Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose (H-R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D', is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

Topological solitons in the CPN model

We investigate the solitons in the CPN supercript stop model in terms of the decomposition of gauge potential. Based on the phi-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component. Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored also.

A quasi-synoptic interpretation of water mass distribution and circulation in the western North Pacific II: Circulation

Using the data of conductivity-temperature-depth (CTD) intensive observations conducted during Oct.-Nov. 2005, this study provides the first three-dimension quasi-synoptic description of the circulation in the western North Pacific. Several novel phenomena are revealed, especially in the deep ocean where earlier observations were very sparse. During the observations, the North Equatorial Current (NEC) splits at about 12A degrees N near the sea surface. This bifurcation shifts northward with depth, reaching about 20A degrees N at 1 000 m, and then remains nearly unchanged to as deep as 2 000 m. The Luzon Undercurrent (LUC), emerging below the Kuroshio from about 21A degrees N, intensifies southward, with its upper boundary surfacing around 12A degrees N. From there, part of the LUC separates from the coast, while the rest continues southward to join the Mindanao Current (MC). The MC extends to 2 000 m near the coast, and appears to be closely related to the subsurface cyclonic eddies which overlap low-salinity water from the North Pacific. The Mindanao Undercurrent (MUC), carrying waters from the South Pacific, shifts eastward upon approaching the Mindanao coast and eventually becomes part of the eastward undercurrent between 10A degrees N and 12A degrees N at 130A degrees E. In the upper 2 000 dbar, the total westward transport across 130A degrees E between 7.5A degrees N and 18A degrees N reaches 65.4 Sv (1 Sv = 10(-6) m(3)s(-1)), the northward transport across 18A degrees N from Luzon coast to 130A degrees E is up to 35.0 Sv, and the southward transport across 7.5A degrees N from Mindanao coast to 130A degrees E is 27.9 Sv.

Origin of mitochondrial DNA diversity of domestic yaks

Background: The domestication of plants and animals was extremely important anthropologically. Previous studies have revealed a general tendency for populations of livestock species to include deeply divergent maternal lineages, indicating that they were domesticated in multiple, independent events from genetically discrete wild populations. However, in water buffalo, there are suggestions that a similar deep maternal bifurcation may have originated from a single population. These hypotheses have rarely been rigorously tested because of a lack of sufficient wild samples. To investigate the origin of the domestic yak (Poephagus grunnies), we analyzed 637 bp of maternal inherited mtDNA from 13 wild yaks (including eight wild yaks from a small population in west Qinghai) and 250 domesticated yaks from major herding regions.Results: The domestic yak populations had two deeply divergent phylogenetic groups with a divergence time of > 100,000 yrs BP. We here show that haplotypes clustering with two deeply divergent maternal lineages in domesticated yaks occur in a single, small, wild population. This finding suggests that all domestic yaks are derived from a single wild gene pool. However, there is no clear correlation of the mtDNA phylogenetic clades and the 10 morphological types of sampled yaks indicating that the latter diversified recently. Relatively high diversity was found in Qinghai and Tibet around the current wild distribution, in accordance with previous suggestions that the earliest domestications occurred in this region. Conventional molecular clock estimation led to an unrealistic early dating of the start of the domestication. However, Bayesian estimation of the coalescence time allowing a relaxation of the mutation rateConclusion: The information gathered here and the previous studies of other animals show that the demographic histories of domestication of livestock species were highly diverse despite the common general feature of deeply divergent maternal lineages. The results further suggest that domestication of local wild prey ungulate animals was a common occurrence during the development of human civilization following the postglacial colonization in different locations of the world, including the high, arid Qinghai-Tibetan Plateau.

降雨触发滑坡的非线性模型与斜坡演化的混沌效应

This paper analyzes landsliding process by nonlinear theories, especially the influence mechanism of external factors (such as rainfall and groundwater) on slope evolution. The author investigates landslide as a consequence of the catastrophic slide of initially stationary or creeping slope triggered by a small perturbation. A fully catastrophe analysis is done for all possible scenarios when a continuous change is imposed to the control parameters. As the slip surface continues and erosion due to rainfall occurs, control parameters of the slip surface may evolve such that a previously stable slope may become unstable (e.g. catastrophe occurs), when a small perturbation is imposed. Thus the present analysis offers a plausible explanation to why slope failure occurs at a particular rainfall, which is not the largest in the history of the slope. It is found, by analysis on the nonlinear dynamical model of the evolution process of slope built, that the relationship between the action of external environment factors and the response of the slope system is complicatedly nonlinear. When the nonlinear action of slope itself is equivalent to the acting ability of external environment, the chaotic phenomenon appears in the evolution process of slope, and its route leading to chaos is realized with bifurcation of period-doublings. On the basis of displacement time series of the slope, a nonlinear dynamic model is set up by improved Backus generalized linear inversion theory in this paper. Due to the equivalence between autonomous gradient system and catastrophe model, a standard cusp catastrophe model can be obtained through variable substitution. The method is applied to displacement data of Huangci landslide and Wolongsi landslide, to show how slopes evolve before landsliding. There is convincing statistical evidence to believe that the nonlinear dynamic model can make satisfied prediction results. Most important of all, we find that there is a sudden fall of D, which indicates the occurrence of catastrophe (when D=0).

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.

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.

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.