Lattice congruences of the weak order

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let \eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show that the fibers of \eta_K constitute the smallest lattice congruence with 1\equiv s for every s\in(S-K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure

CD-independent subsets in meet-distributive lattices

A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt proved that any two maximal CD-independent subsets of a finite distributive lattice have the same number of elements. In this paper, we prove that if $L$ is a finite meet-distributive lattice, then the size of every CD-independent subset of $L$ is at most the number of atoms of $L$ plus the length of $L$. If, in addition, there is no three-element antichain of meet-irreducible elements, then we give a recursive description of maximal CD-independent subsets. Finally, to give an application of CD-independent subsets, we give a new approach to count islands on a rectangular board.Comment: 14 pages, 4 figure

Diabetes and lipid screening among patients in primary care: A cohort study

<p>Abstract</p> <p>Background</p> <p>Obesity is associated with increased cardiovascular diseases and diabetes mellitus. Guidelines call for intensified glucose and lipid screening among overweight and obese patients. Data on compliance with these guidelines are scarce. The purpose of this study was to assess rates of diabetes and lipid screening in primary care according to demographic variables and weight status.</p> <p>Methods</p> <p>Over a 3-year follow-up period, we assessed screening rates for blood glucose, triglycerides, and HDL- and LDL-cholesterol among 5025 patients in primary care. From proportional hazards models we estimated screening rates among low, moderate, high, and very-high risk patients and compared them with recommendations of the American Diabetes Association (ADA), National Cholesterol Education Program (ATP III) and U.S. Preventive Services Task Force (USPSTF).</p> <p>Results</p> <p>Mean (SD) age was 47.4 (15.6); 69% were female, 21% were non-white, and 30% of males and 25% of females were obese (BMI ≥ 30 kg/m²). For both diabetes and lipid screening, the adjusted hazard was 260–330% higher among ≥65 than <35 year-olds, 50–90% higher in persons with BMI ≥ 35 than <25 kg/m², 10–30% lower for females than males, and not lower among racial/ethnic minorities. Screening rates were at least 80% among very-high risk persons, which we defined as 55–64 years old, BMI ≥ 35 kg/m², non-white, with baseline hypertension. In contrast, high-risk persons who were younger (35–44 years old) and less obese (BMI 30–<35 kg/m²) were screened less often (43% for LDL-cholesterol among females to 83% for diabetes among males) even though ADA, ATP III and USPSTF recommend diabetes and lipid screening among them.</p> <p>Conclusion</p> <p>Patients with higher BMI or age were more likely to be screened for cardiometabolic risk factors. Women were screened at lower rates than men. Even in a highly structured medical group practice, some obese patients were under-screened for diabetes and dyslipidemia.</p

Improving the physician-patient cardiovascular risk dialogue to improve statin adherence

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to evaluate the effectiveness of a patient education program developed to facilitate statin adherence.</p> <p>Methods</p> <p>A controlled trial was designed to test the effectiveness of a multifaceted patient education program to facilitate statin adherence. The program included a brief, in-office physician counseling kit followed by patient mailings. The primary end point was adherence to filling statin prescriptions during a 120-day period. Patients new to statins enrolled and completed a survey. Data from a national pharmacy claims database were used to track adherence.</p> <p>Results</p> <p>Patients new to statin therapy exposed to a patient counseling and education program achieved a 12.4 higher average number of statin prescription fill days and were 10% more likely to fill prescriptions for at least 120 days (<it>p </it>= .01).</p> <p>Conclusion</p> <p>Brief in-office counseling on cardiovascular risk followed by patient education mailings can be effective in increasing adherence. Physicians found a one-minute counseling tool and pocket guidelines useful in counseling patients.</p

Adherence with statins in a real-life setting is better when associated cardiovascular risk factors increase: a cohort study

<p>Abstract</p> <p>Background</p> <p>While the factors for poor adherence for treatment with statins have been highlighted, the impact of their combination on adherence is not clear.</p> <p>Aims</p> <p>To estimate adherence for statins and whether it differs according to the number of cardiovascular risk factors.</p> <p>Methods</p> <p>A cohort study was conducted using data from the main French national health insurance system reimbursement database. Newly treated patients with statins between September 1 and December 31, 2004 were included. Patients were followed up 15 months. The cohort was split into three groups according to their number of additional cardiovascular risk factors that included age and gender, diabetes mellitus and cardiovascular disease (using co-medications as a <it>proxy</it>). Adherence was assessed for each group by using four parameters: <it>(i) </it>proportion of days covered by statins, <it>(ii) </it>regularity of the treatment over time, <it>(iii) </it>persistence, and <it>(iv) </it>the refill delay.</p> <p>Results</p> <p>16,397 newly treated patients were identified. Of these statin users, 21.7% did not have additional cardiovascular risk factors. Thirty-one percent had two cardiovascular risk factors and 47% had at least three risk factors. All the parameters showed a sub-optimal adherence whatever the group: days covered ranged from 56% to 72%, regularity ranged from 23% to 33% and persistence ranged from 44% to 59%, but adherence was better for those with a higher number of cardiovascular risk factors.</p> <p>Conclusions</p> <p>The results confirm that long-term drug treatments are a difficult challenge, particularly in patients at lower risk and invite to the development of therapeutic education.</p

Abstract Concept Lattices

International audienceWe present a view of abstraction based on a structure preserving reduction of the Galois connection between a language of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties