COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Loss of interest, depressed mood and impact on the quality of life: Cross-sectional survey

Abstract Background Depressive symptoms and chronic disease have adverse effects on patients' health-related quality of life (H-RQOL). However, little is known about this effect on H-RQOL when only the two core depressive symptoms - loss of interest and depressed mood - are considered. The objective of this study is to investigate H-RQOL in the presence of loss of interest and depressed mood at a general medical outpatient unit. Methods We evaluated 553 patients at their first attendance at a general medical outpatient unit of a teaching hospital. H-RQOL was assessed with the Medical Outcomes Study 36-item Short-Form Health Survey (SF-36). Depressed mood and loss of interest were assessed by the Primary Care Evaluation of Mental Disorders (PRIME-MD)-Patient Questionnaire. A physician performed the diagnosis of chronic diseases by clinical judgment and classified them in 13 possible pre-defined categories. We used multiple linear regression to investigate associations between each domain of H-RQOL and our two core depression symptoms. The presence of chronic diseases and demographic variables were included in the models as covariates. Results Among the 553 patients, 70.5% were women with a mean age of 41.0 years (range 18-85, SD ± 15.4). Loss of interest was reported by 54.6%, and depressed mood by 59.7% of the patients. At least one chronic disease was diagnosed in 59.5% of patients; cardiovascular disease was the most prevalent, affecting 20.6% of our patients. Loss of interest and depressed mood was significantly associated with decreased scores in all domains of H-RQOL after adjustment for possible confounders. The presence of any chronic disease was associated with a decrease in the domain of vitality. The analysis of each individual chronic disease category revealed that no category was associated with a decrease in more than one domain of H-RQOL. Conclusion Loss of interest and depressed mood were associated with significant decreases in H-RQOL. We recommend these simple tests for screening in general practice.

Pre- and Postoperative Quantitative Analysis of Contour Abnormalities in Graves Upper Eyelid Retraction

Purpose: One of the most common problems of the surgical management of Graves upper eyelid retraction is the occurrence of eyelid contour abnormalities. In the present study, the postoperative contour of a large sample of eyelids of patients with Graves orbitopathy was measured. Methods: The postoperative upper eyelid contour of 62 eyes of 43 patients with Graves orbitopathy was subjectively classified by 3 experienced surgeons in 3 categories: poor, fair, and good. The shape of the eyelid contours in each category was then measured with a recently developed custom-made software by measuring multiple midpupil eyelid distances each 15 degrees along the palpebral fissure. The upper eyelid contour of 60 normal subjects was also quantified as a control group. Results: The mean ratio between the sum of the lateral and medial midpupil eyelid distances (lateral/medial ratio) was 1.10 +/- 0.11 standard deviation in controls and 1.15 +/- 0.13 standard deviation in patients. Postoperatively, the mean midpupil eyelid distance at 90 degrees was 4.16 +/- 1.13 mm standard deviation. The distribution lateral/medial ratios of the eyelids judged as having good contours was similar to the distribution of the controls with a modal value centered on the interval between 1.0 and 1.10. The distribution of lateral/medial ratios of the eyelids judged as having poor contour was bimodal, with eyelids with low and high lateral/medial ratios. Low lateral/medial ratios occurred when there was a lateral overcorrection, giving the eyelid a flat or a medial ptosis appearance. High lateral/medial ratios were due to a central or medial overcorrection or a lateral peak maintenance. Conclusions: Postoperative upper eyelid contour abnormalities can be quantified by comparing the sum of multiple midpupil eyelid distances of the lateral and medial sectors of the eyelid. Low and high lateral/medial ratios are anomalous and judged as unpleasant. (Ophthal Plast Reconstr Surg 2012;28:429-433)

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.