Best polynomial approximation

U některých matematických úloh nedokážeme nalézt řešení exaktně, ale pouze přibližně metodami numerické matematiky. Klíčovým konceptem je pak nahrazení neboli aproximace. Mezi nejčastěji používané metody patří například polynomiální interpolace, nicméně chyba této metody může být v některých bodech intervalu velmi vysoká. Aproximace, která v každém bodě daného intervalu minimalizuje maximum chyby, se nazývá nejlepší stejnoměrná aproximace (best approximation). Obecně existuje právě jedno řešení úlohy nalezení nejlepší polynomiální aproximace, ale nelze ji vypočítat přesně. K přibližnému řešení se lze dopracovat například použitím Remezova algoritmu. Překvapivě dobré (near-best approximation) řešení nám také nabízí interpolace v Čebyševových uzlech. Cílem naší práce je zejména nastudovat a naimplementovat Remezův algoritmus a otestovat jeho funkčnost. Remezův algoritmus nakonec porovnáme s Lagrangeovou interpolací v Čebyševových uzlech.For some mathematical problems we are not able to find solutions exactly, but only approximately by using methods of numerical mathematics. The key concept is then replacement or in other words approximation. One of the most used methods is, for example, polynomial interpolation, however at some points of the interval the error of this method might be significant. The approximation which minimizes the maximum error at every point of the interval is called the best approximation. Generally, there is a unique solution to the problem of finding the best polynomial approximation, but it is not possible to calculate it exactly. The approximate solution can be obtained, for example, by using the Remez algorithm. The interpolation at Chebyshev nodes also yields surprisingly good results, generally being near-best approximations. The goal of our thesis is namely to study and implement the Remez algorithm and test its functionality. Finally, we compare the Remez algorithm with Lagrange interpolation at Chebyshev nodes.470 - Katedra aplikované matematikyvýborn

Creation of dashboards in the tool QlikView

This diploma thesis deals with performance dashboards and QlikView tool which serves for creation of these dashboards. The work is divided into seven parts. The first and the second part together focus on defining the theoretical foundations of Business Intelligence and Corporate Performance Management, which create basis for performance dashboards. The focus of the third part lies in definition of term performance dashboard and clarifying its major advantages and benefits for a company. An important part is also the description of performance dashboard composition in terms of their usability, layered structure and division into various types. The forth part analyses existing criteria for evaluating of tools dedicated for creation of dashboards. Its goal is, according to the forgone analysis, to make the own list of criteria for evaluating these tools. The aim of the fifth part of this work is to describe QlikView platform. It provides a brief overview of the platform in terms of its most important components and their purpose and also provides an insight into basic architecture of this platform and compares it with traditional BI solutions. The sixth part describes basic principles of work in QlikView. Its goal is to demonstrate the basic procedure of dashboards creation in this environment on sample examples, which should also serve as a simple guide for beginner users of this tool. The last seventh part deals with evaluation of QlikView solution. Its main purpose is to review possibilities and capabilities of this tool for dashboard creation according to the predetermined criteria which are applied to the tool during its evaluation

Does atorvastatin therapy change the anti‐Xa activity in xabans‐treated patients with atrial fibrillation?

Abstract Atorvastatin and direct oral factor Xa inhibitors (xabans) are frequently co‐administrated in patients with atrial fibrillation (AF). However, no studies investigating the possibility of the pharmacologic interaction between these agents have been conducted. The aim of this prospective observational study was to determine the impact of atorvastatin therapy on anti‐Xa activity in xabans‐treated patients with AF. We enrolled 115 AF patients on long‐term rivaroxaban (52 patients) and long‐term apixaban (63 patients) therapy. Long‐term atorvastatin (40 mg once daily) was administrated to 28 rivaroxaban‐treated patients and to 28 apixaban‐treated patients. Trough and peak samples were tested for anti‐Xa activity with drug‐specific anti‐Xa chromogenic analysis. For rivaroxaban, there were no significant differences in trough activity (45.5 ± 39.5 ng/ml vs. 46.2 ± 30.1 ng/ml; p = .34) and peak anti‐Xa activity (179.2 ± 108.8 ng/ml vs. 208.1 ± 104.1 ng/ml; p = .94) between atorvastatin‐treated patients and those without atorvastatin. Similarly, atorvastatin did not impact the trough activity (127.7 ± 71.1 ng/ml vs. 100.8 ± 61.1 ng/ml; p = .12) or peak anti‐Xa activity (213.8 ± 103.6 ng/ml vs. 179.3 ± 72.9 ng/ml; p = .14) among apixaban‐treated patients with AF. This observational study did not show a significant impact of atorvastatin on trough and peak anti‐Xa activity in xabans‐treated patients with AF

Viscoelastic Hemostatic Assays and Platelet Function Testing in Patients with Atherosclerotic Vascular Diseases

Platelets play crucial role in acute vascular atherosclerotic diseases, including myocardial infarction and stroke. Additionally, platelet aggregation is a key target of antiplatelet agents, forming the keystone of pharmacotherapy of various atherosclerotic cardiovascular diseases. Thromboelastography and thromboelastometry, representing currently available viscoelastic hemostatic assays (VHA), are designed as whole blood, real-time analyzers of clot formation and clot resolution. These assays could, in theory, overcome some limitations of currently available platelet function testing assays. This article reviews the current experience with the use of VHA for platelet function testing and for monitoring of the response to antiplatelet therapy

Tailored Direct Oral Anticoagulation in Patients with Atrial Fibrillation: The Future of Oral Anticoagulation?

Direct oral anticoagulants (DOAC) are currently the drug of choice for drug prevention of stroke or systemic embolism in patients with atrial fibrillation (AF). However, repeated ischemic stroke or systemic embolism and bleeding while on DOAC is still a challenging clinical phenomenon in the management of future long-term anticoagulation. It is not known whether tailoring the DOAC therapy to achieve optimal therapeutic drug levels could improve the clinical course of DOAC therapy. To be able to tailor the therapy, it is necessary to have a valid laboratory method for DOAC level assessment, to be aware of factors influencing DOAC levels and to have clinical options to tailor the treatment. Furthermore, the data regarding clinical efficacy/safety of tailored DOAC regimes are still lacking. This article reviews the current data on tailored direct oral anticoagulation in patients with AF

Resistance on the Latest Oral and Intravenous P2Y12 ADP Receptor Blockers in Patients with Acute Coronary Syndromes: Fact or Myth?

Novel P2Y12 ADP receptor blockers (ADPRB) should be preferred in dual-antiplatelet therapy in patients with acute coronary syndrome. Nevertheless, there are still patients who do not respond optimally to novel ADP receptor blocker therapy, and this nonoptimal response (so-called “high on-treatment platelet reactivity” or “resistance”) could be connected with increased risk of adverse ischemic events, such as myocardial re-infarction, target lesion failure and stent thrombosis. In addition, several risk factors have been proposed as factors associated with the phenomenon of inadequate response on novel ADPRB. These include obesity, multivessel coronary artery disease, high pre-treatment platelet reactivity and impaired metabolic status for prasugrel, as well as elderly, concomitant therapy with beta-blockers, morphine and platelet count for ticagrelor. There is no literature report describing nonoptimal therapeutic response on cangrelor, and cangrelor therapy seems to be a possible approach for overcoming HTPR on prasugrel and ticagrelor. However, the optimal therapeutic management of “resistance” on novel ADPRB is not clear and this issue requires further research. This narrative review article discusses the phenomenon of high on-treatment platelet reactivity on novel ADPRB, its importance in clinical practice and approaches for its therapeutic overcoming

The Impact of Type 2 Diabetes on the Efficacy of ADP Receptor Blockers in Patients with Acute ST Elevation Myocardial Infarction: A Pilot Prospective Study

Background. The aim of this study was to validate the impact of type 2 diabetes (T2D) on the platelet reactivity in patients with acute ST elevation myocardial infarction (STEMI) treated with adenosine diphosphate (ADP) receptor blockers. Methods. A pilot prospective study was performed. Totally 67 patients were enrolled. 21 patients had T2D. Among all study population, 33 patients received clopidogrel and 34 patients received prasugrel. The efficacy of ADP receptor blocker therapy had been tested in two time intervals using light transmission aggregometry with specific inducer and vasodilator-stimulated phosphoprotein phosphorylation (VASP-P) flow cytometry assay. Results. There were no significant differences in platelet aggregability among T2D and nondiabetic (ND) group. The platelet reactivity index of VASP-P did not differ significantly between T2D and ND group (59.4±30.9% versus 60.0±25.2% and 33.9±25.3% versus 38.6±29.3% in second testing). The number of ADP receptor blocker nonresponders did not differ significantly between T2D and ND patients. The time interval from ADP receptor blocker loading dosing to the blood sampling was similar in T2D and ND patients in both examinations. Conclusion. This prospective study did not confirm the higher platelet reactivity and higher prevalence of ADP receptor blocker nonresponders in T2D acute STEMI patients

The Impact of Type 2 Diabetes on the Efficacy of ADP Receptor Blockers in Patients with Acute ST Elevation Myocardial Infarction: A Pilot Prospective Study

Background. The aim of this study was to validate the impact of type 2 diabetes (T2D) on the platelet reactivity in patients with acute ST elevation myocardial infarction (STEMI) treated with adenosine diphosphate (ADP) receptor blockers. Methods. A pilot prospective study was performed. Totally 67 patients were enrolled. 21 patients had T2D. Among all study population, 33 patients received clopidogrel and 34 patients received prasugrel. The efficacy of ADP receptor blocker therapy had been tested in two time intervals using light transmission aggregometry with specific inducer and vasodilator-stimulated phosphoprotein phosphorylation (VASP-P) flow cytometry assay. Results. There were no significant differences in platelet aggregability among T2D and nondiabetic (ND) group. The platelet reactivity index of VASP-P did not differ significantly between T2D and ND group (59.4 ± 30.9% versus 60.0 ± 25.2% and 33.9 ± 25.3% versus 38.6 ± 29.3% in second testing). The number of ADP receptor blocker nonresponders did not differ significantly between T2D and ND patients. The time interval from ADP receptor blocker loading dosing to the blood sampling was similar in T2D and ND patients in both examinations. Conclusion. This prospective study did not confirm the higher platelet reactivity and higher prevalence of ADP receptor blocker nonresponders in T2D acute STEMI patients. Background Type 2 diabetes (T2D) is a strong and independent risk factor of cardiovascular disease in both men and women Methods Study Design and Patients. A single centre, pilot prospective observational study in patients with acute STEMI was performed. All patients underwent coronary angiography and primary percutaneous coronary intervention (pPCI) of culprit coronary lesion. Totally 67 consecutive presentations of patients (37 men and 30 women; mean age 67 years; the youngest patient was 34-year-old and the oldest patient was 89-year-old) with acute STEMI and pPCI of coronary lesion were enrolled in this study. Patients with multivessel coronary disease planned for surgical revascularization, patients treated only conservatively, and hemodynamically unstable patients (i.e., patients in Killip class IV) had been excluded from this study. Additionally, patients with hypertensive crisis, kidney, and liver failure had been also excluded from study population. Moreover, patients with medication which could interfere with the action of ADP receptor blockers, such as omeprazole, fluconazole, or morphine were also excluded from this study. All patients should be ADPRB naïve prior to myocardial infarction. Patients with known and correctly diagnosed history of T2D had been assigned to T2D group. This group included 21 patients. In all patients without previous history of T2D the glycated hemoglobin (HbA1C) levels were assessed in order to exclude patients with undiagnosed T2D. Patients with HbA1C levels > 5.7% DCCT were considered to be patients with possibly undiagnosed T2D and these patients had been excluded from the study. Subsequently, a standard oral glucose tolerance test (75 g of glucose was administrated in 100 mL of water and a venous blood sample was taken two hours after the glucose administration) was performed in the rest of the patients without previous history of T2D one month after the hospital discharge. Patients with blood glucose value > 7.8 mmol/L two hours after the glucose administration had been also excluded from the study. Patients without previous history of T2D, with HbA1C levels < 5.7% DCCT and blood glucose value < 7.8 mmol/L shown in oral glucose tolerance test had been assigned to nondiabetic (ND) group. The basic demographic data and concomitant medication in the study population are shown in Platelet Function Testing. Blood samples had been taken using 3.8% citrate vacutainer blood collection tubes. Blood samples had been immediately analyzed within first 2 hours from blood sampling. The samples had been taken in the following time intervals: Sample 1, at the time of patient arrival to cath laboratory: this sample aimed to test the efficacy of ADP receptor blocker given in loading doses prior to the urgent coronary angiography and pPCI of coronary lesion. Sample 2, one hour after the administration of first ADP receptor blocker maintenance dose: this sample aimed to test the efficacy of in-hospital ADP receptor blocker therapy given in maintenance dosage. The platelet reactivity was tested using light transmission aggregometry (LTA) with specific inducer (ADP) and vasodilator-stimulated phosphoprotein phosphorylation (VASP-P) flow cytometry assay. Light Transmission Aggregometry (LTA) . this method represents recently the "golden standard" of platelet function testing. ADP (10 mol/L) was used as specific inducer for ADP receptor blocker efficacy testing. LTA was examined with Chrono-Log model 700 (Chronolog Corporation, Havertown, PA, USA). The platelet aggregability was assessed on the basis of the change in the plasma turbidity after the addition of the specific inducer. Residual platelet aggregability > 50% after the addition of ADP was considered to be high ontreatment platelet reactivity (HTPR). VASP-P Flow Cytometry Assay. In this analysis, we used PLT VASP/P2Y12 assay kits (Diagnostica Stago, France). Sample of citrate blood was incubated with prostaglandin E1 (PGE1) and PGE1 + ADP (activated platelets). After cellular permeabilization by nonionic detergent, VASP-P is labeled by indirect no-wash immunofluorescence using a specific monoclonal antibody. Dual color flow cytometry analysis then allowed comparison of the 2 tested conditions. Analysis was carried out on FACSCalibur flow cytometer (BD Biosciences, San Jose, California). In the final step, the platelet reactivity index (PRI) was calculated using corrected mean VASP fluorescence intensities (MFIc) in the presence of PGE1 alone (resting platelets) or PGE1 + ADP simultaneously (activated platelets). Index represented the ratio of activated/resting platelets and was calculated according to the following equation: The resulting value described PRI to ADP treatment in the range of 0% to 100%. Values of PRI above 50% were considered as determinant of HTPR and inadequate response to treatment. Normally distributed continuous or interval-scaled variables are presented as mean ± standard deviation (SD); otherwise median (M) and quartile ranges from the lower quartile to the upper quartile were used. Group effects (i.e., differences between T2D and ND groups) were tested with t-test in the case of normally distributed data or with Mann-Whitney U test when data distribution was asymmetrical. Differences between proportions (e.g., number of patients in T2D and ND groups) were tested with binominal tests. Categorical variables grouped in 2-way contingency tables were analyzed using chi-square tests. The significance of < 0.05 was considered as a criterion for comparison between data sets with equal and unequal variances. The statistical analysis was performed with Statistica v. 7.0 (StatSoft Inc., Dell Software, Tulsa, Oklahoma, USA). Sample size calculation was based on the assumption of the incidence of HTPR among ADP receptor blockerstreated T2D patients reported in previously published studies Results The time interval from ADP receptor blocker loading dose administration to the collection of sample 1 was 1.8 ± 0.9 hours and to the collection of sample 2 was 20.5 ± 2.1 hours. The mean platelet aggregability after the induction with ADP was 52.5 ± 23.6% in sample 1 and 39.7 ± 24.5% in sample 2. Examination of VASP phosphorylation showed mean PRI 59.7±26.9% in sample 1 and mean PRI 37.0±27.8% in sample 2, respectively. When comparing the T2D and ND group Prasugrel induced in this preliminary study significantly more potent platelet inhibition Discussion T2D is a strong and independent risk factor of acute STEMI. T2D increases the risk of future complications in acute STEMI patients. Endothelial dysfunction On the other hand, the results of this preliminary prospective observation did not confirm the significantly higher residual platelet reactivity or significantly higher prevalence of HTPR in T2D acute STEMI patients undergoing pPCI of culprit coronary lesion. The exact explanation of this observation is recently missing. The time interval from drug administration to blood sample collection did not differ significantly in T2D and ND patients neither in sample 1 nor in sample 2. The differences in time interval from drug Journal of Diabetes Research 5 dosing to blood sampling therefore cannot explain the results obtained in this study. Another possible explanation may be the fact that the majority of studies pointing on the higher prevalence of HTPR among T2D patients were performed on a sample of stable coronary/ischemic heart disease patients. It is generally accepted that patients with acute STEMI represent a special group with different clinical and risk profile. It is therefore possible that results obtained from the studies on stable patients might not be fully applicable in high risk ACS patients. However, study performed by Cuisset et al. identified high prevalence of clopidogrel nonresponders (50% of patients) also in T2D patients undergoing PCI for ACS An alternative explanation of similar on-treatment platelet reactivity in T2D and ND patients in this study might be a possibility that the failure in antiplatelet response is in T2D patients specifically associated with clopidogrel. The administration of newer ADP receptor blockers might not be connected with such a failure in on-treatment response Limitations There were some important limitations of our analysis. First, this study had a prospective observational design and not a randomized double blinded one. The decision on ADP receptor blocker therapy strategy (clopidogrel versus prasugrel) was left to the physician who performed the diagnostic ECG record (general practitioner, cardiologist, ED physician, etc.). Therefore the data obtained in this study do not have the evidence power of data from a randomized double blinded trial. Second, a low sample size might be a limitation of the study. A relatively small patient sample cannot guarantee significant power. Third, a relatively short time interval from ADPRB loading dosing to first sampling (especially in the settings of acute coronary syndrome) might be another limitation of this study. It is already known that time to peak platelet inhibition is generally prolonged in acute STEMI patients and also in stable coronary artery disease patients with T2D Conclusion This prospective study did not confirm the higher residual platelet reactivity and higher prevalence of HTPR in T2D acute STEMI patients undergoing pPCI of culprit coronary lesion. However, the results of this study are preliminary and further studies on larger sample sizes would be definitely needed for the final clarification of this issue

High On-Treatment Platelet Reactivity in Patients Undergoing Complex Percutaneous Coronary Interventions

Patient response to P2Y12 inhibitor therapy is heterogeneous, and those with high on-treatment platelet reactivity (HTPR) are at an increased risk of thrombotic complications. The aim of our study was to determine whether selecting a high-risk patient group of individuals after complex percutaneous coronary intervention (PCI) would show the clinical benefit of HTPR testing for preventing thrombotic complications. Blood samples of patients after complex PCI were acquired 1 day and 1 month after the intervention. The samples were tested using vasodilator-stimulated phosphoprotein phosphorylation (VASP-P) and platelet function assay (PFA). The occurrence of clinically significant stent thrombosis with repeated revascularization of the target vessel was observed over a 1-year period. One day after PCI, 37% of patients had HTPR as established by VASP-P. One month after PCI, the percentage of patients with HTPR decreased to 30.9%. According to PFA, 1 day after PCI, 33.3% of patients had HTPR. This percentage declined to 19.8% after 1 month. All measurements identified a significantly higher proportion of HTPR in patients on clopidogrel compared to ticagrelor and prasugrel. Two cases of early stent thrombosis and 1 case of late stent thrombosis were identified. Further study of adenosine diphosphate receptor blocker on-treatment response in patients undergoing complex PCI is necessary

DNA Polymorphisms in Pregnant Women with Sticky Platelet Syndrome

Sticky platelet syndrome (SPS) is a thrombophilia caused by the increased aggregability of platelets in response to the addition of low concentrations of epinephrine (EPI) and/or adenosine diphosphate (ADP). Some of the single nucleotide polymorphisms (SNP), alleles and haplotypes of platelet glycoprotein receptors were proved to have a role in the etiology of thrombotic episodes When comparing SPS and the control group, in VEGFA rs3025039, the p value for both CC vs. TT and CT vs. TT analyses was <0.001. Interestingly, no minor TT genotype was present in the SPS group, suggesting the thrombotic pathogenesis of recurrent spontaneous abortions (RSA) in these patients. Moreover, we found a significant difference in the presence of AT containing a risky A allele and TT genotype of ALPP rs13026692 (p = 0.034) in SPS patients when compared with the controls. Additionally, we detected a decreased frequency of the GG (CC) genotype of FOXP3 rs3761548 in patients with SPS and RSA when compared with the control group (p value for the CC (GG) vs. AA (TT) 0.021). This might indicate an evolutionary protective mechanism of the A (T) allele in the SPS group against thrombotic complications in pregnancy. These results can be used for antithrombotic management in such pregnant patients