Cultures of caste and rural development in the social network of a south Indian village

Cultures of caste in much of rural India have become entangled with institutions of rural development. In community-driven development, emphasis on “local resource persons” and “community spokespersons” has created new opportunities for brokerage and patronage within some villages, which interact with existing forms of authority and community afforded by caste identity and intra-caste headmanship. In this article, we study how these entangled cultures of caste and development translate into social network structures using data on friendship ties from a south Indian village. We find that although caste continues to be important in shaping community structures and leadership in the village’s network, its influence varies across different communities. This fluidity of caste’s influence on community network structures is argued to be the result of multiple distinct yet partially overlapping cultural-political forces, which include sharedness afforded by caste identity and new forms of difference and inequality effected through rural development

Regularity of squarefree monomial ideals

We survey a number of recent studies of the Castelnuovo-Mumford regularity of squarefree monomial ideals. Our focus is on bounds and exact values for the regularity in terms of combinatorial data from associated simplicial complexes and/or hypergraphs.Comment: 23 pages; survey paper; minor changes in V.

Stellar theory for flag complexes

Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag complexes, each obtained from the previous one by either an edge subdivision or its inverse. For flag spheres we pose new conjectures on their combinatorial structure forced by their face numbers, analogous to the extremal examples in the upper and lower bound theorems for simplicial spheres. Furthermore, we show that our algorithm to test the conjectures searches through the entire space of flag PL spheres of any given dimension.Comment: 12 pages, 2 figures. Notation unified and presentation of proofs improve

Domination in Functigraphs

Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid u \in V(G_1), v \in V(G_2), v=f(u)\}$. A functigraph is a generalization of a \emph{permutation graph} (also known as a \emph{generalized prism}) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let $\gamma(G)$ denote the domination number of $G$. It is readily seen that $\gamma(G) \le \gamma(C(G,f)) \le 2 \gamma(G)$. We investigate for graphs generally, and for cycles in great detail, the functions which achieve the upper and lower bounds, as well as the realization of the intermediate values.Comment: 18 pages, 8 figure

Privacy as personal resistance: exploring legal narratology and the need for a legal architecture for personal privacy rights

Different cultures produce different privacies – both architecturally and legally speaking – as well as in their different legal architectures. The ‘Simms principle’ can be harnessed to produce semi-constitutional privacy protection through statute; building on the work already done in ‘bringing rights home’ through the Human Rights Act 1998. This article attempts to set out a notion of semi-entrenched legal rights, which will help to better portray the case for architectural, constitutional privacy, following an examination of the problems with a legal narrative for privacy rights as they currently exist. I will use parallel ideas from the works of W.B. Yeats and Costas Douzinas to explore and critique these assumptions and arguments. The ultimate object of this piece is an argument for the creation of a legal instrument, namely an Act of Parliament, in the United Kingdom; the purpose of which is to protect certain notions of personal privacy from politically-motivated erosion and intrusion