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

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]

Exploiting lattice structures in shape grammar implementations

The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible

Repression of DNA-binding dependent glucocorticoid receptor-mediated gene expression

The glucocorticoid receptor (GR) affects the transcription of genes involved in diverse processes, including energy metabolism and the immune response, through DNA-binding dependent and independent mechanisms. The DNA-binding dependent mechanism occurs by direct binding of GR to glucocorticoid response elements (GREs) at regulatory regions of target genes. The DNA-binding independent mechanism involves binding of GR to transcription factors and coactivators that, in turn, contact DNA. A small molecule that competes with GR for binding to GREs could be expected to affect the DNA-dependent pathway selectively by interfering with the protein-DNA interface. We show that a DNA-binding polyamide that targets the consensus GRE sequence binds the glucocorticoid-induced zipper (GILZ) GRE, inhibits expression of GILZ and several other known GR target genes, and reduces GR occupancy at the GILZ promoter. Genome-wide expression analysis of the effects of this polyamide on a set of glucocorticoid-induced and -repressed genes could help to elucidate the mechanism of GR regulation for these genes

Complexity of Networks (reprise)

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as species enter an ecosystem via migration or speciation, and leave via extinction. In a previous paper, a complexity measure of networks was proposed based on the {\em complexity is information content} paradigm. To apply this paradigm to any object, one must fix two things: a representation language, in which strings of symbols from some alphabet describe, or stand for the objects being considered; and a means of determining when two such descriptions refer to the same object. With these two things set, the information content of an object can be computed in principle from the number of equivalent descriptions describing a particular object. The previously proposed representation language had the deficiency that the fully connected and empty networks were the most complex for a given number of nodes. A variation of this measure, called zcomplexity, applied a compression algorithm to the resulting bitstring representation, to solve this problem. Unfortunately, zcomplexity proved too computationally expensive to be practical. In this paper, I propose a new representation language that encodes the number of links along with the number of nodes and a representation of the linklist. This, like zcomplexity, exhibits minimal complexity for fully connected and empty networks, but is as tractable as the original measure. ...Comment: Accepted in Complexit

An exploration of ebook selection behavior in academic library collections

Academic libraries have offered ebooks for some time, however little is known about how readers interact with them while making relevance decisions. In this paper we seek to address that gap by analyzing ebook transaction logs for books in a university library

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

Seiberg duality, quiver gauge theories, and Ihara's zeta function

We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory