On the Distribution of MIMO Mutual Information: An In-Depth Painlev\'{e} Based Characterization

This paper builds upon our recent work which computed the moment generating function of the MIMO mutual information exactly in terms of a Painlev\'{e} V differential equation. By exploiting this key analytical tool, we provide an in-depth characterization of the mutual information distribution for sufficiently large (but finite) antenna numbers. In particular, we derive systematic closed-form expansions for the high order cumulants. These results yield considerable new insight, such as providing a technical explanation as to why the well known Gaussian approximation is quite robust to large SNR for the case of unequal antenna arrays, whilst it deviates strongly for equal antenna arrays. In addition, by drawing upon our high order cumulant expansions, we employ the Edgeworth expansion technique to propose a refined Gaussian approximation which is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and for moderate deviations into the tails (where the Gaussian approximation fails remarkably). For stronger deviations where the Edgeworth expansion becomes unwieldy, we employ the saddle point method and asymptotic integration tools to establish new analytical characterizations which are shown to be very simple and accurate. Based on these results we also recover key well established properties of the tail distribution, including the diversity-multiplexing-tradeoff.Comment: Submitted to IEEE Transaction on Information Theory (under revision

Anisotropic pair-superfluidity of trapped two-component Bose gases

We theoretically investigate the pair-superfluid phase of two-component ultracold gases with negative inter-species interactions in an optical lattice. We establish the phase diagram for filling $n=1$ at zero and finite temperature, by applying Bosonic Dynamical Mean-Field Theory, and confirm the stability of pair-superfluidity for asymmetric hopping of the two species. While the pair superfluid is found to be robust in the presence of a harmonic trap, we observe that it is destroyed already by a small population imbalance of the two species.Comment: 7 pages, 11 figure

Equilibrium asset pricing evaluation of real estate risk and return across four quadrants

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 38-40).The major objective of this study is to test equilibrium asset pricing models with respect to how well they price risk across multiple asset classes; including the four quadrants of real estate. While using the Geltner (1999) paper as a springboard for our approach, this thesis both updates Professor Geltner's earlier work and extends its scope through the testing of additional models and asset classes. Using historical data to derive beta estimates, we empirically test several variations of the Capital Asset Pricing Model (CAPM). These variations include the traditional, single-beta, Sharpe-Lintner CAPM, as well as the multi-beta, Fama-French CAPM. For the single-factor formula we explore the use of two different market portfolio proxies, the S&P 500 Index and the National Wealth Portfolio (NWP). We also apply the single-factor formula to a non-wealth based, consumption oriented approach. Test results show the NWP based CAPM to be the strongest model, being both robust and statistically significant in its pricing of asset volatility. When using the traditional S&P 500 index as the market proxy, the basic CAPM performs surprisingly well, though not as well as the NWP version. The multi-beta Fama-French model explains a large amount of price variation, however, only the market and size factors prove to be statistically significant at the 95% confidence level.(cont.) In a dramatic departure from what was found roughly fifteen years ago, the consumption model's performance was lackluster; supporting a widespread belief that there may be empirical issues with the measurement of quarterly consumption. The most interesting finding across all models tested was the behavior of the housing asset class. Housing appears to be an outlier that doesn't seem to fit in with the rest of the asset classes using linear pricing models. All the models display a statistically significant intercept, suggesting that there is a component of risk, perhaps a significant component (as perceived by investors relative to treasury bills), that is not captured in any of these risk models.by Nan Li and Steven McKay Price.S.M

Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

We investigate MIMO eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly-correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.Comment: 32 pages, 6 figures, to appear in IEEE Transactions on Information Theor

Moessbauer and Electron Microprobe Studies of Density Separates of Martian Nakhlite Mil03346: Implications for Interpretation of Moessbauer Spectra Acquired by the Mars Exploration Rovers

Martian meteorite MIL03346 is described as an augite-rich cumulate rock with approx.80%, approx.3%, and approx.21% modal phase proportions of augite (CPX), olivine and glassy mesostasis, respectively, and is classified as a nakhlite [1]. The Mossbauer spectrum for whole rock (WR) MIL 03346 is unusual for Martian meteorites in that it has a distinct magnetite subspectrum (~7% subspectral area) [2]. The meteorite also has products of pre-terrestrial aqueous alteration ("iddingsite") that is associated primarily with the basaltic glass and olivine. The Mossbauer spectrometers on the Mars Exploration Rovers have measured the Fe oxidation state and the Fe mineralogical composition of rocks and soils on the planet s surface since their landing in Gusev Crater and Meridiani Planum in January, 2004 [3,4]. The MIL 03346 meteorite provides an opportunity to "ground truth" or refine Fe phase identifications. This is particularly the case for the so-called "nanophase ferric oxide" (npOx) component. NpOx is a generic name for a ferric rich product of oxidative alteration. On Earth, where we can take samples apart and study individual phases, examples of npOx include ferrihydrite, schwertmannite, akagaaneite, and superparamagnetic (small particle) goethite and hematite. It is also possible for ferric iron to be associated to some unknown extent with igneous phases like pyroxene. We report here an electron microprobe (EMPA) and Moessbauer (MB) study of density separates of MIL 03346. The same separates were used for isotopic studies by [5]. Experimental techniques are described by [6,7]

Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups

We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as SU(6,2) covariant bases. E_{8(-24)} has E_7 X SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d=3. For the corresponding U-duality group E_{8(8)} of the maximal supergravity theory the minimal realization was given in hep-th/0109005. The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E_{8(-24)} and E_{8(8)}. By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E_{8(-24)} as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in hep-th/0008063.Comment: 28 pages. Latex commands removed from the abstract for the arXiv. No changes in the manuscrip

Alternative Transcript Initiation and Splicing as a Response to DNA Damage

Humans are exposed to the DNA damaging agent, ionizing radiation (IR), from background radiation, medical treatments, occupational and accidental exposures. IR causes changes in transcription, but little is known about alternative transcription in response to IR on a genome-wide basis. These investigations examine the response to IR at the exon level in human cells, using exon arrays to comprehensively characterize radiation-induced transcriptional expression products. Previously uncharacterized alternative transcripts that preferentially occur following IR exposure have been discovered. A large number of genes showed alternative transcription initiation as a response to IR. Dose-response and time course kinetics have also been characterized. Interestingly, most genes showing alternative transcript induction maintained these isoforms over the dose range and times tested. Finally, clusters of co-ordinately up- and down-regulated radiation response genes were identified at specific chromosomal loci. These data provide the first genome-wide view of the transcriptional response to ionizing radiation at the exon level. This study provides novel insights into alternative transcripts as a mechanism for response to DNA damage and cell stress responses in general