Analysis of Algorithms for Permutations Biased by Their Number of Records

The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of parameter $\theta$ for records on permutations: the weight $\theta^r$ of a permutation depends on its number $r$ of records. We show that this model is meaningful for the notion of presortedness, while still being mathematically tractable. Our results describe the expected value of several classical permutation statistics in this model, and give the expected running time of three algorithms: the Insertion Sort, and two variants of the Min-Max search

Good Predictions Are Worth a Few Comparisons

Most modern processors are heavily parallelized and use predictors to guess the outcome of conditional branches, in order to avoid costly stalls in their pipelines. We propose predictor-friendly versions of two classical algorithms: exponentiation by squaring and binary search in a sorted array. These variants result in less mispredictions on average, at the cost of an increased number of operations. These theoretical results are supported by experimentations that show that our algorithms perform significantly better than the standard ones, for primitive data types

Merge Strategies: from Merge Sort to TimSort

The introduction of TimSort as the standard algorithm for sorting in Java and Python questions the generally accepted idea that merge algorithms are not competitive for sorting in practice. In an at- tempt to better understand TimSort algorithm, we define a framework to study the merging cost of sorting algorithms that relies on merges of monotonic subsequences of the input. We design a simpler yet competi- tive algorithm in the spirit of TimSort based on the same kind of ideas. As a benefit, our framework allows to establish the announced running time of TimSort, that is, O(n log n)

On the Worst-Case Complexity of TimSort

TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently implemented in Python and in Java respectively. We propose a pedagogical and insightful proof that the Python version runs in O(n log n). The approach we use in the analysis also applies to the Java version, although not without very involved technical details. As a byproduct of our study, we uncover a bug in the Java implementation that can cause the sorting method to fail during the execution. We also give a proof that Python\u27s TimSort running time is in O(n + n log rho), where rho is the number of runs (i.e. maximal monotonic sequences), which is quite a natural parameter here and part of the explanation for the good behavior of TimSort on partially sorted inputs

Learning Multiple Belief Propagation Fixed Points for Real Time Inference

In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of correlations among a large set of N variables, is encoded into a graphical model; this encoding is optimized with respect to an approximate decoding procedure LBP, which is used to infer hidden variables from an observed subset. We focus on the situation where the underlying data have many different statistical components, representing a variety of independent patterns. Considering a single parameter family of models we show how LBP may be used to encode and decode efficiently such information, without solving the NP hard inverse problem yielding the optimal MRF. Contrary to usual practice, we work in the non-convex Bethe free energy minimization framework, and manage to associate a belief propagation fixed point to each component of the underlying probabilistic mixture. The mean field limit is considered and yields an exact connection with the Hopfield model at finite temperature and steady state, when the number of mixture components is proportional to the number of variables. In addition, we provide an enhanced learning procedure, based on a straightforward multi-parameter extension of the model in conjunction with an effective continuous optimization procedure. This is performed using the stochastic search heuristic CMAES and yields a significant improvement with respect to the single parameter basic model.Comment: RR Inria 6887, 26 pages, 7 figure

Angiotensin {II}-induced redox-sensitive {SGLT}1 and 2 expression promotes high glucose-induced endothelial cell senescence

High glucose (HG)-induced endothelial senescence and dysfunction contribute to the increased cardiovascular risk in diabetes. Empagliflozin, a selective sodium glucose co-transporter2 (SGLT2) inhibitor, reduced the risk of cardiovascular mortality in type 2 diabetic patients but the protective mechanism remains unclear. This study examines the role of SGLT2 in HG-induced endothelial senescence and dysfunction. Porcine coronary artery cultured endothelial cells (ECs) or segments were exposed to HG (25 mmol/L) before determination of senescence-associated beta-galactosidase activity, protein level by Western blot and immunofluorescence staining, mRNA by RT-PCR, nitric oxide (NO) by electron paramagnetic resonance, oxidative stress using dihydroethidium and glucose uptake using 2-NBD-glucose. HG increased ECs senescence markers and oxidative stress, down-regulated eNOS expression and NO formation, and induced the expression of VCAM-1, tissue factor, and the local angiotensin system, all these effects were prevented by empagliflozin. Empagliflozin and LX-4211 (dual SGLT1/2 inhibitor) reduced glucose uptake stimulated by HG and H2O2 in ECs. HG increased SGLT1 and 2 protein levels in cultured ECs and native endothelium. Inhibition of the angiotensin system prevented HG-induced ECs senescence and SGLT1 and 2 expression. Thus, HG-induced ECs ageing is driven by the local angiotensin system via the redox-sensitive up-regulation of SGLT1 and 2, and, in turn, enhanced glucotoxicity

Redox-Sensitive Induction of Src/PI3-kinase/Akt and MAPKs Pathways Activate eNOS in Response to EPA:DHA 6:1

AIMS: Omega-3 fatty acid products containing eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have vasoprotective effects, in part, by stimulating the endothelial formation of nitric oxide (NO). This study determined the role of the EPA:DHA ratio and amount, and characterized the mechanism leading to endothelial NO synthase (eNOS) activation. METHODS AND RESULTS: EPA:DHA 6ratio1 and 9ratio1 caused significantly greater endothelium-dependent relaxations in porcine coronary artery rings than EPA:DHA 3ratio1, 1ratio1, 1ratio3, 1ratio6, 1ratio9, EPA and DHA alone, and EPA:DHA 6ratio1 with a reduced EPA + DHA amount, which were inhibited by an eNOS inhibitor. Relaxations to EPA:DHA 6ratio1 were insensitive to cyclooxygenase inhibition, and reduced by inhibitors of either oxidative stress, Src kinase, PI3-kinase, p38 MAPK, MEK, or JNK. EPA:DHA 6ratio1 induced phosphorylation of Src, Akt, p38 MAPK, ERK, JNK and eNOS; these effects were inhibited by MnTMPyP. EPA:DHA 6ratio1 induced the endothelial formation of ROS in coronary artery sections as assessed by dihydroethidium, and of superoxide anions and hydrogen peroxide in cultured endothelial cells as assessed by electron spin resonance with the spin probe CMH, and the Amplex Red based assay, respectively. CONCLUSION: Omega-3 fatty acids cause endothelium-dependent NO-mediated relaxations in coronary artery rings, which are dependent on the EPA:DHA ratio and amount, and involve an intracellular activation of the redox-sensitive PI3-kinase/Akt and MAPKs pathways to activate eNOS

ENDOTHELIUM-INDEPENDENT AND ENDOTHELIUM-DEPENDENT VASORELAXATION BY A DICHLOROMETHANE FRACTION FROM ANOGEISSUS LEIOCARPUS (DC) GUILL. ET PERR. (COMBRETACEAE): POSSIBLE INVOLVEMENT OF CYCLIC NUCLEOTIDE PHOSPHODIESTERASE INHIBITION.

Many traditional medicinal herbs from Burkina Faso are used to treat arterial hypertension (HTA). Among them, Anogeissus leiocarpus (A. Leiocarpus) which is well known and widely used in Burkina traditional medicine. Herein we assess the effects of dichloromethane fraction from A. leiocarpus stem bark (ALF), selected as the most active on cyclic nucleotide phosphodiesterases (PDEs) and characterized its specificity towards purified vascular PDE1 to PDE5 isoenzymes and study its effects on a vascular model. ALF potently and preferentially inhibits (IC50=1.6 ± 0.6 µg/mL) the calmodulin-dependent phosphodiesterase PDE1, being mainly present in vascular smooth muscle and preferentially hydrolyses cGMP. In the same range (IC50 =2.8 ±0.2 µg/ml) ALF inhibits PDE2, a cGMP-activated enzyme that is only present in endothelial cells and hydrolyses both cAMP and cGMP. PDE5, which specifically hydrolyses cGMP and which mainly contributes to cGMP hydrolysis is also potently inhibited by ALF (IC50=7.6±3.5 µg/ml). The potencies of ALF on cAMP hydrolyzing isoenzymes was lesser, being more effective on PDE4 (IC50= 17.6±3.5 µg/ml) than on PDE3 (60.9 ± 1.8 µg/ml). Since the major effect of ALF were against cGMP hydrolysis and since cGMP is implicated in endothelium-dependent relaxation, the endothelium-dependent vasorelaxation was studied on isolated porcine coronary arteries rings pre-contracted with U46619. The endothelium-dependent vasorelaxation is significantly inhibited by Nω-nitro-L-arginine (LNA 300 µmol/L, an inhibitor of endothelial NO synthase), but not affected by charybdotoxin (CTX, 100nM) plus apamin (APA, 100nM) (two inhibitors of EDHF-mediated responses). The combination of 4-aminopyridine (4-AP, 1 mmol/L, inhibitor of voltage-dependent potassium channels, Kv) plus baryum (Ba2+, 30 µmol/L, inhibitor of the potassium channels with entering correction, Kir) plus ouabain (3 µmol/L, inhibitor of ATPase Na+/K+ channels) partially inhibits endothelium-independent vasorelaxant effect. This endothelium-independent relaxant effect was also sensitive to combination of 1H-[1,2,4]-oxadiazole-[4,3-α]-quinoxalin-1-one (ODQ, 10 µM, soluble guanylyl cyclase inhibitor) and N-[2-(p-Bromocinnamylamino)ethyl]-5-isoquinoline sulfonamide dihydrochloride (H89, 100 nM, Protein Kinase A inhibitor). Taken together, these results indicate that ALF is a powerful vasodilator modulated by the formation of NO from endothelium, but also act by directly relaxing the vascular smooth muscle cells, by inhibiting cGMP hydrolyzing PDEs (PDE1, PDE2 and PDE5) and to a lesser extend on cAMP degradation (PDE3 and PDE4), cAMP and cGMP being second messengers involved in vascular relaxation

PloS one

AIMS: Portal hypertension characterized by generalized vasodilatation with endothelial dysfunction affecting nitric oxide (NO) and endothelium-dependent hyperpolarization (EDH) has been suggested to involve bacterial translocation and/or the angiotensin system. The possibility that ingestion of probiotics prevents endothelial dysfunction in rats following common bile duct ligation (CBDL) was evaluated. METHODS: Rats received either control drinking water or the probiotic VSL#3 solution (50 billion bacteria.kg body wt(-)(1).day(-)(1)) for 7 weeks. After 3 weeks, rats underwent surgery with either resection of the common bile duct or sham surgery. The reactivity of mesenteric artery rings was assessed in organ chambers, expression of proteins by immunofluorescence and Western blot analysis, oxidative stress using dihydroethidium, and plasma pro-inflammatory cytokine levels by flow cytometry. RESULTS: Both NO- and EDH-mediated relaxations to acetylcholine were reduced in the CBDL group compared to the sham group, and associated with a reduced expression of Cx37, Cx40, Cx43, IKCa and SKCa and an increased expression of endothelial NO synthase (eNOS). In aortic sections, increased expression of NADPH oxidase subunits, angiotensin converting enzyme, AT1 receptors and angiotensin II, and formation of ROS and peroxynitrite were observed. VSL#3 prevented the deleterious effect of CBDL on EDH-mediated relaxations, vascular expression of connexins, IKCa, SKCa and eNOS, oxidative stress, and the angiotensin system. VSL#3 prevented the CBDL-induced increased plasma TNF-alpha, IL-1alpha and MCP-1 levels. CONCLUSIONS: These findings indicate that VSL#3 ingestion prevents endothelial dysfunction in the mesenteric artery of CBDL rats, and this effect is associated with an improved vascular oxidative stress most likely by reducing bacterial translocation and the local angiotensin system