Exploiting Spatial Interference Alignment and Opportunistic Scheduling in the Downlink of Interference Limited Systems

In this paper we analyze the performance of single stream and multi-stream spatial multiplexing (SM) systems employing opportunistic scheduling in the presence of interference. In the proposed downlink framework, every active user reports the post-processing signal-to-interference-plus-noise-power-ratio (post-SINR) or the receiver specific mutual information (MI) to its own transmitter using a feedback channel. The combination of scheduling and multi-antenna receiver processing leads to substantial interference suppression gain. Specifically, we show that opportunistic scheduling exploits spatial interference alignment (SIA) property inherent to a multi-user system for effective interference mitigation. We obtain bounds for the outage probability and the sum outage capacity for single stream and multi stream SM employing real or complex encoding for a symmetric interference channel model. The techniques considered in this paper are optimal in different operating regimes. We show that the sum outage capacity can be maximized by reducing the SM rate to a value less than the maximum allowed value. The optimum SM rate depends on the number of interferers and the number of available active users. In particular, we show that the generalized multi-user SM (MU SM) method employing real-valued encoding provides a performance that is either comparable, or significantly higher than that of MU SM employing complex encoding. A combination of analysis and simulation is used to describe the trade-off between the multiplexing rate and sum outage capacity for different antenna configurations

Smoothing nilpotent actions on 1-manifolds

Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0, 1]$, or $S^1$, and let \Homeo_+(M) (resp. \Diff_+^1(M)) be the group of orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It is a classical result that if $N$ is a finitely-generated, torsion-free nilpotent group, then there exist 1-1 homomorphisms \phi\colon N \to \Homeo_+(M). Farb and Franks show that, in fact, there exists a 1-1 homomorphism N \to \Diff_+^1(M). In this paper we obtain a stronger result: every action \phi\colon N \to \Homeo_+(M) is topologically conjugate to an action \tilde{\phi}\colon N \to \Diff_+^1(M).Comment: 16 page

Completed K-theory and Equivariant Elliptic Cohomology

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. I present a $G$-equivariant version of their construction, which is a completed version of the Freed-Hopkins-Teleman model of $K$-theory for local quotient groupoids and resolves the issues concerning twisting and degree that arise in a first attempt to relate their work to elliptic cohomology.Comment: 23 page

Thinking Fragments: Adisciplinary Reflections on Feminisms and Environmental Justic

Feminisms and environmental justice are some of the names of struggles to understand nature-culture linkages and conceptualize just worlds for non-humans and their human kin. In this paper, I revisit my journey of doing environmental justice research, i.e. of my feminist scientific practice in Asia and Latin America. In this retrospective telling I highlight how gender, political economy, and race were and remain fundamental in producing the subjects and objects of my research and analysis. I discuss how an implicit feminism helped me grapply with the complex nature-culture linkages I observed in the field. Postcolonial and marxist insights supplement and complement feminisms in the questions I pose as we attempt to imagine new nature-cultures

The Eternal Unprovability Filter – Part I

I prove both the mathematical conjectures P ≠ NP and the Continuum Hypothesis are eternally unprovable using the same fundamental idea. Starting with the Saunders Maclane idea that a proof is eternal or it is not a proof, I use the indeterminacy of human biological capabilities in the eternal future to show that since both conjectures are independent of Axioms and have definitions connected with human biological capabilities, it would be impossible to prove them eternally without the creation and widespread acceptance of new axioms. I also show that the same fundamental concepts cannot be used to demonstrate the eternal unprovability of many other mathematical theorems and open conjectures. Finally I investigate the idea’s implications for the foundations of mathematics including its relation to Godel’s Incompleteness Theorem and Tarsky’s Undefinability Theorem

Character Formulas from Matrix Factorisations

(With an Appendix by Constantin Teleman) In the spirit of Freed, Hopkins, and Teleman I establish an equivalence between the category of discrete series representations of a real semisimple Lie group G and a category of equivariant matrix factorisations on a subset of the dual of the Lie algebra, in analogy with the situation in [FT] which treated the case when G is compact or a loop group thereof. The equivalence is implemented by a version of the Dirac operator used in [FHT1-3], squaring to the superpotential W defining the matrix factorisations. Using the structure of the resulting matrix factorisation category as developed in [FT] I deduce the Kirillov character formula for compact Lie groups and the Rossman character formula for the discrete series of a real semi-simple Lie group. The proofs are a calculation of Chern characters and use the Dirac family constructed in [FHT1-3]. Indeed, the main theorems of [FHT3] and [FT] are a categorification of the Kirillov correspondence, and this paper establishes that this correspondence can be recovered at the level of characters.Comment: Appendix (by Constantin Teleman) to appear in final versio