Relays for Interference Mitigation in Wireless Networks

Wireless links play an important role in the last mile network connectivity. In contrast to the strictly centralized approach of today's wireless systems, the future promises decentralization of network management. Nodes potentially engage in localized grouping and organization based on their neighborhood to carry out complex goals such as end-to-end communication. The quadratic energy dissipation of the wireless medium necessitates the presence of certain relay nodes in the network. Conventionally, the role of such relays is limited to passing messages in a chain in a point-point hopping architecture. With the decentralization, multiple nodes could potentially interfere with each other. This work proposes a technique to exploit the presence of relays in a way that mitigates interference between the network nodes. Optimal spatial locations and transmission schemes which enhance this gain are identified

Samplers and Extractors for Unbounded Functions

Blasiok (SODA\u2718) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions f from {0,1}^m to the real numbers such that f(U_m) has subgaussian tails, and asked for explicit constructions. In this work, we give the first explicit constructions of subgaussian samplers (and in fact averaging samplers for the broader class of subexponential functions) that match the best known constructions of averaging samplers for [0,1]-bounded functions in the regime of parameters where the approximation error epsilon and failure probability delta are subconstant. Our constructions are established via an extension of the standard notion of randomness extractor (Nisan and Zuckerman, JCSS\u2796) where the error is measured by an arbitrary divergence rather than total variation distance, and a generalization of Zuckerman\u27s equivalence (Random Struct. Alg.\u2797) between extractors and samplers. We believe that the framework we develop, and specifically the notion of an extractor for the Kullback-Leibler (KL) divergence, are of independent interest. In particular, KL-extractors are stronger than both standard extractors and subgaussian samplers, but we show that they exist with essentially the same parameters (constructively and non-constructively) as standard extractors

Implications of δlCP∼270∘\delta^{CP}_l\sim 270^\circ and θ23≳45∘\theta_{23}\gtrsim 45^\circ for texture specific lepton mass matrices and 0νββ0\nu \beta \beta decay

We study the phenomenological consequences of recent results from atmospheric and accelerator neutrino experiments, favoring normal neutrino mass ordering $m_1 < m_2 < m_3$, a near maximal lepton Dirac CP phase $\delta_{l}\sim 270^\circ$ along with $\theta_{23}\gtrsim 45^\circ$, for possible realization of natural structure in the lepton mass matrices characterized by ${({M_{ij}})} \sim O(\sqrt {{m_i}{m_j}})$ for $i,j=1,2,3$. It is observed that deviations from parallel texture structures for $M_{l}$ and $M_{\nu}$ are essential for realizing such structures. In particular, such hierarchical neutrino mass matrices are not supportive for a vanishing neutrino mass $m_{\nu 1}\rightarrow 0$ characterized by Det$M_{\nu}\ne 0$ and predict ${m_{\nu 1}} \simeq (0.1 - 8.0)$ $meV$ , ${m_{\nu 2}} \simeq (8.0 - 13.0)$ $meV$, ${m_{\nu 3}} \simeq (47.0 - 52.0)$ $meV$, $\Sigma \simeq (56.0 - 71.0)$ $meV$ and $\left\langle {{m_{ee}}} \right\rangle \simeq (0.01 - 10.0)$ $meV$, respectively, indicating that the task of observing a $0\nu \beta \beta$ decay may be rather challenging for near future experiments.Comment: 12 pages, 10 figures, 2 table