Ovidiu Lipan

Extensive and divergent circadian gene expression in liver and heart

Many mammalian peripheral tissues have circadian clocks; endogenous oscillators that generate transcriptional rhythms thought to be important for the daily timing of physiological processes. The extent of circadian gene regulation in peripheral tissues is unclear, and to what degree circadian regulation in different tissues involves common or specialized pathways is unknown. Here we report a comparative analysis of circadian gene expression in vivo in mouse liver and heart using oligonucleotide arrays representing 12,488 genes. We find that peripheral circadian gene regulation is extensive (≥8–10% of the genes expressed in each tissue), that the distributions of circadian phases in the two tissues are markedly different, and that very few genes show circadian regulation in both tissues. This specificity of circadian regulation cannot be accounted for by tissue-specific gene expression. Despite this divergence, the clock-regulated genes in liver and heart participate in overlapping, extremely diverse processes. A core set of 37 genes with similar circadian regulation in both tissues includes candidates for new clock genes and output genes, and it contains genes responsive to circulating factors with circadian or diurnal rhythms.

Quantum Integrable Models and Discrete Classical Hirota Equations

Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota’s bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice with open boundaries. The standard objects of quantum integrable models are identified with elements of classical nonlinear integrable difference equation. In particular, elliptic solutions of Hirota’s equation give complete set of eigenvalues of the quantum transfer matrices. Eigenvalues of Baxter’s Q-operator are solutions to the auxiliary linear problems for classical Hirota’s equation. The elliptic solutions relevant to Bethe ansatz are studied. The nested Bethe ansatz equations for Ak−1-type models appear as discrete time equations of motions for zeros of classical τ -functions and Baker-Akhiezer functions. Determinant representations of the general solution to bilinear discrete Hirota’s equation and a new determinant formula for eigenvalues of the quantum transfer matrices are obtained. Department of Mathematics of Columbia University and Landau Institute for Theoretical Physics Kosygina str. 2, 117940 Moscow, Russia James Franck Institute of the University of Chicago, 5640 S.Ellis Avenue, Chicago, IL 60637, USA James Franck Institute and and Enrico Fermi Institute of the University of Chicago, 5640 S.Ellis Avenue, Chicago, IL 60637, USA and Landau Institute for Theoretical Physics Joint Institute of Chemical Physics, Kosygina str. 4, 117334, Moscow, Russia and ITEP, 117259, Moscow, Russia 1

GoSurfer: a graphical interactive tool for comparative analysis of large gene sets in Gene Ontology space.

UNLABELLED The analysis of complex patterns of gene regulation is central to understanding the biology of cells, tissues and organisms. Patterns of gene regulation pertaining to specific biological processes can be revealed by a variety of experimental strategies, particularly microarrays and other highly parallel methods, which generate large datasets linking many genes. Although methods for detecting gene expression have improved substantially in recent years, understanding the physiological implications of complex patterns in gene expression data is a major challenge. This article presents GoSurfer, an easy-to-use graphical exploration tool with built-in statistical features that allow a rapid assessment of the biological functions represented in large gene sets. GoSurfer takes one or two list(s) of gene identifiers (Affymetrix probe set ID) as input and retrieves all the Gene Ontology (GO) terms associated with the input genes. GoSurfer visualises these GO terms in a hierarchical tree format. With GoSurfer, users can perform statistical tests to search for the GO terms that are enriched in the annotations of the input genes. These GO terms can be highlighted on the GO tree. Users can manipulate the GO tree in various ways and interactively query the genes associated with any GO term. The user-generated graphics can be saved as graphics files, and all the GO information related to the input genes can be exported as text files. AVAILABILITY GoSurfer is a Windows-based program freely available for noncommercial use and can be downloaded at http://www.gosurfer.org. Datasets used to construct the trees shown in the figures in this article are available at http://www.gosurfer.org/download/GoSurfer.zip.

Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations

In spite of the diversity of solvable models of quantum field theory and the vast variety of methods, the final results display dramatic unification: the spectrum of an integrable theory with a local interaction is given by a sum of elementary energies

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

E = \sum\limits_i {\varepsilon \left( {{u_i}} \right)}

Fusion Rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds

(1.1) where u i obey a system of algebraic or transcendental equations known as Bethe equations [1], [2]. The major ingredients of Bethe equations are determined by the algebraic structure of the problem. A typical example of a system of Bethe equations (related to A i -type models with elliptic R-matrix) is

Optimal discovery of a stochastic genetic network

{e^{ - 4\eta \nu }}\frac{{\phi \left( {{u_j}} \right)}}{{\phi \left( {{u_j} - 2} \right)}} = - \mathop \Pi \limits_k \frac{{\sigma \left( {\eta \left( {{u_j} - {u_k} + 2} \right)} \right)}}{{\sigma \left( {\eta \left( {{u_j} - {u_k} - 2} \right)} \right)}}