Exit Measure Research Articles

Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on “boundary statistics” of the exit measure $X_{D}$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_{D}$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_{D}$ and conditioning on $X_{D}$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin’s formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_{D}=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants’ total contribution to the exit measure. The particle’s spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle’s death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.

Cognitive and affective reassurance and patient outcomes in primary care: A systematic review

In the context of uncertainty about aetiology and prognosis, good clinical practice commonly recommends both affective (creating rapport, showing empathy) and cognitive reassurance (providing explanations and education) to increase self-management in groups with nonspecific pain conditions. The specific impact of each of these components in reference to patients’ outcomes has not been studied. This review aimed to systematically evaluate the evidence from prospective cohorts in primary care that measured patient–practitioner interactions with reference to patient outcomes. We carried out a systematic literature search and appraisal of study methodology. We extracted measures of affective and cognitive reassurance in consultations and their associations with consultation exit and follow-up measures of patients’ outcomes. We identified 16 studies from 16,059 abstracts. Eight studies were judged to be high in methodological quality. Pooling could not be achieved as a result of heterogeneity of samples and measures. Affective reassurance showed inconsistent findings with consultation exit outcomes. In 3 high-methodology studies, an association was found between affective reassurance and higher symptom burden and less improvement at follow-up. Cognitive reassurance was associated with higher satisfaction and enablement and reduced concerns directly after the consultations in 8 studies; with improvement in symptoms at follow-up in 7 studies; and with reduced health care utilization in 3 studies. Despite limitations, there is support for the notion that cognitive reassurance is more beneficial than affective reassurance. We present a tentative model based on these findings and propose priorities for future research.

Effect of orifice inner lip radius on synthetic jet efficiency

A synthetic jet is formed by periodic oscillation of a fluid through an orifice. The oscillatory motion is driven by a diaphragm or other driver. Previous studies have demonstrated that synthetic jet formation and time-averaged cavity pressure are a function of the orifice shape. Traditionally, the performance of the jet is evaluated with varying configurations of fixed driver input voltage or fixed driver displacement. Neither of these measures accurately reflect the efficiency of the actuator. Defining efficiency as “desired output divided by required input,” these traditional measures may not account for increase in required driving current or force. A sharp inside edge of a thin synthetic jet orifice can result in separated flow and increased momentum flux (due to the decreased flow area) for a fixed driver displacement. This can lead one to believe that efficiency has been improved, when, in reality, much more power was required for the driver. Acoustic power, which is the time-average of volume flow rate through the orifice multiplied by the driving pressure, accurately accounts for the power required to drive the actuator. For any synthetic jet actuator, the power to the driver is the power to the fluid (acoustic power) divided by the driver efficiency. If we assume that the driver efficiency is not a strong function of the load, any change to the acoustic power will result in the same proportional change in the driver input power. This study investigates the efficiency of a round (axisymmetric) synthetic jet actuator as a function of the radius of curvature of the interior edge of the orifice. Simultaneous particle image velocimetry measurements at the jet exit and cavity pressure measurements are used to measure the acoustic power required to generate the jet. The resultant momentum flux of the jet is used as a measure of output of the jet. Results are obtained for a range of displacement amplitudes (or stroke lengths) and radii of curvature, while Reynolds number is held fixed.

An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier

We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki, Kyprianou and Murillo-Salas (2011). In particular, by considering existing results for branching Brownian motion due to Harris and Kyprianou (2006) and Maillard (2011), we obtain, with relative ease, conclusions regarding the growth in the right-most point in the support, analytical properties of the associated one-sided Fisher-Kolmogorov-Petrovskii-Piscounov wave equation, as well as the distribution of mass on the exit measure associated with the barrier.

An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier

We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki, Kyprianou and Murillo-Salas (2011). In particular, by considering existing results for branching Brownian motion due to Harris and Kyprianou (2006) and Maillard (2011), we obtain, with relative ease, conclusions regarding the growth in the right-most point in the support, analytical properties of the associated one-sided Fisher-Kolmogorov-Petrovskii-Piscounov wave equation, as well as the distribution of mass on the exit measure associated with the barrier.

Uncertainty assessment of species measurements in acetone counterflow diffusion flames

To quantitatively understand the uncertainty of intrusive species sampling measurements using a microprobe, velocity and speciation profiles of acetone counterflow diffusion flames have been experimentally investigated with cross validations using non-intrusive particle image velocimetry (PIV) and laser induced fluorescence (LIF) measurements. It is shown that the separation distance between the fuel and oxidizer nozzles needs to be sufficiently large to achieve uniform radial velocity profiles at the nozzle exit and accurate measurements of fuel concentration distributions in flames. The impacts of the diffusion flame location relative to the stagnation plane and the diffusion flame thickness on quantitative species sampling are investigated by varying the fuel to oxygen ratio as well as nitrogen and helium as fuel diluents. The results show that the diffusion flame needs to be located on the fuel side far from the stagnation plane in order to obtain reliable speciation measurements of fuel oxidation-related species. For helium dilution in the fuel side, a significant deviation from the model prediction is found due to the excessively fast diffusion velocity of helium. The impact of the intrusive probe on the flow field and the structure of the counterflow diffusion flame are identified by acetone and OH LIF measurements. The uncertainty in the speciation measurement associated with flow perturbations by the probe is quantified and found to be comparable to the outer diameter of the probe, ±0.3mm. A simple Reynolds number analysis shows that the flow near the probe is just on the outskirts of the Stokes regime. Finally, the structure of the acetone diffusion flame is measured quantitatively with species measurements of ethane, ethylene, and acetylene. The comparison between predictions and measurements indicate that the current C2 kinetic mechanism needs to be improved for quantitative prediction of the acetone flame structures.

Evaluation of an online study skills course

This article describes the evaluation of an online study skills course unit designed, using evidence-based principles, to support undergraduate students. A mixed-methods approach was employed to establish the extent to which the unit was (a) fit for purpose and (b) effective. Data were obtained from an online survey ( n = 63) conducted on entry to the unit and on exit several months later and from face-to-face interviews with students ( n = 12). Moderate to large positive and statistically significant changes between entry and exit measures of student knowledge and confidence in a variety of study-related skills were identified in the survey data. Positive data regarding confidence were also evident in the interview data, which further revealed that, although the unit was generally seen as fit for purpose, there were some issues regarding feedback to students and the supporting face-to-face tutorials that were provided. The literature would benefit from larger-scale and more robustly designed research in this area.

The effect of a supervised exercise program on arm girth measurements in breast cancer survivors.

9115 Background: There is minimal research examining the effect of cardiovascular and resistance exercise after surgery and/or radiation treatment to the breast and axillary area. Currently there are no guidelines for activity restrictions; however, medical providers historically have recommended limiting activity of the affected arm in an attempt to prevent the development of lymphedema. This could potentially affect future quality of life and other medical issues in breast cancer survivors. Methods: Female breast cancer survivors (n=79) completed an 8-week group exercise program meeting two days per week for cardiovascular and resistance training. Participants were also encouraged to exercise independently in addition to their group sessions. Bilateral arm girth measurements were performed on all participants upon program entry and exit. Measurements were taken distal to the ulnar styloid process (wrist) and three inches above (upper arm) and below (elbow) the lateral epicondyle of the elbow. All participants included in this analysis attended ≥ 70% of the group exercise sessions and had complete entry and exit measurements. Results: Participants attended an average of 15.94 ± 3.75 exercise sessions during the 8 week program. Changes in arm girth measurement were compared for the surgical side and non-surgical sides of the body using paired t-tests. Arm girth changes in the surgical side of the body were compared to the non-surgical side of the body using the Wilcoxon Ranked Sum test. The surgical and the non-surgical arm girths did not significantly increase at the wrist (p=0.55 and p=0.76), elbow (p=0.31 and p=0.24) or upper arm (p=0.18 and p=0.42). The changes in arm girth observed on the surgical body side were not significantly different from the changes observed on the non-surgical side (wrist (p=0.67), elbow (p=0.44), and upper arm (p=0.36). Conclusions: A structured, group-based exercise program involving both cardiovascular and resistance training did not significantly increase arm girth measurements in breast cancer survivors.

In vivo dosimetry for head and neck carcinoma: determination of target absorbed dose from entrance and exit absorbed dose measurements

The aims of this work were to measure the entrance and exit dose for patient treated for head and neck tumors. The target absorbed dose was determined from the exit and entrance dose measurement. Twenty patients were evaluated. The results were compared to the calculated values and the midline dose was determinate and compared with the prescribed dose. 80 entrance doses and 80 exit doses measurements were performed. The average difference from expected values was 1.93% for entrance dose (SD 1.92%) and –0.34% for exit dose (SD 4.1%). The target absorbed dose differed from prescribed dose values by 2.94% (1.97%) for the results using the Noel method and 3.34% (SD: 2.29%) with the Rizzotti method. The total uncertainty budget in the measurement of the absorbed entrance and exit dose with diode, including diode reading, correction factors and diode calibration coefficient, is determined as 3.02% (1 s). Simple in vivo dose measurements are an additional safeguard against major setup errors and calculation or transcription errors that were missed during pre-treatment chart check.

Noisy heteroclinic networks

We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distribution in a special topology to a piecewise constant process that jumps between saddle points along the heteroclinic orbits of the network. We also obtain precise asymptotics for the exit measure for a domain containing the starting point of the diffusion.

Treatment Goals in Addiction Healthcare: the Perspectives of Patients and Clinicians

Little is known about the perspectives of either patients or clinicians regarding treatment goals in addiction healthcare. In general, treatment goals involve abstinence or at least reduction of substance use. To examine and compare the treatment goals indicated by both patients and clinicians at baseline, interim and exit measurement. A descriptive study was performed with multiple measurements of treatment goals. Patients (n = 111) and clinicians (n = 20) were recruited from three addiction treatment centres in the Netherlands. A Shared Decision Making Intervention (SDMI) was undertaken to promote and evaluate treatment agreement. Patients identified treatment goals of daytime activities and abstinence or reduced alcohol consumption as most important. Clinicians indicated psychological distress, daytime activities and substance use as most important. Differences between patients and clinicians were found for the treatment goals of physical health (patient > clinician) and psychological distress (clinician > patient). The results further showed that treatment goals of both patients and clinicians become more closely aligned during the course of treatment. SDMI provides a method to explore and discuss discrepancy between patients' and clinicians' goals of treatment which leads to convergence. Such convergence is likely to be a necessary prerequisite for positive treatment outcomes.

TH-D-BRB-07: Skin Dose Determination for Various IMRT Delivery Methods

Purpose: To examine the effect of various methods of IMRT delivery on skin dose. Method and Materials:MLC based optimized IMRT plans were created using Pinnacle® TPS: two controlled cases — a 6‐step step‐wedge and a 4‐field forward planned IMRT plans — and one clinical case for abdomen treatment. For the same cases, optimized fluence maps were used to define the corresponding thickness distribution of brass compensators using the p.d software (.decimal) The planned compensator apertures were imported in Pinnacle® TPS for dose calculation using the same geometry with the MLC plans (isocentric method on a 30cm diameter cylindrical phantom). Equivalence between the MLC and compensator calculated plans were verified through isodose lines and Dose Volume Histogram comparisons. All measurements were performed using a 23Ex Varian accelerator with 120MLC and the compensators were fitted at the wedge tray location. Absolute dose measurements using ionization chambers were also performed at the center of the phantom geometry for plan verification purposes. Entrance, exit and total skin dose measurements were done using ultra thin TLDs and gafchromic EBT film. Results: Measurements of the entrance skin dose was shown to be reduced for the compensator based plan for the controlled cases up to 45% (step‐wedge plan) and the effect was even more prominent for thicker compensator material. However, the exit and total skin dose measurements were higher for the compensator IMRT plans than the respective MLC ones for the most part of the surface area. Conclusion: Preliminary results showed that the hardening of the beam when using compensator based IMRT delivery affects the patient's skin dose reducing the entrance skin dose but leading to higher skin doses when accounting for the total plan delivery. Current and future work includes Monte Carlo simulations for verification purposes. Conflict of Interest: Research sponsored by .decimal.

Prediction of tumour response by FDG-PET in patients with adenocarcinomas of the oesophagogastric junction

Dear Sirs, We congratulate the authors on this interesting paper [1]. The authors report that positron emission tomography with glucose analog fluorodeoxyglucose (FDG-PET) had a high accuracy to predict tumour response to neoadjuvant chemotherapy. In patients with adenocarcinoma of the oesophagogastric junction, metabolic changes within the first 2 weeks of therapy were at least as predictive as histopathologic response. It is remarkable, however, that the graphically depicted exit measurements for the standard uptake value (SUV mean) of FDG-PET show a minimal range of variation. The graph presents a mean tumour FDG uptake of 10.7, with a standard deviation of ±1.2 at baseline for responders and 7.1± 0.1 for non-responders (Fig. 1a). Based on this graph, one might consider it possible to predict therapeutic response with the PET examination even prior to initiation of therapy. The authors discuss this and conclude that the difference between exit measurements and the SUV value after 2 weeks allows even better differentiation between responders and non-responders. However, it is also remarkable that PET measurements of advanced tumours in 24 patients should show so little variation. The data assembled in the table do not correspond with those in Fig. 1a. A proper plotting of the data corresponding to the “Patients and methods” section of this paper yields a completely different picture. Fig. 1b depicts the results with the correct values. It is clear that both the exit values and the values after therapy are subject to large variations. Similarly, if the correct graphic presentation is used, the significant difference of the average reduction of SUV mean values between histopathologic responders and nonresponders is no longer evident (Figs. 2a and b). The authors identified a cut-off for SUV values to predict response to neoadjuvant chemotherapy after 2 weeks of therapy. They found an optimum threshold value of −33% to differentiate between minor and major response. The receiver operating characteristic (ROC) curve demonstrated that the highest accuracy for differentiation of histopathologically responding and non-responding tumours was achieved by applying this cut-off value of a 33% decrease of baseline FDG uptake. In a ROC curve, the true positive rate (sensitivity) is plotted as a function of the false positive rate (100 minus specificity) for different cut-off points. Each point on the ROC plot represents a sensitivity/specificity pair corresponding to a particular decision threshold. A test with perfect discrimination (no overlap in the two distributions) has an ROC plot that passes through the upper left corner (100% sensitivity, 100% specificity). Therefore, the closer a ROC plot is to the upper left corner, the higher the overall accuracy of the test [2]. In the current case, the published ROC curve is reproducible from the given data. However, adding 95% confidence intervals to this curve confuses the results (Fig. 3). The 95% confidence interval is the interval in which the true (population) area under the ROC curve lies within 95% confidence. Eur J Nucl Med Mol Imaging (2008) 35:1742–1743 DOI 10.1007/s00259-008-0851-9

Multiscale analysis of exit distributions for random walks in random environments

We present a multiscale analysis for the exit measures from large balls in $$\mathbb{Z}^d, d\geq 3$$ , of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large ball, approaches the exit measure of a simple random walk from the same ball, in the sense that the variational distance between smoothed versions of these measures converges to zero. We also prove the transience of the random walk in random environment. The analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in random environment and that of simple random walk, in addition to estimates on the variational distance between smoothed versions of these quantities.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R d , (0 < α < 2), whose branching rate function is dt, and branching mechanism is of the form Ψ( z) = z 1+β. Let X τ and Y τ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of X τ and Y τ are discussed.

Multicentric and multifocal breast cancer: additional value of whole-breast ultrasound in preoperative evaluation

In the context of uncertainty about aetiology and prognosis, good clinical practice commonly recommends both affective (creating rapport, showing empathy) and cognitive reassurance (providing explanations and education) to increase self-management in groups with nonspecific pain conditions. The specific impact of each of these components in reference to patients’ outcomes has not been studied. This review aimed to systematically evaluate the evidence from prospective cohorts in primary care that measured patient–practitioner interactions with reference to patient outcomes. We carried out a systematic literature search and appraisal of study methodology. We extracted measures of affective and cognitive reassurance in consultations and their associations with consultation exit and follow-up measures of patients’ outcomes. We identified 16 studies from 16,059 abstracts. Eight studies were judged to be high in methodological quality. Pooling could not be achieved as a result of heterogeneity of samples and measures. Affective reassurance showed inconsistent findings with consultation exit outcomes. In 3 high-methodology studies, an association was found between affective reassurance and higher symptom burden and less improvement at follow-up. Cognitive reassurance was associated with higher satisfaction and enablement and reduced concerns directly after the consultations in 8 studies; with improvement in symptoms at follow-up in 7 studies; and with reduced health care utilization in 3 studies. Despite limitations, there is support for the notion that cognitive reassurance is more beneficial than affective reassurance. We present a tentative model based on these findings and propose priorities for future research.

A note on $X$-harmonic functions

The Martin boundary theory allows one to describe all positive harmonic functions in an arbitrary domain $E$ of a Euclidean space starting from the functions $k^y(x)=\sfrac{g(x,y)}{g(a,y)}$, where $g(x,y)$ is the Green function of the Laplacian and $a$ is a fixed point of $E$. In two previous papers a similar theory was developed for a class of positive functions on a space of measures. These functions are associated with a superdiffusion $X$ and we call them $X$-harmonic. Denote by $\M_c(E)$ the set of all finite measures $\mu$ supported by compact subsets of $E$. $X$-harmonic functions are functions on $\M_c(E)$ characterized by a mean value property formulated in terms of exit measures of a superdiffusion. Instead of the ratio $\sfrac{g(x,y)}{g(a,y)}$ we use a Radon-Nikodym derivative of the probability distribution of an exit measure of $X$ with respect to the probability distribution of another such measure. The goal of the present note is to find an expression for this derivative.

Non-linear Neumann's condition for the heat equation: a probabilistic representation using catalytic super-Brownian motion

Let D be a bounded domain in R d with smooth boundary ∂ D. We give a probabilistic representation formula for the non-negative solution of the mixed Dirichlet non-linear Neumann boundary value problem (DNP) { Δ u = 0 in D , u = φ on F 2 , ∂ n u + 2 u 2 = 0 on F 1 , where ( F 1 , F 2 ) is a non-trivial partition of ∂ D, φ is a non-negative, bounded and continuous function defined on F 2 , and ∂ n denotes the outward normal derivative on the boundary of D. To solve the DNP, we consider a catalytic super-Brownian motion with underlying motion a Brownian motion reflected on ∂ D, killed when it reaches F 2 and catalysed by the set F 1 , i.e. the branching rate is given by the local time of the paths on F 1 . Then we prove that the log-Laplace transform of φ integrated with respect to the exit measure of the catalytic process on F 2 , is a non-negative weak solution of the DNP. In a second part we show that we still have a probabilistic representation formula if the Dirichlet condition on F 2 is replaced by a Neumann condition.

Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion

This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1+β)-stable branching mechanism. It establishes the continuity of the density in dimension d=2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutions of the partial differential equation Δu=u1+β.

Random trees and applications

We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous’ theorem giving the convergence in distribution of the contour process of conditioned Galton-Watson trees towards the normalized Brownian excursion. We also briefly discuss applications to combinatorial trees. In the continuous setting, we use the formalism of real trees, which yields an elegant formulation of the convergence of rescaled discrete trees towards continuous objects. We explain the coding of real trees by functions, which is a continuous version of the well-known coding of discrete trees by Dyck paths. We pay special attention to random real trees coded by Brownian excursions, and in a particular we provide a simple derivation of the marginal distributions of the CRT. The last section is an introduction to the theory of the Brownian snake, which combines the genealogical structure of random real trees with independent spatial motions. We introduce exit measures for the Brownian snake and we present some applications to a class of semilinear partial differential equations.