Publications

We consider unconstrained randomized optimization of smooth convex objective functions in the gradient-free setting. We analyze Random Pursuit (RP) algorithms with fixed (F-RP) and variable metric (V-RP). The algorithms only use zeroth-order information about the objective function and compute an approximate solution by repeated optimization over randomly chosen one-dimensional subspaces. The distribution of search directions is dictated by the chosen metric. Variable Metric RP uses novel variants of a randomized zeroth-order Hessian approximation scheme recently introduced by Leventhal and Lewis (D. Leventhal and A. S. Lewis., Optimization 60(3), 329--245, 2011). We here present (i) a refined analysis of the expected single step progress of RP algorithms and their global convergence on (strictly) convex functions and (ii) novel convergence bounds for V-RP on strongly convex functions. We also quantify how well the employed metric needs to match the local geometry of the function in order for the RP algorithms to converge with the best possible rate. Our theoretical results are accompanied by numerical experiments, comparing V-RP with the derivative-free schemes CMA-ES, Implicit Filtering, Nelder-Mead, NEWUOA, Pattern-Search and Nesterov's gradient-free algorithms.

The present invention relates to oxopiperazines that mimic helix αB of the C-terminal transactivation domain of HIF1α. Also disclosed are pharmaceutical compositions containing these oxopiperazines and methods of using these oxopiperazines (e.g., to reduce gene transcription, treat or prevent disorders mediated by interaction of HIF1a with CREB-binding protein and/or p300, reduce or prevent angiogenesis in a tissue, induce apoptosis, and decrease cell survival and/or proliferation).

16S ribosomal RNA (rRNA) gene and other environmental sequencing techniques provide snapshots of microbial communities, revealing phylogeny and the abundances of microbial populations across diverse ecosystems. While changes in microbial community structure are demonstrably associated with certain environmental conditions (from metabolic and immunological health in mammals to ecological stability in soils and oceans), identification of underlying mechanisms requires new statistical tools, as these datasets present several technical challenges. First, the abundances of microbial operational taxonomic units (OTUs) from amplicon-based datasets are compositional. Counts are normalized to the total number of counts in the sample. Thus, microbial abundances are not independent, and traditional statistical metrics (e.g., correlation) for the detection of OTU-OTU relationships can lead to spurious results. Secondly, microbial sequencing-based studies typically measure hundreds of OTUs on only tens to hundreds of samples; thus, inference of OTU-OTU association networks is severely under-powered, and additional information (or assumptions) are required for accurate inference. Here, we present SPIEC-EASI (SParse InversE Covariance Estimation for Ecological Association Inference), a statistical method for the inference of microbial ecological networks from amplicon sequencing datasets that addresses both of these issues. SPIEC-EASI combines data transformations developed for compositional data analysis with a graphical model inference framework that assumes the underlying ecological association network is sparse. To reconstruct the network, SPIEC-EASI relies on algorithms for sparse neighborhood and inverse covariance selection. To provide a synthetic benchmark in the absence of an experimentally validated gold-standard network, SPIEC-EASI is accompanied by a set of computational tools to generate OTU count data from a set of diverse underlying network topologies. SPIEC-EASI outperforms state-of-the-art methods to recover edges and network properties on synthetic data under a variety of scenarios. SPIEC-EASI also reproducibly predicts previously unknown microbial associations using data from the American Gut project.

The diagnosis of Parkinson's disease (PD) is usually not established until advanced neurodegeneration leads to clinically detectable symptoms. Previous blood PD transcriptome studies show low concordance, possibly resulting from the use of microarray technology, which has high measurement variation. The Leucine-rich repeat kinase 2 (LRRK2) G2019S mutation predisposes to PD. Using preclinical and clinical studies, we sought to develop a novel statistically motivated transcriptomic-based approach to identify a molecular signature in the blood of Ashkenazi Jewish PD patients, including LRRK2 mutation carriers. Using a digital gene expression platform to quantify 175 messenger RNA (mRNA) markers with low coefficients of variation (CV), we first compared whole-blood transcript levels in mouse models (1) overexpressing wild-type (WT) LRRK2, (2) overexpressing G2019S LRRK2, (3) lacking LRRK2 (knockout), and (4) and in WT controls. We then studied an Ashkenazi Jewish cohort of 34 symptomatic PD patients (both WT LRRK2 and G2019S LRRK2) and 32 asymptomatic controls. The expression profiles distinguished the four mouse groups with different genetic background. In patients, we detected significant differences in blood transcript levels both between individuals differing in LRRK2 genotype and between PD patients and controls. Discriminatory PD markers included genes associated with innate and adaptive immunity and inflammatory disease. Notably, gene expression patterns in levodopa-treated PD patients were significantly closer to those of healthy controls in a dose-dependent manner. We identify whole-blood mRNA signatures correlating with LRRK2 genotype and with PD disease state. This approach may provide insight into pathogenesis and a route to early disease detection.

Tissue and cell-type identity lie at the core of human physiology and disease. Understanding the genetic underpinnings of complex tissues and individual cell lineages is crucial for developing improved diagnostics and therapeutics. We present genome-wide functional interaction networks for 144 human tissues and cell types developed using a data-driven Bayesian methodology that integrates thousands of diverse experiments spanning tissue and disease states. Tissue-specific networks predict lineage-specific responses to perturbation, identify the changing functional roles of genes across tissues and illuminate relationships among diseases. We introduce NetWAS, which combines genes with nominally significant genome-wide association study (GWAS) P values and tissue-specific networks to identify disease-gene associations more accurately than GWAS alone. Our webserver, GIANT, provides an interface to human tissue networks through multi-gene queries, network visualization, analysis tools including NetWAS and downloadable networks. GIANT enables systematic exploration of the landscape of interacting genes that shape specialized cellular functions across more than a hundred human tissues and cell types.

The linear sequence of the genome has been extremely valuable in mapping regulatory elements relative to the genes they control. However, it has become increasingly evident that characterizing the three-dimensional organization of the genome is critical to get a better understanding of long-range regulation. Early studies using fluorescent in-situ hybridization (FISH) revealed that individual chromosomes occupy distinct spaces in the nucleus with minimal intermingling between territories[1]. Recent advances using chromosome conformation capture (3C) techniques have confirmed these findings and further improved the depth at which we can determine the organization of chromosomes and the physical interactions that occur within and between them[2, 3]. Variations of the 3C technique include (i) Hi-C, to capture all pairwise interactions, (ii) 5C, to capture interactions within and between loci of interest and (iii) 4C-Seq, to capture all interactions with a single locus of interest. The choice of technique depends on the biological question being asked and the scale at which this needs to be examined. While Hi-C has been instrumental in characterizing higher-order organization of chromosomes in the nucleus, it lacks the resolution that is required for analysis of specific interactions, such as between enhancers and promoters. This can be achieved with 4C-Seq, which allows interrogation of interactions from a single viewpoint or bait, to the rest of the genome. Several studies have used 4C-Seq to better understand phenomena such as X chromosome inactivation[4], enhancer-promoter interactions[5, 6], organization of antigen receptor loci[7], choice of translocation partners[8, 9] and collinear transcriptional regulation[10]. Here we aim to focus on the current state of the 4C-Seq method and the limitations and challenges of the associated computational analysis.

The present invention relates to oligooxopiperzines for modulating the p53-Mdm2 interaction. Methods of using the oligooxopiperazines are also disclosed.

MOTIVATION:
Leveraging the large compendium of genomic data to predict biomedical pathways and specific mechanisms of protein interactions genome-wide in metazoan organisms has been challenging. In contrast to unicellular organisms, biological and technical variation originating from diverse tissues and cell-lineages is often the largest source of variation in metazoan data compendia. Therefore, a new computational strategy accounting for the tissue heterogeneity in the functional genomic data is needed to accurately translate the vast amount of human genomic data into specific interaction-level hypotheses.

RESULTS:
We developed an integrated, scalable strategy for inferring multiple human gene interaction types that takes advantage of data from diverse tissue and cell-lineage origins. Our approach specifically predicts both the presence of a functional association and also the most likely interaction type among human genes or its protein products on a whole-genome scale. We demonstrate that directly incorporating tissue contextual information improves the accuracy of our predictions, and further, that such genome-wide results can be used to significantly refine regulatory interactions from primary experimental datasets (e.g. ChIP-Seq, mass spectrometry).

AVAILABILITY AND IMPLEMENTATION:
An interactive website hosting all of our interaction predictions is publically available at http://pathwaynet.princeton.edu. Software was implemented using the open-source Sleipnir library, which is available for download at https://bitbucket.org/libsleipnir/libsleipnir.bitbucket.org.

Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. By starting with the SNMF cost function we derive an online algorithm, which can be implemented by a biologically plausible network with local learning rules. We demonstrate that such network performs soft clustering of the data as well as sparse feature discovery. The derived algorithm replicates many known aspects of sensory anatomy and biophysical properties of neurons including unipolar nature of neuronal activity and synaptic weights, local synaptic plasticity rules and the dependence of learning rate on cumulative neuronal activity. Thus, we make a step towards an algorithmic theory of neuronal function, which should facilitate large-scale neural circuit simulations and biologically inspired artificial intelligence.

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.