The Population Genetic Signature of Polygenic Local Adaptation

Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loci to estimate the mean additive genetic value for a given phenotype across many populations as simple weighted sums of allele frequencies. We first describe a general model of neutral genetic value drift for an arbitrary number of populations with an arbitrary relatedness structure. Based on this model we develop methods for detecting unusually strong correlations between genetic values and specific environmental variables, as well as a generalization of $Q_{ST}/F_{ST}$ comparisons to test for over-dispersion of genetic values among populations. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles, and also significantly outperform methods that do not account for population structure. We apply our tests to the Human Genome Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation, type 2 diabetes, body mass index, and two inflammatory bowel disease datasets. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.Comment: 42 pages including 8 figures and 3 tables; supplementary figures and tables not included on this upload, but are mostly unchanged from v

On Distributed and Acoustic Sensing for Situational Awareness

Recent advances in electronics enable the development of small-sized, low-cost, low-power, multi-functional sensor nodes that possess local processing capability as well as to work collaboratively through communications. They are able to sense, collect, and process data from the surrounding environment locally. Collaboration among the nodes are enabled due to their integrated communication capability. Such a system, generally referred to as sensor networks are widely used in various of areas, such as environmental monitoring, asset tracking, indoor navigation, etc. This thesis consists of two separate applications of such mobile sensors. In this first part, we study decentralized inference problems with dependent observations in wireless sensor networks. Two separate problems are addressed in this part: one pertaining to collaborative spectrum sensing while the other on distributed parameter estimation with correlated additive Gaussian noise. In the second part, we employ a single acoustic sensor with co-located microphone and loudspeaker to reconstruct a 2-D convex polygonal room shape. For spectrum sensing, we study the optimality of energy detection that has been widely used in the literature. This thesis studies the potential optimality (or sub-optimality) of the energy detector in spectrum sensing. With a single sensing node, we show that the energy detector is provably optimal for most cases and for the case when it is not theoretically optimal, its performance is nearly indistinguishable from the true optimal detector. For cooperative spectrum sensing where multiple nodes are employed, we use a recently proposed framework for distributed detection with dependent observations to establish the optimality of energy detector for several cooperative spectrum sensing systems and point out difficulties for the remaining cases. The second problem in decentralized inference studied in this thesis is to investigate the impact of noise correlation on decentralized estimation performance. For a tandem network with correlated additive Gaussian noises, we establish that threshold quantizer on local observations is optimal in the sense of maximizing Fisher information at the fusion center; this is true despite the fact that subsequent estimators may differ at the fusion center, depending on the statistical distribution of the parameter to be estimated. In addition, it is always beneficial to have the better sensor (i.e. the one with higher signal-to-noise ratio) serve as the fusion center in a tandem network for all correlation regimes. Finally, we identify different correlation regimes in terms of their impact on the estimation performance. These include the well known case where negatively correlated noises benefit estimation performance as it facilitates noise cancellation, as well as two distinct regimes with positively correlated noises compared with that of the independent case. In the second part of this thesis, a practical problem of room shape reconstruction using first-order acoustic echoes is explored. Specifically, a single mobile node, with co-located loudspeaker, microphone and internal motion sensors, is deployed and times of arrival of the first-order echoes are measured and used to recover room shape. Two separate cases are studied: the first assumes no knowledge about the sensor trajectory, and the second one assumes partial knowledge on the sensor movement. For either case, the uniqueness of the mapping between the first-order echoes and the room geometry is discussed. Without any trajectory information, we show that first-order echoes are sufficient to recover 2-D room shapes for all convex polygons with the exception of parallelograms. Algorithmic procedure is developed to eliminate the higher-order echoes among the collected echoes in order to retrieve the room geometry. In the second case, the mapping is proved for any convex polygonal shapes when partial trajectory information from internal motion sensors is available.. A practical algorithm for room reconstruction in the presence of noise and higher order echoes is proposed

Suppression of acoustic noise in speech using spectral subtraction

technical reportA stand alone noise suppression algorithm is presented for reducing the spectral effects of acoustically added noise in speech. Effective performance of digital speech processors operating in practical environments may require suppression of noise from the digital waveform. Spectral subtraction offers a computationally efficient, processor independent, approach to effective digital speech analysis. The method, requiring about the same computation as high-speed convolution, suppresses stationary noise for speech by subtracting the spectral noise bias calculated during non-speech activity. Secondary procedures and then applied to attenuate the residual noise left after subtraction. Since the algorithm resynthesizes a speech waveform, it can be used as a preprocessor to narrow band voice communications systems, speech recognition systems or speaker authentication systems

Multiple Hypothesis Testing Framework for Spatial Signals

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from multiple hypothesis testing to identify such regions. A discrete spatial grid is assumed for the monitored environment. The spatial grid points associated with different hypotheses are identified while controlling the false discovery rate at a pre-specified level. Measurements are acquired using a large-scale sensor network. We propose a novel, data-driven method to estimate local false discovery rates based on the spectral method of moments. Our method is agnostic to specific spatial propagation models of the underlying physical phenomenon. It relies on a broadly applicable density model for local summary statistics. In between sensors, locations are assigned to regions associated with different hypotheses based on interpolated local false discovery rates. The benefits of our method are illustrated by applications to spatially propagating radio waves.Comment: Submitted to IEEE Transactions on Signal and Information Processing over Network

Black box simulation optimization:Generalized response surface methodology

The thesis consists of three papers in the area of Response Surface Methodology (RSM). The first paper deals with optimization problems with a single random objective. The contributions of that paper are a scale independent search direction and possible solutions for the step size. The second paper considers optimization problems with a single random objective and multiple random constraints, as well as deterministic box constraints. That paper extends RSM to cope with constraints, using ideas from interior point methods. Furthermore, it provides a heuristic to reach quickly a neighborhood of the optimum. The third paper copes with optimization problems with a single random objective and multiple random constraints. The contribution of that paper is an asymptotic stopping rule that tests the first-order necessary optimality conditions at a feasible point.

Subspace Representations and Learning for Visual Recognition

Pervasive and affordable sensor and storage technology enables the acquisition of an ever-rising amount of visual data. The ability to extract semantic information by interpreting, indexing and searching visual data is impacting domains such as surveillance, robotics, intelligence, human- computer interaction, navigation, healthcare, and several others. This further stimulates the investigation of automated extraction techniques that are more efficient, and robust against the many sources of noise affecting the already complex visual data, which is carrying the semantic information of interest. We address the problem by designing novel visual data representations, based on learning data subspace decompositions that are invariant against noise, while being informative for the task at hand. We use this guiding principle to tackle several visual recognition problems, including detection and recognition of human interactions from surveillance video, face recognition in unconstrained environments, and domain generalization for object recognition.;By interpreting visual data with a simple additive noise model, we consider the subspaces spanned by the model portion (model subspace) and the noise portion (variation subspace). We observe that decomposing the variation subspace against the model subspace gives rise to the so-called parity subspace. Decomposing the model subspace against the variation subspace instead gives rise to what we name invariant subspace. We extend the use of kernel techniques for the parity subspace. This enables modeling the highly non-linear temporal trajectories describing human behavior, and performing detection and recognition of human interactions. In addition, we introduce supervised low-rank matrix decomposition techniques for learning the invariant subspace for two other tasks. We learn invariant representations for face recognition from grossly corrupted images, and we learn object recognition classifiers that are invariant to the so-called domain bias.;Extensive experiments using the benchmark datasets publicly available for each of the three tasks, show that learning representations based on subspace decompositions invariant to the sources of noise lead to results comparable or better than the state-of-the-art

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis