A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Three-dimensional kinetic simulations of active suspensions: effect of chemotaxis and steric interaction

In this work, the effects of chemotaxis and steric interactions in active suspensions are analyzed by extending the kinetic model proposed by Saintillan and Shelley [1, 2]. In this model, a conservation equation for the active particle configuration is coupled to the Stokes equation for the flow arising from the force dipole exerted by the particles on the fluid. The fluid flow equations are solved spectrally and the conservation equation is solved by second-order finite differencing in space and second-order Adams-Bashforth time marching. First, the dynamics in suspensions of oxytactic run-and-tumble bacteria confined in thin liquid films surrounded by air is investigated. These bacteria modify their tumbling behavior by making temporal comparisons of the oxygen concentration, and, on average, swim towards high concentrations of oxygen. The kinetic model proposed by Saintillan and Shelley [1, 2] is modified to include run-and-tumble effects and oxygentaxis. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady states. Above a critical film thickness (approximately 200 micron), a transition to chaotic dynamics is observed and is characterized by turbulent-like 3D motion, the formation of bacterial plumes, enhanced oxygen mixing and transport into the film, and hydrodynamic velocities of magnitudes up to 7 times the single bacterial swimming speed. The simulations demonstrate that the combined effects of hydrodynamic interactions and oxygentaxis create collective three-dimensional instabilities which enhances oxygen availability for the bacteria. Our simulation results are consistent with the experimental findings of Sokolov et al. [3], who also observed a similar transition with increasing film thickness. Next, the dynamics in concentrated suspensions of active self-propelled particles in a 3D periodic domain are analyzed. We modify the kinetic model of Saintillan and Shelley [1, 2] by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards [4]). Large-scale three- dimensional simulations show that, in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations and are characterized by highly nematic structures. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation will be presented. Our analysis shows that steric interactions have a destabilizing effect in active suspensions.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.

Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network.

States' Responding Behavior in Conflict: Asymmetric Response and Strategic Conflict Avoidance

State responses to external threats and aggression are studied with focus on two different rationales: (1) to make credible deterrent threats to avoid being exploited, and (2) to minimize the risk of escalation to unwanted war. Given external aggression, the target state's responding behavior has three possibilities: concession (under-response), reciprocation, and escalation. This study focuses on the first two possibilities and investigates how the strategic nature of crisis interaction can explain the intentional choice of concession or avoidance of retaliation. I build a two-level bargaining model that accounts for the domestic bargaining situation between the leader and the challenger for each state. The model's equilibrium shows that the responding behavior is determined not only by inter-state level variables (e.g. balance of power between two states, or cost of war that each state is supposed to pay), but also the domestic variables of both states. Next, the strategic interaction is rationally explained by the model: as the responding state believes that the initiating state has strong domestic challenges and, hence, the aggression is believed to be initiated for domestic political purposes (a rally-around-the-flag effect), the response tends to decrease. The concession is also predicted if the target state leader has strong bargaining power against her domestic challengers \emph{and} she believes that the initiating leader suffers from weak domestic standing. To test the model's prediction, I conduct a lab experiment and case studies. The experimental result shows that under an incentivized bargaining situation, individual actors are observed to react to hostile action as the model predicts: if the opponent is believed to suffer from internally driven difficulties, the subject will not punish hostile behavior of the other player as severely as she would without such a belief. The experiment also provides supporting evidence for the choice of concession: when the player finds herself in a favorable situation while the other has disadvantages, the player is more likely to make concessions in the controlled dictator game. Two cases are examined to discuss how the model can explain the choice of either reciprocation or concession. From personal interviews and fieldwork in South Korea, I find that South Korea's reciprocating behavior during the 2010 Yeonpyeong Island incident is explained by a combination of `low domestic power of initiating leader (Kim Jong-il)' and `low domestic power of responding leader (Lee Myung-bak).' On the other hand, the case of EC-121 is understood as a non-response or concession outcome. Declassified documents show that Nixon and his key advisors interpreted the attack as a result of North Korea's domestic political instabilities (low domestic power of initiating leader) and that Nixon did not have difficulties at domestic politics during the first few months of his presidency (high domestic power of responding leader).

Modelagem da propagação sonora em dutos : abordagem matemática no domínio da frequência e do tempo utilizando transformada de laplace

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Faculdade de Tecnologia, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2016.

THE IMPACT OF UPPER-LEVEL PROCESSES ON THE INTENSITY AND STRUCTURAL CHANGES OF HURRICANE SANDY (2012)

The first part of this study examines the relative roles of frontogenesis and tropopause undulation in determining the intensity and structural changes of Hurricane Sandy (2012) using a high-resolution cloud-resolving model. A 138-h simulation reproduces Sandy’s four distinct development stages: (i) rapid intensification, (ii) weakening, (iii) steady maximum surface wind but with large continued sea-level pressure (SLP) falls, and (iv) re-intensification. Results show typical correlations between intensity changes, sea-surface temperature and vertical wind shear during the first two stages. The large SLP falls during the last two stages are mostly caused by Sandy’s moving northward into lower-tropopause regions associated with an eastward-propagating midlatitude trough, where the associated lower-stratospheric warm air wraps into the storm and its surrounding areas. The steady maximum surface wind occurs because of the widespread SLP falls with weak pressure gradients lacking significant inward advection of absolute angular momentum (AAM). Meanwhile, there is a continuous frontogenesis in the outer region during the last three stages. Cyclonic inward advection of AAM along each frontal rainband accounts for the continued expansion of the tropical-storm-force wind and structural changes, while deep convection in the eyewall and merging of the final two survived frontal rainbands generate a spiraling jet in Sandy’s northwestern quadrant, leading to its re-intensification prior to landfall. The physical, kinematic and dynamic aspects of an upper-level outflow layer and its possible impact on the re-intensification of Sandy are examined in the second part of this study. Above the outflow layer isentropes are tilted downward with radius as a result of the development of deep convection and an approaching upper-level trough, causing weak subsidence. Its maximum outward radial velocity is located above the cloud top, so the outflow channel experiences cloud-induced long-wave cooling. Because Sandy has two distinct convective regions (an eyewall and a frontal rainband), it has multiple outflow layers, with the eyewall’s outflow layer located above that of the frontal rainband. During the re-intensification stage, the eyewall’s outflow layer interacts with a jet stream ahead of the upper-level trough axis. Because of the presence of inertial instability on the anticyclonic side of the jet stream and symmetric instability in the inner region of the outflow layer, Sandy’s secondary circulation intensifies. Its re-intensification ceases when these instabilities disappear. The relationship between the intensity of the secondary circulation and dynamic instabilities of the outflow layer suggests that the re-intensification occurs in response to these instabilities. Additionally, it is verified that the long-wave cooling in the outflow layer helps induce symmetric instability by reducing static stability.

Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Past, present and future of epigenetics applied to livestock breeding

This article reviews the concept of Lamarckian inheritance and the use of the term epigenetics in the field of animal genetics. Epigenetics was first coined by Conrad Hal Waddington (1905–1975), who derived the term from the Aristotelian word epigenesis. There exists some controversy around the word epigenetics and its broad definition. It includes any modification of the expression of genes due to factors other than mutation in the DNA sequence. This involves DNA methylation, post-translational modification of histones, but also linked to regulation of gene expression by non-coding RNAs, genome instabilities or any other force that could modify a phenotype. There is little evidence of the existence of transgenerational epigenetic inheritance in mammals, which may commonly be confounded with environmental forces acting simultaneously on an individual, her developing fetus and the germ cell lines of the latter, although it could have an important role in the cellular energetic status of cells. Finally, we review some of the scarce literature on the use of epigenetics in animal breeding programs.

Vector self-pulsing in erbium-doped fiber lasers

Insight into instabilities of fiber laser regimes leading to complex self-pulsing operations is an opportunity to unlock the high power and dynamic operation tunability of lasers. Though many models have been suggested, there is no complete covering of self-pulsing complexity observed experimentally. Here, I further generalized our previous vector model of erbium-doped fiber laser and, for the first time, to the best of my knowledge, map tunability of complex vector self-pulsing on Poincare sphere (limit cycles and double scroll polarization attractors) for laser parameters, e.g., power, ellipticity of the pump wave, and in-cavity birefringence. Analysis validated by extensive numerical simulations demonstrates good correspondence to the experimental results on complex self-pulsing regimes obtained by many authors during the last 20 years.

Temporal solitonic crystals and non-Hermitian informational lattices

Clusters of temporal optical solitons—stable self-localized light pulses preserving their form during propagation—exhibit properties characteristic of that encountered in crystals. Here, we introduce the concept of temporal solitonic information crystals formed by the lattices of optical pulses with variable phases. The proposed general idea offers new approaches to optical coherent transmission technology and can be generalized to dispersion-managed and dissipative solitons as well as scaled to a variety of physical platforms from fiber optics to silicon chips. We discuss the key properties of such dynamic temporal crystals that mathematically correspond to non-Hermitian lattices and examine the types of collective mode instabilities determining the lifetime of the soliton train. This transfer of techniques and concepts from solid state physics to information theory promises a new outlook on information storage and transmission.