Branching Brownian motion with absorption and the all-time minimum of branching Brownian motion with drift

We study a dyadic branching Brownian motion on the real line with absorption at 0, drift $\mu \in \mathbb{R}$ and started from a single particle at position $x>0.$ When $\mu$ is large enough so that the process has a positive probability of survival, we consider $K(t),$ the number of individuals absorbed at 0 by time $t$ and for $s\ge 0$ the functions $\omega_s(x):= \mathbb{E}^x[s^{K(\infty)}].$ We show that $\omega_s<\infty$ if and only of $s\in[0,s_0]$ for some $s_0>1$ and we study the properties of these functions. Furthermore, for $s=0, \omega(x) := \omega_0(x) =\mathbb{P}^x(K(\infty)=0)$ is the cumulative distribution function of the all time minimum of the branching Brownian motion with drift started at 0 without absorption. We give three descriptions of the family $\omega_s, s\in [0,s_0]$ through a single pair of functions, as the two extremal solutions of the Kolmogorov-Petrovskii-Piskunov (KPP) traveling wave equation on the half-line, through a martingale representation and as an explicit series expansion. We also obtain a precise result concerning the tail behavior of $K(\infty)$. In addition, in the regime where $K(\infty)>0$ almost surely, we show that $u(x,t) := \mathbb{P}^x(K(t)=0)$ suitably centered converges to the KPP critical travelling wave on the whole real line.Comment: Grant information adde

Seeing but not perceiving: Inattentional blindness as a cause of missed cues in the general practice (GP) consultation

Background It is well known that healthcare professionals, including GPs, frequently fail to respond to cues made by their patients. A possible explanation for this behaviour is that the phenomenon of IB could lead to a failure to observe the cue, rather than a deliberate choice to ignore it. This study sought to explore that possibility, and to consider whether GP trainees are more susceptible to IB than GP trainers. Aim A pre-recorded video of a simulated consultation was used, where the patient gave two significant cues which were not picked up by the doctor in the video. The aim was to compare the rates with which both trainee GPs and GP trainers observed these missed cues. Methods The research was a case study involving two groups of participants - GP trainees and GP trainers from a localised GP Training Scheme. Actors were used to record a video of a pre-defined GP consultation involving a patient affected by headaches, who gave two significant cues which were not responded to in the video. Participants observed the video while being asked to focus on the diagnosis and management of the patient’s headaches, following which they completed a questionnaire, including questions about the cues. Results Cues were missed by 24-53% of participants, suggesting a high rate of IB within the GP consultation. Unexpected findings included the recording by some participants of false observations from the video. There was no significant difference between trainers and trainees in the rates of IB. Conclusions IB appears to be a real and significant phenomenon within the GP consultation, and is likely to have important implications for patient care. More research is needed to confirm these findings, establish IB rates as a cause of missed cues among healthcare professionals and evaluate possible interventions to reduce susceptibility to IB

Controlling the composition of a confined fluid by an electric field

Starting from a generic model of a pore/bulk mixture equilibrium, we propose a novel method for modulating the composition of the confined fluid without having to modify the bulk state. To achieve this, two basic mechanisms - sensitivity of the pore filling to the bulk thermodynamic state and electric field effect - are combined. We show by Monte Carlo simulation that the composition can be controlled both in a continuous and in a jumpwise way. Near the bulk demixing instability, we demonstrate a field induced population inversion in the pore. The conditions for the realization of this method should be best met with colloids, but being based on robust and generic mechanisms, it should also be applicable to some molecular fluids.Comment: 9 pages, 5 figure

How genealogies are affected by the speed of evolution

In a series of recent works it has been shown that a class of simple models of evolving populations under selection leads to genealogical trees whose statistics are given by the Bolthausen-Sznitman coalescent rather than by the well known Kingman coalescent in the case of neutral evolution. Here we show that when conditioning the genealogies on the speed of evolution, one finds a one parameter family of tree statistics which interpolates between the Bolthausen-Sznitman and Kingman's coalescents. This interpolation can be calculated explicitly for one specific version of the model, the exponential model. Numerical simulations of another version of the model and a phenomenological theory indicate that this one-parameter family of tree statistics could be universal. We compare this tree structure with those appearing in other contexts, in particular in the mean field theory of spin glasses

An Intrisic Topology for Orthomodular Lattices

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.Comment: Under submission to the International Journal of Theoretical Physic

Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential

We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the right-most particle for this system is already known; in this article we give large deviations probabilities for particles following "difficult" paths, growth rates along "easy" paths, the total population growth rate, and we derive the optimal paths which particles must follow to achieve this growth rate.Comment: 56 pages, 1 figur

Sensible and latent heat flux from radiometric surface temperatures at the regional scale: methodology and validation

The CarboEurope Regional Experiment Strategy (CERES) was designed to develop and test a range of methodologies to assess regional surface energy and mass exchange of a large study area in the south-western part of France. This paper describes a methodology to estimate sensible and latent heat fluxes on the basis of net radiation, surface radiometric temperature measurements and information obtained from available products derived from the Meteosat Second Generation (MSG) geostationary meteorological satellite, weather stations and ground-based eddy covariance towers. It is based on a simplified bulk formulation of sensible heat flux that considers the degree of coupling between the vegetation and the atmosphere and estimates latent heat as the residual term of net radiation. Estimates of regional energy fluxes obtained in this way are validated at the regional scale by means of a comparison with direct flux measurements made by airborne eddy-covariance. The results show an overall good matching between airborne fluxes and estimates of sensible and latent heat flux obtained from radiometric surface temperatures that holds for different weather conditions and different land use types. The overall applicability of the proposed methodology to regional studies is discusse

Conceptual Frameworks for Multimodal Social Signal Processing

This special issue is about a research area which is developing rapidly. Pentland gave it a name which has become widely used, ‘Social Signal Processing’ (SSP for short), and his phrase provides the title of a European project, SSPnet, which has a brief to consolidate the area. The challenge that Pentland highlighted was understanding the nonlinguistic signals that serve as the basis for “subconscious discussions between humans about relationships, resources, risks, and rewards”. He identified it as an area where computational research had made interesting progress, and could usefully make more

Ultra-high vacuum seals operating under pressure and at 1.8 K

The Large Hadron Collider (LHC) project will be the next major high energy physics facility at CERN. Superconducting magnets operating at a magnetic field of 8.4 Tesla in a superfluid helium bath at 1.8 K are required to guide the high energy beams of protons on their trajectory. As part of the magnet qualification tests, magnetic measurements are made using a special device where demountable seals are required. The seals must be leak tight to vacuum and must be able to resist for short periods to pressure bursts up to 20 bar during resistive transitions (quench). Two types of seals have been qualified. Maximum leak rates were in the range 6.10-10 to 1.10-9 mbar.l.s-1, in the worst conditions (20 bar, superfluid helium at 1.8 K)

Duality in interacting particle systems and boson representation

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those with continuous state space. We clarify that using a generating function approach and the Doi-Peliti method, a birth-death process (or discrete random walk model) is naturally connected to a differential equation with continuous variables, which would be interpreted as a dual Markov process. The key point in the derivation is to use bosonic coherent states as a bra state, instead of a conventional projection state. As examples, we apply the scheme to a simple birth-coagulation process and a Brownian momentum process. The generator of the Brownian momentum process is written by elements of the SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same scheme is available.Comment: 13 page