A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

The role of hydrological transience in peatland pattern formation

The sloping flanks of peatlands are commonly patterned with non-random, contour-parallel stripes of distinct microhabitats such as hummocks, lawns and hollows. Patterning seems to be governed by feedbacks among peatland hydrological processes, plant micro-succession, plant litter production and peat decomposition. An improved understanding of peatland patterning may provide important insights into broader aspects of the long-term development of peatlands and their likely response to future climate change.

Pattern formation for a reaction-diffusion system: Catalytic-dependent diffusion coefficients

[ES]Se considera un modelo de reacción-difusión para dos reactantes en presencia de un tercero, que actúa de catalizador. La escala temporal para el catalizador se compara con la de los reactantes y los coeficientes de difusión dependen solamente de la concentración en el estado de equilibrio del catalizador. Se realizan experimentos para diferentes cinéticas

The spatiotemporal pattern of auditory cortical responses during verbal hallucinations

Functional magnetic resonance imaging (fMRI) studies can provide insight into the neural correlates of hallucinations. Commonly, such studies require self-reports about the timing of the hallucination events. While many studies have found activity in higher-order sensory cortical areas, only a few have demonstrated activity of the primary auditory cortex during auditory verbal hallucinations. In this case, using self-reports as a model of brain activity may not be sensitive enough to capture all neurophysiological signals related to hallucinations. We used spatial independent component analysis (sICA) to extract the activity patterns associated with auditory verbal hallucinations in six schizophrenia patients. SICA decomposes the functional data set into a set of spatial maps without the use of any input function. The resulting activity patterns from auditory and sensorimotor components were further analyzed in a single-subject fashion using a visualization tool that allows for easy inspection of the variability of regional brain responses. We found bilateral auditory cortex activity, including Heschl's gyrus, during hallucinations of one patient, and unilateral auditory cortex activity in two more patients. The associated time courses showed a large variability in the shape, amplitude, and time of onset relative to the self-reports. However, the average of the time courses during hallucinations showed a clear association with this clinical phenomenon. We suggest that detection of this activity may be facilitated by examining hallucination epochs of sufficient length, in combination with a data-driven approach.

Neurogranin controls the spatiotemporal pattern of postsynaptic Ca2+/CaM signaling.

Neurogranin (Ng) is a postsynaptic IQ-motif containing protein that accelerates Ca(2+) dissociation from calmodulin (CaM), a key regulator of long-term potentiation and long-term depression in CA1 pyramidal neurons. The exact physiological role of Ng, however, remains controversial. Two genetic knockout studies of Ng showed opposite outcomes in terms of the induction of synaptic plasticity. To understand its function, we test the hypothesis that Ng could regulate the spatial range of action of Ca(2+)/CaM based on its ability to accelerate the dissociation of Ca(2+) from CaM. Using a mathematical model constructed on the known biochemistry of Ng, we calculate the cycle time that CaM molecules alternate between the fully Ca(2+) saturated state and the Ca(2+) unbound state. We then use these results and include diffusion of CaM to illustrate the impact that Ng has on modulating the spatial profile of Ca(2+)-saturated CaM within a model spine compartment. Finally, the first-passage time of CaM to transition from the Ca(2+)-free state to the Ca(2+)-saturated state was calculated with or without Ng present. These analyses suggest that Ng regulates the encounter rate between Ca(2+) saturated CaM and its downstream targets during postsynaptic Ca(2+) transients.

Comparative studies of Hox genes in mammalian limb and vertebral pattern formation

Divergence of anterior-posterior (AP) limb pattern and differences in vertebral column morphology are the two main examples of mammalian evolution. The Hox genes (homeobox containing gene) have been implicated in driving evolution of these structures. However, regarding Hox genes, how they contribute to the generation of mammalian morphological diversities, is still unclear. Implementing comparative gene expression and phenotypic rescue studies for different mammalian Hox genes could aid in unraveling this mystery. In the first part of this thesis, the expression pattern of Hoxd13 gene, a key Hox gene in the establishment of the limb AP pattern, was examined in developing limbs of bats and mice. Bat forelimbs exhibit a pronounced asymmetric AP pattern and offer a good model to study the molecular mechanisms that contribute to the variety of mammalian limbs. The data showed that the expression domain of bat Hoxd13 was shifted prior to the asymmetric limb plate expansion, whereas its domain in mice was much more symmetric. This finding reveals a correlation between the divergence of Hoxd13 expression and the AP patterning difference in limb development. The second part of this thesis details a phenotypic rescue approach by human HOXB1-9 transgenes in mice with Hoxb1-9 deletion, The mouse mutants displayed homeosis in cervical and anterior thoracic vertebrae. The human transgenes entirely rescued the mouse mutants, suggesting that these human HOX genes have similar functions to their mouse orthologues in anterior axial skeletal patterning. The anterior expressing human HOXB transgenes such as HOXB1-3 were expressed in the mouse embryonic trunk in a similar manner as their murine orthologues. However, the anterior boundary of human HOXB9 expression domain was more posterior than that of the mouse Hoxb9 by 2-3 somites. These data provide the molecular support for the hypothesis that Hox genes are responsible for maintaining similar anterior axial skeletal architectures cervical and anterior thoracic regions, but different architectures in lumbar and posterior thoracic regions between humans and mice. ^

Pattern formation of parametrically driven surface waves induced by vibration

Esta tesis se centra en la generación de ondas superficiales subarmónicas en fluidos sometidos a vibración forzada en el régimen gravitatorio capilar con líquidos de baja viscosidad. Tres problemas diferentes han sido estudiados: un contenedor rectangular con vibración horizontal, la misma geometría pero con una combinación de vibración vertical y horizontal y un obstáculo completamente sumergido vibrado verticalmente en un contenedor grande. Se deriva una ecuación de amplitud desde primeros principios para describir las ondas subarmónicas con forzamiento parámetrico inducido por la vibración. La ecuación es bidimensional mientras que el problema original es tridimensional y admite un forzamiento espacial no uniforme. Usando esta ecuación los tres sistemas han sido analizados, centrándose en calcular la amplitud crítica, la orientación de los patrones y el carácter temporal de los patrones espaciotemporales, que pueden ser estrictamente subarmónicos o cuasiperiodicos con una frecuencia de modulación temporal. La dependencia con los parámetros adimensionales también se considera. La teoría será comparada con los experimentos disponibles en la literatura. Abstract This thesis focus on the generation of subharmonic surface waves on fluids subject to forced vibration in the gravity-capillary regime with liquids of small viscosity. Three different problems have been considered: a rectangular container under horizontal vibration; the same geometry but under a combination of horizontal and vertical vibration; and a fully submerged vertically vibrated obstacle in a large container. An amplitude equation is derived from first principles that fairly precisely describes the subharmonic surfaces waves parametrically driven by vibration. That equation is two dimensional while the underlying problem is three-dimensional and permits spatially nonuniform forcing. Using this equation, the three systems have been analyzed, focusing on the calculation of the threshold amplitude, the pattern orientation, and the temporal character of the spatio-temporal patterns, which can be either strictly subharmonic or quasi-periodic, showing an additional modulation frequency. Dependence on the non-dimensional parameters is also considered. The theory is compared with the experiments available in the literature.

Metabolism to a response pathway selective retinoid ligand during axial pattern formation

We report identification of 9-cis-4-oxo-retinoic acid (9-cis-4-oxo-RA) as an in vivo retinoid metabolite in Xenopus embryos. 9-Cis-4-oxo-RA bound receptors (RARs) α, β, and γ as well as retinoid X receptors (RXRs) α, β, and γ in vitro. However, this retinoid displayed differential RXR activation depending on the response pathway used. Although it failed to activate RXRs in RXR homodimers, it activated RXRs and RARs synergistically in RAR-RXR heterodimers. 9-Cis-4-oxo-RA thus acted as a dimer-specific agonist. Considering that RAR-RXR heterodimers are major functional units involved in transducing retinoid signals during embryogenesis and that 9-cis-4-oxo-RA displayed high potency for modulating axial pattern formation in Xenopus, metabolism to 9-cis-4-oxo-RA may provide a mechanism to target retinoid action to this and other RAR-RXR heterodimer-mediated processes.

Molecular genetics of pattern formation in the inner ear: Do compartment boundaries play a role?

The membranous labyrinth of the inner ear establishes a precise geometrical topology so that it may subserve the functions of hearing and balance. How this geometry arises from a simple ectodermal placode is under active investigation. The placode invaginates to form the otic cup, which deepens before pinching off to form the otic vesicle. By the vesicle stage many genes expressed in the developing ear have assumed broad, asymmetrical expression domains. We have been exploring the possibility that these domains may reflect developmental compartments that are instrumental in specifying the location and identity of different parts of the ear. The boundaries between compartments are proposed to be the site of inductive interactions required for this specification. Our work has shown that sensory organs and the endolymphatic duct each arise near the boundaries of broader gene expression domains, lending support to this idea. A further prediction of the model, that the compartment boundaries will also represent lineage-restriction compartments, is supported in part by fate mapping the otic cup. Our data suggest that two lineage-restriction boundaries intersect at the dorsal pole of the otocyst, a convergence that may be critical for the specification of endolymphatic duct outgrowth. We speculate that the patterning information necessary to establish these two orthogonal boundaries may emanate, in part, from the hindbrain. The compartment boundary model of ear development now needs to be tested through a variety of experimental perturbations, such as the removal of boundaries, the generation of ectopic boundaries, and/or changes in compartment identity.

Synaptic pattern formation during cellular recognition

Cell–cell recognition often requires the formation of a highly organized pattern of receptor proteins (a synapse) in the intercellular junction. Recent experiments [e.g., Monks, C. R. F., Freiberg, B. A., Kupfer, H., Sciaky, N. & Kupfer, A. (1998) Nature (London) 395, 82–86; Grakoui, A., Bromley, S. K., Sumen, C., Davis, M. M., Shaw, A. S., Allen, P. M. & Dustin, M. L. (1999) Science 285, 221–227; and Davis, D. M., Chiu, I., Fassett, M., Cohen, G. B., Mandelboim, O. & Strominger, J. L. (1999) Proc. Natl. Acad. Sci. USA 96, 15062–15067] vividly demonstrate a complex evolution of cell shape and spatial receptor–ligand patterns (several microns in size) in the intercellular junction during immunological synapse formation. The current view is that this dynamic rearrangement of proteins into organized supramolecular activation clusters is driven primarily by active cytoskeletal processes [e.g., Dustin, M. L. & Cooper, J. A. (2000) Nat. Immunol. 1, 23–29; and Wulfing, C. & Davis, M. M. (1998) Science 282, 2266–2269]. Here, aided by a quantitative analysis of the relevant physico-chemical processes, we demonstrate that the essential characteristics of synaptic patterns observed in living cells can result from spontaneous self-assembly processes. Active cellular interventions are superimposed on these self-organizing tendencies and may also serve to regulate the spontaneous processes. We find that the protein binding/dissociation characteristics, protein mobilities, and membrane constraints measured in the cellular environment are delicately balanced such that the length and time scales of spontaneously evolving patterns are in near-quantitative agreement with observations for synapse formation between T cells and supported membranes [Grakoui, A., Bromley, S. K., Sumen, C., Davis, M. M., Shaw, A. S., Allen, P. M. & Dustin, M. L. (1999) Science 285, 221–227]. The model we present provides a common way of analyzing immunological synapse formation in disparate systems (e.g., T cell/antigen-presenting cell junctions with different MHC-peptides, natural killer cells, etc.).

Auxin as a positional signal in pattern formation in plants.

By using a novel, extremely sensitive and specific gas chromatography-mass spectrometry technique we demonstrate in Pinus sylvestris (L.) trees the existence of a steep radial concentration gradient of the endogenous auxin, indole-3-acetic acid, over the lateral meristem responsible for the bulk of plant secondary growth, the vascular cambium. This is the first evidence that plant morphogens, such as indole-3-acetic acid, occur in concentration gradients over developing tissues. This finding gives evidence for a regulatory system in plants based on positional signaling, similar to animal systems.

Pattern formation in volumetrically heated fluids

Finite element simulations have been performed along side normal mode analysis on the linear stability that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.