A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection

According to the Smoluchowski-Kramers approximation, the solution of the equation ${\mu}\ddot{q}^{\mu}_t=b(q^{\mu}_t)-\dot{q}^{\mu}_t+{\Sigma}(q^{\mu}_t)\dot{W}_t, q^{\mu}_0=q, \dot{q}^{\mu}_0=p$ converges to the solution of the equation $\dot{q}_t=b(q_t)+{\Sigma}(q_t)\dot{W}_t, q_0=q$ as {\mu}->0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.Comment: 14 pages, 2 figure

Importance Sampling for Multiscale Diffusions

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided

Influence of thoracic epidural analgesia on cardiovascular autonomic control after thoracic surgery

Background. Thoracic epidural analgesia (TEA) is effective in alleviating pain after major thoracoabdominal surgery and may also reduce postoperative mortality and morbidity. This study investigated cardiovascular autonomic control in patients undergoing elective thoracic surgery and its modulation by continuous TEA. Methods. Thirty‐eight patients were randomly assigned to receive patient‐controlled analgesia (PCA group) or thoracic epidural analgesia (TEA group) with doses of bupivacaine (0.25% during operation, 0.125% after operation) and fentanyl (2 µgml-1). Heart rate variability (HRV), baroreflex function and pressure response to nitroglycerine and phenylephrine were assessed before operation, 4 h after the end of surgery (POD 0) and on the first and second postoperative days (POD1 and POD2). Results. Early after surgery, all HRV variables and baroreflex sensitivities were markedly decreased in both groups. In the TEA group, total HRV and its high‐frequency components (HF) increased towards preoperative values at POD1 and POD2, whereas the ratio of low to high frequencies (LF/HF) was significantly reduced (mean (sd), -44 (15)% at POD 0, -38 (17)% at POD1, -37 (18%) at POD2) and associated with blunting of the postoperative increase in heart rate and blood pressure. In the PCA group, the ratio of LF/HF remained unchanged and the decrements in HRV variables persisted until POD2. In the two groups, baroreflex sensitivities and pressure responses recovered preoperative values at POD2. Conclusions. In contrast with PCA management, TEA using low concentrations of bupivacaine and fentanyl blunted cardiac sympathetic neural drive, resulting in vagal predominance, while HRV variables were better restored after surgery. Br J Anaesth 2003; 91: 525-3

Early improvement of respiratory function after surgical plication for unilateral diaphragmatic paralysis

We reported an unusual case of symptomatic diaphragmatic paralysis in an elderly patient with progressive respiratory-dependent limitation of her daily activities. Surgical plication of the affected hemidiaphragm resulted in early clinical and physiological improvement

Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplers

Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which directly discretize Langevin dynamics to estimate expectations over the target distribution. We study the use of transport maps that approximately normalize a target distribution as a way to precondition and accelerate the convergence of Langevin dynamics. We show that in continuous time, when a transport map is applied to Langevin dynamics, the result is a Riemannian manifold Langevin dynamics (RMLD) with metric defined by the transport map. We also show that applying a transport map to an irreversibly-perturbed ULA results in a geometry-informed irreversible perturbation (GiIrr) of the original dynamics. These connections suggest more systematic ways of learning metrics and perturbations, and also yield alternative discretizations of the RMLD described by the map, which we study. Under appropriate conditions, these discretized processes can be endowed with non-asymptotic bounds describing convergence to the target distribution in 2-Wasserstein distance. Illustrative numerical results complement our theoretical claims.Comment: 28 pages, 12 figure

Large Deviations Principle for a Large Class of One-Dimensional Markov Processes

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator $D_{v}D_{u}$, where $v$ and $u$ are two strictly increasing functions, $v$ is right continuous and $u$ is continuous. In this paper, we study large deviations principle for Markov processes whose infinitesimal generator is $\epsilon D_{v}D_{u}$ where $0<\epsilon\ll 1$. This result generalizes the classical large deviations results for a large class of one dimensional "classical" stochastic processes. Moreover, we consider reaction-diffusion equations governed by a generalized operator $D_{v}D_{u}$. We apply our results to the problem of wave front propagation for these type of reaction-diffusion equations.Comment: 23 page

Management of the Industry/Research Organisation Interface

The purpose of a consultancy undertaken to assess management processes in research projects to improve communication between research organisations and the mining industry through the development of an improved mode of operation and customer interface is discussed. The consultancy was conducted using the Nadler and Tushman Congruency Model of Organisational Behaviour to asses components of a project\u27s inputs, transformation process and outputs for their degree of congruence or \u27fit\u27. As an example the University of Queensland (UQ) managed ACARP Project \u27Maximising Coal Production in the Presence of Hydrogen Sulphide (H₂S) Seam Gas\u27 was used for illustration. An action research process was used to collect data on the project organisation and history, observations made of group project meetings and interviews undertaken with project staff and representatives of the mining industry and the UQ. The findings highlighted major differences in culture between the university and industry, inadequate planning and strategy development, ineffective intergroup communication, high and conflicting demands on time, and in some cases a poor fit between individuals and tasks. Recommendations proposed to address these issues are presented as two groups, those applicable to the current H₂S Project and those for future similar research projects. They involve improved strategies for intergroup and interpersonal communication, role clarification, project administration and organisational learning and assessment. The proposed interventions are relatively simple, easily implemented and inexpensive. They have the potential to improve the fit between the components of the organisation as well as between the organisation and its environment, enhance efficiency and effectiveness and improve the relationship between the university and industry to ensure future collaborative research projects and access to external funding

Perioperative mortality and major cardio-pulmonary complications after lung surgery for non-small cell carcinoma

Objectives: A database of patients operated of lung cancer was analyzed to evaluate the predictive risk factors of operative deaths and life-threatening cardiopulmonary complications. Methods: From 1990 to 1997, data were collected concerning 634 consecutive patients undergoing lung resection for non-small cell carcinoma in an academic medical centre and a regional hospital. Operations were managed by a team of experienced surgeons, anaesthesiologists and chest physicians. Operative mortality was defined as death within 30 days of operation and/or intra-hospital death. Respiratory failure, myocardial infarct, heart failure, pulmonary embolism and stroke were considered as major non-fatal complications. Preoperative risk factors, extent of surgery, pTNM staging, perioperative mortality and major cardiopulmonary complications were recorded and evaluated using chi-square statistics and multivariate logistic regression. Results: Complete data were obtained in 621 cases. The overall operative mortality was 3.2% (n=19). Cardiovascular complications (n=10), haemorrhage (n=4) and sepsis or acute lung injury (n=5) were incriminated as the main causative factors. In addition, there were 13 life-threatening complications (2.1%) consisting in strokes (n=4), myocardial infarcts (n=5), pulmonary embolisms (n=1), acute lung injury (n=1) and respiratory failure (n=2). Four independent predictors of operative death were identified: pneumonectomy, evidence of coronary artery disease (CAD), ASA class 3 or 4 and period 1990-93. In addition, the risk of major complications was increased in hypertensive patients and in those belonging to ASA class 3 or 4. A trend towards improved outcome was observed during the second period, from 1994 to 97. Conclusion: Our data demonstrate that perioperative mortality is mainly dependent on the extent of surgery, the presence of CAD and provision of adequate medical and nursing care. Preoperative testing and interventions to reduce the cardiovascular risk factors may help to further improve perioperative outcom