Estimation of MIMO transmit-antenna number using higher-order moments based hypothesis testing

This letter proposes a higher-order-moment based hypothesis testing algorithm to estimate the transmit-antenna number for multiple-input multiple-output (MIMO) systems. Exploiting the asymptotic normal distribution of the moments composed by noise eigenvalues, the proposed algorithm improves the estimation performance for low signal-to-noise ratios (SNRs). Moreover, since the empirical distribution of the moments converges quickly to the normal distribution when the number of samples increases, our algorithm can make a reliable estimation in a sample starved condition. Computer simulations are provided to demonstrate that the proposed algorithm outperforms the conventional algorithms

Applied stochastic eigen-analysis

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2007The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest (“signal”) eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded. The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) “free probability” theory. The class of “algebraic” random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional “eigenvector distribution.” The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.I am grateful to the National Science Foundation for supporting this work via grant DMS-0411962 and the Office of Naval Research Graduate Traineeship awar

The biophysics of bacterial collective motion: Measuring responses to mechanical and genetic cues

Mechanobiology is an emerging field investigating mechanical signals as a necessary component of cellular and developmental regulation. These mechanical signals play a well-established role in the differentiation of animal cells, whereby cells with identical genes specialize their function and create distinct tissues depending on the physical properties of their environment, such as shear stiffness. These differences arise from the cell’s ability to use those incoming signals to inform which genes it expresses and what molecular machinery it builds and activates. Understanding the various missing factors that cause cells with specific genes to express an emergent phenotype is termed the genotype-to-phenotype problem, and mechanical signaling pathways present themselves as a significant piece of this puzzle. Despite the strong evidence for mechanosensing in eukaryotes, the pathways by which prokaryotes respond to mechanical stimuli are still largely unknown. Bacteria are among the simplest and yet most abundant forms of life. Many of their survival strategies depend on multicellular development and the coordinated formation of a colony into functional structures that may also feature cellular differentiation. This dissertation employs bacteria as a model system to investigate multiple biophysical questions of collective motion through novel experimental and analytical techniques. This work addresses the understudied mechanical relationship between a bacterial colony and the substrate it colonizes by asking “what is the effect of substrate stiffness on colony growth?” This is done by measuring bacterial growth on hydrogel substrates that decouple the effects of substrate stiffness from other material properties of the substrate that vary with stiffness. We report a previously unobserved effect in which bacteria colonize stiffer substrates faster than softer substrates, in opposition to previous studies done on agar, where permeability, viscoelasticity, and other material properties vary with stiffness.A second theme of this work probes the genetic inputs to the genotype-to-phenotype problem in multicellular development. The bacterial species Myxococcus xanthus producing macroscopic aggregates called fruiting bodies is used as a model organism for these studies. It has long been conjectured that genes may stand in for each other functionally, allowing for development to be more consistent and stable, but the extent of this redundancy has resisted measurement. We approach the question “how does redundancy among related genes lead to robust collective behavior?” by quantifying developmental phenotype in a large dataset of time lapse microscopy videos that show development in many mutant strains. We observe that when knocking out multiple genes that have a common origin (i.e. homologous genes), the resulting phenotypes differ from wild-type in a similar way. These phenotype clusters also differ from knockouts from other homologous gene families. These distinct phenotypic clusters provide evidence for the existence of networks of redundant genes that are larger than could previously be tested directly. Because of this robustness, the effects of individual gene mutations can be hidden or damped. We thus develop our analytical techniques further to address the question “how can subtle changes in phenotype be measured?” This involves quantifying the breadth of variation observed in wild-type development and creating a statistical technique to distinguish probabilistic distributions of phenotypic outcomes. We present a coherent method of visualizing large phenotypic datasets that include multiple metrics that we use to distinguish small developmental differences from wild-type, giving each mutant strain a phenotypic fingerprint that can be used in future studies on gene annotation and environmental impacts on phenotype

MAGESTIC: Magnetically Enabled Structures Using Interacting Coils

In our NIAC Phase I study, awarded September 2011, the MIT Space Systems Lab (MIT SSL) began investigating a new structural and mechanical technique aimed at reducing the mass and increasing the stowed-to-deployed ratio of spacecraft systems. This technique uses the magnetic fields from current passing through coils of high temperature superconductors (HTSs) to support spacecraft structures and deploy them to operational configurations from their positions as stowed inside a launch vehicle fairing. These electromagnetic coils are tethered or hinged together in such a way that their motion in some directions or around some axes is constrained, as in Figure 1. Our Phase II study,awarded in Fall 2012, continued this work on electromagnetic structures, with an added focus on developing a new thermal system, investigating additional, non-structural electromagnet functions, and creating a maturation roadmap and plan for addressing barriers to feasibility of the technology. We now call the project MAGESTIC, or Magnetically Enabled STructures using Interacting Coils

Removal Period Cherokee Households in Southwestern North Carolina: Material Perspectives on Ethnicity and Cultural Differentiation

Nineteenth century accounts of Cherokee Indian society consistently refer to the existence of two classes among the Cherokees: the acculturated mixed blood[s], who speak English and are considered the intelligent and wealthy class and the culturally conservative fullbloods, whom white observers denigrated as backward, indolent, and ignorant pagans. This perceived dichotomy reflected the poles of a socioeconomic and cultural continuum that developed as a result of the differential Westernization of Cherokee individuals and households during the post-Revolutionary War era. As these socioeconomic classes diverged, they developed as the primary axis of competition and conflict within Cherokee society. Because these groups were progressively distinguished by ancestry, language use, lifestyle, and ideology, they may be characterized as emergent ethnic groups subsumed within the Cherokee national polity. As identity-conscious groups in competition for economic resources and political power, the Cherokee-speaking fullblood majority and the English-speaking metis minority used various media, including material goods and property, to construct and maintain ethnic boundaries. This study examines documentary and archaeological evidence for the use of such material media by Cherokee families in southwestern North Carolina during the Removal period. (1835-1838) and seeks to define material patterning that distinguished the English-speaking metis minority from the Cherokee-speaking fullblood majority. Four independent primary datasets are successively analyzed and discussed to accomplish a synthetic overview of Cherokee wealthholding and material culture. Bioracial, linguistic, and certain aspects of economic variation within the study population are defined through examination of the 1835 War Department census of the Cherokee Nation east of the Mississippi. General trends of bioracial endogamy, community composition, and wealth distribution evident in the 1835 census indicate active ethnic differentiation within the Cherokee population of southwestern North Carolina. The population of the study area was ethnically and socioeconomically homogeneous, with a dominant component of monolingual Cherokee fullblood subsistence farmers who formed a distinctly conservative and materially impoverished aboriginal stratum of Cherokee society. Contrasted with this majority was a small group of Anglo-Cherokee households who exhibited high rates of English literacy and slaveholding, and who managed extensive market farms in the larger river and creek valleys in the southern portion of the study area A relatively small number of fullblood and AngloCherokee families were arrayed between these extremes, forming a heavily skewed socioeconomic continuum largely reflective of household ethnicity. The improved real properties of Cherokee households in southwestern North Carolina are documented by U.S. government property appraisals conducted in the winter of 1836-1837. These appraisals include narrative descriptions and dimensions of dwellings and other buildings, cultivated fields and other cleared or fenced land, fruit trees, ditches, wells, mills, and other facilities present on 684 properties. Hierarchical agglomerative (Ward\u27s method) cluster analysis is used to define types of properties based upon similarities in the values assigned to dwellings, nonresidential structures, and agricultural improvements by the federal appraisers. The resultant cluster solution is interpreted as a series of farmstead models that can be ranked from those more traditional in composition to those more closely resembling Western agrarian modes. These analyses indicate that Cherokee properties in the study area were remarkably homogeneous in composition; more than 85% of the Cherokee farmsteads in southwestern North Carolina consisted of twelve or fewer acres of cropland, small, cribbed log dwellings valued less than $32.00, and few outbuildings other than corn cribs and an occasional asi. Properties owned by a small number of Anglo-Cherokees families contrast sharply with this traditional farmstead mode, and reflect thorough incorporation and integration of Western agrarian material modes of life. The largest and most highly valued Cherokee properties included substantial, hewn log dwellings valued in excess of$70.00, 35 or more acres of cropland, and a wide array of ancillary domestic structures (e.g. kitchens, springhouses, smokehouses), farm buildings (e.g. stables, cribs, barns), and specialized facilities (e.g. stores, mills, blacksmith shops). These farms substantially resembled the typical holdings of Anglo-American middling farmers and small planters in the southern highlands, and the Cherokee owners of such properties occupied a socioeconomic status parallel to the upper middle class of the Anglo-American rural South. A relatively small sector of Anglo-Cherokee and fullblood Cherokee families maintained homes and farms that formed a continuum between these extremes. Contrastive modes of farmstead composition are interpreted as evidence for the operation of distinct Western and traditional systems of household economy and material lifeways. These distinct systems are largely, but not exclusively, correlated with the bioracial and linguistic affinities of Cherokee households, and contrastive farmstead composition is interpreted as evidence for ethnic differentiation among Cherokee households in southwestern North Carolina. Spoliation claims which Cherokees from the study area filed against the United States government following forced removal of 1838 document losses of clothing, furniture, household goods, cookware and tableware, agricultural equipment and other tools, livestock, and other material possessions by more than 400 Cherokee households from the study area. These data are initially explored through univariate comparisons of the distributions of major functional groups of chattel property among bioracial/linguistic subsets of the study population to determine differential patterns of ownership. Hierarchical agglomerative cluster analysis is applied to classify individual household cases by inventory composition. The membership of these groups of households is then evaluated with respect to racial/ethnic affinity to determine whether ethnicity played a significant role in the formation of household assemblages. Analyses of the chattel properties data. reveal patterning similar to that of the real properties data, with a large, homogeneous group of relatively poor, predominantly fullblood families forming the basal economic stratum of Cherokee society contrasted with a small, predominantly English-speaking, group of wealthy Cherokees. A relatively small group of both fullblood and Anglo-Cherokee households span these extremes. These patterns are interpreted as evidence for a traditional-Western continuum in material lifestyles and economic modes; the poles of this continuum appear to represent the contrastive content of an ethnic dichotomy. Archaeological data present a collateral, yet independent gauge of variation in the material lifeways of Removal Period Cherokee households in the study area. To illustrate the differences in material culture that distinguish more Westernized from more traditionally oriented Cherokee households, artifact assemblages representing one Anglo-Cherokee metis occupation, and six fullblood Cherokee household occupations are compared and contrasted in terms of diversity, content, and relative composition. Archaeological assemblages recovered from surface and excavated contexts at these farmstead sites evince a high degree of interhousehold variation in scale and content; this variability is interpreted as evidence of differential acculturation and contrastive cultural orientations. Most of these assemblages are dominated by Qualla series ceramics and other goods reflective of indigenous traditions; these configurations suggest that many of the Cherokee inhabitants of southwestern North Carolina retained strong native identities expressed through continuity of traditional technologies. However, high frequencies of commercially manufactured goods associated with the metis household (the Christies) occupation also indicate substantially higher levels of material wealth and construction of a Westernized material lifestyle informed by AngloAmerican models. which commercial consumption was particularly prominent. These analyses illustrate the broad themes of variation in Cherokee material culture on the eve of the removal of 1838. The extremes of variation evident in these datasets are interpreted as evidence for differential Westernization of Cherokee households, and illustrate the material modes that conservative Cherokees and Westernized Anglo-Cherokees used to define and distinguish their communities of association as nascent ethnic groups struggling over the cultural identity and political fate of the Cherokee Nation

Uncovering the Roles and Evolved Sequence Grammar of Hypervariable Intrinsically Disordered Proteins in Bacterial Cell Division

Across all domains of life, a defining hallmark of the onset of cell division is the formation of a cytokinetic ring at the center of the cell. Cell division is a tightly controlled process that involves various regulatory factors that modulate the assembly of the cytokinetic ring. In rod-shaped bacteria, the ring is termed the Z-ring after the protein FtsZ, which is foundational to ring formation and is the bacterial homolog of tubulin. Like tubulin, FtsZ is an assembling GTPase, where GTP binding promotes the cooperative assembly into FtsZ polymers that laterally associate to form bundles. While the GTPase domain drives FtsZ polymerization, the formation of these higher-order structures requires domains outside the folded core. FtsZ has a bristled architecture, where a disordered tail, called the C-terminal tail (CTT), flanks the folded domain. The essentiality of the CTT was established through deletion experiments; however, the exact role that the CTT plays within the context of FtsZ function remained unclear. Here, we establish that the CTT, containing an intra-and intermolecular interaction motif (CTP) and a disordered linker (CTL), has a sticker-and-spacer architecture, where the CTL modulates the interactions of the CTP. We find that the modules of the CTT not only influence FtsZ assembly but also impact the catalytic efficiency of the GTPase domain. These findings add to recent findings that implicate disordered regions tethered to enzymes in auto-regulatory activities. The findings summarized above were obtained by focusing our investigations on the CTT of the FtsZ protein from B. subtilis (Bs-FtsZ). Is the stickers-and-spacers model applicable to understanding the functions of CTTs from other bacterial FtsZs? We analyzed the sequences of 1208 orthologous FtsZs, and the results show that while the CTPs and the core domains are reasonably well conserved, the CTLs are hypervariable across orthologs. The results of the sequence analysis have several implications: It might reflect a form of convergent evolution whereby different CTL sequences are interoperable with one other because different sequences serve the functionality of being spacers. Alternatively, the variation could be an example of divergent evolution, whereby changes to the CTLs engender different functionalities in different bacteria. Answering these questions will require methods to identify common sequence patterns across orthologous CTLs, and this cannot be achieved using traditional multiple sequence alignment approaches. Accordingly, we introduce computational methods that enable the quantitative analysis of conserved / distinct sequence-ensemble relationships across a family of IDRs. Additionally, we introduce a new method to uncover cryptic sequence patterns that define disordered regions as random versus non-random. These methods are shown to be applicable for high-throughput analysis of CTLs derived from different FtsZs. They are also effective in uncovering sequence patterns that are cryptic but conserved in intrinsically disordered regions (IDRs) from other bacterial proteins. Given the role of sequence-ensemble relationships and non-random motifs in IDP/IDR function, we hypothesized that these features might influence function and, therefore, might be encoded for within the amino acid sequence of the FtsZ CTL. This implies that designed CTL sequence variants that result in significant changes to these sequence features and to the ability of the CTL to function as a spacer could perturb function. To test this hypothesis, we developed scrambled sequence variants of the B. subtilis FtsZ CTL using the patterning of oppositely charged residues as a design parameter. Leveraging new methodologies, we found that the designed variants caused changes to the sequence-ensemble relationships, the non-random sequence patterning, and / or the spacer properties. Each variant was tested for complementary functions to wild type in vitro and in vivo. Indeed, deviations from wild type features had phenotypic impacts and / or influenced FtsZ assembly and activity, showing that the CTL is not a random disordered sequence but instead has specifically encoded sequence features that dictate function. As the global need to combat antibiotic-resistant infections continues to mount, studies that further understand the functions that IDRs contribute to essential bacterial processes such as cell division can be leveraged to create next-generation antibiotics

Mobile Robots Navigation

Mobile robots navigation includes different interrelated activities: (i) perception, as obtaining and interpreting sensory information; (ii) exploration, as the strategy that guides the robot to select the next direction to go; (iii) mapping, involving the construction of a spatial representation by using the sensory information perceived; (iv) localization, as the strategy to estimate the robot position within the spatial map; (v) path planning, as the strategy to find a path towards a goal location being optimal or not; and (vi) path execution, where motor actions are determined and adapted to environmental changes. The book addresses those activities by integrating results from the research work of several authors all over the world. Research cases are documented in 32 chapters organized within 7 categories next described