Parametric Polyhedra with at least kk Lattice Points: Their Semigroup Structure and the k-Frobenius Problem

Given an integral $d \times n$ matrix $A$, the well-studied affine semigroup \mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be stratified by the number of lattice points inside the parametric polyhedra $P_A(b)=\{x: Ax=b, x\geq0\}$. Such families of parametric polyhedra appear in many areas of combinatorics, convex geometry, algebra and number theory. The key themes of this paper are: (1) A structure theory that characterizes precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{ Sg}(A) such that $P_A(b) \cap {\mathbb Z}^n$ has at least $k$ solutions. We demonstrate that this set is finitely generated, it is a union of translated copies of a semigroup which can be computed explicitly via Hilbert bases computations. Related results can be derived for those right-hand-side vectors $b$ for which $P_A(b) \cap {\mathbb Z}^n$ has exactly $k$ solutions or fewer than $k$ solutions. (2) A computational complexity theory. We show that, when $n$, $k$ are fixed natural numbers, one can compute in polynomial time an encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function, using a short sum of rational functions. As a consequence, one can identify all right-hand-side vectors of bounded norm that have at least $k$ solutions. (3) Applications and computation for the $k$-Frobenius numbers. Using Generating functions we prove that for fixed $n,k$ the $k$-Frobenius number can be computed in polynomial time. This generalizes a well-known result for $k=1$ by R. Kannan. Using some adaptation of dynamic programming we show some practical computations of $k$-Frobenius numbers and their relatives

Use of ticagrelor alongside fibrinolytic therapy in patients with ST-segment elevation myocardial infarction: Practical perspectives based on data from the TREAT study

All Clinical Cardiology articles are published under the terms of the Creative Commons Attribution License (CC BY) which allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by a Wiley Open Access journal is retained by the author(s).Primary percutaneous coronary intervention (PCI) is the preferred reperfusion method in patients with ST‐segment elevation myocardial infarction (STEMI). In patients with STEMI who cannot undergo timely primary PCI, pharmacoinvasive treatment is recommended, comprising immediate fibrinolytic therapy with subsequent coronary angiography and rescue PCI if needed. Improving clinical outcomes following fibrinolysis remains of great importance for the many patients globally for whom rapid treatment with primary PCI is not possible. For patients with acute coronary syndrome who underwent primary PCI, the PLATO trial demonstrated superior efficacy of ticagrelor relative to clopidogrel. Results in the predefined subgroup of patients with STEMI were consistent with the overall PLATO trial. Patients who received fibrinolytic therapy in the 24 hours before randomization were excluded from PLATO, and there is thus a lack of data on the safety of using ticagrelor in conjunction with fibrinolytic therapy in the first 24 hours after STEMI. The TREAT study addresses this knowledge gap; patients with STEMI who had symptom onset within the previous 24 hours and had received fibrinolytic therapy (of whom 89.4% had also received clopidogrel) were randomized to treatment with ticagrelor or clopidogrel (median time between fibrinolysis and randomization: 11.5 hours). At 30 days, ticagrelor was found to be non‐inferior to clopidogrel for the primary safety outcome of Thrombolysis in Myocardial Infarction (TIMI)‐defined first major bleeding. Considering together the results of the PLATO and TREAT studies, initiating or switching to treatment with ticagrelor within the first 24 hours after STEMI in patients receiving fibrinolysis is reasonable

Derivatives of 9-phosphorylated acridine as butyrylcholinesterase inhibitors with antioxidant activity and the ability to inhibit β-amyloid self-aggregation: potential therapeutic agents for Alzheimer’s disease

We investigated the inhibitory activities of novel 9-phosphoryl-9,10-dihydroacridines and 9-phosphorylacridines against acetylcholinesterase (AChE), butyrylcholinesterase (BChE), and carboxylesterase (CES). We also studied the abilities of the new compounds to interfere with the self-aggregation of β-amyloid (Aβ42) in the thioflavin test as well as their antioxidant activities in the ABTS and FRAP assays. We used molecular docking, molecular dynamics simulations, and quantum-chemical calculations to explain experimental results. All new compounds weakly inhibited AChE and off-target CES. Dihydroacridines with aryl substituents in the phosphoryl moiety inhibited BChE; the most active were the dibenzyloxy derivative 1d and its diphenethyl bioisostere 1e (IC50 = 2.90 ± 0.23 µM and 3.22 ± 0.25 µM, respectively). Only one acridine, 2d, an analog of dihydroacridine, 1d, was an effective BChE inhibitor (IC50 = 6.90 ± 0.55 μM), consistent with docking results. Dihydroacridines inhibited Aβ42 self-aggregation; 1d and 1e were the most active (58.9% ± 4.7% and 46.9% ± 4.2%, respectively). All dihydroacridines 1 demonstrated high ABTS•+-scavenging and iron-reducing activities comparable to Trolox, but acridines 2 were almost inactive. Observed features were well explained by quantum-chemical calculations. ADMET parameters calculated for all compounds predicted favorable intestinal absorption, good blood–brain barrier permeability, and low cardiac toxicity. Overall, the best results were obtained for two dihydroacridine derivatives 1d and 1e with dibenzyloxy and diphenethyl substituents in the phosphoryl moiety. These compounds displayed high inhibition of BChE activity and Aβ42 self-aggregation, high antioxidant activity, and favorable predicted ADMET profiles. Therefore, we consider 1d and 1e as lead compounds for further in-depth studies as potential anti-AD preparations

Antithrombotic therapy after acute coronary syndrome or PCI in atrial fibrillation

BACKGROUND: Appropriate antithrombotic regimens for patients with atrial fibrillation who have an acute coronary syndrome or have undergone percutaneous coronary intervention (PCI) are unclear. METHODS: In an international trial with a two-by-two factorial design, we randomly assigned patients with atrial fibrillation who had an acute coronary syndrome or had undergone PCI and were planning to take a P2Y12 inhibitor to receive apixaban or a vitamin K antagonist and to receive aspirin or matching placebo for 6 months. The primary outcome was major or clinically relevant nonmajor bleeding. Secondary outcomes included death or hospitalization and a composite of ischemic events. RESULTS: Enrollment included 4614 patients from 33 countries. There were no significant interactions between the two randomization factors on the primary or secondary outcomes. Major or clinically relevant nonmajor bleeding was noted in 10.5% of the patients receiving apixaban, as compared with 14.7% of those receiving a vitamin K antagonist (hazard ratio, 0.69; 95% confidence interval [CI], 0.58 to 0.81; P<0.001 for both noninferiority and superiority), and in 16.1% of the patients receiving aspirin, as compared with 9.0% of those receiving placebo (hazard ratio, 1.89; 95% CI, 1.59 to 2.24; P<0.001). Patients in the apixaban group had a lower incidence of death or hospitalization than those in the vitamin K antagonist group (23.5% vs. 27.4%; hazard ratio, 0.83; 95% CI, 0.74 to 0.93; P = 0.002) and a similar incidence of ischemic events. Patients in the aspirin group had an incidence of death or hospitalization and of ischemic events that was similar to that in the placebo group. CONCLUSIONS: In patients with atrial fibrillation and a recent acute coronary syndrome or PCI treated with a P2Y12 inhibitor, an antithrombotic regimen that included apixaban, without aspirin, resulted in less bleeding and fewer hospitalizations without significant differences in the incidence of ischemic events than regimens that included a vitamin K antagonist, aspirin, or both. (Funded by Bristol-Myers Squibb and Pfizer; AUGUSTUS ClinicalTrials.gov number, NCT02415400.)

Searching for diagnostic correlations in female patients after ischemic stroke

Aim. To perform a comparative analysis of clinical and laboratory parameters in groups of young women (pregnant or in early postpartum period) with stroke. Materials and methods. The study included 17 pregnant or in early postpartum period women (group 1) and 17 non-pregnant women (group 2) matched by disease severity with mean age 27.7±14.4 years in acute period of stroke in cerebral hemispheres of medium severity. Results. At the discharge improvement in NIH scale results was observed in women in both groups and there were no significant differences in outcomes. Not statistically significant differences of partial pressure of oxygen in venous blood (VB) from the median cubital vein (MCV) and the jugular vein (JV) in both groups at study period were acquired in comparative time interval. Differences in pH levels in VB from the MCV and the JV were observed during hospital stay. In patients from 2 groups pH levels were more acidic in the JV VB than in the MCV VB. Differences in lactate levels in blood from the MCV and the JV were observed. Lactate levels were lower in the MCV VB than in the JV VB during hospital stay in patients from both groups. In patients from both groups glycemia level in the JV VB was lower than in the MCV VB during the whole study period. At the discharge in patients from both groups a decrease in glucose level in arterial and venous blood from the MCV was observed. Arteriovenous oxygen difference (AVOD) in JV VB in 2 study groups was decreasing over time from admission to discharge. Differences in AVOD of VB from JV and MCV and AVOD in JV VB were higher in both study groups during the follow up period. Conclusion. In the conducted study of neurological status, brain and system metabolism charachteristics in patients with brain infarction in dynamics there were no differences found in 2 grops of women of fertile age. The reported changes suggest macroergic compounds deficit, and oxidative stress reactions pro­ducts utilization disorders in brain tissue

Pharmacodynamic and Pharmacokinetic Profiles of Sacubitril/Valsartan (LCZ696) in Patients with Heart Failure and Reduced Ejection Fraction

Aims: Concomitant renin–angiotensin–aldosterone system blockade and natriuretic peptide system enhancement may provide unique therapeutic benefits to patients with heart failure and reduced ejection fraction (HFrEF). This study assessed the pharmacodynamics and pharmacokinetics of LCZ696 in patients with HFrEF. Methods: This was an open-label, noncontrolled single-sequence study. After a 24-h run-in period, patients (n = 30) with HFrEF (EF ≤ 40%; NYHA class II–IV) received LCZ696 100 mg twice daily (bid) for 7 days and 200 mg bid for 14 days, along with standard treatment for heart failure (HF) (except angiotensin-converting enzyme inhibitors [ACEIs] or angiotensin receptor blockers [ARBs]). Results: On Day 21, significant increases were observed in the plasma biomarkers indicative of neprilysin and RAAS inhibition (ratio-to-baseline: cyclic guanosine monophosphate [cGMP], 1.38; renin concentration and activity, 3.50 and 2.27, respectively; all, P < 0.05). Plasma NT-proBNP levels significantly decreased at all the time points on Days 7 and 21; plasma aldosterone and endothelin-1 levels significantly decreased on Day 21 (all, P < 0.05). Following administration of LCZ696, the Cmax of sacubitril (neprilysin inhibitor prodrug), LBQ657 (active neprilysin inhibitor), and valsartan were reached within 0.5, 2.5, and 2 h. Between 100- and 200-mg doses, the Cmax and AUC0–12 h for sacubitril and LBQ657 were approximately dose-proportional while that of valsartan was less than dose-proportional. Conclusions: Treatment with LCZ696 for 21 days was well tolerated and resulted in plasma biomarker changes indicative of neprilysin and RAAS inhibition in patients with HF. The pharmacokinetic exposure of the LCZ696 analytes in patients with HF observed in this study is comparable to that observed in the pivotal Phase III study

Invasive and antiplatelet treatment of patients with non-ST-segment elevation myocardial infarction: Understanding and addressing the global risk-treatment paradox

Clinical guidelines for the treatment of patients with non-ST-segment elevation myocardial infarction (NSTEMI) recommend an invasive strategy with cardiac catheterization, revascularization when clinically appropriate, and initiation of dual antiplatelet therapy regardless of whether the patient receives revascularization. However, although patients with NSTEMI have a higher long-term mortality risk than patients with ST-segment elevation myocardial infarction (STEMI), they are often treated less aggressively; with those who have the highest ischemic risk often receiving the least aggressive treatment (the treatment-risk paradox). Here, using evidence gathered from across the world, we examine some reasons behind the suboptimal treatment of patients with NSTEMI, and recommend approaches to address this issue in order to improve the standard of healthcare for this group of patients. The challenges for the treatment of patients with NSTEMI can be categorized into four P factors that contribute to poor clinical outcomes: patient characteristics being heterogeneous; physicians underestimating the high ischemic risk compared with bleeding risk; procedure availability; and policy within the healthcare system. To address these challenges, potential approaches include: developing guidelines and protocols that incorporate rigorous definitions of NSTEMI; risk assessment and integrated quality assessment measures; providing education to physicians on the management of long-term cardiovascular risk in patients with NSTEMI; and making stents and antiplatelet therapies more accessible to patients