Overlap properties of geometric expanders

The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) ∈ (0, 1] such that no matter how we map the vertices of H into ℝd, there is a point covered by at least a c(H)-fraction of the simplices induced by the images of its hyperedges. Motivated by the search for an analogue of the notion of graph expansion for higher dimensional simplicial complexes, we address the question whether or not there exists a sequence of arbitrarily large (d + 1)-uniform hypergraphs with bounded degree for which . Using both random methods and explicit constructions, we answer this question positively by constructing infinite families of (d + 1)-uniform hypergraphs with bounded degree such that their overlap numbers are bounded from below by a positive constant c = c(d). We also show that, for every d, the best value of the constant c = c(d) that can be achieved by such a construction is asymptotically equal to the limit of the overlap numbers of the complete (d + 1)-uniform hypergraphs with n vertices, as n → ∞. For the proof of the latter statement, we establish the following geometric partitioning result of independent interest. For any h, s and any ɛ > 0, there exists K = K(ɛ, h, s) satisfying the following condition. For any k ≧ K and for any semi-algebraic relation R on h-tuples of points in a Euclidean space ℝd with description complexity at most s, every finite set P ⫅ ℝd has a partition P = P1 ∪ ⋯ ∪ Pk into k parts of sizes as equal as possible such that all but at most an ɛ-fraction of the h-tuples (Pi1,   , Pih) have the property that either all h-tuples of points with one element in each Pij are related with respect to R or none of them ar

Overlap properties of geometric expanders

The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map the vertices of $H$ into $\R^d$, there is a point covered by at least a $c(H)$-fraction of the simplices induced by the images of its hyperedges. In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph expansion for higher dimensional simplicial complexes, it was asked whether or not there exists a sequence $\{H_n\}_{n=1}^\infty$ of arbitrarily large $(d+1)$-uniform hypergraphs with bounded degree, for which $\inf_{n\ge 1} c(H_n)>0$. Using both random methods and explicit constructions, we answer this question positively by constructing infinite families of $(d+1)$-uniform hypergraphs with bounded degree such that their overlap numbers are bounded from below by a positive constant $c=c(d)$. We also show that, for every $d$, the best value of the constant $c=c(d)$ that can be achieved by such a construction is asymptotically equal to the limit of the overlap numbers of the complete $(d+1)$-uniform hypergraphs with $n$ vertices, as $n\rightarrow\infty$. For the proof of the latter statement, we establish the following geometric partitioning result of independent interest. For any $d$ and any $\epsilon>0$, there exists $K=K(\epsilon,d)\ge d+1$ satisfying the following condition. For any $k\ge K$, for any point $q \in \mathbb{R}^d$ and for any finite Borel measure $\mu$ on $\mathbb{R}^d$ with respect to which every hyperplane has measure $0$, there is a partition $\mathbb{R}^d=A_1 \cup \ldots \cup A_{k}$ into $k$ measurable parts of equal measure such that all but at most an $\epsilon$-fraction of the $(d+1)$-tuples $A_{i_1},\ldots,A_{i_{d+1}}$ have the property that either all simplices with one vertex in each $A_{i_j}$ contain $q$ or none of these simplices contain $q$

Female Characters in the Novels of Kyallo Wadi Wamitila

Feminism, namely its post-colonial version, is one of the most used theoretical and ideological platforms in modern African literature. Indian scholar Raj-Kumar Mishra in one of his works gives the post-colonial feminism the following characterization: “The matter of fact is that postcolonial women refuse to remain passive and continue to bear male-oppressive environments. These women seek to emancipate themselves through education, struggle, and hard work. The postcolonial men re-colonized the bodies and minds of their women in the name of preserving their cultural values. Postcolonial feminism is primarily concerned with deplorable plight of women in postcolonial environment […] Postcolonial feminists argue for women emancipation that is subalternized by social, cultural, or economic structures across the world.” (132-3). And thus: “Postcolonial feminism […] comprises non-western feminisms which negotiate the political demands of nationalism, socialist feminism, liberalism, and ecofeminism, alongside the social challenge of everyday patriarchy, typically supported by its institutional and legal discrimination: of domestic violence, sexual abuse, rape, honour killings, dowry deaths, female foeticide, child abuse”

Kenyan Women’s Literature in Swahili as a Factor of Female Rights Development

In a previously published article, the author of this study asserted that feminism, as a system of views establishing and defending equal rights and opportunities for women, has acquired a profound stand in Kenyan literature already since its formation period, the first decades of the country’s independence, in the works of such writers as Grace Ogot, Rebecca Njau, Marjorie Oludhe-Macgoye and others, whose names now rightfully and deservedly form the treasury of Kenyan writing. In their books these writers were addressing the whole variety of problems that modern Kenyan women were faced with, forming new post-colonial mentality in concern with these problems and their solutions both in female and male audiences (primarily addressing the former) – and thus contributing to the advancement of Kenyan society (see Gromov 2017)

East African Literature: Essays on Written and Oral Traditions. Ed. by J.K.S. Makokha, Egara Kabaji and Dominica Dipio. Berlin: Logos Verlag, 2011, 513 pp. ISBN 978-3-8325-2816-4: Review

Book review of the collection titled ´East African literature: Essays on Written and Oral Tradition´ edited by J.K.S. Makokha, Egara Kabaji and Dominica Dipi

BILINGUAL LITERATURE OF TANZANIA AS A SPECIFIC INTER-LITERARY COMMUNITY

Modern literary theory has created a variety of approaches to describe dynamic processes emerging in a literary field. This may be especially significant in the case of relatively young literary traditions, characterized by rather high level of dynamics.Among various theories of significance is a theory launched in the last quarter of the last century by a Slovakian scholar of comparative literature, Dionýz Ďurišin (1929-1997), who came up with the theory of the so-called specific inter-literary communities. The works of Ďurišin and other scholars, mainly from East European countries (such as Joseph Grmela, Libuša Vajdova, Irina Nikiforova, Yuri Azarov, and others) were published in the 1980s, 1990s and early 2000s in a variety of collection.KEY WORDS: literary, inter-literary, community, Tanzania

Three novels of John Habwe: Social criticism through “new enlightenment”

 John Habwe is one of the most established and prolific writers in modern Kenyan literature in Swahili language, whose writing career now spans for more than two decades 1. Despite his productivity and fame in the literary and reading circles, Habwe so far seems to have gained a rather timid attention from the critics. His first three novels were reviewed, among others, by Kyallo Wadi Wamitila in his survey of Kenyan novel in the new edition of Outline of Swahili Literature (Bertoncini et al., 2009). In that survey Wamitila noticed, along with other traits, Habwe’s tangible inclination towards “Enlightenment-type” didacticism. Thus, before we start the analysis of the texts chosen for this study, it would be advisable to provide a brief outline of the main traits of Enlightenment and its literature.Key words: Habwe, enlightenment, Swahili, literature, Keny

JOHN HABWE’S SAFARI YA LAMU (2011) AS A TRAVELOGUE

The genre of travelogue may be regarded almost as old as the human civilization. Iain Manley in his survey of the genre (Manley 2011) traces the history of travelogue in the world literature from The Epic of Gilgamesh (13th-7th centuries BC), Homer’s Odyssey (8th century BC), accounts of ancient travelers, like the Greeks Arrianus and Pausanius (1-2 centuries), the Chinese Faxian and Xuanzang (5th and 7th centuries), to the medieval texts of the venetian Marco Polo (13th century) and Arabian traveler Ibn Batutta (14th century), Christopher Columbus of Spain (15th century), and Fernão Mendes Pinto of Portugal (16th century AD). Key words: John Habwe, travelogue, Lamu, Safar

THE PRESENT STATE OF SWAHILI LITERATURE AS AN ARTISTIC AND SOCIAL PHENOMENON

This study is aimed at giving an overall picture of present state of creative writing in the language of Swahili in the Eastern part of the African continent, i.e. its condition after the year 2000.Key words: Kiswahili, literature, East Africa, novel