Seminars archive

Rapid development of next generation sequencing technologies produces a plethora of large-scale epigenome profiling data. Given the quantity of available epigenome datasets, obtaining a clear and comprehensive picture of the underlying regulatory network remains a challenge. The multitude of cell type heterogeneity and temporal changes in the epigenome make it impossible to assay all epigenome events for each type of cell. Computational model shows its advantages in capturing intrinsic correlations among epigenetic features and adaptively predicting epigenome marks in a dynamic scenario. Current progress in machine learning provides opportunities to uncover higher level patterns of epigenome interactions and integrating regulatory signals from different resources. My works aim to utilize public data resources to characterize, predict and understand the epigenome-wide regulatory relationship. The first part of my work is a novel computational model to predict in vivo transcription factor (TF) binding using base-pair resolution methylation data. The model combines cell-type specific methylation patterns and static genomic features, and accurately predicts binding sites of a variety of TFs among diverse cell types. The second part of my work is a computational framework to integrate sequence, gene expression and epigenome data for genome wide TF binding prediction. This extended supervised framework integrates motif features, context-specific gene expression and chromatin accessibility profiles across multiple cell types and scale up the TF prediction task beyond the limits of candidate sites with limited known motifs. The third part of my work is a novel computational strategy for functional annotation of non-coding genomic regions. It takes advantage of the newly emerged, genome-wide and tissue-specific expression quantitative trait loci (eQTL) information to help annotate a set of genomic intervals in terms of transcription regulation. This method builds a bridge connecting genomic intervals with biological pathways and pre-defined biological-meaningful gene sets. Tissue specificity analysis provides additional evidence of the distinct roles of different tissues in the disease mechanisms

SQL (Structural Query Language) and Relational Algebra are two important languages to manipulate relational database. SQL is an international standard language used to express queries on data stored in a database. Relational Algebra is a Mathematical language with operations on sets. SQL queries are first translated to an equivalent expression in Relational Algebra in query processing. The thesis explores the translation from SQL to Relational Algebra to gain a deeper understanding in database systems. The thesis begins with an introduction to the problem (including motivation to working on the translation), the related background knowledge to handle the translation, and follows with the project design. It then discusses the evaluation of the result, reflects on my learning experience from the project, and makes suggestion about further improvement.

Multiphysics and multiscale simulations often need to solve discretized sparse algebraic systems that are highly indefinite, nonsymmetric and extremely ill-conditioned. For such problems, factorization based algorithms are often at the core of the solvers toolchain. Compared to pure iterative methods, the higher computation and communication costs in factorization methods present serious hurdles to utilizing extreme-scale hardware. I will present several research vignettes aimed at reducing those costs. By incorporating data-sparse low-rank structures, such as hierarchical matrix algebra, we can obtain lower arithmetic complexity as well as robust preconditioner. By replicating small amount of data in sparse factorization, we can avoid communication with provablly lower communication complexity. By means of asynchronous, custermized broadcast/reduction, we can reduce the dominating latency cost in sparse triangular solution. The effectiveness of these techniques will be demonstrated with our open source software STRUMPACK and SuperLU. <br> <br> Bio: <br> Sherry Li is a Senior Scientist at Lawrence Berkeley National Laboratory. She has worked on diverse problems in high performance scientific computations, including parallel computing, sparse matrix computations, high precision arithmetic, and combinatorial scientific computing She has (co)authored over 100 publications. She is the lead developer of SuperLU sparse direct solver library, and has contributed to several other widely-used mathematical libraries, including ARPREC, LAPACK, STRUMPACK, and XBLAS. She received Ph.D. in Computer Science from UC Berkeley in 1996. She is a SIAM Fellow and an ACM Senior Member.

In recent years, improvements in medical imaging and image-reconstruction algorithms have led to increased interest in the use of Computational Fluid Dynamics (CFD) as a clinical tool in hemodynamics. While such methods have long been employed in the design of medical devices and in basic medical research, many of the techniques commonly employed in these contexts are not ideal in the clinical setting. In particular, in clinical settings typically one is faced with more demanding turnaround times for simulations, less powerful computational resources, and noisy, incomplete, or missing data.\\ \\ In this thesis, we discuss these challenges and introduce CFD methods which are more practical for direct clinical application. Frequently in these settings, the variable of interest is the temporal average of some time-periodic quantity, such as wall shear-stress, over a cardiac cycle. In these cases, the standard procedure is to perform an unsteady simulation over several cardiac cycles and then to take the time average of the last one. Here, we propose to instead surrogate the unsteady time-averaged solution with the solution of a steady-state problem, allowing us to compute it directly. This approach, if properly applied, can dramatically lower computational cost as we show here; however in many respects the steady problem is arguably more difficult numerically than its unsteady counterpart.\\ \\ We will address these difficulties and propose effective workarounds. In particular, we aim to develop methods for steady solvers that are \textit{efficient}, \textit{stable}, and \textit{reliable}. Roughly speaking, this work is divided into three parts, with each part focusing on one of these aspects. Concerning efficiency, we extend the inexact algebraic factorization approach popular for the unsteady problem into the steady setting. We will address the issue of stability by taking inspiration from nonlinear filtering techniques used in turbulence modeling to develop stabilization techniques for the steady problem. Finally, we will develop and validate methods for assigning boundary conditions in data-deficient settings while maintaining reliability. Throughout each section, we will provide both theoretical and numerical justification for our methods.

Varieties that fail to have rational points despite having local points for each prime are said to fail the Hasse principle. A systematic tool accounting for these failures is called the Brauer-Manin obstruction, which uses [subsets of] the Brauer group, Br X, to preclude the existence of rational points on a variety X. After fixing numerical invariants such as dimension, it is natural to ask which birational classes of varieties fail the Hasse principle, and moreover whether the Brauer group (or certain distinguished subsets) always explains this failure. In this talk, we will focus on K3 surfaces (e.g. a double cover of the plane branched along a smooth sextic curve) which are relatively simple surfaces in terms of geometric complexity, but whose arithmetic is more mysterious. For example, in 2014, Skorobogatov asked whether any odd torsion in the Brauer group of a K3 surface could obstruct the Hasse principle. We answer this question in the affirmative; via a purely geometric approach, we construct a 3-torsion transcendental Brauer class on a degree 2 K3 surface which obstructs the Hasse principle. Moreover, we do this without needing to explicitly write down a central simple algebra. This is joint work with Tony Varilly-Alvarado.

In this talk we prove theorems at the intersection of the additive and multiplicative branches of number theory, bringing together ideas from partition theory, $q$-series, algebra, modular forms and analytic number theory. We present a natural multiplicative theory of integer partitions (which are usually considered in terms of addition), and explore new classes of partition-theoretic zeta functions and Dirichlet series --- as well as ``Eulerian'' $q$-hypergeometric series --- enjoying many interesting relations. We find a number of theorems of classical number theory and analysis arise as particular cases of extremely general combinatorial structure laws.\\ \\ Among our applications, we prove explicit formulas for the coefficients of the $q$-bracket of Bloch-Okounkov, a partition-theoretic operator from statistical physics related to quasi-modular forms; we prove partition formulas for arithmetic densities of certain subsets of the integers, giving $q$-series formulas to evaluate the Riemann zeta function; we study $q$-hypergeometric series related to quantum modular forms and the ``strange'' function of Kontsevich; and we show how Ramanujan's odd-order mock theta functions (and, more generally, the universal mock theta function $g_3$ of Gordon-McIntosh) arise from the reciprocal of the Jacobi triple product via the $q$-bracket operator, connecting also to unimodal sequences in combinatorics and quantum modular-like phenomena.

In 1988, Mathur, Mukhi, and Sen studied rational conformal field theories in terms of differential equations satisfied by their characters. These differential equations are modular invariant, and the solutions they obtain for order 2 equations have relationships with certain Lie algebras. In fact, the Lie algebras in the Deligne Exceptional series appear, whose study is motivated by uniformities which appear in their representation theory. This thesis studies the Deligne Exceptional Series from these two perspectives, and gives a sequence of finite groups which has analogies with the Deligne series.

Singular value decompositions are a particularly attractive matrix factorization for ill-posed problems because singular value magnitudes reveal information about the relative importance of data in the matrix. However, computing a singular value decomposition is typically computationally infeasible for large problems, as the cost for traditional methods, such as Lanczos bidiagonalization-based approaches and randomized methods, scales linearly with the number of entries in the matrix times the number of singular values computed. In this work we present two new algorithms and one new hybrid approach for computing the singular value decomposition of matrices cheaply approximable as an ordered Kronecker summation decomposition. Unlike previous work using ordered Kronecker summation decompositions, the factorizations these methods produce are more accurate for certain classes of matrices and have nonnegative singular values. The three proposed methods are also faster, with lower computational and spatial complexity, although also lower accuracy, than traditional methods. Our Kronecker-based methods therefore enable singular value decomposition approximations on larger matrices than traditional methods, while providing more accurate results in many cases than previous Kronecker-based singular value decompositions. We demonstrate the efficacy of these methods on a variety of image deconvolution problems for which the image is modeled as a regular grid of data.

Starting in 2009, Harbater and Hartmann introduced a new patching setup for semi-global fields, establishing a patching framework for vector spaces, central simple algebras, quadratic forms and other algebraic structures. In subsequent work with Krashen, the patching framework was refined and extended to torsors and certain Galois cohomology groups. After describing this framework, we will discuss an extension of the patching equivalence to bitorsors and gerbes. Building up on these results, we then proceed to derive a characterisation of a local- global principle for gerbes and bitorsors in terms of factorization. These results can be expressed in the form of a Mayer-Vietoris sequence in non-abelian hypercohomology with values in the crossed-module $G->Aut(G)$. After proving the local-global principle for certain bitorsors and gerbes using the characterization mentioned above, we conclude with an application on rational points for homogeneous spaces.

This dissertation is about arithmetic information encoded by analytic characteristics (such as Fourier coefficients) of classical modular forms and a real-analytic generalization of modular forms called harmonic Maass forms. For example, I use the theory of harmonic Maass forms to extend and refine a theorem of Wiles on class number divisibility. I also prove asymptotic bounds for Rankin-Selberg shifted convolution L-functions in shift aspect. In partition theory, I use the circle method to describe the expected distribution of parts of integer partitions over residue classes, and I use effective estimates for partition functions to obtain simple formulas for functions arising in group theory.