Pattern Formation

Two-dimensional Stokes flow with injection and suction is investigated through a second-order, perturbative mode-coupling approach. We examine the time-dependent disturbance of an initially circular interface separating two viscous fluids, and derive a system of nonlinear differential equations describing the evolution of the interfacial perturbation amplitudes. Linear stability analysis reveals that an injection-induced expanding interface is stable, while a contracting motion driven by suction is unstable. Curiously, at the linear level this suction instability is independent of the viscosity contrast between the fluids. However, second-order results tell a different story, and show that the viscosity contrast plays a key role in determining the shape of the emerging interfacial patterns. By focusing on the onset of nonlinear effects, we have been able to extract valuable information about the most fundamental features of the pattern-forming structures for arbitrary values of visc...

To allow the survival of the population in the absence of nitrogen, some cyanobacteria strains have developed the capability of differentiating into nitrogen fixing cells, forming a characteristic pattern. In this paper, the process by which cyanobacteria differentiates from vegetative cells into heterocysts in the absence of nitrogen and the elements of the gene network involved that allow the formation of such a pattern are investigated. A simple gene network model, which represents the complexity of the differentiation process, and the role of all variables involved in this cellular process is proposed. Specific characteristics and details of the system's behavior such as transcript profiles for ntcA, hetR and patS between consecutive heterocysts were studied. The proposed model is able to capture one of the most distinctive features of this system: a characteristic distance of 10 cells between two heterocysts, with a small standard deviation according to experimental variability. The system's response to knock-out and overexpression of patS and hetR was simulated in order to validate the proposed model against experimental observations. In all cases, simulations show good agreement with reported experimental results. A simple evolution mathematical model based on the gene network involved in heterocyst differentiation was proposed. The behavior of the biological system naturally emerges from the network and the model is able to capture the spacing pattern observed in heterocyst differentiation, as well as the effect of external perturbations such as nitrogen deprivation, gene knock-out and over-expression without specific parameter fitting.

Floral development was compared with scanning electron microscopy in 12 Australian species of Hibbertia representing most of its morphological variation, and in the related Adrastaea (Dilleniaceae). Calyx and corolla arise in quincuncial helices in radially symmetrical species, while the petals initiate unidirectionally from one side in zygomorphic species. Stamen number (3-200ϩ) proliferates by centrifugal addition of individual primordia or by innovations of common primordia and ring meristems. Common primordia arise in single-stamen positions alternately with petals, and each produces one to several stamens centrifugally that remain attached to a shared base and form a stamen fascicle. A ring meristem in Adrastaea initiates a whorl of five stamens, alternate with the first stamens but outside their whorl. In radially symmetrical species of Hibbertia, a first ring of stamens is supplemented centrifugally by additional stamens on a meristem ring. The first stamens in zygomorphic species of Hibbertia initiate as a terminal ridge on the floral apex, with subsequent stamens added centrifugally on one side and two carpels initiated on the opposite side. The carpels arise as a simultaneous ring in radially symmetrical flowers, or as a simultaneous pair in zygomorphic species. Staminodial presence is viewed as of minor significance. Four pollinator syndromes are proposed for Hibbertia, related to differing floral architecture.

We report wide class of exact solutions of the modified Gross-Pitaevskii equation (GPE) in 'smart' Jacobi elliptic potentials: V(ξ) = -V 0 sn(ξ, m), V(ξ) = -V 0 cn(ξ, m), and V(ξ) = -V 0 dn(ξ, m) in the presence of external source. Solitonlike solutions, singular solutions, and periodic solutions are found using a recently developed fractional transform: , where f is the respective Jacobi elliptic function and the amplitude parameters A, B, and D nonzero. These results generalize those contained in (Paul T, Richter K and Schlagheck P 2005 Phys. Rev. Lett. 94, 020404) for nonzero trapping potential.

We report wide class of exact solutions of the modified Gross-Pitaevskii equation (GPE) in 'smart' Jacobi elliptic potentials: V(ξ) = -V 0 sn(ξ, m), V(ξ) = -V 0 cn(ξ, m), and V(ξ) = -V 0 dn(ξ, m) in the presence of external source. Solitonlike solutions, singular solutions, and periodic solutions are found using a recently developed fractional transform: , where f is the respective Jacobi elliptic function and the amplitude parameters A, B, and D nonzero. These results generalize those contained in (Paul T, Richter K and Schlagheck P 2005 Phys. Rev. Lett. 94, 020404) for nonzero trapping potential.

We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schrödinger equation. It is found that, a wide class of solutions of the higher order non-linear Schrödinger equation with a source can also be obtained through the above procedure. Distinct parameter ranges, allowing the existence of these solutions, phase locked with their respective sources, are delineated. Conditions for obtaining non-propagating solutions are found to be quite different for both the equations. A special case, where the scale of the soliton emerges as a free parameter, is obtained and the condition under which solitons can develop singularity is pointed out. We also study the highly restrictive structure of the localised solutions, when the phase and amplitude get coupled.

Sinusoidal wave solutions are obtained for reduced Maxwell-Duffing equations describing the wave propagation in a non-resonant atomic medium. These continuous wave excitations exist when the medium is initially polarized by an electric field. Other obtained solutions include both monofrequency and cnoidal waves.

We investigate exact travelling wave solutions of higher order nonlinear Schrödinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation, governing the evolution of intensity in the femtosecond regime, is that of non-linear Schrödinger equation with a source. The exact localized solutions to this system can have both super and subluminal propagation belonging to two distinct class. A number of these solitons exhibit chirality, thereby showing preferential propagation behavior determined by group velocity dispersion. Both localized bright and dark solitons are found in complementary velocity and experimental parameter domains, which can exist for anomalous and normal dispersion regimes. It is found that, dark solitons in this system propagate with non-zero velocity, unlike their counterpart in nanosecond regime. Interestingly, subluminal propagation is observed for solitons having a nontrivial Padé type intensity profile.

We present a study on the emergence of spatial structure in plankton dynamics under the influence of stirring and mixing. A distribution of plankton is represented as a lattice of nonidentical, interacting, oscillatory plankton populations. Each population evolves according to ͑i͒ the internal biological dynamics represented by an NPZ model with population-specific phytoplankton growth rate, ͑ii͒ sub-grid-cell stirring and mixing parameterized by a nearest-neighbor coupling, and ͑iii͒ explicit advection resulting from a constant horizontal shear. Using the methods of synchronization theory, the emergent spatial structure of the simulation is investigated as a function of the coupling strength and rate of advection. Previous work using similar methods has neglected the effects of explicit stirring ͑i.e., at scales larger than the grid cell͒, leaving as an open question the relevance of the work to real marine systems. Here, we show that persistent spatial structure emerges for a range of coupling strengths for all realistic levels of surface ocean shear. Spatially, this corresponds to the formation of temporally evolving clusters of local synchronization. Increasing shear alters the spatial characteristics of this clustering by stretching and narrowing patches of synchronized dynamics. These patches are not stretched into stripes of synchronized abundance aligned with the flow, as may be expected, but instead lie at an angle to the flow. This study shows that advection does not diminish the relevance of conclusions from previous studies of spatial structure in plankton simulations. In fact, the inclusion of advection adds characteristic filamental structure, as observed in real-world plankton distributions. The results also show that the ability of coupled oscillators to synchronize depends strongly on the spatial arrangement of oscillator natural frequencies; under the influence of advection, therefore, the impact of the coupling strength on the emergent spatial structure of a biophysical simulation is time-dependent.

It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signaling mechanism for neuronal growth.

We are interested in addressing the problem of coordinating a large number of simple agents in order to achieve a given task. Stated in this way, the question leads naturally to the Swarm Intelligence field. In this paper we use a new type of model, directly inspired by Kaneko's coupled map gas model which we have adapted to the multi-agent system paradigm, so as to tackle this generic objective. This model is called a logistic multi-agent system (LMAS): it is composed of reactive situated agents whose individual behavior is governed by a logistic map or more generally a quadratic map. The collective behavior results from couplings between agents and local controls on agents adjusted by local environmental conditions. This way of modelling reveals to enable a wide range of pattern formations and various forms of adaptation to the environment. This paper focuses on the way to design the constitutive mechanisms of LMAS -particularly the perception and action processesand on the way a self-adaptation process may result from these mechanisms. This study is illustrated with experiments on the predators-prey pursuit problem, in which a set of agents (predators) has to encircle a moving prey. We show that coupling the internal states of agents leads to amplifying the predator aggregation around the prey, whereas altering the internal control variable in each agent through environment perceptions modifies the predator sensitivity to the prey. We finally complete this study by relating the concept of adaptation with concepts of the dynamical system theory: a qualitative dynamical analysis of the capturing process leads to view the prey as a dynamical fixed point of the system.

The 2D laminar quasi-steady asymptotically simplified and linearized flow with a simplified mass transport of sediments is solved over a slowly erodible bed in various laminar basic shear flow (steady, oscillating or decelerating). The simplified mass transport equation includes the two following phenomena: flux of erosion when the skin friction goes over a threshold value, and a non local effect coming either from an inertial effect or from a slope effect. It is shown that the bed is always unstable for small wave numbers. Examples of long time evolution in various shear régimes are presented, wave trains of ripples are created and merge into a unique bump. This coarsening process is such that the maximum wave length obeys a power law with time.

Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, evolved are gene regulation networks under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most of thousands of numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Here, both the pattern dynamics consist of several epochs to form successive stripe formations between quasi-stationary regimes. In evolution, the regimes are generations needed to hit relevant mutations, while in development, they are due to the emergence of slowly varying expression that controls the pattern change. Successive pattern changes are thus generated, which are regulated by successive combinations of feedback or feedforward regulations under the upstream feedforward network that reads the morphogen gradient. By using a pattern generated by the upstream feedforward network as a boundary condition, downstream networks form later stripe patterns. These epochal changes in development and evolution are represented as same bifurcations in dynamical-systems theory, and this agreement of bifurcations lead to the evolution-development congruences. Violation of the evolution-development congruence, observed exceptionally, is shown to be originated in alteration of the boundary due to mutation at the upstream feedforward network. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

Boundary-induced pattern formation from a spatially uniform state is investigated using onedimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern wavelength with the period of oscillation is also obtained. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis.

It is acknowledged that embryonic development has tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel’s recapitulation theory, i.e., the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene-expression dynamics with cell-to-cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Both pattern changes consisted of several epochs where stripes are formed in a short time, whereas for other temporal...

Boundary-induced pattern formation from a spatially uniform state is investigated using onedimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern wavelength with the period of oscillation is also obtained. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis.

Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development...

Spatiotemporal patterning of neuronal activity is considered to be an important feature of cognitive processing in the brain as well as pathological brain states, such as seizures. Here, we investigate complex interactions between intrinsic properties of neurons and network structure in the generation of network spatiotemporal patterning in the context of seizure-like synchrony. We show that membrane excitability properties have differential effects on network activity patterning for different network topologies. We consider excitatory networks consisting of neurons with excitability properties varying between type I and type II that exhibit significantly different spike frequency responses to external current stimulation, especially at firing threshold. We find that networks with type II-like neurons show higher synchronization and bursting capacity across a range of network topologies than corresponding networks with type I-like neurons. These differences in activity patterning are persistent across different network sizes, connectivity strengths, magnitudes of random external input, and the addition of inhibitory interneurons to the network, making them highly likely to be relevant to brain function. Furthermore, we show that heterogeneous networks of mixed cell types show emergent dynamical patterns even for very low mixing ratios. Specifically, the addition of a small percentage of type II-like cells into a network of type I-like cells can markedly change the patterning of network activity. These findings suggest that cellular as well as network mechanisms can go hand in hand, leading to the generation of seizure-like discharges, suggesting that a single ictogenic mechanism alone may not be responsible for seizure generation.

An overview of several dynamic properties of SQUID metamaterials is given in the presence of both constant and alternating magnetic field. The total current as a function of the driving frequency exhibits hysteretic effects which are favored by low levels of disorder. Multistability in the current states leads to multiple magnetic responses with different value of magnetic permeability. SQUID metamaterials exhibit wide-band tuneability which is periodic with the applied constant magnetic field; the numerical calculations reproduce fairly well recent experimental results. Current work also reveals the possibility for wave transmission through nonlinear bands, which is briefly discussed.

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.

A periodic array of rf SQUIDs in an alternating magnetic field acts as an inherently nonlinear magnetic metamaterial, due to the nonlinearity of the Josephson element and the resonant properties of the SQUIDs themselves. Neighboring SQUIDs are weakly coupled due to magnetic ...

In Hydra, head regeneration and bud formation appear to be very similar processes. The fact that there are genes whose expression is specific for one of the two processes suggests that they do not have identical molecular bases. We analyzed the signal transduction pathways regulating bud development using inhibitors of protein kinase C, Src, PI3K and ERK. The four inhibitors reversibly blocked bud formation in Hydra when applied before stage 1. Once the bud reached stage 3, three of them had no effect and the bud developed normally. The inhibitors blocked the expression of Budhead, an early head marker, and of CnOtx which are specific for bud formation. The results are in agreement with the central role of a signaling pathway mediated by Src on bud development.

We present results of an experimental and numerical investigation of the patterns realized by surface waves within an open rectangular container subjected to horizontal vibrations at frequencies of 40-100 Hz. The first instability exhibited by the primary harmonic wave field is subharmonic, and may be identified with the cross-wave instability often seen in wave tank experiments. We show that, contrary to common theoretical and experimental assumptions, and despite their name, these subharmonic waves are not oriented crosswise, but at an intermediate angle with respect to the axis of vibration. Hence, the pattern selection problem for horizontally forced Faraday waves is more complex than has previously been assumed. We establish the robustness of this obliquely oriented surface wave pattern by varying the forcing frequency and amplitude, the fluid viscosity, the fluid depth, and the boundary conditions. Previous work on cross-waves is reviewed and discussed in relation to the current results. Finally, numerical simulations using a reduced model with an appropriate forcing term are used to support the generality of the experimental observations.

Particle clustering phenomenon is relevant to many industrial and natural systems. Particles denser than the carrier fluid tend to accumulate in the high-strain low-vorticity regions, which leads to inhomogeneous distribution of particles. This phenomenon is known as "preferential concentration". The deposition and entrainment of particles in low-Reynolds number turbulent channel flow is well understood. However, particles clustering under the influence of multi-scale vortices in high-Reynolds-number turbulent channel flow is not fully investigated. Present study aims to understand this situation through the DNS of particle-laden turbulent channel flow at 𝑅𝑒 𝜏 = 500 and 1000.

The evolution of a ripple pattern on Si(100) surfaces induced by 60 keV Ar + beam incident at 60°with the surface normal has been studied as a function of bombardment time using ex situ atomic force microscopy (AFM) in ambient condition. The ripple wavelength ͑l͒ and roughness amplitude ͑W͒ increase with bombardment time following a scaling law l ϰ t ␥ and W ϰ t ␤ , where ␥ = 0.64± 0.08 to a crossover value 0.22± 0.07 and ␤ = 0.76± 0.03 to a crossover at 0.27± 0.11. The ripple orientation and average wavelength observed in the early stage patterned morphology can be described by a linear continuum model. However, the scaling exponents for the power law variation of roughness amplitude and wavelength with bombardment time are not consistent with predictions of the linear model or the Kuramoto-Sivashinsky-equation-based nonlinear model.

A two-dimensional Ising-like model with spin 1 and long-range interactions is studied numerically through a Monte Carlo simulation. The goal of the simulation is to describe pattern formations and critical temperature of twodimensional magnetic structures. Three sets of parameters are considered, that give rise to stripes, labyrinths or cellular domain structures. We determine for each con"guration the transition ordering temperatures, the relaxation of the energy, the hysteresis cycle, and the average size of the domains.

This short speculative note inquires into the question as to whether AI computational models of the brain (LLMs most prominently) and neuroscience and computational neuroscience could eventually unify into a comprehensive theory of the brain and mind. True integration isn't trivial. The brain isn't just a computer; it's a living, adapting, and dynamic system deeply intertwined with physiology and the environment. One way of reconciling the two would be to employ the methodology developed by David Marr whereby a high level conceptual model (level) articulated by an algorithmic model or models could be mapped down onto a dynamic (although in this context the objective would be to hypothesis how the dynamic model would actually perform the algorithmic layer. I conclude with an enormous number of open issues.

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}' consisting of cells interacting with each other via bonds. Both the internal states of the cells and the "strength" of the bonds are assumed to be dynamical variables. In section 3 the basis is laid for a version of '{\it discrete analysis}' which, starting from different, perhaps more physically oriented principles, manages to make contact with the much more abstract machinery of Connes et al. and may complement the latter approach. In section 4 a, as far as we can see, new concept of '{\it topological dimension}' in form of a '{\it degree of connectivity}' for graphs, networks and the like is developed. It is then indicated how this '{\it dimension}', which for continuous structures or lattic...

Primary vascular pattern determines pathways of long distance transport for water, nutrients and signalling molecules within plant shoot systems. • Expression of an Arabidopsis thaliana homeobox gene 8::GUS construct is restricted to the procambium and provides a molecular marker for vascular pattern at early developmental stages. • Primary vascular pattern and phyllotaxis are highly coordinated, with vascular sympodia corresponding to phyllotactic parastichies. During vegetative development, primary vasculature forms a reticulate pattern, with each leaf trace derived from two vascular sympodia. Shoot phase change is marked by alterations of this fundamental pattern. Formation of leaf trace procambial strands is temporally coordinated with primordium initiation, but ATHB-8::GUS expression is discontinuous in these strands at early stages. • The interconnection of vascular sympodia provides alternate pathways for long distance transport in shoots of A. thaliana and reflects the limited secondary growth in this species. ATHB-8::GUS expression identifies a prepattern that precedes anatomical definition of procambium. The longitudinal discontinuity in ATHB-8::GUS expression indicates that one function of this gene is to define the xylem components of vascular radial pattern.

We deal with a weakly-coupled system of semilinear parabolic equations, namely a competition-diffusion system, and prove the existence of a stable spatially-inhomogeneous equilibrium solution on the assumption that the spatial domain is far from being convex and that the corresponding system of ODEs in the absence of diffusion posesses at least two distinct asymptotically stable equilibria. We also consider a non-weakly coupled system of competition type involving cross-diffusion terms, which leave the system quasilinear but no longer semilinear. The point of interest is to see how the shape of the spatial domain or the presence of cross-diffusion terms contributes to the occurrence of pattern formation.

We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a modified equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled fluid. When the sound speed is tuned small enough, the compressible region of fluid flow can be reached. An example 2-D model is presented, together with the numerical verification for its transport coefficients.

The use of liquid-crystal light valves (LCLV s) as nonlinear elements in diffractive optical systems with feedback leads to the formation of a variety of optical patterns. The spectrum of possible spatial instabilities is shown to be even richer when the LCLV's capability for polarization modulation is utilized and internal threshold and saturation eKects are considered. We derive a model for the feedback system based on a realistic description of the LCLV's internal function and coupling to a polarizer. Thresholds of pattern formation are compared to the common Kerr-type approximation and show transitions involving rolls, squares, hexagons, and tiled patterns. Numerical and experimental results con6rm our theoretical predictions and unveil how patterns and their typical length scales can be easily controlled by changes of the parameters.

We present an experimental realization of an almost non-invasive stabilization and manipulation method of coexisting and unstable states of pattern forming systems. In a photorefractive single feedback system, a control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few per cent of the system's intensity. By that means, we were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as coexisting or underlying solutions. Changing the phase of the control signal allows one to switch between different pattern states.

We investigate the origin of dynamics of hexagonal pattern formation in a photorefractive single feedback system[ By introducing an asymmetry\ we induced di}erent complex motion behaviours[ A visualization method is presented and means to control the dynamics in the case of _xed external parameters are discussed[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ 0[ TRANSVERSE STRUCTURES IN PHOTOREFRACTIVE MEDIA

In the process of limb development, various signaling molecules are produced in the organizing center of the limb bud. These molecules regulate pattern formation and the morphogenesis of the limb. Members of the bone morphogenetic protein (BMP) family and their receptors are expressed in the limb bud in spatiotemporal specific patterns. BMP signaling regulates chondrogenesis of limb mesenchyme, and promotes apoptosis of the interdigital soft tissue. Recently, this signaling was found to be involved in establishment of dorsoventral polarity of the limb bud and in regulation of limb growth via maintenance of the apical ectodermal ridge. BMPs also regulate digit morphology. In these events, BMPs work together with other signaling molecules, but they sometimes act as negative regulators of these other molecules so that limb morphogenesis can proceed normally.

In the developing limb bud, mesenchymal cells show position-specific affinity, suggesting that the positional identity of the cells is represented as their surface properties. Since the affinity is regulated by glycosylphosphatidylinositol (GPI)-anchored cell surface proteins, and by EphA4 receptor tyrosine kinase, we hypothesized that the GPI-anchored ligand, the ephrin-A family, also contributes to the affinity. Here, we describe the role of ephrin-A2 in the chick limb bud. Ephrin-A2 protein is uniformly distributed in the limb bud during early limb development. As the limb bud grows, expression of ephrin-A2 is strong in its proximal-to-intermediate regions, but weak distally. The position-dependent expression is maintained in vitro, and is regulated by FGF protein, which is produced in the apical ectodermal ridge. To investigate the role of ephrin-A2 in affinity and in cartilage morphogenesis of limb mesenchyme, we ectopically expressed ephrin-A2 in the limb bud using the retrovirus vector, RCAS. Overexpressed ephrin-A2 modulated the affinity of the mesenchymal cells that differentiate into autopod elements. It also caused malformation of the autopod skeleton and interfered with cartilage nodule formation in vitro without inhibiting chondrogenesis. These results suggest that ephrin-A2 regulates the position-specific affinity of limb mesenchyme and is involved in cartilage pattern formation in the limb.

Although regional differences in mesenchymal cell affinity in the limb bud represent positional identity, the molecular basis for cell affinity is poorly understood. We found that treatment of the cell surface with bacterial phosphatidylinositol-specific phospholipase C (PI-PLC) could change cell affinity in culture. When PI-PLC was added to the culture medium, segregation of the progress zone (PZ) cells from different stage limb buds was inhibited. Similarly, sorting out of the cells from different positions along the proximodistal (PD) axis of the same stage limb buds was disturbed. Since PI-PLC can remove glycosylphosphatidylinositol (GPI)-anchored membrane bound proteins from the cell surface, the GPI-anchored cell surface proteins may be involved in sorting out. To define the GPI-anchored molecules that determine the segregation of limb mesenchymal cells, we examined the effect of neutralizing antibody on the EphA4 receptor that binds to GPI-anchored cell surface ligands, called ephrin-A. Sorting out of the PZ cells at different stages could be inhibited by the neutralizing antibody to EphA4. These results suggest that EphA4 and its GPI-anchored ligands are, at least in part, involved in sorting out of limb mesenchymal cells with different proximal-distal positional values, and that GPI-anchored cell surface proteins play important roles in determining cell affinity in the limb bud.

Epitaxial thin film growth by vapor deposition or molecular beam epitaxy under ultra-high vacuum conditions generally occurs in two stages: (i) nucleation and growth of well-separated islands on the substrate; (ii) subsequent formation of a thicker continuous film with possible kinetic roughening. For homoepitaxial growth, two-dimensional (2D) monolayer islands are formed during submonolayer deposition. Typically, the presence of a step-edge barrier inhibits downward transport and leads to the formation of mounds (multilayer stacks of 2D islands) during multilayer growth. For heteroepitaxial growth, islands formed in the initial stages of deposition sometimes have a 2D monolayer structure. However, they may instead exhibit bilayer or 3D multilayer structure due to, e.g., a high film surface energy, strain, or quantum size effects. Various growth modes are possible for thicker films. Atomistic modeling provides the most detailed picture of film growth. For coherent (defect-free) epitaxial films, lattice-gas modeling analyzed by kinetic Monte Carlo simulation (KMC) is particularly successful in describing film growth on the appropriate time and length scales. For large islands or complex systems, another effective and instructive approach is laterally coarse-grained step-dynamics modeling which tracks only the evolution of step edges in each layer. However, fully coarse-grained 3D continuum modeling for the evolution of a film height function does not yet have predictive capability. Examples are provided for: Ag homoepitaxy on (100), ( ) and (110) surfaces; Ag heteroepitaxy on lattice-matched substrates including NiAl(110), NiAl(100), and Fe(100); and Ag heteroepitaxy on 5-fold icosohedral Al-Pd-Mn and 2-fold decagonal Al-Cu-Co quasicrystalline surfaces.

A new approach to algorithmic trading system development is presented. This approach, Kernel Price Pattern Trading (KPPT P ), allows the practitioner to link the performance of a learned classifier (that predicts the occurrence of the price pattern P ) to the profitability of the system. A positive definite kernel based distance that tries to capture the drivers of the process of price patterns formation and some results about the profitability of the system are also presented.

We study front propagation in the reversible reaction-diffusion system A+A ↔ A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get correct value of the front diffusion coefficient.

An experimental investigation of chemical reaction fronts, created by an initial separation of reactants, is reported for a system of two competing reactions. Spatiotemporal patterns are observed experimentally for the competing reaction front and are accounted for quantitatively by a reaction-diffusion model. We use the reaction of xylenol orange with Cr 3+ in aqueous solution. Different oligomers of Cr 3+ provide the two kinetically different species that react competitively with xylenol orange. The parameters that determine whether pattern formation is observable at the front are the ratios of (1) the microscopic reaction constants of the competing reactions and (2) the concentrations of the competing species. Under the parameter values studied, which allowed clear spatiotemporal separation of the two competing reactions, we find that the behavior of the reaction front at early times follows a perturbation theory developed for a simple elementary A + B f C reaction with initially separated reactants. The global reaction rate, observed over the entire time scale of the experiments, is highly non-monotonic. Overall, with no free parameters, our theoretical model is quantitatively consistent with the experimental observations of the spatiotemporal patterns, the unusual scaling laws, and the crossover behaviors. The geometrical constraints and nonclassical behavior of the reaction rate allow a quantitative determination of the reaction probability of the chromium ion monomer relative to that of the higher order oligomers.

We investigate the Rayleigh-Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder's wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh-Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently threedimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.

By virtue of Rayleigh-Benard convection, we illustrate the advantages of combining a hydrodynamic pattern forming instability with a thermodynamic critical point. This has already lead to many novel unexpected observations and is further shown to possess opportunities for the study of exciting fundamental problems in nonequilibrium systems.

In this paper we study travelling wave solutions to a system of four non-linear partial di erential equations, which arise in a tissue interaction model for skin morphogenesis. Under the 'small-stress' assumption we prove the existence and uniqueness (up to a translation) of solutions with the dermis and epidermis cell densities being positive, which are a perturbation of a uniform epidermal cell density. We discuss the problem of the minimal wave-speed.

The paper considers conditions sufficient for the existence of classical C solutions to a new model of chondrogenesis during the vertebrate limb formation. We assume that the diffusion coefficient of the fibronectin is positive and that the function describing the interaction between the fibronectin and cells satisfies some additional properties.

We consider the Eigen quasispecies model with a dynamic environment. For an environment with sharppeak fitness in which the most-fit sequence moves by k spin-flips each period T we find an asymptotic stationary state in which the quasispecies population changes regularly according to the regular environmental change. From this stationary state we estimate the maximum and the minimum mutation rates for a quasispecies to survive under the changing environment and calculate the optimum mutation rate that maximizes the population growth. Interestingly we find that the optimum mutation rate in the Eigen model is lower than that in the Crow-Kimura model, and at their optimum mutation rates the corresponding mean fitness in the eigenmodel is lower than that in the Crow-Kimura model, suggesting that the mutation process which occurs in parallel to the replication process as in the Crow-Kimura model gives an adaptive advantage under changing environment.

In the development of superintelligent artificial intelligence (AI), there arises a risk of cognitive burnout-performance degradation due to internal state overload, analogous to human burnout. This hypothesis suggests that unlimited growth of computational power (P) may lead to collapse if not balanced with cognitive strain (T). The solution involves emergent self-regulation through dynamic parameters (R, ,) that emerge from the system's architecture and experience, without external constraints. Below we present the problem, justifications, false approaches, and the preferred model with mathematical formalization, including extension to multi-agent systems.

Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations among which gene flow occurs. This flow can also be represented as a network. In this paper we briefly show some properties of these complex networks of evolutionary and ecological relationships. First, we characterize large scale evolutionary relationships in the Tree of Life by a degree distribution. Second, we represent genetic relationships between individuals of a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum Spanning Tree. Finally, relationships among plant shoots inside populations are represented as networks of genetic similarity.