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

Extensions and reductions of square-free words

A word is square-free if it does not contain a nonempty word of the form $XX$ as a factor. A famous 1906 result of Thue asserts that there exist arbitrarily long square-free words over a $3$-letter alphabet. We study square-free words with additional properties involving single-letter deletions and extensions of words. A square-free word is steady if it remains square-free after deletion of any single letter. We prove that there exist infinitely many steady words over a $4$-letter alphabet. We also demonstrate that one may construct steady words of any length by picking letters from arbitrary alphabets of size $7$ assigned to the positions of the constructed word. We conjecture that both bounds can be lowered to $4$, which is best possible. In the opposite direction, we consider square-free words that remain square-free after insertion of a single (suitably chosen) letter at every possible position in the word. We call them bifurcate. We prove a somewhat surprising fact, that over a fixed alphabet with at least three letters, every steady word is bifurcate. We also consider families of bifurcate words possessing a natural tree structure. In particular, we prove that there exists an infinite tree of doubly infinite bifurcate words over alphabet of size $12$.Comment: 11 pages, 1 figur

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

Nanoparticles for Directed Immunomodulation: Mannose-Functionalized Glycodendrimers Induce Interleukin-8 in Myeloid Cell Lines

New therapeutic strategies for personalized medicine need to involve innovative pharmaceutical tools, for example, modular nanoparticles designed for direct immunomodulatory properties. We synthesized mannose-functionalized poly(propyleneimine) glycodendrimers with a novel architecture, where freely accessible mannose moieties are presented on poly(ethylene glycol)-based linkers embedded within an open-shell maltose coating. This design enhanced glycodendrimer bioactivity and led to complex functional effects in myeloid cells, with specific induction of interleukin-8 expression by mannose glycodendrimers detected in HL-60 and THP-1 cells. We concentrated on explaining the molecular mechanism of this phenomenon, which turned out to be different in both investigated cell lines: in HL-60 cells, transcriptional activation via AP-1 binding to the promoter predominated, while in THP-1 cells (which initially expressed less IL-8), induction was mediated mainly by mRNA stabilization. The success of directed immunomodulation, with synthetic design guided by assumptions about mannose-modified dendrimers as exogenous regulators of pro-inflammatory chemokine levels, opens new possibilities for designing bioactive nanoparticles. © 2021 The Authors. Published by American Chemical Society

Szybka metoda oceny stężenia witaminy A, witaminy E oraz kotyniny w surowicy krwi kobiet z śródnabłonkową neoplazją (CIN)i rakiem szyjki macicy

Abstract Objective: The aim of this study was to elaborate on the analytical method for quantitative determination of retinol and α-tocopherol in serum of women diagnosed with CIN and cervical cancer. The basic problem in the analysis of the vitamins content in biological material is their low physiological concentration level and instability. Liquid chromatography with diode array detector (DAD) was applied. Material and methods: The material consisted of serum and urine collected from 12 women diagnosed with cervical intraepithelial neoplasia (CIN) and 16 diagnosed with cervical cancer. The method was evaluated for the following parameters: linearity, recovery, sensitivity, precision, accuracy, selectivity, stability, limit of quantification (LOQ) and limit of detection (LOD). Results: Results showed good linearity (r2 ≥0,99) in the range 0,1μg/ml-10mg/ml for retinol and 0,25μg/ml-15μg/ml for α-tocopherol. The Lower Limit of Detection was 0,15μg/ml for vitamin E and 0,05μg/ml for vitamin A. The within-run R.S.Ds were below 5,2% at all concentration levels and the between-run R.S.Ds were below 10,0% at all concentration levels. Conclusions: The advantage of this method is that it measures both compounds in a more rapid, reproducible and accurate manner when compared to the previous HPLC studies. The compounds (vitamin A and E and internal standards) are measured in the same sample at the same time. Quantitative determination of cotinine may reveal active smokers and subjects exposed to environmental tobacco smoke, which is independent measurable carcinogenetic co-factor. The following study is a part of a project determining non-viral causative agents in cervical carcinogenesis.Streszczenie Cel pracy: Celem niniejszej pracy jest ocena przydatności analitycznej metody oznaczania ilościowego retinolu i alfa-tokoferolu w surowicy kobiet z rozpoznaną śródnabłonkową neoplazją (CIN) i rakiem szyjki macicy. Głównym problemem w analizowaniu zawartości witamin w materiale biologicznym jest ich niskie fizjologiczne stężenie i niestabilność. W niniejszym badaniu zastosowano metodę ciekłej chromatografii z detektorem diodowym (DAD). Materiał i metodyka: Materiał badawczy stanowiło osocze i mocz, 12 kobiet z rozpoznaną śródnabłonkową neoplazją szyjki macicy (CIN) i 16 z rakiem szyjki macicy. Metodę oceniono pod kątem następujących parametrów: liniowość, powtarzalność, czułość, precyzja, dokładność, selektywność, stabilność, granica kwantyfikacji (limit of quantification - LOQ) i detekcji (limit of detection - LOD). Wyniki: Uzyskano wysoka liniowość (r2 ≥0,99) w zasięgu 0,1μg/ml-10mg/ml dla retinolu i 0,25μg/ml-15μg/ml dla alfa-tokoferolu. Dolna granica wykrywalności wyniosła 0,15μg/ml dla witaminy E i 0,05μg/ml dla witaminy A. Zasięg metody R.S.Ds wyniósł 5,2% we wszystkich poziomach stężeń a interwałowy zasięg R.S.Ds poniżej 10,0% we wszystkich poziomach stężeń. Wnioski: Zaleta zbadanej metody jest fakt, iż można przy jej pomocy uzyskać wyniki w szybszy, bardziej powtarzalny i dokładniejszy sposób, niż w opisywanych w literaturze badaniach z użyciem HPLC. Dodatkową zaleta stosowanej metody jest możliwość pomiaru z tej samej próbki witamin A i E. Ilościowa ocena stężenia kotyniny może wskazać pacjentki, będące aktywnymi palaczkami lub narażonymi na palenie bierne. W aspekcie karcinogenezy w obrębie szyjki macicy może być to cenna wiadomość dotycząca istotnego a często zatajanego kofaktora nowotworzenia. Niniejsze badanie jest częścią projektu oceniającego pozawirusowe czynniki onkogenne w procesie karcinogenezy w obr´bie szyjki macicy

Cervical cancer - is there anything to worry about? Research on knowledge and awareness of cervical cancer among Poles

Cervical cancer poses a global health challenge, being one of the most common cancers of the reproductive organs and a leading cause of morbidity and mortality worldwide. The disease, resulting from infection with the human papillomavirus (HPV), tends to develop in advanced stages, significantly complicating effective treatment. Despite advancements in medicine, diagnostics, and therapy, cervical cancer remains a serious public health threat. Periodic surveillance through screening has significantly reduced the incidence of cervical cancer; however, in Poland, there is a notable gap between potentially available preventive measures and their actual utilization by the population. It has been observed that only around 20% of Polish women participate in screening programs, contributing to Poland having one of the highest rates of incidence and mortality from this type of cancer in Europe. This leads to the conclusion that cervical cancer constitutes an unresolved oncological and epidemiological problem in Poland. In the context of these challenges, a crucial aspect is understanding the level of public knowledge about cervical cancer, its risk factors, and available preventive measures. This study focuses on evaluating the societal knowledge regarding the risk factors of cervical cancer, identifying existing gaps, and suggesting potential areas for educational interventions

Bouveret's Syndrome: Diagnostic Dilemmas and Therapeutic Strategies - A Comprehensive Educational Approach for Healthcare Professionals

Bouveret's syndrome, a rare complication of gallstone disease, poses a significant diagnostic and therapeutic challenge, particularly in elderly individuals with multiple comorbidities. The mortality rate ranges from 12-30%, emphasizing the importance of prompt and accurate diagnosis. Nonspecific symptoms, such as nausea, vomiting, and abdominal pain, contribute to delayed diagnosis. Healthcare professionals, especially those involved in gastroenterology and surgery, require comprehensive education on Bouveret's syndrome. Training should emphasize the diverse diagnostic modalities, including the use of imaging techniques such as X-rays, ultrasound, and MRI. Awareness of the syndrome's rarity and collaboration among specialists from various fields are crucial for effective management. Additionally, educational programs should underscore the need for individualized treatment plans, considering patient parameters such as age, comorbidities, and the inflammatory state of surrounding tissues. While endoscopic procedures exhibit lower success rates, they are often preferred due to the high risk associated with open surgical procedures in elderly patients. Continuous medical education should also highlight the potential link between diabetes and Bouveret's syndrome, emphasizing the importance of recognizing risk factors and ensuring timely medical intervention. In conclusion, enhancing the knowledge base of healthcare professionals through targeted education is essential for improving the diagnosis and management of Bouveret's syndrome, ultimately contributing to better patient outcomes