Problems and results on 1-cross intersecting set pair systems

The notion of cross intersecting set pair system of size $m$, $\Big(\{A_i\}_{i=1}^m, \{B_i\}_{i=1}^m\Big)$ with $A_i\cap B_i=\emptyset$ and $A_i\cap B_j\ne\emptyset$, was introduced by Bollob\'as and it became an important tool of extremal combinatorics. His classical result states that $m\le {a+b\choose a}$ if $|A_i|\le a$ and $|B_i|\le b$ for each $i$. Our central problem is to see how this bound changes with the additional condition $|A_i\cap B_j|=1$ for $i\ne j$. Such a system is called $1$-cross intersecting. We show that the maximum size of a $1$-cross intersecting set pair system is -- at least $5^{n/2}$ for $n$ even, $a=b=n$, -- equal to $\bigl(\lfloor\frac{n}{2}\rfloor+1\bigr)\bigl(\lceil\frac{n}{2}\rceil+1\bigr)$ if $a=2$ and $b=n\ge 4$, -- at most $|\cup_{i=1}^m A_i|$, -- asymptotically $n^2$ if $\{A_i\}$ is a linear hypergraph ($|A_i\cap A_j|\le 1$ for $i\ne j$), -- asymptotically ${1\over 2}n^2$ if $\{A_i\}$ and $\{B_i\}$ are both linear hypergraphs

Design, synthesis and biological evaluation of thiosemicarbazones, hydrazinobenzothiazoles and arylhydrazones as anticancer agents with a potential to overcome multidrug resistance

There is a constant need for new therapies against multidrug resistant (MDR) cancer. An attractive strategy is to develop chelators that display significant antitumor activity in multidrug resistant cancer cell lines overexpressing the drug efflux pump P-glycoprotein. In this study we used a panel of sensitive and MDR cancer cell lines to evaluate the toxicity of picolinylidene and salicylidene thiosemicarbazone, arylhydrazone, as well as picolinylidene and salicylidene hydrazino-benzothiazole derivatives. Our results confirm the collateral sensitivity of MDR cells to isatin-β-thiosemicarbazones, and identify several chelator scaffolds with a potential to overcome multidrug resistance. Analysis of structure-activity-relationships within the investigated compound library indicates that NNS and NNN donor chelators show superior toxicity as compared to ONS derivatives regardless of the resistance status of the cells. © 2016 Elsevier Masson SAS

Positive Impulsive Control of Tumor Therapy - A Cyber-Medical Approach

Chemotherapy optimization based on mathematical models is a promising direction of personalized medicine. Personalizing, thus optimizing treatments, may have multiple advantages, from fewer side effects to lower costs. However, personalization is a complicated process in practice. We discuss a mathematical model of tumor growth and therapy optimization algorithms that can be used to personalize therapies. The therapy generation is based on the concept of keeping the drug level over a specified value. A mixed-effect model is used for parametric identification, and the doses are calculated using a two-compartment model for drug pharmacokinetics, and a nonlinear pharmacodynamics and tumor dynamics model. We propose personalized therapy generation algorithms for having a maximal effect and minimal effective doses. We handle inter-and intra-patient variability for the minimal effective dose therapy. Results from mouse experiments for the personalized therapy are discussed and the algorithms are compared to a generic protocol based on overall survival. The experimental results show that the introduced algorithms significantly increased the overall survival of the mice, demonstrating that by control engineering methods an efficient modality of cancer therapy may be possible

Celecoxib Prevents Doxorubicin-Induced Multidrug Resistance in Canine and Mouse Lymphoma Cell Lines.

BACKGROUND: Treatment of malignancies is still a major challenge in human and canine cancer, mostly due to the emergence of multidrug resistance (MDR). One of the main contributors of MDR is the overexpression P-glycoprotein (Pgp), which recognizes and extrudes various chemotherapeutics from cancer cells. METHODS: To study mechanisms underlying the development of drug resistance, we established an in vitro treatment protocol to rapidly induce Pgp-mediated MDR in cancer cells. Based on a clinical observation showing that a 33-day-long, unplanned drug holiday can reverse the MDR phenotype of a canine diffuse large B-cell lymphoma patient, our aim was to use the established assay to prevent the emergence of drug resistance in the early stages of treatment. RESULTS: We showed that an in vitro drug holiday results in the decrease of Pgp expression in MDR cell lines. Surprisingly, celecoxib, a known COX-2 inhibitor, prevented the emergence of drug-induced MDR in murine and canine lymphoma cell lines. CONCLUSIONS: Our findings suggest that celecoxib could significantly improve the efficiency of chemotherapy by preventing the development of MDR in B-cell lymphoma

Celecoxib Prevents Doxorubicin-Induced Multidrug Resistance in Canine and Mouse Lymphoma Cell Lines

Background: Treatment of malignancies is still a major challenge in human and canine cancer, mostly due to the emergence of multidrug resistance (MDR). One of the main contributors of MDR is the overexpression P-glycoprotein (Pgp), which recognizes and extrudes various chemotherapeutics from cancer cells. Methods: To study mechanisms underlying the development of drug resistance, we established an in vitro treatment protocol to rapidly induce Pgp-mediated MDR in cancer cells. Based on a clinical observation showing that a 33-day-long, unplanned drug holiday can reverse the MDR phenotype of a canine diffuse large B-cell lymphoma patient, our aim was to use the established assay to prevent the emergence of drug resistance in the early stages of treatment. Results: We showed that an in vitro drug holiday results in the decrease of Pgp expression in MDR cell lines. Surprisingly, celecoxib, a known COX-2 inhibitor, prevented the emergence of drug-induced MDR in murine and canine lymphoma cell lines. Conclusions: Our findings suggest that celecoxib could significantly improve the efficiency of chemotherapy by preventing the development of MDR in B-cell lymphoma

Diszkrét matematika = Discrete mathematics

A pályázat résztvevői igen aktívak voltak a 2006-2008 években. Nemcsak sok eredményt értek el, miket több mint 150 cikkben publikáltak, eredményesen népszerűsítették azokat. Több mint 100 konferencián vettek részt és adtak elő, felerészben meghívott, vagy plenáris előadóként. Hagyományos gráfelmélet Több extremális gráfproblémát oldottunk meg. Új eredményeket kaptunk Ramsey számokról, globális és lokális kromatikus számokról, Hamiltonkörök létezéséséről. a crossig numberről, gráf kapacitásokról és kizárt részgráfokról. Véletlen gráfok, nagy gráfok, regularitási lemma Nagy gráfok "hasonlóságait" vizsgáltuk. Különféle metrikák ekvivalensek. Űj eredeményeink: Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit. Hipergráfok, egyéb kombinatorika Új Sperner tipusú tételekte kaptunk, aszimptotikusan meghatározva a halmazok max számát bizonyos kizárt struktőrák esetén. Több esetre megoldottuk a kizárt hipergráf problémát is. Elméleti számítástudomány Új ujjlenyomat kódokat és bioinformatikai eredményeket kaptunk. | The participants of the project were scientifically very active during the years 2006-2008. They did not only obtain many results, which are contained in their more than 150 papers appeared in strong journals, but effectively disseminated them in the scientific community. They participated and gave lectures in more than 100 conferences (with multiplicity), half of them were plenary or invited talks. Traditional graph theory Several extremal problems for graphs were solved. We obtained new results for certain Ramsey numbers, (local and global) chromatic numbers, existence of Hamiltonian cycles crossing numbers, graph capacities, and excluded subgraphs. Random graphs, large graphs, regularity lemma The "similarities" of large graphs were studied. We show that several different definitions of the metrics (and convergence) are equivalent. Several new results like the Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit were proved Hypergraphs, other combinatorics New Sperner type theorems were obtained, asymptotically determining the maximum number of sets in a family of subsets with certain excluded configurations. Several cases of the excluded hypergraph problem were solved. Theoretical computer science New fingerprint codes and results in bioinformatics were found

Identification and Validation of Compounds Selectively Killing Resistant Cancer: Delineating Cell Line-Specific Effects from P-Glycoprotein-Induced Toxicity.

Despite significant progress, resistance to chemotherapy is still the main reason why cancer remains a deadly disease. An attractive strategy is to target the collateral sensitivity of otherwise multidrug resistant (MDR) cancer. In this study, our aim was to catalog various compounds that were reported to elicit increased toxicity in P-glycoprotein (Pgp)-overexpressing MDR cells. We show that the activity of most of the serendipitously identified compounds reported to target MDR cells is in fact cell-line specific, and is not influenced significantly by the function of Pgp. In contrast, novel 8-hydroxyquinoline derivatives that we identify in the National Cancer Institute (NCI) drug repository possess a robust Pgp-dependent toxic activity across diverse cell lines. Pgp expression associated with the resistance of the doxorubicin-resistant Brca1-/-;p53-/- spontaneous mouse mammary carcinoma cells could be eliminated by a single treatment with NSC57969, suggesting that MDR-selective compounds can effectively revert the MDR phenotype of cells expressing Pgp at clinically relevant levels. The discovery of new MDR-selective compounds shows the potential of this emerging technology and highlights the 8-hydroxyquinoline scaffold as a promising starting point for the development of compounds targeting the Achilles heel of drug-resistant cancer. Mol Cancer Ther; 16(1); 45-56. (c)2016 AACR