Rapid alteration of thalamocortical axon morphology follows peripheral damage in the neonatal rat.

The effect of day of birth (postnatal day 0; P0) infraorbital nerve section on the morphology of individual thalamocortical axons in rat somatosensory cortex was examined on P3. Thalamic fibers were labeled in fixed brains with the carbocyanine dye 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate, and individual photo-converted thalamocortical fibers were reconstructed. In normal animals on P3, axon arbor terminal formation within layer IV has commenced and terminal arbor width is comparable to that of a cortical "barrel." After infraorbital nerve section, the average width of thalamocortical terminal arbors is significantly greater than is the average arbor width of normal rats of the same age; however, neither the number of branches per terminal arbor nor total arbor length differs between groups. These observations suggest that the role of the periphery in guiding terminal arbor formation is exerted both very rapidly and at the level of the single thalamic axon. Further, these results indicate a close association between individual axon terminal arbor morphology and pattern formation in the rat somatosensory cortex.

Contexto e modularização em redes neurais recorrentes para aprendizagem de seqüências temporais

Este trabalho apresenta um sistema neural modular, que processa separadamente informações de contexto espacial e temporal, para a tarefa de reprodução de sequências temporais. Para o desenvolvimento do sistema neural foram considerados redes neurais recorrentes, modelos estocásticos, sistemas neurais modulares e processamento de informações de contexto. Em seguida, foram estudados três modelos com abordagens distintas para aprendizagem de seqüências temporais: uma rede neural parcialmente recorrente, um exemplo de sistema neural modular e um modelo estocástico utilizando a teoria de modelos markovianos escondidos. Com base nos estudos e modelos apresentados, esta pesquisa propõe um sistema formado por dois módulos sucessivos distintos. Uma rede de propagação direta (módulo estimador de contexto espacial) realiza o processamento de contexto espacial identificando a seqüência a ser reproduzida e fornecendo um protótipo do contexto para o segundo módulo. Este é formado por uma rede parcialmente recorrente (módulo de reprodução de sequências temporais) para aprender as informações de contexto temporal e reproduzir em suas saídas a seqüência identificada pelo módulo anterior. Para a finalidade mencionada, este mestrado utiliza a distribuição de Gibbs na saída do módulo para contexto espacial de forma que este forneça probabilidades de contexto espacial, indicando o grau de certeza do módulo e possibilitando a utilização de procedimentos especiais para os casos de dúvida. O sistema neural foi testado em conjuntos contendo trajetórias abertas, fechadas, e com diferentes situações de ambigüidade e complexidade. Duas situações distintas foram avaliadas: (a) capacidade do sistema em reproduzir trajetórias a partir de pontos iniciais treinados; e (b) capacidade de generalização do sistema reproduzindo trajetórias considerando pontos iniciais ou finais em situações não treinadas. A situação (b) é um problema de difícil ) solução em redes neurais devido à falta de contexto temporal, essencial na reprodução de seqüências. Foram realizados experimentos comparando o desempenho do sistema modular proposto com o de uma rede parcialmente recorrente operando sozinha e um sistema modular neural (TOTEM). Os resultados sugerem que o sistema proposto apresentou uma capacidade de generalização significamente melhor, sem que houvesse uma deterioração na capacidade de reproduzir seqüências treinadas. Esses resultados foram obtidos em sistema mais simples que o TOTEM.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Universality of quantum critical dynamics in a planar optical parametric oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the quantum image critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Knockdown of zebrafish crim1 results in a bent tail phenotype with defects in somite and vascular development

The Crim1 gene encodes a transmembrane protein containing six cysteine-rich repeats similar to those found in the BMP antagonist, chordin (chd). To investigate its physiological role, zebrafish crim1 was cloned and shown to be both maternally and zygotically expressed during zebrafish development in sites including the vasculature, intermediate cell mass. notochord, and otic vesicle. Bent or hooked tails with U-shaped somites were observed in 85% of morphants from 12 hpf. This was accompanied by a loss of muscle pioneer cells. While morpholino knockdown of crim1 showed some evidence of ventralisation, including expansion of the intermediate cell mass (ICM), reduction in head size bent tails and disruption to the somites and notochord, this did not mimic the classically ventralised phenotype, as assessed by the pattern of expression of the dorsal markers chordin, otx2 and the ventral markers eve1, pax2.1, tall and gata1 between 75% epiboly and six-somites. From 24 hpf, morphants displayed an expansion of the ventral mesoderm-derived ICM, as evidenced by expansion of tall. Imo2 and crim1 itself. Analysis of the crim1 morphant phenotype in Tg(fli:EGFP) fish showed a clear reduction in the endothelial cells forming the intersegmental vessels and a loss of the dorsal longitudinal anastomotic vessel (DLAV). Hence, the primary role of zebrafish crim1 is likely to be the regulation of somitic and vascular development. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

The design of a real-time nowcasting system for localised weather

National meteorological offices are largely concerned with synoptic-scale forecasting where weather predictions are produced for a whole country for 24 hours ahead. In practice, many local organisations (such as emergency services, construction industries, forestry, farming, and sports) require only local short-term, bespoke, weather predictions and warnings. This thesis shows that the less-demanding requirements do not require exceptional computing power and can be met by a modern, desk-top system which monitors site-specific ground conditions (such as temperature, pressure, wind speed and direction, etc) augmented with above ground information from satellite images to produce `nowcasts'. The emphasis in this thesis has been towards the design of such a real-time system for nowcasting. Local site-specific conditions are monitored using a custom-built, stand alone, Motorola 6809 based sub-system. Above ground information is received from the METEOSAT 4 geo-stationary satellite using a sub-system based on a commercially available equipment. The information is ephemeral and must be captured in real-time. The real-time nowcasting system for localised weather handles the data as a transparent task using the limited capabilities of the PC system. Ground data produces a time series of measurements at a specific location which represents the past-to-present atmospheric conditions of the particular site from which much information can be extracted. The novel approach adopted in this thesis is one of constructing stochastic models based on the AutoRegressive Integrated Moving Average (ARIMA) technique. The satellite images contain features (such as cloud formations) which evolve dynamically and may be subject to movement, growth, distortion, bifurcation, superposition, or elimination between images. The process of extracting a weather feature, following its motion and predicting its future evolution involves algorithms for normalisation, partitioning, filtering, image enhancement, and correlation of multi-dimensional signals in different domains. To limit the processing requirements, the analysis in this thesis concentrates on an `area of interest'. By this rationale, only a small fraction of the total image needs to be processed, leading to a major saving in time. The thesis also proposes an extention to an existing manual cloud classification technique for its implementation in automatically classifying a cloud feature over the `area of interest' for nowcasting using the multi-dimensional signals.

Generation of primary hepatocyte microarrays by piezoelectric printing

We demonstrate a single-step method for the generation of collagen and poly-l-Lysine (PLL) micropatterns on a poly(ethylene glycol) (PEG) functionalized glass surface for cell based assays. The method involves establishing a reliable silanization method to create an effective non-adhesive PEG layer on glass that inhibits cell attachment, followed by the spotting of collagen or PLL solutions using non-contact piezoelectric printing. We show for the first time that the spotted protein micropatterns remain stable on the PEG surface even after extensive washing, thus significantly simplifying protein pattern formation. We found that adherence and spreading of NIH-3T3 fibroblasts was confined to PLL and collagen areas of the micropatterns. In contrast, primary rat hepatocytes adhered and spread only on collagen micropatterns, where they formed uniform, well defined functionally active cell arrays. The differing affinity of hepatocytes and NIH-3T3 fibroblasts for collagen and PLL patterns was used to develop a simple technique for creating a co-culture of the two cell types. This has the potential to form structured arrays that mimic the in vivo hepatic environment and is easily integrated within a miniaturized analytical platform for developing high throughput toxicity analysis in vitro.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Nonparametric Estimation in the Class of Bisexual Processes with Population-Size Dependent Mating

2000 Mathematics Subject Classification: 60J80, 62M05

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

Interactions between endothelin receptor B and transcription factors Sox10 and Pax3 in the melanocyte lineage

Genetic interactions that underlie developmental processes such as cell differentiation and pattern formation are complex and difficult to elucidate. Neural Crest (NC) cells and their derivatives offer an optimal system in which to probe for these complex interactions as they acquire different cell fates and constitute a variety of structures. The transcription factors Sox10 and Pax3 as well as the transmembrane receptor Endothelin receptor b (Ednrb) are temporally and spatially co-expressed early in NC cells and mutations in these genes lead to similar hypopigmentation phenotypes due to a reduced number of NC-derived melanocyte precursors, the melanoblasts. The goal of this study was to establish whether Sox10 and Ednrb or Pax3 and Ednrb interact to promote normal murine melanocyte development. Crosses of Sox10 or Pax3 with Ednrb heterozygous mutants showed that the double heterozygous hypopigmentation phenotype was significantly more pronounced than phenotypes of single heterozygotes, implying that a synergistic interaction exists between Sox10 and Ednrb and Pax3 and Ednrb. This interaction was further explored by the attempt to rescue the Sox10 and Pax3 hypopigmentation phenotypes by the transgenic addition of Ednrb to melanoblasts. Pigmentation was completely restored in the Sox10 and partially restored in the Pax3 mutant mice. The comparison of the number of melanoblasts in transgenic and non-transgenic Sox10 mutant embryos showed that the transgenic rescue occurred as early as E11.5, a critical time for melanoblast population expansion. Cell survival assays indicated that the rescue was not due to an effect of the transgene on melanoblast survival. A novel phenotype arose when studying the interaction between Ednrb and Pax3. Newborns appeared normal but by 3.5 weeks of age, the affected pups were smaller than normal littermates and developed a dome-shaped head; some also developed thoracic kyphosis. Affected pups were dead by 4 weeks of age: 80% were Pax3Sp/+ and 75% were female. When compared to normal littermates, affected mice had brains with enlarged 4th ventricles and more glia while skeletal staining showed kyphosis, wider rib cages and pelvic differences. An epistatic interaction resulting from the mixing of genetic backgrounds that is exacerbated in the presence of Pax3 heterozygosity is suspected.

Interactions between Endothelin Receptor B and Transcription Factors Sox10 and Pax3 in the Melanocyte Lineage

Genetic interactions that underlie developmental processes such as cell differentiation and pattern formation are complex and difficult to elucidate. Neural Crest (NC) cells and their derivatives offer an optimal system in which to probe for these complex interactions as they acquire different cell fates and constitute a variety of structures. The transcription factors Sox10 and Pax3 as well as the transmembrane receptor Endothelin receptor b (Ednrb) are temporally and spatially co-expressed early in NC cells and mutations in these genes lead to similar hypopigmentation phenotypes due to a reduced number of NC-derived melanocyte precursors, the melanoblasts. The goal of this study was to establish whether Sox10 and Ednrb or Pax3 and Ednrb interact to promote normal murine melanocyte development. Crosses of Sox10 or Pax3 with Ednrb heterozygous mutants showed that the double heterozygous hypopigmentation phenotype was significantly more pronounced than phenotypes of single heterozygotes, implying that a synergistic interaction exists between Sox10 and Ednrb and Pax3 and Ednrb. This interaction was further explored by the attempt to rescue the Sox10 and Pax3 hypopigmentation phenotypes by the transgenic addition of Ednrb to melanoblasts. Pigmentation was completely restored in the Sox10 and partially restored in the Pax3 mutant mice. The comparison of the number of melanoblasts in transgenic and non-transgenic Sox10 mutant embryos showed that the transgenic rescue occurred as early as E11.5, a critical time for melanoblast population expansion. Cell survival assays indicated that the rescue was not due to an effect of the transgene on melanoblast survival. A novel phenotype arose when studying the interaction between Ednrb and Pax3. Newborns appeared normal but by 3.5 weeks of age, the affected pups were smaller than normal littermates and developed a dome-shaped head; some also developed thoracic kyphosis. Affected pups were dead by 4 weeks of age: 80% were Pax3Sp/+ and 75% were female. When compared to normal littermates, affected mice had brains with enlarged 4th ventricles and more glia while skeletal staining showed kyphosis, wider rib cages and pelvic differences. An epistatic interaction resulting from the mixing of genetic backgrounds that is exacerbated in the presence of Pax3 heterozygosity is suspected.