Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems.

The topological behaviour of 3D null points in the Sun's corona

Brown D. S. and Priest E. R. 2001, The topological behaviour of 3D null points in the Sun's corona, Astronomy and Astrophysics, 367, 339-346

A Topological Analysis of the Magnetic Breakout Model for an Eruptive Solar Flare

Maclean, R., Beveridge, C., Longcope, D.W., Brown, D.S. and Priest, E.R., 2005, A topological analysis of the magnetic breakout model for an eruptive solar flare, Proc. Roy. Soc., 461, 2099-2120. Sponsorship: PPARC/STFC

Centres and limit cycles for an extended Kukles system

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Centres and limit cycles for an extended Kukles system', Electronic Journal of Differential Equations, Vol. 2007(2007), No. 119, pp. 1-23.

A Neural Pattern Generator that Exhibits Arousal-Dependant Human Gait Transitions

A neural pattern generator based upon a non-linear cooperative-competitive feedback neural network is presented. It can generate the two standard human gaits: the walk and the run. A scalar arousal or GO signal causes a bifurcation from one gait to the next. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The model simulates the walk and the run via qualitatively different waveform shapes. The fraction of cycle that activity is above threshold distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Two closely coupled lasers, dynamics & applications

The dynamics of two mutually coupled identical single-mode semi-conductor lasers are theoretically investigated. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities whilst at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable two-colour states, where both single-mode lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. For low coupling but possibly large separation, the frequency of the relaxation oscillations of the freerunning lasers defines the dynamics. Chaotic and quasi-periodic states are identified and shown to be stable. For weak coupling undamped relaxation oscillations dominate where each laser is locked to three or more odd number of colours spaced by the relaxation oscillation frequency. It is shown that the instabilities that lead to these states are directly connected to the two colour mechanism where the change in the number of optical colours due to a change in the plane of oscillation. At initial coupling, in-phase and anti-phase one colour states are shown to emerge from “on” uncoupled lasers using a perturbation method. Similarly symmetry-broken one-colour states come from considering one free-running laser initially “on” and the other laser initially “off”. The mechanism that leads to a bi-stability between in-phase and anti-phase one-colour states is understood. Due to an equivariant phase space symmetry of being able to exchange the identical lasers, a symmetric and symmetry-broken variant of all states mentioned above exists and is shown to be stable. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour, symmetric and symmetry-broken two-colour, symmetric and symmetry-broken undamped relaxation oscillations, symmetric and symmetry-broken quasi-periodic, and symmetric and symmetry-broken chaotic states. As symmetry-broken states always exist in pairs, they naturally give rise to bi-stability. Several of these states show multistabilities between symmetric and symmetry-broken variants and among states. Three memory elements on the basis of bi-stabilities in one and two colour states for two coupled single-mode lasers are proposed. The switching performance of selected designs of optical memory elements is studied numerically.

Vascular structures for volumetric cooling and mechanical strength

When solid material is removed in order to create flow channels in a load carrying structure, the strength of the structure decreases. On the other hand, a structure with channels is lighter and easier to transport as part of a vehicle. Here, we show that this trade off can be used for benefit, to design a vascular mechanical structure. When the total amount of solid is fixed and the sizes, shapes, and positions of the channels can vary, it is possible to morph the flow architecture such that it endows the mechanical structure with maximum strength. The result is a multifunctional structure that offers not only mechanical strength but also new capabilities necessary for volumetric functionalities such as self-healing and self-cooling. We illustrate the generation of such designs for strength and fluid flow for several classes of vasculatures: parallel channels, trees with one, two, and three bifurcation levels. The flow regime in every channel is laminar and fully developed. In each case, we found that it is possible to select not only the channel dimensions but also their positions such that the entire structure offers more strength and less flow resistance when the total volume (or weight) and the total channel volume are fixed. We show that the minimized peak stress is smaller when the channel volume (φ) is smaller and the vasculature is more complex, i.e., with more levels of bifurcation. Diminishing returns are reached in both directions, decreasing φ and increasing complexity. For example, when φ=0.02 the minimized peak stress of a design with one bifurcation level is only 0.2% greater than the peak stress in the optimized vascular design with two levels of bifurcation. © 2010 American Institute of Physics.

High-field FMRI reveals brain activation patterns underlying saccade execution in the human superior colliculus.

BACKGROUND: The superior colliculus (SC) has been shown to play a crucial role in the initiation and coordination of eye- and head-movements. The knowledge about the function of this structure is mainly based on single-unit recordings in animals with relatively few neuroimaging studies investigating eye-movement related brain activity in humans. METHODOLOGY/PRINCIPAL FINDINGS: The present study employed high-field (7 Tesla) functional magnetic resonance imaging (fMRI) to investigate SC responses during endogenously cued saccades in humans. In response to centrally presented instructional cues, subjects either performed saccades away from (centrifugal) or towards (centripetal) the center of straight gaze or maintained fixation at the center position. Compared to central fixation, the execution of saccades elicited hemodynamic activity within a network of cortical and subcortical areas that included the SC, lateral geniculate nucleus (LGN), occipital cortex, striatum, and the pulvinar. CONCLUSIONS/SIGNIFICANCE: Activity in the SC was enhanced contralateral to the direction of the saccade (i.e., greater activity in the right as compared to left SC during leftward saccades and vice versa) during both centrifugal and centripetal saccades, thereby demonstrating that the contralateral predominance for saccade execution that has been shown to exist in animals is also present in the human SC. In addition, centrifugal saccades elicited greater activity in the SC than did centripetal saccades, while also being accompanied by an enhanced deactivation within the prefrontal default-mode network. This pattern of brain activity might reflect the reduced processing effort required to move the eyes toward as compared to away from the center of straight gaze, a position that might serve as a spatial baseline in which the retinotopic and craniotopic reference frames are aligned.

Metabolic programming and PDHK1 control CD4+ T cell subsets and inflammation.

Activation of CD4+ T cells results in rapid proliferation and differentiation into effector and regulatory subsets. CD4+ effector T cell (Teff) (Th1 and Th17) and Treg subsets are metabolically distinct, yet the specific metabolic differences that modify T cell populations are uncertain. Here, we evaluated CD4+ T cell populations in murine models and determined that inflammatory Teffs maintain high expression of glycolytic genes and rely on high glycolytic rates, while Tregs are oxidative and require mitochondrial electron transport to proliferate, differentiate, and survive. Metabolic profiling revealed that pyruvate dehydrogenase (PDH) is a key bifurcation point between T cell glycolytic and oxidative metabolism. PDH function is inhibited by PDH kinases (PDHKs). PDHK1 was expressed in Th17 cells, but not Th1 cells, and at low levels in Tregs, and inhibition or knockdown of PDHK1 selectively suppressed Th17 cells and increased Tregs. This alteration in the CD4+ T cell populations was mediated in part through ROS, as N-acetyl cysteine (NAC) treatment restored Th17 cell generation. Moreover, inhibition of PDHK1 modulated immunity and protected animals against experimental autoimmune encephalomyelitis, decreasing Th17 cells and increasing Tregs. Together, these data show that CD4+ subsets utilize and require distinct metabolic programs that can be targeted to control specific T cell populations in autoimmune and inflammatory diseases.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

Challenges in modelling biofluids in microchannels

This paper presents the challenges encountered in modelling biofluids in microchannels. In particular blood separation implemented in a T-microchannel device is analysed. Microfluids behave different from the counterparts in the microscale and a different approach has been adopted here to model them, which emphasize the roles of viscous forces, high shear rate performance and particle interaction in microscope. A T-microchannel design is numerically analysed by means of computational fluid dynamics (CFD) to investigate the effectiveness of blood separation based on the bifurcation law and other bio-physical effects. The simulation shows that the device can separate blood cells from plasma.

Integrated biomedical device for blood preparation

The separation of red blood cells from plasma flowing in microchannels is possible by bio-physical effects such as an axial migration effect and Zweifach-Fung bifurcation law. In the present study, subchannels are placed alongside a main channel to collect cells and plasma separately. The addition of a constriction in the main microchannel creates a local high shear force region, forcing the cells to migrate and concentrate towards the centre of the channel. The resulting lab-on-a-chip was manufactured using biocompatible materials. Purity efficiency was measured for mussel and human blood suspensions as different parameters including flow rate and geometries of parent and daughter channels were varied.

Parametrical modeling and design optimization of blood plasma separation device with microchannel mechanism

This paper presents an analysis of biofluid behavior in a T-shaped microchannel device and a design optimization for improved biofluid performance in terms of particle liquid separation. The biofluid is modeled with single phase shear rate non-Newtonian flow with blood property. The separation of red blood cell from plasma is evident based on biofluid distribution in the microchannels against various relevant effects and findings, including Zweifach-Fung bifurcation law, Fahraeus effect, Fahraeus-Lindqvist effect and cell free phenomenon. The modeling with the initial device shows that this T-microchannel device can separate red blood cell from plasma but the separation efficiency among different bifurcations varies largely. In accordance with the imbalanced performance, a design optimization is conducted. This includes implementing a series of simulations to investigate the effect of the lengths of the main and branch channels to biofluid behavior and searching an improved design with optimal separation performance. It is found that changing relative lengths of branch channels is effective to both uniformity of flow rate ratio among bifurcations and reduction of difference of the flow velocities between the branch channels, whereas extending the length of the main channel from bifurcation region is only effective for uniformity of flow rate ratio.

Effect of fluid dynamics and device mechanism on biofluid behaviour in microchannel systems: modelling biofluids in a microchannel biochip separator

Biofluid behaviour in microchannel systems is investigated in this paper through the modelling of a microfluidic biochip developed for the separation of blood plasma. Based on particular assumptions, the effects of some mechanical features of the microchannels on behaviour of the biofluid are explored. These include microchannel, constriction, bending channel, bifurcation as well as channel length ratio between the main and side channels. The key characteristics and effects of the microfluidic dynamics are discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. The effects include the Fahraeus and Fahraeus-Lindqvist effects, the Zweifach-Fung bifurcation law, the cell-free layer phenomenon. The characteristics of the microfluid dynamics include the properties of the laminar flow as well as particle lateral or spinning trajectories. In this paper the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviours to investigate the effect of the viscosity on flow and separation efficiency. It is found that, for a flow rate controlled Newtonian flow system, viscosity and outlet pressure have little effect on velocity distribution. When the fluid is assumed to be Non-Newtonian more fluid is separated than observed in the Newtonian case, leading to reduction of the flow rate ratio between the main and side channels as well as the system pressure as a whole.