High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder

Diamond "lattices" are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, $A$ and $B$. The construction recipe for diamond graphs depends on a branching number $b\in \mathbb{N}$ and a segmenting number $s\in \mathbb{N}$, for which a larger value of the ratio $s/b$ intuitively corresponds to more opportunities for intersections between two randomly chosen paths. By attaching i.i.d. random variables to the bonds of the graphs, I construct a random Gibbs measure on the set of directed paths by assigning each path an "energy" given by summing the random variables along the path. For the case $b=s$, I propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs, and the partition function (the normalization factor of the Gibbs measure) appears to converge in law. I prove that all of the positive integer moments of the partition function converge in this limiting regime. The motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the $b<s$ case.Comment: 28 pages, 1 figur

Recent Decisions

Comments on recent decisions by John F. Mendoza, William J. Verdonk, William G. Greif, James L. O\u27Brien, F. Richard Kramer, Louis Albert Hafner, Peter F. Flaherty, Wilmer L. McLaughlin, Louis F. DiGiovanni, Vincent C. A. Scully, Bernard L. Weddel, and William B. Wombacher

Recent Decisions

Comments on recent decisions by Francis W. Collopy, William J. Verdonk, Vincent C. A. Scully, John F. Mendoza, James L. O\u27Brien, Bernard L. Weddel, William B. Wombacher, Thomas L. Smith, Henry M. Shine, Jr., James D. Matthews, Clifford A. Goodrich, Jr., Wilmer L. McLaughlin, and William M. Dickson

Improvement in hypercapnia does not predict survival in COPD patients on chronic noninvasive ventilation

Purpose: It has recently been shown that chronic noninvasive ventilation (NIV) improves a number of outcomes including survival, in patients with stable hypercapnic COPD. However, the mechanisms responsible for these improved outcomes are still unknown. The aim of the present study was to identify parameters associated with: 1) an improved arterial partial pressure of carbon dioxide (PaCO2) and 2) survival, in a cohort of hypercapnic COPD patients treated with chronic NIV. Patients and methods: Data from 240 COPD patients treated with chronic NIV were analyzed. Predictors for the change in PaCO2 and survival were investigated using multivariate linear and Cox regression models, respectively. Results: A higher level of bicarbonate before NIV initiation, the use of higher inspiratory ventilator pressures, the presence of anxiety symptoms, and NIV initiated following an exacerbation compared to NIV initiated in stable disease were associated with a larger reduction in PaCO2. A higher body mass index, a higher FEV1, a lower bicarbonate before NIV initiation, and younger age and NIV initiation in stable condition were independently associated with better survival. The change in PaCO2 was not associated with survival, neither in a subgroup of patients with a PaCO2 >7.0 kPa before the initiation of NIV. Conclusion: Patients with anxiety symptoms and a high bicarbonate level at NIV initiation are potentially good responders in terms of an improvement in hypercapnia. Also, higher inspiratory ventilator pressures are associated with a larger reduction in PaCO2. However, the improvement in hypercapnia does not seem to be associated with an improved survival and emphasizes the need to look beyond PaCO2 when considering NIV initiation

Managing the complexity of doing it all : an exploratory study on students' experiences when trained stepwise in conducting consultations

Background: At most medical schools the components required to conduct a consultation, medical knowledge, communication, clinical reasoning and physical examination skills, are trained separately. Afterwards, all the knowledge and skills students acquired must be integrated into complete consultations, an art that lies at the heart of the medical profession. Inevitably, students experience conducting consultations as complex and challenging. Literature emphasizes the importance of three didactic course principles: moving from partial tasks to whole task learning, diminishing supervisors' support and gradually increasing students' responsibility. This study explores students' experiences of an integrated consultation course using these three didactic principles to support them in this difficult task. Methods: Six focus groups were conducted with 20 pre-clerkship and 19 clerkship students in total. Discussions were audiotaped, transcribed and analysed by Nvivo using the constant comparative strategy within a thematic analysis. Results: Conducting complete consultations motivated students in their learning process as future physician. Initially, students were very much focused on medical problem solving. Completing the whole task of a consultation obligated them to transfer their theoretical medical knowledge into applicable clinical knowledge on the spot. Furthermore, diminishing the support of a supervisor triggered students to reflect on their own actions but contrasted with their increased appreciation of critical feedback. Increasing students' responsibility stimulated their active learning but made some students feel overloaded. These students were anxious to miss patient information or not being able to take the right decisions or to answer patients' questions, which sometimes resulted in evasive coping techniques, such as talking faster to prevent the patient asking questions. Conclusion: The complex task of conducting complete consultations should be implemented early within medical curricula because students need time to organize their medical knowledge into applicable clinical knowledge. An integrated consultation course should comprise a step-by-step teaching strategy with a variety of supervisors' feedback modi, adapted to students' competence. Finally, students should be guided in formulating achievable standards to prevent them from feeling overloaded in practicing complete consultations with simulated or real patients

Heart Failure and Pancreas Exocrine Insufficiency:Pathophysiological Mechanisms and Clinical Point of View

Heart failure is associated with decreased tissue perfusion and increased venous congestion that may result in organ dysfunction. This dysfunction has been investigated extensively for many organs, but data regarding pancreatic (exocrine) dysfunction are scarce. In the present review we will discuss the available data on the mechanisms of pancreatic damage, how heart failure can lead to exocrine dysfunction, and its clinical consequences. We will show that heart failure causes significant impairment of pancreatic exocrine function, particularly in the elderly, which may exacerbate the clinical syndrome of heart failure. In addition, pancreatic exocrine insufficiency may lead to further deterioration of cardiovascular disease and heart failure, thus constituting a true vicious circle. We aim to provide insight into the pathophysiological mechanisms that constitute this reciprocal relation. Finally, novel treatment options for pancreatic dysfunction in heart failure are discussed

Accuracy of magnetic resonance studies in the detection of chondral and labral lesions in femoroacetabular impingement : systematic review and meta-analysis

Background: Several types of Magnetic resonance imaging (MRI) are commonly used in imaging of femoroacetabular impingement (FAI), however till now there are no clear protocols and recommendations for each type. The aim of this meta-analysis is to detect the accuracy of conventional magnetic resonance imaging (cMRI), direct magnetic resonance arthrography (dMRA) and indirect magnetic resonance arthrography (iMRA) in the diagnosis of chondral and labral lesions in femoroacetabular impingement (FAI). Methods: A literature search was finalized on the 17th of May 2016 to collect all studies identifying the accuracy of cMRI, dMRA and iMRA in diagnosing chondral and labral lesions associated with FAI using surgical results (arthroscopic or open) as a reference test. Pooled sensitivity and specificity with 95% confidence intervals using a random-effects meta-analysis for MRI, dMRA and iMRA were calculated also area under receiver operating characteristic (ROC) curve (AUC) was retrieved whenever possible where AUC is equivocal to diagnostic accuracy. Results: The search yielded 192 publications which were reviewed according inclusion and exclusion criteria then 21 studies fulfilled the eligibility criteria for the qualitative analysis with a total number of 828 cases, lastly 12 studies were included in the quantitative meta-analysis. Meta-analysis showed that as regard labral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.864, 0.833 and 0.88 and for dMRA were 0.91, 0.58 and 0.92. While in chondral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.76, 0.72 and 0.75 and for dMRA were 0.75, 0.79 and 0.83, while for iMRA were sensitivity of 0.722 and specificity of 0.917. Conclusions: The present meta-analysis showed that the diagnostic test accuracy was superior for dMRA when compared with cMRI for detection of labral and chondral lesions. The diagnostic test accuracy was superior for labral lesions when compared with chondral lesions in both cMRI and dMRA. Promising results are obtained concerning iMRA but further studies still needed to fully assess its diagnostic accuracy