Splaying Preorders and Postorders

Let $T$ be a binary search tree. We prove two results about the behavior of the Splay algorithm (Sleator and Tarjan 1985). Our first result is that inserting keys into an empty binary search tree via splaying in the order of either $T$'s preorder or $T$'s postorder takes linear time. Our proof uses the fact that preorders and postorders are pattern-avoiding: i.e. they contain no subsequences that are order-isomorphic to $(2,3,1)$ and $(3,1,2)$, respectively. Pattern-avoidance implies certain constraints on the manner in which items are inserted. We exploit this structure with a simple potential function that counts inserted nodes lying on access paths to uninserted nodes. Our methods can likely be extended to permutations that avoid more general patterns. Second, if $T'$ is any other binary search tree with the same keys as $T$ and $T$ is weight-balanced (Nievergelt and Reingold 1973), then splaying $T$'s preorder sequence or $T$'s postorder sequence starting from $T'$ takes linear time. To prove this, we demonstrate that preorders and postorders of balanced search trees do not contain many large "jumps" in symmetric order, and exploit this fact by using the dynamic finger theorem (Cole et al. 2000). Both of our results provide further evidence in favor of the elusive "dynamic optimality conjecture.

A Fistful of Dollars: Formalizing Asymptotic Complexity Claims via Deductive Program Verification

Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018International audienceWe present a framework for simultaneously verifying the functional correctness and the worst-case asymptotic time complexity of higher-order imperative programs. We build on top of Separation Logic with Time Credits, embedded in an interactive proof assistant. We formalize the O notation, which is key to enabling modular specifications and proofs. We cover the subtleties of the multivariate case, where the complexity of a program fragment depends on multiple parameters. We propose a way of integrating complexity bounds into specifications, present lemmas and tactics that support a natural reasoning style, and illustrate their use with a collection of examples

In Vitro Comparison of Novel Polyurethane Aortic Valves and Homografts After Seeding and Conditioning

The aim of the study was to compare the behavior of seeded cells on synthetic and natural aortic valve scaffolds during a low-flow conditioning period. Polyurethane (group A) and aortic homograft valves (group B) were consecutively seeded with human fibroblasts (FB), and endothelial cells (EC) using a rotating seeding device. Each seeding procedure was followed by an exposure to low pulsatile flow in a dynamic bioreactor for 5 days. For further analysis, samples were taken before and after conditioning. Scanning electron microscopy showed confluent cell layers in both groups. Immunohistochemical analysis showed the presence of EC and FB before and after conditioning as well as the establishment of an extracellular matrix (ECM) during conditioning. A higher expression of ECM was observed on the scaffolds’ inner surface. Real-time polymerase chain reaction showed higher inflammatory response during the conditioning of homografts. Endothelialization caused a decrease in inflammatory gene expression. The efficient colonization, the establishment of an ECM, and the comparable inflammatory cell reaction to the scaffolds in both groups proved the biocompatibility of the synthetic scaffold. The newly developed bioreactor permits conditioning and cell adaption to shear stress. Therefore, polyurethane valve scaffolds may offer a new option for aortic valve replacement

Sirtuin1, not NAMPT, possesses anti-inflammatory effects in epicardial, pericardial and subcutaneous adipose tissue in patients with CHD

Background Inflammation in cardiac adipose tissue (AT) is associated with atherosclerosis. We investigated whether the epicardial-, pericardial and pre-sternal subcutaneous AT (EAT, PAT and SAT) expression of Sirtuin1 (SIRT1) and nicotinamide phosphoribosyl transferase (NAMPT) are involved in the inflammatory process in coronary heart disease (CHD), and potentially associated to nod-like receptor family pyrin domain containing 3 (NLRP3) inflammasome-related markers, macrophage polarization markers, cell markers and the cardiometabolic profile.Methods In this cohort study performed between 2016 and 2018, EAT, PAT and SAT biopsies were retrieved from 52 CHD patients (77% men, median age 67) undergoing open-chest coronary artery bypass grafting (CABG), and 22 patients (50% men, median age 69) undergoing aortic valve replacement serving as controls. AT samples were snapfrozen at - 80 degrees C until RNA extraction and AT expression of actual markers, relatively quantified by PCR. Circulating SIRT1 and NAMPT were measured with Enzyme-linked immunosorbent assays (ELISAs). Non-parametric statistical tests were mainly used, including Friedman's test coupled to Wilcoxon signed-rank test and Spearman Correlation.Results SIRT1 and NAMPT levels were similar in CHD and controls. In CHD, SIRT1 and NAMPT were inter-correlated in all AT compartments (r = 0.37-0.56, p < 0.01, all), and differently expressed between compartments, with the highest expression in SAT, significantly different from EAT (p < 0.01, both). Circulating SIRT1 and NAMPT levels were inversely associated (r = - 0.32, p = 0.024). In EAT and SAT, SIRT1 expression was inversely associated with IL-18 (r = - 0.43 and r = - 0.38, p < 0.01, both), whereas NAMPT expression was positively associated with the NLRP3 inflammasomerelated markers in all compartments (r = 0.37-0.55, p < 0.01, all). While SIRT1 and NAMPT correlated to nitric oxide synthase 2 (NOS2), especially in SAT (r = 0.50-0.52, p <= 0.01, both), SIRT1 expression was related to endothelial cells, and NAMPT to macrophages. SIRT1 levels were correlated to weight and waist (r = 0.32 and r = 0.38, p < 0.03, both) and inversely to triglycerides and glycated haemoglobin (HbA1c) (r = - 0.33-- 0.37, p < 0.03, all), the latter positively correlated to NAMPT concentration (r = 0.39, p = 0.010).Conclusion The study indicates that targeting SIRT1, with its anti-inflammatory properties, may be a novel antiinflammatory strategy in preventing atherosclerosis and CHD progression. NAMPT may be an early player in AT inflammation, mediating/reflecting a pro-inflammatory state