Forthcoming events in this series
Abstract available upon request - Ruth Preston @email
Self-renewal and pluripotency of mouse embryonic stem (ES) cells are controlled by a complex transcriptional regulatory network (TRN) which is rich in positive feedback loops. A number of key components of this TRN, including Nanog, show strong temporal expression fluctuations at the single cell level, although the precise molecular basis for this variability remains unknown. In this talk I will discuss recent work which uses a genetic complementation strategy to investigate genome-wide mRNA expression changes during transient periods of Nanog down-regulation. Nanog removal triggers widespread changes in gene expression in ES cells. However, we found that significant early changes in gene expression were reversible upon re-induction of Nanog, indicating that ES cells initially adopt a flexible “primed” state. Nevertheless, these changes rapidly become consolidated irreversible fate decisions in the continued absence of Nanog. Using high-throughput single cell transcriptional profiling we observed that the early molecular changes are both stochastic and reversible at the single cell level. Since positive feedback commonly gives rise to phenotypic variability, we also sought to determine the role of feedback in regulating ES cell heterogeneity and commitment. Analysis of the structure of the ES cell TRN revealed that Nanog acts as a feedback “linchpin”: in its presence positive feedback loops are active and the extended TRN is self-sustaining; while in its absence feedback loops are weakened, the extended TRN is no longer self-sustaining and pluripotency is gradually lost until a critical “point-of-no-return” is reached. Consequently, fluctuations in Nanog expression levels transiently activate different sub-networks in the ES cell TRN, driving transitions between a (Nanog expressing) feedback-rich, robust, self-perpetuating pluripotent state and a (Nanog-diminished), feedback-depleted, differentiation-sensitive state. Taken together, our results indicate that Nanog- dependent feedback loops play a central role in controlling both early fate decisions at the single cell level and cell-cell variability in ES cell populations.
Motivated by industrial and biological applications, the Waves
Group at Manchester has in recent years been interested in
developing methods for obtaining the effective properties of
complex composite materials. As time allows we shall discuss a
number of issues, such as differences between composites
with periodic and aperiodic distributions of inclusions, and
modelling of nonlinear composites.
I discuss models for the planar spreading of a viscous fluid between an elastic lid and an underlying rigid plane. These have application to the growth of magmatic intrusions, as well as to other industrial and biological processes; simple experiments of an inflated blister will be used for motivation. The height of the fluid layer is described by a sixth order non-linear diffusion equation, analogous to the fourth order equation that describes surface tension driven spreading. The dynamics depend sensitively on the conditions at the contact line, where the sheet is lifted from the substrate and where some form of regularization must be applied to the model. I will explore solutions with a pre-wetted film or a constant-pressure fluid lag, for flat and inclined planes, and compare with the analogous surface tension problems.
When a rubber membrane tube is inflated, a localized bulge will initiate when the internal pressure reaches a certain value known as the initiation pressure. As inflation continues, the bulge will grow in diameter until it reaches a maximum size, after which the bulge will spread in both directions. This simple phenomenon has previously been studied both experimentally, numerically, and analytically, but surprisingly it is only recently that the character of the initiation pressure has been fully understood. In this talk, I shall first show how the entire inflation process can be described analytically, and then apply the ideas to the mathematical modelling of aneurysm initiation in human arteries.
It is generally believed that in order to generate waves, a small object (like an insect) moving at the air-water surface must exceed the minimum wave speed (about 23 centimeters per second). We show that this result is only valid for a rectilinear uniform motion, an assumption often overlooked in the literature. In the case of a steady circular motion (a situation of particular importance for the study of whirligig beetles), we demonstrate that no such velocity threshold exists and that even at small velocities a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. The results presented should be important for a better understanding of the propulsion of water-walking insects. For example, it would be very interesting to know if whirligig beetles can take advantage of such spirals for echolocation purposes.
The essential information contained in most large data sets is
small when compared to the size of the data set. That is, the
data can be well approximated using relatively few terms in a
suitable transformation. Compressed sensing and matrix completion
show that this simplicity in the data can be exploited to reduce the
number of measurements. For instance, if a vector of length $N$
can be represented exactly using $k$ terms of a known basis
then $2k\log(N/k)$ measurements is typically sufficient to recover
the vector exactly. This can result in dramatic time savings when
k
The periodic orbits of a discrete dynamical system can be described as
permutations. We derive the composition law for such permutations. When
the composition law is given in matrix form the composition of
different periodic orbits becomes remarkably simple. Composition of
orbits in bifurcation diagrams and decomposition law of composed orbits
follow directly from that matrix representation.
We propose a model to reproduce qualitatively and quantitatively the experimental behavior obtained by the AFM techniques for the titin. Via an energetic based minimization approach we are able to deduce a simple analytical formulations for the description of the mechanical behavior of multidomain proteins, giving a physically base description of the unfolding mechanism. We also point out that our model can be inscribed in the led of the pseudo-elastic variational damage model with internal variable and fracture energy criteria of the continuum mechanics. The proposed model permits simple analytical calculations and
to reproduce hard-device experimental AFM procedures. The proposed model also permits the continuum limit approximation which maybe useful to the development of a three-dimensional multiscale constitutive model for biological tissues.
Ultracold atomic gases have recently proven to be enormously rich
systems from the perspective of a condensed matter physicist. With
the advent of optical lattices, such systems can now realise idealised
model Hamiltonians used to investigate strongly correlated materials.
Conversely, ultracold atomic gases can exhibit quantum phases and
dynamics with no counterpart in the solid state due to their extra
degrees of freedom and unique environments virtually free of
dissipation. In this talk, I will discuss examples of such behaviour
arising from spinor degrees of freedom on which my recent research has
focused. Examples will include bosons with artificially induced
spin-orbit coupling and the non-equilibrium dynamics of spinor
condensates.
In this talk I shall describe two rather different, but not entirely unrelated,
problems involving thin-film flow of a viscous fluid which I have found of interest
and which may have some application to a number of practical situations,
including condensation in heat exchangers and microfluidics.
The first problem,
which is joint work with Adam Leslie and Brian Duffy at the University of Strathclyde,
concerns the steady three-dimensional flow of a thin, slowly varying ring of fluid
on either the outside or the inside of a uniformly rotating large horizontal cylinder.
Specifically, we study ``full-ring'' solutions, corresponding to a ring of continuous,
finite and non-zero thickness that extends all the way around the cylinder.
These full-ring solutions may be thought of as a three-dimensional generalisation of
the ``full-film'' solutions described by Moffatt (1977) for the corresponding two-dimensional problem.
We describe the behaviour of both the critical and non-critical full-ring solutions.
In particular,
we show that, while for most values of the rotation speed and the load the azimuthal velocity is
in the same direction as the rotation of the cylinder, there is a region of parameter space close
to the critical solution for sufficiently small rotation speed in which backflow occurs in a
small region on the upward-moving side of the cylinder.
The second problem,
which is joint work with Phil Trinh and Howard Stone at Princeton University,
concerns a rigid plate moving steadily on the free surface of a thin film of fluid.
Specifically, we study two problems
involving a rigid flat (but not, in general, horizontal) plate:
the pinned problem, in which the upstream end of plate is pinned at a fixed position,
the fluid pressure at the upstream end of the plate takes a prescribed value and there is a free surface downstream of the plate, and
the free problem, in which the plate is freely floating and there are free surfaces both upstream and downstream of the plate.
For both problems, the motion of the fluid and the position of the plate
(and, in particular, its angle of tilt to the horizontal) depend in a non-trivial manner on the
competing effects of the relative motion of the plate and the substrate,
the surface tension of the free surface, and of the viscosity of the fluid,
together with the value of the prescribed pressure in the pinned case.
Specifically, for the pinned problem we show that,
depending on the value of an appropriately defined capillary number and on the value of the
prescribed fluid pressure, there can be either none, one, two or three equilibrium solutions
with non-zero tilt angle.
Furthermore, for the free problem we show that the solutions
with a horizontal plate (i.e.\ zero tilt angle) conjectured by Moriarty and Terrill (1996)
do not, in general, exist, and in fact there is a unique equilibrium solution with,
in general, a non-zero tilt angle for all values of the capillary number.
Finally, if time permits some preliminary results for an elastic plate will be presented.
Part of this work was undertaken while I was a
Visiting Fellow in the Department of Mechanical and Aerospace Engineering
in the School of Engineering and Applied Science at Princeton University, Princeton, USA.
Another part of this work was undertaken while I was a
Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM),
University of Oxford, United Kingdom.
This publication was based on work supported in part by Award No KUK-C1-013-04,
made by King Abdullah University of Science and Technology (KAUST).
Recent years have seen increasing attention to the subtle effects on
intracellular transport caused when multiple molecular motors bind to
a common cargo. We develop and examine a coarse-grained model which
resolves the spatial configuration as well as the thermal fluctuations
of the molecular motors and the cargo. This intermediate model can
accept as inputs either common experimental quantities or the
effective single-motor transport characterizations obtained through
systematic analysis of detailed molecular motor models. Through
stochastic asymptotic reductions, we derive the effective transport
properties of the multiple-motor-cargo complex, and provide analytical
explanations for why a cargo bound to two molecular motors moves more
slowly at low applied forces but more rapidly at high applied forces
than a cargo bound to a single molecular motor. We also discuss how
our theoretical framework can help connect in vitro data with in vivo
behavior.
We study a thin liquid film on a vertical fibre. Without gravity, there
is a Rayleigh-Plateau instability in which surface tension reduces the
surface area of the initially cylindrical film. Spherical drops cannot
form because of the fibre, and instead, the film forms bulges of
roughly twice the initial thickness. Large bulges then grow very slowly
through a ripening mechanism. A small non-dimensional gravity moves the
bulges. They leave behind a thinner film than that in front of them, and
so grow. As they grow into large drops, they move faster and grow
faster. When gravity is stronger, the bulges grow only to finite
amplitude solitary waves, with equal film thickness behind and in front.
We study these solitary waves, and the effect of shear-thinning and
shear-thickening of the fluid. In particular, we will be interested in
solitary waves of large amplitudes, which occur near the boundary
between large and small gravity. Frustratingly, the speed is only
determined at the third term in an asymptotic expansion. The case of
Newtonian fluids requires four terms.
Some striking, and potentially useful, effects in electrokinetics occur for
bipolar membranes: applications are in medical diagnostics amongst other areas.
The purpose of this talk is to describe the experiments, the dominant features observed
and then model the phenomena: This uncovers the physics that control this process.
Time-periodic reverse voltage bias
across a bipolar membrane is shown to exhibit transient hysteresis.
This is due to the incomplete depletion of mobile ions, at the junction
between the membranes, within two adjoining polarized layers; the layer thickness depends on
the applied voltage and the surface charge densities. Experiments
show that the hysteresis consists of an Ohmic linear rise in the
total current with respect to the voltage, followed by a
decay of the current. A limiting current is established for a long
period when all the mobile ions are depleted from the polarized layer.
If the resulting high field within the two polarized layers is
sufficiently large, water dissociation occurs to produce proton and
hydroxyl travelling wave fronts which contribute to another large jump
in the current. We use numerical simulation and asymptotic analysis
to interpret the experimental results and
to estimate the amplitude of the transient hysteresis and the
water-dissociation current.
The use of formal mathematical models in sociology started in the 1940s and attracted mathematicians such as Frank Harary in the 1950s. The idea is to take the rather intuitive ideas described in social theory and express these in formal mathematical terms. Social network analysis is probably the best known of these and it is the area which has caught the imagination of a wider audience and has been the subject of a number of popular books. We shall give a brief over view of the field of social networks and will then look at three examples which have thrown up problems of interest to the mathematical community. We first look at positional analysis techniques and give a formulation that tries to capture the notion of social role by using graph coloration. We look at algebraic structures, properties, characterizations, algorithms and applications including food webs. Our second and related example looks at core-periphery structures in social networks. Our final example relates to what the network community refer to as two-mode data and a general approach to analyzing networks of this form. In all cases we shall look at the mathematics involved and discuss some open problems and areas of research that could benefit from new approaches and insights.
The computational analysis of a mathematical model describing a complex system is often based on the following roadmap: first, an experiment is conceived, in which the measured data are (either directly or indirectly) related to the input data of the model equations; second, such equations are computationally solved to provide iconographic reconstructions of the unknown physical or physiological parameters of the system; third, the reconstructed images are utilized to validate the model or to inspire appropriate improvements. This talk will adopt such framework to investigate three applied problems, respectively in solar physics, neuroscience and physiology. The solar physics problem is concerned with the exploitation of hard X-ray data for the comprehension of energy transport mechanisms in solar flares. The neuroscientific problem is the one to model visual recognition in humans with the help of a magnetocencephalography experiment. Finally, the physiological problem investigates the kinetics of the kidney-bladder system by means of nuclear data.
Complex networks have been used to model almost any
real-world complex systems. An especially important
issue regards how to related their structure and dynamics,
which contributes not only for the better understanding of
such systems, but also to the prediction of important
dynamical properties from specific topological features.
In this talk I revise related research developed recently
in my group. Particularly attention is given to the concept
of accessibility, a new measurement integrating topology
and dynamics, and the relationship between frequency of
visits and node degree in directed modular complex
networks. Analytical results are provided that allow accurate
prediction of correlations between structure and dynamics
in systems underlain by directed diffusion. The methodology
is illustrated with respect to the macaque cortical network.
In this seminar we discuss the gas dynamics of chimneys, solar updraft towers and energy towers. The main issue is to discuss simple fluid dynamic models which still describe the main features of the mentioned applications. We focus first on one dimensional compressible models. Then we apply a small Mach number asymptotics to reduce to complexity and to avoid the known problems
of fully compressible models in the small Mach number regime. In case of the energy tower in addition we have to model the evaporation process.
Finally we obtain a much simpler fluid dynamic model which allows robust and very fast numerical simulations. We discuss the qualitative behaviour and the good agreement with expermental data (in cases such data are available).
The displacement of a liquid by an air finger is a generic two-phase flow that
underpins applications as diverse as microfluidics, thin-film coating, enhanced
oil recovery, and biomechanics of the lungs. I will present two intriguing
examples of such flows where, firstly, oscillations in the shape of propagating
bubbles are induced by a simple change in tube geometry, and secondly, flexible
vessel boundaries suppress viscous fingering instability.
1) A simple change in pore geometry can radically alter the behaviour of a
fluid displacing air finger, indicating that models based on idealized pore
geometries fail to capture key features of complex practical flows. In
particular, partial occlusion of a rectangular cross-section can force a
transition from a steadily-propagating centred finger to a state that exhibits
spatial oscillations via periodic sideways motion of the interface at a fixed
location behind the finger tip. We characterize the dynamics of the
oscillations and show that they arise from a global homoclinic connection
between the stable and unstable manifolds of a steady, symmetry-broken
solution.
2) Growth of complex dendritic fingers at the interface of air and a viscous
fluid in the narrow gap between two parallel plates is an archetypical problem
of pattern formation. We find a surprisingly effective means of suppressing
this instability by replacing one of the plates with an elastic membrane. The
resulting fluid-structure interaction fundamentally alters the interfacial
patterns that develop and considerably delays the onset of fingering. We
analyse the dependence of the instability on the parameters of the system and
present scaling arguments to explain the experimentally observed behaviour.
Feature Selection is a ubiquitous problem in across data mining,
bioinformatics, and pattern recognition, known variously as variable
selection, dimensionality reduction, and others. Methods based on
information theory have tremendously popular over the past decade, with
dozens of 'novel' algorithms, and hundreds of applications published in
domains across the spectrum of science/engineering. In this work, we
asked the question 'what are the implicit underlying statistical
assumptions of feature selection methods based on mutual information?'
The main result I will present is a unifying probabilistic framework for
information theoretic feature selection, bringing almost two decades of
research on heuristic methods under a single theoretical interpretation.
Hollow vortices are vortices whose interior is at rest. They posses vortex sheets on their boundaries and can be viewed as a desingularization of point vortices. We give a brief history of point vortices. We then obtain exact solutions for hollow vortices in linear and nonlinear strain and examine the properties of streets of hollow vortices. The former can be viewed as a canonical example of a hollow vortex in an arbitrary flow, and its stability properties depend. In the latter case, we reexamine the hollow vortex street of Baker, Saffman and Sheffield and examine its stability to arbitrary disturbances, and then investigate the double hollow vortex street. Implications and extensions of this work are discussed.
Nematic liquid crystals (NLCs) are materials that flow like liquids, but have some crystalline features. Their molecules are typically long and thin, and tend to align locally, which imparts some elastic character to the NLC. Moreover at interfaces between the NLC and some other material (such as a rigid silicon substrate, or air) the molecules tend to have a preferred direction (so-called "surface anchoring"). This preferred behaviour at interfaces, coupled with the internal "elasticity", can give rise to complex instabilities in spreading free surface films. This talk will discuss modelling approaches to describe such flows. The models presented are capable of capturing many of the key features observed experimentally, including arrested spreading (with or without instability). Both 2D and 3D spreading scenarios will be considered, and simple ways to model nontrivial surface anchoring patterns, and "defects" within the flows will also be discussed.
In a variety of problems in engineering and applied science, the goal is to design or control a network of dynamical agents so as to achieve some desired asymptotic behaviour. Examples include consensus and rendez-vous problems in robotics, synchronization of generator angles in power grids or coordination of oscillations in bacterial populations. A pressing challenge in all of these problems is to derive appropriate analytical tools to prove convergence towards the target behaviour. Such tools are not only invaluable to guarantee the desired performance, but can also provide important guidelines for the design of decentralized control strategies to steer the collective behaviour of the network of interest in a desired manner. During this talk, a methodology for analysis and design of convergence in networks will be presented which is based on the use of a classical, yet not fully exploited, tool for convergence analysis: contraction theory. As opposed to classical methods for stability analysis, the idea is to look at convergence between trajectories of a system of interest rather that at their asymptotic convergence towards some solution of interest. After introducing the problem, a methodology will be derived based on the use of matrix measures induced by non-Euclidean norms that will be exploited to design strategies to control the collective behaviour of networks of dynamical agents. Representative examples will be used to illustrate the theoretical results.
TALK 1 -- social media for OII:
TITLE: Computational Perspectives on the Structure and Information
Flows in On-Line Networks
ABSTRACT:
With an increasing amount of social interaction taking place in on-line settings, we are accumulating massive amounts of data about phenomena that were once essentially invisible to us: the collective behavior and social interactions of hundreds of millions of people Analyzing this massive data computationally offers enormous potential both to address long-standing scientific questions, and also to harness and inform the design of future social computing applications: What are emerging ideas and trends? How is information being created, how it flows and mutates as it is passed from a node to node like an epidemic?
We discuss how computational perspective can be applied to questions involving structure of online networks and the dynamics of information flows through such networks, including analysis of massive data as well as mathematical models that seek to abstract some of the underlying phenomena.
TALK 2 -- Community detection:
TITLE: Networks, Communities and the Ground-Truth
ABSTRACT: Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities. Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.