Coloring triangle-free rectangle overlap graphs with O(log⁡log⁡n)O(\log\log n) colors

Recently, it was proved that triangle-free intersection graphs of $n$ line segments in the plane can have chromatic number as large as $\Theta(\log\log n)$. Essentially the same construction produces $\Theta(\log\log n)$-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected sets in $\mathbb{R}^2$ closed under horizontal scaling, vertical scaling, and translation, except for axis-parallel rectangles. We show that this construction is asymptotically optimal for intersection graphs of boundaries of axis-parallel rectangles, which can be alternatively described as overlap graphs of axis-parallel rectangles. That is, we prove that triangle-free rectangle overlap graphs have chromatic number $O(\log\log n)$, improving on the previous bound of $O(\log n)$. To this end, we exploit a relationship between off-line coloring of rectangle overlap graphs and on-line coloring of interval overlap graphs. Our coloring method decomposes the graph into a bounded number of subgraphs with a tree-like structure that "encodes" strategies of the adversary in the on-line coloring problem. Then, these subgraphs are colored with $O(\log\log n)$ colors using a combination of techniques from on-line algorithms (first-fit) and data structure design (heavy-light decomposition).Comment: Minor revisio

Coloring intersection graphs of arc-connected sets in the plane

A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line $L$ if the intersection of its any member with $L$ is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.Comment: Minor changes + some additional references not included in the journal versio

Triangle-free geometric intersection graphs with large chromatic number

Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $X$ in $\mathbb{R}^2$ that is not an axis-aligned rectangle and for any positive integer $k$ produces a family $\mathcal{F}$ of sets, each obtained by an independent horizontal and vertical scaling and translation of $X$, such that no three sets in $\mathcal{F}$ pairwise intersect and $\chi(\mathcal{F})>k$. This provides a negative answer to a question of Gyarfas and Lehel for L-shapes. With extra conditions, we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries, and equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the line.Comment: Small corrections, bibliography updat

Triangle-free intersection graphs of line segments with large chromatic number

In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer $k$, we construct a triangle-free family of line segments in the plane with chromatic number greater than $k$. Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number.Comment: Small corrections, bibliography updat

Coloring Intersection Graphs of Arc-Connected Sets in the Plane

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line $$L$$ L if the intersection of any member with $$L$$ L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $$X$$ X in $$\mathbb{R }^2$$ R 2 that is not an axis-aligned rectangle and for any positive integer $$k$$ k produces a family $$\mathcal{F }$$ F of sets, each obtained by an independent horizontal and vertical scaling and translation of $$X$$ X , such that no three sets in $$\mathcal{F }$$ F pairwise intersect and $$\chi (\mathcal{F })>k$$ χ ( F ) > k . This provides a negative answer to a question of Gyárfás and Lehel for L-shapes. With extra conditions we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries or equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the lin

"Heterobasidion annosum" induces apoptosis in DLD-1 cells and decreases colon cancer growth in In vivo model

Application of substances from medicinal mushrooms is one of the interesting approaches to improve cancer therapy. In this study, we commenced a new attempt in the field of Heterobasidion annosum (Fr.) Bref. sensu lato to further extend our knowledge on this basidiomycete fungus. For this purpose, analysis of the active substances of Heterobasidion annosum methanolic extract and also its influence on colorectal cancer in terms of in vitro and in vivo experiments were performed. In vivo studies on mice were conducted to verify its acute toxicity and to further affirm its anticancer potential. Results indicated that all the most common substances of best known medicinal mushrooms that are also responsible for their biological activity are present in tested extracts. In vitro tests showed a high hemocompatibility and a significant decrease in viability and proliferation of DLD-1 cells in a concentration-dependent manner of Heterobasidion annosum extract. The studies performed on xenograft model of mice showed lower tendency of tumor growth in the group of mice receiving Heterobasidion annosum extract as well as mild or moderate toxicity. Obtained results suggest beneficial potential of Heterobasidion annosum against colon cancer as cytotoxic agent or as adjuvant anticancer therapy

Multicenter registry of Impella-assisted high-risk percutaneous coronary interventions and cardiogenic shock in Poland (IMPELLA-PL)

Background: Impella is a percutaneous mechanical circulatory support device for treatment of cardiogenic shock (CS) and high-risk percutaneous coronary interventions (HR-PCIs). IMPELLA-PL is a national retrospective registry of Impella-treated CS and HR-PCI patients in 20 Polish interventional cardiological centers, conducted from January 2014 until December 2021.Aims: We aimed to determine the efficacy and safety of Impella using real-world data from IMPELLA-PL and compare these with other registries.Methods: IMPELLA-PL data were analyzed to determine primary endpoints: in-hospital mortality and rates of mortality and major adverse cardiovascular and cerebrovascular events (MACCE) at 12 months post-discharge.Results: Of 308 patients, 18% had CS and 82% underwent HR-PCI. In-hospital mortality rates were 76.4% and 8.3% in the CS and HR-PCI groups, respectively. The 12-month mortality rates were 80.0% and 18.2%, and post-discharge MACCE rates were 9.1% and 22.5%, respectively. Any access site bleeding occurred in 30.9% of CS patients and 14.6% of HR-PCI patients, limb ischemia in 12.7% and 2.4%, and hemolysis in 10.9% and 1.6%, respectively.Conclusions: Impella is safe and effective during HR-PCIs, in accordance with previous registry analyses. The risk profile and mortality in CS patients were higher than in other registries, and the potential benefits of Impella in CS require investigation

Maintenance of surface made of cement concrete. Currant concrete condition after 83 years of exploitation –18th national road

Droga krajowa nr 18 łączy przejście graniczne w Olszynie z najkrótszą autostradą w Polsce – A18 (węzeł Golnice) a dalej z autostradą A4. W latach 1936–1945 był to fragment autostrady Reichsautobahn 9 (RAB 9), która łączyła Berlin z Wrocławiem (Breslau). Pod koniec roku 2019, po ok. 83 latach eksploatacji, rozpoczęto prace na jezdni południowej – prawej, które polegają na wyburzeniu starej konstrukcji i ułożeniu nowych warstw nawierzchni. Przed całkowitą destrukcją, pobrano próbki i wykonano badania laboratoryjne oraz petrograficzne. W artykule przedstawiono wyniki tych badań i omówiono kondycję betonu nawierzchniowego.The national road number 18 connects the border crossing in Olszyna with the shortest motorway in Poland A18 (Golnice junction) and then connects with the A4 motorway. In the years 1936–1945 it was connected to the section of the Reichsautobahn 9 (RAB9) motorway that used to connect Berlin with Breslau (today Wroclaw). At the end of 2019, after approximately 83 years of operation, work began on the southern-right roadway which involves demolishing the old structure and laying new layers of pavement.Before the complete destruction, samples were taken and laboratory and petrographic test were performed. The article presents the results of these test and discusses the condition of the pavement concrete