On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage

The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve minimum repair bandwidth (matching the cutset lower bound) for arbitrary admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on interference alignment techniques and uses vector linear codes which allow to split symbols into arbitrarily small subsymbols.Comment: 20 pages, 6 figure

The Essence of Intuitive Set Theory

Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does not appear, nonLebesgue measurable sets are not possible, and the unit interval splits into a set of infinitesimals

Unmournable Bodies: Gothic Postcolonialism and The Spectre of Loss in Arundhati Roy\u27s The God of Small Things and Anuradha Roy\u27s Sleeping on Jupiter

My thesis compares Arundhati Roy’s The God of Small Things and Anuradha Roy’s Sleeping on Jupiter in order to demonstrate how a) each text is a product of its moment and a reflection of corresponding critical thought and b) how an inversion of gothic tropes in Sleeping reflects a changed world dynamic, a melancholic exploration of epistemological and traumatic loss that can be seen not only as a recognition of the continued power of oppressive systems but a reflection on the failure of cosmopolitanism to “rescue” the global subject from her own isolation and recolonization. I claim that this is not only demonstrated by a change in form and how gothic tropes are presented, but in how homosexuality and deviant sexuality in particular is treated, a reminder that even in texts that attempt to condemn and reject colonizing tendencies, the political moment and its theoretical appendages continue to haunt postcolonial discourse, enabling recolonization and restratifying spaces of resistance. I claim that this recognition need not be totalizing or nihilistic, but that in the recognition itself lies the possibility for resistance, an act of rebellion that must be constantly re-enacted in order to deterritorialize what has been captured and displaced, a fluid and imaginative negotiation that, much like literature, is limitless in interpretation and offers readers constant and multiplicitous possibilities for agency in the face of equally fluid oppressive systems. --Provided by the author