Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Web Graph

Slides and an essay on the Web Graph, search engines and how Google calculates Page Rank

Spectra info & resources

Resources and info updates for the Spectra Roadshow. SPECTRA LOGO for use on posters, etc...

Graph Theory and Social Networks Tutorial

For COMP60

Infra red spectra

Spectra taken using the Spectroscopy in a Suitcase spectrometer sponsored by the RSC. Spectra taken during the University of Southampton's School of Chemistry Twilight outreach events 2015.

Speak to me graph.

Se compone de diez actividades destinadas a ayudar a los profesores a desarrollar las capacidades de análisis e interpretación de datos de los alumnos de ciencias. Cada actividad incluye una hoja de preguntas y una hoja de datos, ésta última, disponible en archivos de Excel, para que los estudiantes utilicen las nuevas tecnologías para crear gráficos. Los ejercicios están pensados para el nivel superior de la etapa 2 (key stage 2) del currículo nacional inglés y para la etapa 3, es decir, para primaria y secundaria, y se centran en el contenido de 'Sc2 Life and Living Proceses'.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Testing the influence of small crystals on ice size spectra using Doppler lidar observations

Analysis of the vertical velocity of ice crystals observed with a 1.5micron Doppler lidar from a continuous sample of stratiform ice clouds over 17 months show that the distribution of Doppler velocity varies strongly with temperature, with mean velocities of 0.2m/s at -40C, increasing to 0.6m/s at -10C due to particle growth and broadening of the size spectrum. We examine the likely influence of crystals smaller than 60microns by forward modelling their effect on the area-weighted fall speed, and comparing the results to the lidar observations. The comparison strongly suggests that the concentration of small crystals in most clouds is much lower than measured in-situ by some cloud droplet probes. We argue that the discrepancy is likely due to shattering of large crystals on the probe inlet, and that numerous small particles should not be included in numerical weather and climate model parameterizations.

Rotational spectra induced by vibrations

Mizushima and Venkateswarlu showed in 1953 that certain molecules have the property that excited vibrational states may possess rotational spectra even when the rotational spectrum of the ground vibrational state is forbidden by symmetry. We call such a spectrum a vibrationally induced rotational spectrum, and have made a systematic examination of the point groups which permit such behaviour. We also give formulae for the approximate line frequencies and intensities in these spectra, and discuss some of the problems involved in observing them. The spectra can only arise from degenerate vibrational states, and are of three possible types: i) symmetric top perpendicular spectra, shown by molecules belonging to the point groups Dnh, Dn and Cnh, where n is odd; (ii) symmetric top parallel spectra, shown by molecules belonging to Dnd and S2n, where n is even; and (iii) spherical top spectra, shown by molecules belonging to T or Td. Excited vibrational states of polar molecules of point groups Cnv or Cn, where n is odd, may also possess vibrationally induced perpendicular components of type (i), in addition to their ordinary parallel spectra. In addition to the above limitations on the point groups there are, in general, limitations on the symmetry species of the degenerate vibrational states.

Microwave spectra and centrifugal distortion constants of oxetane

The microwave spectra of oxetane (trimethylene oxide) and its three symmetrically deuterated isotopic species have been observed on a Hewlett-Packard microwave spectrometer from 26.5 to 40 GHz. For the parent species, the β-d2 and the αα′-d4 species, about 300 lines have been assigned for each molecule, and for the d6 species more than 600 lines have been assigned. The assignments range from v = 0 to v = 5 in the puckering vibration; although they are mostly Q transitions, either 3 or 4 R transitions have been observed for each vibrational state. The spectra have been interpreted using an effective rotational hamiltonian for each vibrational state, including five quartic distortion constants according to Watson's formulation, and a variable number of sextic distortion constants; in general, the lines are fitted to about ± 10 kHz. The distortion constants show an anomalous zig-zag dependence on the puckering vibrational quantum number, similar to that first observed for the rotational constants by Gwinn and coworkers. This is interpreted according to a simple modification of the standard theory of centrifugal distortion, involving the double minimum potential function in the puckering coordinate.