Ward identities in N=1\mathcal{N}=1 supersymmetric SU(3) Yang-Mills theory on the lattice

The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e.\ Poincar{\'e} invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills theory causes an additional soft breaking of supersymmetry. We employ the lattice form of SUSY Ward identities, imposing that their continuum form would be recovered when removing the lattice regulator, to obtain the critical hopping parameter where broken symmetries can be recovered.Comment: Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017

Inferring Dynamic Signatures of Microbes in Complex Host Ecosystems

The human gut microbiota comprise a complex and dynamic ecosystem that profoundly affects host development and physiology. Standard approaches for analyzing time-series data of the microbiota involve computation of measures of ecological community diversity at each time-point, or measures of dissimilarity between pairs of time-points. Although these approaches, which treat data as static snapshots of microbial communities, can identify shifts in overall community structure, they fail to capture the dynamic properties of individual members of the microbiota and their contributions to the underlying time-varying behavior of host ecosystems. To address the limitations of current methods, we present a computational framework that uses continuous-time dynamical models coupled with Bayesian dimensionality adaptation methods to identify time-dependent signatures of individual microbial taxa within a host as well as across multiple hosts. We apply our framework to a publicly available dataset of 16S rRNA gene sequences from stool samples collected over ten months from multiple human subjects, each of whom received repeated courses of oral antibiotics. Using new diversity measures enabled by our framework, we discover groups of both phylogenetically close and distant bacterial taxa that exhibit consensus responses to antibiotic exposure across multiple human subjects. These consensus responses reveal a timeline for equilibration of sub-communities of micro-organisms with distinct physiologies, yielding insights into the successive changes that occur in microbial populations in the human gut after antibiotic treatments. Additionally, our framework leverages microbial signatures shared among human subjects to automatically design optimal experiments to interrogate dynamic properties of the microbiota in new studies. Overall, our approach provides a powerful, general-purpose framework for understanding the dynamic behaviors of complex microbial ecosystems, which we believe will prove instrumental for future studies in this field

Scalable learning of interpretable rules for the dynamic microbiome domain [preprint]

The microbiome, which is inherently dynamic, plays essential roles in human physiology and its disruption has been implicated in numerous human diseases. Linking dynamic changes in the microbiome to the status of the human host is an important problem, which is complicated by limitations and complexities of the data. Model interpretability is key in the microbiome field, as practitioners seek to derive testable biological hypotheses from data or develop diagnostic tests that can be understood by clinicians. Interpretable structure must take into account domainspecific information key to biologists and clinicians including evolutionary relationships (phylogeny) and dynamic behavior of the microbiome. A Bayesian model was previously developed in the field, which uses Markov Chain Monte Carlo inference to learn human interpretable rules for classifying the status of the human host based on microbiome time-series data, but that approach is not scalable to increasingly large microbiome datasets being produced. We present a new fully-differentiable model that also learns human-interpretable rules for the same classification task, but in an end-to-end gradient-descent based framework. We validate the performance of our model on human microbiome data sets and demonstrate our approach has similar predictive performance to the fully Bayesian method, while running orders-of-magnitude faster and moreover learning a larger set of rules, thus providing additional biological insight into the effects of diet and environment on the microbiome

Improved results for the mass spectrum of N=1 supersymmetric SU(3) Yang-Mills theory

This talk summarizes the results of the DESY-M\"unster collaboration for $\mathcal{N}=1$ supersymmetric Yang-Mills theory with the gauge group SU(3). It is an updated status report with respect to our preliminary data presented at the last conference. In order to control the lattice artefacts we have now considered a clover improved fermion action and different values of the gauge coupling.Comment: Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017

Supermultiplets in N=1 SUSY SU(2) Yang-Mills Theory

We study $\mathcal{N}=1$ supersymmetric Yang-Mills theory (SYM) on the lattice. The non-perturbative nature of supersymmetric field theories is still largely unknown. Similarly to QCD, SYM is confining and contains strongly bound states. Applying the variational method together with different smearing techniques we extract masses of the lightest bound states such as gluino-glue, glueball and mesonic states. As these states should form supermultiplets, this study allows to check whether SYM remains supersymmetric also on the quantum level.Comment: Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017

Computational discovery of gene modules, regulatory networks and expression programs

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2007.Includes bibliographical references (p. 163-181).High-throughput molecular data are revolutionizing biology by providing massive amounts of information about gene expression and regulation. Such information is applicable both to furthering our understanding of fundamental biology and to developing new diagnostic and treatment approaches for diseases. However, novel mathematical methods are needed for extracting biological knowledge from high-dimensional, complex and noisy data sources. In this thesis, I develop and apply three novel computational approaches for this task. The common theme of these approaches is that they seek to discover meaningful groups of genes, which confer robustness to noise and compress complex information into interpretable models. I first present the GRAM algorithm, which fuses information from genome-wide expression and in vivo transcription factor-DNA binding data to discover regulatory networks of gene modules. I use the GRAM algorithm to discover regulatory networks in Saccharomyces cerevisiae, including rich media, rapamycin, and cell-cycle module networks. I use functional annotation databases, independent biological experiments and DNA-motif information to validate the discovered networks, and to show that they yield new biological insights. Second, I present GeneProgram, a framework based on Hierarchical Dirichlet Processes, which uses large compendia of mammalian expression data to simultaneously organize genes into overlapping programs and tissues into groups to produce maps of expression programs. I demonstrate that GeneProgram outperforms several popular analysis methods, and using mouse and human expression data, show that it automatically constructs a comprehensive, body-wide map of inter-species expression programs.(cont.) Finally, I present an extension of GeneProgram that models temporal dynamics. I apply the algorithm to a compendium of short time-series gene expression experiments in which human cells were exposed to various infectious agents. I show that discovered expression programs exhibit temporal pattern usage differences corresponding to classes of host cells and infectious agents, and describe several programs that implicate surprising signaling pathways and receptor types in human responses to infection.by Georg Kurt Gerber.Ph.D