of a random walk on the range of a random walk in the presence of an external field

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon a non-trivial bias is introduced. The proof applies a decomposition of the underlying simple random walk path at its cut-times to relate the associated biased random walk to a one-dimensional random walk in a random environment in Sinai's regime

Clinical Characteristics and Prognosis of Incidentally Detected Lung Cancers

Objective. To evaluate clinical characteristics and outcomes in incidentally detected lung cancer and in symptomatic lung cancer. Material and Methods. We designed a retrospective study including all patients undergoing pulmonary resection with a curative intention for NSCLC. They were classified into two groups according to the presence or absence of cancer-related symptoms at diagnosis in asymptomatic (ASX)—incidental diagnosis—or symptomatic. Results. Of the 593 patients, 320 (53.9%) were ASX. In 71.8% of these, diagnosis was made by chest X-ray. Patients in the ASX group were older (P=0.007), had a higher prevalence of previous malignancy (P=0.002), presented as a solitary nodule more frequently (P<0.001), and were more likely to have earlier-stage disease and smaller cancers (P=0.0001). A higher prevalence of incidental detection was observed in the last ten years (P=0.008). Overall 5-year survival was higher for ASX (P=0.001). Median survival times in pathological stages IIIB-IV were not significantly different. Conclusion. Incidental finding of NSCLC is not uncommon even among nonsmokers. It occurred frequently in smokers and in those with history of previous malignancy. Mortality of incidental diagnosis group was lower, but the better survival was related to the greater number of patients with earlier-stage disease