The perimeter of uniform and geometric words: a probabilistic analysis

Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of $P$. This is applied to uniform and geometric random variables. We also show that, asymptotically, the distribution of $P$ is Gaussian and, seen as a stochastic process, the perimeter converges in distribution to a Brownian motionComment: 13 pages, 7 figure

Low admission LDL-cholesterol is associated with increased 3-year all-cause mortality in patients with non ST segment elevation myocardial infarction

Background: The relationship between admission low-density lipoprotein (LDL) levels and long-term outcomes has not been established in patients with acute coronary syndrome. We tested the hypothesis that patients who develop non-ST segment elevation myocardial infarction (NSTEMI) despite low LDL have a worse cardiovascular outcome in the long term. Methods: Patients admitted with NSTEMI between 1 January 1997 and 31 December 2000 and with fasting lipid profiles measured within 24 hours of admission were selected for analysis. Baseline characteristics and 3-year all-cause mortality were compared between the patients with LDL above and below the median. Multivariate analysis was used to determine the predictors of all-cause mortality, and adjusted survival was analyzed using the Cox proportional hazard model. Results: Of the total of 517 patients, 264 had LDL £ 105 mg/dL and 253 had LDL > 105 mg/dL. There was no difference in age, gender, severity of coronary artery disease, and left ventricular ejection fraction between the 2 groups. Thirty-six percent of patients with LDL £ 105 mg/dL and 24% of patients with LDL > 105 mg/dL were on lipid-lowering therapy on admission. After 3 years, patients with admission LDL £ 105 mg/dL had higher all-cause mortality rate compared to patients with LDL > 105 mg/dL (14.8% vs. 7.1%, p = 0.005). The higher all-cause mortality persisted (OR 1.8, 95% CI 1.0–3.5, p = 0.05) even after adjustment for confounding variables. Conclusions: In our cohort, lower LDL-cholesterol at admission was associated with decreased 3-year survival in patients with NSTEMI. Whether this was a result of current therapy or a marker for worse baseline characteristics needs to be studied further

Systematic review and meta-analysis of mortality and digoxin use in atrial fibrillation

Background: There is growing controversy regarding the association between digoxin and mortality in atrial fibrillation (AF). The aim of this analysis was to systematically review digoxin use and risk of mortality in patients with AF. Methods: MEDLINE, EMBASE, GoogleScholar, CINAHL, meeting abstracts, presentations, and Cochrane central databases were searched from inception through December 2014, without language restrictions. For a study to be selected, it had to report the risk of mortality associated with digoxin use in AF patients as an outcome measure. Data were extracted by 2 independent authors. Evidence tables were created. Results: A total of 16 studies (6 post hoc analyses of randomized controlled trials) with 111,978 digoxin users and 389,643 non-digoxin users were included. In a random effects model, patients treated with digoxin had a 27% increased risk of all-cause mortality (pooled HR 1.27; 95% CI 1.19–1.36) and 21% increased risk of cardiovascular mortality (pooled HR 1.21; 95% CI 1.12–1.30) compared with those who did not use digoxin. In a random effects model, the association of digoxin with all-cause mortality was stronger for AF patients without heart failure (pooled HR 1.47; 95% CI 1.25–1.73) than AF patients with heart failure (pooled HR 1.21; 95% CI 1.07–1.36, interaction p = 0.06). Conclusions: Digoxin use in AF is associated with increased risk of all-cause and cardiovascular mortalities. The effect size was larger for AF patients without heart failure than AF patients with heart failure. The study suggests further directed analyses to study the effect that is suggested by this meta-analysis, especially in AF without heart failure.

Do angiotensin converting enzyme inhibitors or angiotensin receptor blockers prevent diabetes mellitus? A meta-analysis

Background: The prevalence of diabetes mellitus (DM) has increased exponentially in recent years, with 100 million people expected to develop diabetes in the coming 15 years. The impact of medical therapy on the incidence of new onset DM is not clear. We performed a systematic review and meta-analysis to study the impact of angiotensin-converting enzyme inhibitors (ACEIs) and angiotensin receptor blockers (ARBs) on the incidence of new onset DM. Methods: MEDLINE, EMBASE, BIOSIS, Cochrane databases from inception until February 2009 for randomized controlled trials (RCT) that reported new incident DM with ACEI or ARB therapy. A total of 18 RCT are included in this meta-analysis. A random-effect model was used and between-studies heterogeneity was estimated with I2. Results: There were 50,451 patients randomized to ACEI or ARB and 50,397 patients randomized to other therapies. ACEI/ARB use was associated with a decrease in new onset DM (RR 0.78, 95% CI 0.70-0.88, p = 0.003 for ACEI and RR 0.8, 95% CI 0.75-0.86, p < 0.0001 for ARB). Treating 100 patients with ACEI or 50 patients with ARB prevents one case of new onset DM. Conclusions: The cumulative evidence suggests that the use of ACEI/ARB prevents diabetes mellitus. This finding may be of special clinical benefit in patients with hypertension and prediabetes or metabolic syndrome. (Cardiol J 2010; 17, 5: 448-456

Low admission triglyceride and mortality in acute coronary syndrome patients

Background: The relationship between admission triglyceride (TG) levels and long-term outcomes has not been established in patients with acute coronary syndrome. We tested the hypothesis that patients who develop non-ST segment elevation myocardial infarction (NSTEMI) despite low TG have a worse cardiovascular outcome in the long term. Methods: Patients admitted with NSTEMI between 1 January 1997 and 31 December 2000 and with fasting lipid profiles measured within 24 hours of admission were included for analysis. Baseline characteristics and three-year all-cause mortality were compared between the patients with TG above and below the median. Multivariate analysis was used to determine the predictors of all-cause mortality and adjusted survival was analyzed using the Cox proportional hazard model. Results: Of 517 patients, 395 had TG &#163; 200 mg/dL and 124 had TG > 200 mg/dL. Patients with low TG were more often Caucasian, with no significant differences in gender or severity of coronary artery disease between the two groups. There was a trend for increased all-cause mortality at six months (9% vs 3%, p = 0.045) and three years (13.4% vs 5.6%, p = 0.016) in patients with low TG. In multivariate analysis, low TG level at admission was an independent predictor of increased mortality at three years (adjusted OR 2.5, 95% CI = 1.04&#8211;5.9, p = 0.04). Conclusions: In our cohort, lower TG at admission is associated with increased three-year mortality in patients with NSTEMI. Whether this is a result of current therapy, or a marker for worse baseline characteristics, needs to be studied further. (Cardiol J 2011; 18, 3: 297&#8211;303

A Liouville theorem for some Bessel generalized operators

In this paper we establish a Liouville theorem in $\mathcal{H'}_{\mu}$ for a wider class of operators in $(0,\infty)^{n}$ that generalizes the $n$-dimensional Bessel operator. We will present two different proofs, based in two representation theorems for certain distributions "supported in zero"

Predicting diabetes mellitus using SMOTE and ensemble machine learning approach: The Henry Ford ExercIse Testing (FIT) project

Machine learning is becoming a popular and important approach in the field of medical research. In this study, we investigate the relative performance of various machine learning methods such as Decision Tree, Naïve Bayes, Logistic Regression, Logistic Model Tree and Random Forests for predicting incident diabetes using medical records of cardiorespiratory fitness. In addition, we apply different techniques to uncover potential predictors of diabetes. This FIT project study used data of 32,555 patients who are free of any known coronary artery disease or heart failure who underwent clinician-referred exercise treadmill stress testing at Henry Ford Health Systems between 1991 and 2009 and had a complete 5-year follow-up. At the completion of the fifth year, 5,099 of those patients have developed diabetes. The dataset contained 62 attributes classified into four categories: demographic characteristics, disease history, medication use history, and stress test vital signs. We developed an Ensembling-based predictive model using 13 attributes that were selected based on their clinical importance, Multiple Linear Regression, and Information Gain Ranking methods. The negative effect of the imbalance class of the constructed model was handled by Synthetic Minority Oversampling Technique (SMOTE). The overall performance of the predictive model classifier was improved by the Ensemble machine learning approach using the Vote method with three Decision Trees (Naïve Bayes Tree, Random Forest, and Logistic Model Tree) and achieved high accuracy of prediction (AUC = 0.92). The study shows the potential of ensembling and SMOTE approaches for predicting incident diabetes using cardiorespiratory fitness data

Czy inhibitory konwertazy angiotensyny lub blokery receptora dla angiotensyny zapobiegają wystąpieniu cukrzycy? Metaanaliza

Wstęp: Zapadalność na cukrzycę w ciągu ostatnich lat gwałtownie wzrosła, przy czym szacuje się, że w ciągu kolejnych 15 lat choroba ta rozwinie się u 100 milionów osób. Wpływ leczenia na rozwój cukrzycy de novo nie jest jasny. Autorzy badania przeprowadzili systematyczny przegląd i metaanalizę w celu zbadania wpływu inhibitorów konwertazy angiotensyny (ACEI) i blokerów receptora dla angiotensyny (ARB) na wystąpienie cukrzycy de novo. Materiał i metody: Przeszukano bazy danych MEDLINE, EMBASE, BIOSIS, Cochrane od dnia ich powstania aż do lutego 2009 roku. Poszukiwano badań z randomizacją dotyczących świeżych zachorowań na cukrzycę w grupie pacjentów leczonych ACEI lub ARB. Do metaanalizy włączono 18 badań. Zastosowano model efektów losowych i różnice między badaniami oszacowano za pomocą I2. Wyniki: Losowo wybrano 50 451 pacjentów leczonych ACEI lub ARB i 50 397 osób poddanych terapii innymi preparatami. Stosowanie ACEI lub ARB wiązało się ze zmniejszeniem liczby nowych przypadków cukrzycy (RR 0,78, 95% CI 0,70-0,88, p = 0,003 dla ACEI i RR 0,8, 95% CI 0,75-0,86, p < 0,0001 dla ARB). Liczba osób, które należało leczyć, aby zapobiec jednemu nowemu przypadkowi cukrzycy, wyniosła 100 w przypadku ACEI i 50 w przypadku ARB. Wnioski: Zgromadzone dowody wskazują, że stosowanie ACEI/ARB zapobiega rozwojowi cukrzycy. Może to przynieść szczególne korzyści kliniczne pacjentom z nadciśnieniem tętniczym i stanem przedcukrzycowym lub zespołem metabolicznym. (Folia Cardiologica Excerpta 2010; 5, 5: 247-256

Venous Thromboembolism in Cancer: An Update of Treatment and Prevention in the Era of Newer Anticoagulants

Cancer patients are at major risk of developing Venous Thromboembolism (VTE), resulting in increased morbidity and economic burden. While a number of theories try to explain its pathophysiology, its risk stratification can be broadly done in cancer related, treatment related and patient related factors. Studies report the prophylactic use of thrombolytic agents to be safe and effective in decreasing VTE related mortality/ morbidity especially in postoperative cancer patients. Recent data also suggests the prophylactic use of low molecular weight Heparins (LMWH’s) and Warfarin to be effective in reducing VTE’s related to long term Central Venous Catheter (CVC) use. In a double blind, multicenter trial, a new Ultra LMWH Semuloparin has shown to be efficacious in preventing chemotherapy associated VTE’s along with other drugs such as Certoparin and Nadoparin.. LMWH’s are reported to be very useful in preventing recurrent VTE’s in advanced cancers and should be preferred over full dose Warfarin. However their long term safety beyond 6 months has not been established yet. Further, this manuscript discusses the safety and efficacy of different drugs used in the treatment and prevention of recurrent VTE’s including Bemiparin, Semuloparin, oral direct thrombin inhibitors, parenteral and direct oral factor Xa inhibitors