Logarithms and sectorial projections for elliptic boundary problems

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R_-. In the first part of the paper we define and discuss in detail the operator log B; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, zeta(B,0), and it enters in an important way in studies of composed zeta functions zeta(A,B,s)=Tr(AB^{-s}) (pursued elsewhere). There is a similar definition of the operator log_theta B, when the spectral cut is at a general angle theta. When B has spectral cuts at two angles theta < phi, one can define the sectorial projection Pi_{theta,phi}(B) whose range contains the generalized eigenspaces for eigenvalues with argument in ] theta, phi [; this is studied in the last part of the paper. The operator Pi_{theta,phi}(B) is shown to be proportional to the difference between log_theta B and log_phi B, having slightly better symbol properties than they have. We show by examples that it belongs to the Boutet de Monvel calculus in many special cases, but lies outside the calculus in general.Comment: 27 pages, minor adjustments and correction of typos. To appear in Math. Scan

Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis

We show how efficient loop updates, originally developed for Monte Carlo simulations of quantum spin systems at finite temperature, can be combined with a ground-state projector scheme and variational calculations in the valence bond basis. The methods are formulated in a combined space of spin z-components and valence bonds. Compared to schemes formulated purely in the valence bond basis, the computational effort is reduced from up to O(N^2) to O(N) for variational calculations, where N is the system size, and from O(m^2) to O(m) for projector simulations, where m>> N is the projection power. These improvements enable access to ground states of significantly larger lattices than previously. We demonstrate the efficiency of the approach by calculating the sublattice magnetization M_s of the two-dimensional Heisenberg model to high precision, using systems with up to 256*256 spins. Extrapolating the results to the thermodynamic limit gives M_s=0.30743(1). We also discuss optimized variational amplitude-product states, which were used as trial states in the projector simulations, and compare results of projecting different types of trial states.Comment: 12 pages, 9 figures. v2: Significantly expanded, to appear in Phys. Rev.

Betamethasone in prevention of postoperative nausea and vomiting following breast surgery.

To investigate whether betamethasone decreases the incidence of postoperative nausea/vomiting (PONV) and reduces postoperative pain following partial mastectomy

Analysis of the impact of solvent on contacts prediction in proteins

<p>Abstract</p> <p>Background</p> <p>The correlated mutations concept is based on the assumption that interacting protein residues coevolve, so that a mutation in one of the interacting counterparts is compensated by a mutation in the other. Approaches based on this concept have been widely used for protein contacts prediction since the 90s. Previously, we have shown that water-mediated interactions play an important role in protein interfaces. We have observed that current "dry" correlated mutations approaches might not properly predict certain interactions in protein interfaces due to the fact that they are water-mediated.</p> <p>Results</p> <p>The goal of this study has been to analyze the impact of including solvent into the concept of correlated mutations. For this purpose we use linear combinations of the predictions obtained by the application of two different similarity matrices: a standard "dry" similarity matrix (DRY) and a "wet" similarity matrix (WET) derived from all water-mediated protein interfacial interactions in the PDB. We analyze two datasets containing 50 domains and 10 domain pairs from PFAM and compare the results obtained by using a combination of both matrices. We find that for both intra- and interdomain contacts predictions the introduction of a combination of a "wet" and a "dry" similarity matrix improves the predictions in comparison to the "dry" one alone.</p> <p>Conclusion</p> <p>Our analysis, despite the complexity of its possible general applicability, opens up that the consideration of water may have an impact on the improvement of the contact predictions obtained by correlated mutations approaches.</p

Summative assessments are more powerful drivers of student learning than resource intensive teaching formats

BACKGROUND: Electrocardiogram (ECG) interpretation is a core clinical skill that needs to be acquired during undergraduate medical education. Intensive teaching is generally assumed to produce more favorable learning outcomes, but recent research suggests that examinations are more powerful drivers of student learning than instructional format. This study assessed the differential contribution of teaching format and examination consequences to learning outcome regarding ECG interpretation skills in undergraduate medical students. METHODS: A total of 534 fourth-year medical students participated in a six-group (two sets of three), partially randomized trial. Students received three levels of teaching intensity: self-directed learning (two groups), lectures (two groups) or small-group peer teaching facilitated by more advanced students (two groups). One of the two groups on each level of teaching intensity was assessed in a formative, the other in a summative written ECG examination, which provided a maximum of 1% credit points of the total curriculum. The formative examination provided individual feedback without credit points. Main outcome was the correct identification of ≥3 out of 5 diagnoses in original ECG tracings. Secondary outcome measures were time spent on independent study and use of additional study material. RESULTS: Compared with formative assessments, summative assessments increased the odds of correctly identifying at least three out of five ECG diagnoses (OR 5.14; 95% CI 3.26 to 8.09), of spending at least 2 h/week extra on ECG self-study (OR 4.02; 95% CI 2.65 to 6.12) and of using additional learning material (OR 2.86; 95% CI 1.92 to 4.24). Lectures and peer teaching were associated with increased learning effort only, but did not augment examination performance. CONCLUSIONS: Medical educators need to be aware of the paramount role of summative assessments in promoting student learning. Consequently, examinations within medical schools need to be closely matched to the desired learning outcomes. Shifting resources from implementing innovative and costly teaching formats to designing more high-quality summative examinations warrants further investigation