The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.Comment: 4 pages, uses RevTeX 4.

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

Tur\'an numbers for Ks,tK_{s,t}-free graphs: topological obstructions and algebraic constructions

We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.Comment: Fixed a small mistake in the application of Proposition

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

Diophantine Approximation and applications in Interference Alignment

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1]

The lacuna of capital, the state and war? The lost global history and theory of Eastern agency

In this article I seek to constructively engage Alex Anievas’s seminal book that is deservedly the subject of this forum. For Anievas has become a key figure in the revival of Trotskyism in IR and his is one of the first book-length treatments of the New Trotskyist theory of the international. My critique is meant merely as a constructive effort to push his excellent scholarship further in terms of developing his non-Eurocentric approach. In the first section I argue that his book represents a giant leap forward for the New Trotskyist IR. However, in the following sections I argue that although undeniably a brave attempt nevertheless, in the last instance, Anievas falls a few steps short in realising a genuinely non-Eurocentric account of world politics. This is because while he certainly restores or brings in ‘the lost theory and history of IR’ that elevates class forces to a central role in shaping world politics, nevertheless he fails to bring in ‘the lost global theory and history of Eastern agency’ that constitutes, in my view, the key ingredient of a non-Eurocentric approach to world politics. I also argue that while his anti-reductionist ontological credentials are for the most part extremely impressive, nevertheless, I argue that these are compromised in his analysis of Hitler’s racism. Finally, in the conclusion I ask whether the theoretical architecture of the New Trotskyism in IR is capable of developing a non-Eurocentric approach before concluding in the affirmative with respect to its modern revisionist incarnation of which Anievas is in the vanguard

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic

In middle-aged and old obese patients, training intervention reduces leptin level: A meta-analysis

BACKGROUND: Leptin is one of the major adipokines in obesity that indicates the severity of fat accumulation. It is also an important etiological factor of consequent cardiometabolic and autoimmune disorders. Aging has been demonstrated to aggravate obesity and to induce leptin resistance and hyperleptinemia. Hyperleptinemia, on the other hand, may promote the development of age-related abnormalities. While major weight loss has been demonstrated to ameliorate hyperleptinemia, obese people show a poor tendency to achieve lasting success in this field. The question arises whether training intervention per se is able to reduce the level of this adipokine. OBJECTIVES: We aimed to review the literature on the effects of training intervention on peripheral leptin level in obesity during aging, in order to evaluate the independent efficacy of this method. In the studies that were included in our analysis, changes of adiponectin levels (when present) were also evaluated. DATA SOURCES: 3481 records were identified through searching of PubMed, Embase and Cochrane Library Database. Altogether 19 articles were suitable for analyses. STUDY ELIGIBILITY CRITERIA: Empirical research papers were eligible provided that they reported data of middle-aged or older (above 45 years of age) overweight or obese (body mass index above 25) individuals and included physical training intervention or at least fitness status of groups together with corresponding blood leptin values. STATISTICAL METHODS: We used random effect models in each of the meta-analyses calculating with the DerSimonian and Laird weighting methods. I-squared indicator and Q test were performed to assess heterogeneity. To assess publication bias Egger's test was applied. In case of significant publication bias, the Duval and Tweedie's trim and fill algorithm was used. RESULTS: Training intervention leads to a decrease in leptin level of middle-aged or older, overweight or obese male and female groups, even without major weight loss, indicated by unchanged serum adiponectin levels. Resistance training appears to be more efficient in reducing blood leptin level than aerobic training alone. CONCLUSIONS: Physical training, especially resistance training successfully reduces hyperleptinemia even without diet or major weight loss