Randomized contractions meet lean decompositions

We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$, in time $2^{O(k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the following properties: * every adhesion of the tree decomposition is of size at most $k$, and * every bag of the tree decomposition is $(i,i)$-unbreakable in $G$ for every $1 \leq i \leq k$. Here, a set $X \subseteq V(G)$ is $(a,b)$-unbreakable in $G$ if for every separation $(A,B)$ of order at most $b$ in $G$, we have $|A \cap X| \leq a$ or $|B \cap X| \leq a$. The resulting tree decomposition has arguably best possible adhesion size boundsand unbreakability guarantees. Furthermore, the parametric factor in the running time bound is significantly smaller than in previous similar constructions. These improvements allow us to present parameterized algorithms for Minimum Bisection, Steiner Cut, and Steiner Multicut with improved parameteric factor in the running time bound. The main technical insight is to adapt the notion of lean decompositions of Thomas and the subsequent construction algorithm of Bellenbaum and Diestel to the parameterized setting.Comment: v2: New co-author (Magnus) and improved results on vertex unbreakability of bags, v3: final changes, including new abstrac

Predictive role of monocyte count for significant coronary artery disease identification in patients with stable coronary artery disease

Background: The coronary artery disease (CAD) remains the leading cause of morbidity that is characterized by broad spectrum of symptoms. Up to 30% of performed angiographies reveal normal coronary arteries. The aim of the study was to find simple predictor for significant epicardial artery stenosis among patients with chronic coronary syndrome. Methods: There were 187 patients (131 (709%) men and 56 (30%) women) in the median (Q1–Q3) age of 67 [58–72] presenting with stable CAD symptoms enrolled into the present retrospective analysis. The demographical, clinical and laboratory characteristics between patients with normal and significant coronary artery stenosis were compared. Results: The multivariable analysis revealed coexistence of hypercholesterolemia as significant differentiation factor (odds ratio [OR]: 4.38, 95% confidence interval [CI]: 1.78–10.80, p = 0.001) for significant CAD and inverse relation to serum high density lipoprotein (OR: 0.19, 95% CI: 0.05–0.72, p = 0.015) and relation to creatinine concentration (OR: 1.03, 95% CI: 1.00–1.05, p = 0.012). Among whole peripheral blood count analysis, the significant relation was noticed to be hemoglobin concentration (OR: 1.09, 95% CI: 1.10–1.18, p = 0.022) and monocyte count (OR: 32.3, 95% CI: 1.09–653.6, p = 0.017). Receiver operator curve revealed (AUC: 0.641, p = 0.001) with the optimal cut-off value above 0.45 K/uL for monocyte, yelding sensitivity of 81.82% and specificity of 58.06%. Conclusions: The peripheral monocyte count above 0.45 k/uL may be considered as a predictor of significant coronary artery disease in symptomatic patients with chronic coronary syndrome

Problemy cięć w grafach z parametryzowanego punktu widzenia.

W pracy rozważamy następujące dwa problemy:W pierwszym problemie, mamy dany graf G=(V,E), wierzchołek s i nieujemene liczby całkowite p,q. Pytamy się czy istnieje zbiór krawędzi C będący rozmiaru co najwyżej q, taki, że spójna składowa wierzchołka s w G-C ma rozmiar co najwyżej p. Przedstawimy algorytm dla tego problemu, działający w czasie O^{*}(3.87^q), poprawiając aktualne ograniczenie.W drugim problemie, mamy dany graf G=(V,E), zbiór terminali T ⊆ V i nieujemne liczby całkowite k i q. Pytamy się czy istnieje zbiór krawędzi C będący rozmiaru co najwyżej q, taki, że każda ścieżka pomiędzy dowolnymi dwoma terminalami zawiera co najmniej k krawędzi z C. Pokażemy, że ten problem jest "fixed parameter tractable" z parametrem q, dostarczając algorytm działający w czasie O^{*}(4^q).In the thesis we study the following two problems:In the former, we are given a graph G=(V,E), a vertex s and non-negative integers p,q. We ask whether there is a set of edges C of size at most q, such that the component of s in G-C has size at most p. We present a O^{*}(3.87^q) algorithm for this problem, improving previous bound.In the latter, we are given a graph G = (V, E), a set of terminals T ⊆ V and non-negative integers k and q. We ask whether there is a set of edges C of size at most q, such that every path between any two terminals contains at least k edges from C. We show that this problem is fixed parameter tractable with parameter q by providing a O^{*}(4^q) algorithm

Selected Psychosocial Factors, Nutritional Behavior, and the Analysis of Concentrations of Selected Vitamins in Patients with Cardiovascular Diseases

Cardiovascular diseases (CVD) are the leading cause of death worldwide, influenced by the interaction of factors, including age, sex, genetic conditions, overweight/obesity, hypertension, an abnormal lipid profile, vitamin deficiencies, diabetes, and psychological factors. This study aimed to assess the relationships between psychosocial and nutritional factors in a group of 61 patients with CVD (i.e., atherosclerosis, hypertension, ischemic heart disease, and myocardial infarction) and their possible impact on the course of the disease. The plasma concentrations of vitamins A, E, D, and β-carotene were determined using validated HPLC-MS/MS, while the lipid profile was analyzed enzymatically. Psychosocial factors and nutritional behaviors were assessed using author-designed questionnaires. Over 50% of patients had 25-OH-D3 and retinol deficiencies, while >85% of patients exhibited significant deficiencies in α-tocopherol and β-carotene. The lipid profile showed no specific relationship with any particular CVD. Dietary behavior minimally impacted biochemical parameters except for higher β-carotene concentrations in the group with higher fruit and vegetable intake. The negative impact of the CVD on selected parameters of quality of life was noticed. To increase the effectiveness of the prevention and treatment of CVD, the need for interdisciplinary cooperation observed between doctors, psychologists, and specialists in human nutrition seems to be justified

Relation between Systemic Inflammatory Index (SII) and Hair Trace Elements, Metals and Metalloids Concentration in Epicardial Coronary Artery Disease—Preliminary Report

Background: Coronary artery atherosclerosis development and progression are related to generic, clinical, and lifestyle factors combined with inflammatory activation. The relationship between trace element concentration and morbidity is under investigation to gain a clearer understanding of underlying pathological processes. Methods: Thirty-five consecutive patients (22 males and 13 females) with a median [interquartile range (IQR)] age of 67 (61–73) years presenting with anginal symptoms were included in the single center prospective analysis in 2022 and divided into a epicardial coronary artery disease (CAD) and non-CAD group. Scalp hair chemical analysis and inflammatory markers from a peripheral blood count were analyzed. Results: The correlation analysis of elements and inflammatory indexes showed statistical significance between median hair lithium (Li) concentration and the systemic inflammatory index (SII) (r = –0.476, p = 0.046), antimony (Sb) (r = –0.521, p = 0.028) followed by chromium (Cr) (r = –0.478, p = 0.045) and iron (Fe) (r = –0.604, p = 0.008) in the CAD group. Similar correlations were not found in non-CAD group. Conclusions: The correlation between scalp hair lithium (Li), antimony (Sb), chromium (Cr) and iron (Fe) concentration and the systemic inflammatory index (SII) were revealed only in patients with coronary artery disease. Our analysis identified a strong correlation between inflammatory activation and iron concentration