Quantum Enhanced Classical Sensor Networks

The quantum enhanced classical sensor network consists of $K$ clusters of $N_e$ entangled quantum states that have been trialled $r$ times, each feeding into a classical estimation process. Previous literature has shown that each cluster can {ideally} achieve an estimation variance of $1/N_e^2r$ for sufficient $r$. We begin by deriving the optimal values for the minimum mean squared error of this quantum enhanced classical system. We then show that if noise is \emph{absent} in the classical estimation process, the mean estimation error will decay like $\Omega(1/KN_e^2r)$. However, when noise is \emph{present} we find that the mean estimation error will decay like $\Omega(1/K)$, so that \emph{all} the sensing gains obtained from the individual quantum clusters will be lost

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

In this paper, we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple-input multiple-output (MIMO) $d\times d$ antenna amplify-and-forward (AF) relay networks. In particular, we model these networks as random dynamical systems (RDS) and calculate their $d$ Lyapunov exponents. Our analysis can be applied to systems with any per-hop channel fading distribution, although in this contribution we focus on Rayleigh fading. Our main results are twofold: 1) the total transmit power at the $n$th node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the $i$th eigenchannel at the $n$th node will follow a deterministic trajectory through the network governed by the network's $i$th Lyapunov exponent. Before concluding, we concentrate on some applications of our results. In particular, we show how the Lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other, and how this relates to the amplification strategy and number of antennas at each relay. We also use them to determine the extra cost in power associated with each extra multiplexed data stream.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Transactions on Information Theor

Pricing Systems of Trainloading Country Elevator Cooperatives: A Summary

Demand and Price Analysis, Agribusiness,

Symmetric Laplacians, Quantum Density Matrices and their Von-Neumann Entropy

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian's Von Neumann entropy as a measure of bipartite entanglement present between the two parts of the state. We then study extreme values for a connected graph's generalized R\'enyi-$p$ entropy. Specifically, we show that (1) the complete graph achieves maximum entropy, (2) the $2$-regular graph: a) achieves minimum R\'enyi-$2$ entropy among all $k$-regular graphs, b) is within $\log 4/3$ of the minimum R\'enyi-$2$ entropy and $\log4\sqrt{2}/3$ of the minimum Von Neumann entropy among all connected graphs, c) achieves a Von Neumann entropy less than the star graph. Point $(2)$ contrasts sharply with similar work applied to (normalized) combinatorial Laplacians, where it has been shown that the star graph almost always achieves minimum Von Neumann entropy. In this work we find that the star graph achieves maximum entropy in the limit as the number of vertices grows without bound. Keywords: Symmetric; Laplacian; Quantum; Entropy; Bounds; R\'enyi

Outage Performance Analysis of Multicarrier Relay Selection for Cooperative Networks

In this paper, we analyze the outage performance of two multicarrier relay selection schemes, i.e. bulk and per-subcarrier selections, for two-hop orthogonal frequency-division multiplexing (OFDM) systems. To provide a comprehensive analysis, three forwarding protocols: decode-and-forward (DF), fixed-gain (FG) amplify-and-forward (AF) and variable-gain (VG) AF relay systems are considered. We obtain closed-form approximations for the outage probability and closed-form expressions for the asymptotic outage probability in the high signal-to-noise ratio (SNR) region for all cases. Our analysis is verified by Monte Carlo simulations, and provides an analytical framework for multicarrier systems with relay selection

Symmetric Laplacians, quantum density matrices and their Von Neumann entropy

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian's Von Neumann entropy as a measure of bipartite entanglement present between the two parts of the state. We then study extreme values for a connected graph's generalized R\'enyi-p entropy. Specifically, we show that (1) the complete graph achieves maximum entropy, (2) the 2-regular graph: a) achieves minimum R\'enyi-2 entropy among all k-regular graphs, b) is within log4/3 of the minimum R\'enyi-2 entropy and log42‾√/3 of the minimum Von Neumann entropy among all connected graphs, c) achieves a Von Neumann entropy less than the star graph. Point (2) contrasts sharply with similar work applied to (normalized) combinatorial Laplacians, where it has been shown that the star graph almost always achieves minimum Von Neumann entropy. In this work we find that the star graph achieves maximum entropy in the limit as the number of vertices grows without bound

The Effects of Limiting Punitive Damage Awards

In response to concerns that jury awards in tort cases are excessive and unpredictable, nearly every state legislature has enacted some version of tort reform that is intended to curb extravagant damage awards. One of the most important and controversial reforms involves capping (or limiting) the maximum punitive damage award. We conducted a jury analogue study to assess the impact of this reform. In particular, we examined the possibility that capping punitive awards would cause jurors to inflate their compensatory awards to satisfy their desires to punish the defendant, particularly in situations where the defendant’s conduct was highly reprehensible. Relative to a condition in which punitive damages were unlimited, caps on punitive damages did not result in inflation of compensatory awards. However, jurors who had no option to award punitive damages assessed compensatory damages at a significantly higher level than did jurors who had the opportunity to do so. We discuss the policy implications of these findings