Why Does a Kronecker Model Result in Misleading Capacity Estimates?

Many recent works that study the performance of multi-input multi-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigen-bases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this work, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigen-bases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low- and the high-SNR extremes: 1) Sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low-SNR extreme, and 2) Non-regularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.Comment: 39 pages, 5 figures, under review with IEEE Trans. Inform. Theor

Mossbauer neutrinos in quantum mechanics and quantum field theory

We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.Comment: LaTeX, 16 pages, 1 figure; v2: typos corrected; matches published versio

Rewriting P Systems with Conditional Communication: Improved Hierarchies

We consider here a variant of rewriting P systems [1], where communication is controlled by the contents of the strings, not by the evolution rules used for obtaining these strings. Some new characterizations of recursively enumerable languages are obtained by means of P systems with a small number of membranes, which improves some of the known results from [1] and [4]

Quantum versus Semiclassical Description of Selftrapping: Anharmonic Effects

Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that selftrapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement, with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling.Comment: 10 pages, 6 figures, to appear in Phys. Rev.

Mentoring: Who And How

This paper examines the concept of mentoring, defined here as a process where one individual, the mentor, passes on knowledge, experience and advice to another individual, the mentee, in trust and confidence. This process is initiated by a corporation whose purpose it is to recruit, retain and grow talented people in their organization. A survey of the history of the process is reviewed. The benefits and issues of acquiring a mentor and advancing are also covered. Four interviews are reported, the authors feel that this overview of mentoring has many applications and need not be confined to the business community

The Right to be an Exception to a Data-Driven Rule

Data-driven tools are increasingly used to make consequential decisions. They have begun to advise employers on which job applicants to interview, judges on which defendants to grant bail, lenders on which homeowners to give loans, and more. In such settings, different data-driven rules result in different decisions. The problem is: to every data-driven rule, there are exceptions. While a data-driven rule may be appropriate for some, it may not be appropriate for all. As data-driven decisions become more common, there are cases in which it becomes necessary to protect the individuals who, through no fault of their own, are the data-driven exceptions. At the same time, it is impossible to scrutinize every one of the increasing number of data-driven decisions, begging the question: When and how should data-driven exceptions be protected? In this piece, we argue that individuals have the right to be an exception to a data-driven rule. That is, the presumption should not be that a data-driven rule--even one with high accuracy--is suitable for an arbitrary decision-subject of interest. Rather, a decision-maker should apply the rule only if they have exercised due care and due diligence (relative to the risk of harm) in excluding the possibility that the decision-subject is an exception to the data-driven rule. In some cases, the risk of harm may be so low that only cursory consideration is required. Although applying due care and due diligence is meaningful in human-driven decision contexts, it is unclear what it means for a data-driven rule to do so. We propose that determining whether a data-driven rule is suitable for a given decision-subject requires the consideration of three factors: individualization, uncertainty, and harm. We unpack this right in detail, providing a framework for assessing data-driven rules and describing what it would mean to invoke the right in practice.Comment: 22 pages, 0 figure

Generation of arbitrary Dicke states in spinor Bose-Einstein condensates

We demonstrate that the combination of two-body collisions and applied Rabi pulses makes it possible to prepare arbitrary Dicke (spin) states as well as maximally entangled states by appropriate sequencing of external fields.Comment: 5 pages, 2 figure

Low Energy Solar Neutrinos and Spin Flavour Precession

The possibility that the Gallium data effectively indicates a time modulation of the solar active neutrino flux in possible connection to solar activity is examined on the light of spin flavour precession to sterile neutrinos as a subdominant process in addition to oscillations. We distinguish two sets of Gallium data, relating them to high and low solar activity. Such modulation affects principally the low energy neutrinos ($pp$ and $^7 Be$) so that the effect, if it exists, will become most clear in the forthcoming Borexino and LENS experiments and will provide evidence for a neutrino magnetic moment. Using a model previously developed, we perform two separate fits in relation to low and high activity periods to all solar neutrino data. These fits include the very recent charged current spectrum from the SNO experiment. We also derive the model predictions for Borexino and LENS experiments.Comment: 20 pages, 5 ps figures, 1 eps figure, final version to be published in JHE

Features in the Primordial Spectrum from WMAP: A Wavelet Analysis

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper (Shafieloo and Souradeep 2004), we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, `best fit' scale free spectra (\Delta ln L = 25 w.r.t. Harrison Zeldovich, and, \Delta ln L = 11 w.r.t. power law with n_s=0.95). In this paper we use Discrete Wavelet Transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infra-red cut off at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localised at the horizon scale.Comment: 8 pages, 4 figures, uses Revtex4, matches version accepted to Phys. Rev. D, main results and conclusions unchanged, references adde