The alpha-, beta-, and gamma-Protocadherins (gamma-Pcdhs) are cadherin superfamily adhesion molecules encoded by clustered gene families. The 22 gamma-Pcdhs are combinatorially expressed in the central nervous system (CNS) by neurons and astrocytes, and play critical roles in synaptogenesis, dendrite arborization, and the survival of subsets of neurons. The gamma-Pcdhs promiscuously form cis-multimers that interact strictly homophilically in trans (Molumby et al., 2016; Schreiner and Weiner, 2010); the alpha- and beta-Pcdhs were subsequently shown to interact in a similar homophilic manner (Rubinstein et al., 2015; Thu et al., 2014). The Pcdh gene clusters thus have the potential to generate millions of distinct adhesive interfaces, providing CNS cells with molecular identities that shape neuronal morphology. We demonstrated previously that, in mice lacking the gamma-Pcdhs in the cerebral cortex, pyramidal neurons exhibit severely reduced dendrite arborization (Garrett et al., 2012a). This, combined with many studies of gamma-Pcdh interactions in vitro, suggests that homophilic, adhesive gamma-Pcdh interactions between neurons, and between neurons and glia, provide a positive signal for dendrite growth. However, in retinal starburst amacrine cells and cerebellar Purkinje cells, loss of the gamma-Pcdhs resulted in aberrant dendrite fasciculation and self-crossing (Lefebvre et al., 2012), suggesting that these molecules can mediate repulsive self-avoidance between a neuron’s own dendrites. In Chapter I of this thesis I utilized transgenic mice to manipulate expression in vivo, to show that the complexity of a cortical neuron’s dendritic arbor is determined by homophilic gamma-Pcdh isoform matching with other cells. Expression of the same single isoform in a neuron can result in either exuberant, or minimal, dendrite complexity depending on whether surrounding cells express the same isoform. Additionally, loss of gamma-Pcdh in astrocytes, or induced astrocyte-neuron mis-matching, reduces dendrite complexity cell non-autonomously. This indicates a neuron’s pattern of connectivity is indeed regulated by specific interactions between cells that are distinct from the repulsive self-avoidance seen in isoneuronal processes of planar cell types. In addition to modulating dendrite branch development, the gamma-Pcdhs have been shown to regulate the progression of spinal cord synaptogenesis (Garrett and Weiner, 2009). A role for these molecules in cortical dendritic spines and synapses, however, had yet not been examined. In Chapter II of this thesis, I provide evidence that the gamma-Pcdhs negatively regulate synapse formation and spine morphogenesis in forebrain neurons. Mice lacking all gamma-Pcdhs in the cortex exhibit significantly increased spine and synapse density in vivo, while spine density is significantly decreased in mice overexpressing one of the 22 gamma-Pcdh isoforms. To explain this functional result, we present in vitro evidence to show that gamma-Pcdhs physically and functionally interact with the synaptic cell adhesion molecule neuroligin-1. This work suggests a potential new mechanism by which gamma-Pcdhs regulate the “choice” between dendrite arbor growth and formation and/or stabilization of dendritic spines and synapses in the developing brain. Given that disruptions in the pattern and density of dendritic arbors and spines are a hallmark of neurodevelopmental disorders such as autism and Down, Rett, and fragile X syndromes, my work may provide the basic science foundation for future therapeutic approaches focused on Pcdhs and their associated signaling pathways.

Measurements are carried out for dendrite tip growth of succinonitrile-acetone alloys solidifying freely in an undercooled melt. The current experimental investigation is conducted using the equiaxed dendritic solidification experiment (EDSE). This setup allows for precise measurements of the dendrite tip velocity, radius and shape for a range of undercoolings and solute concentrations. The collected data are compared to available theories of free dendritic growth, such as the Lipton-Glicksman-Kurz and Li-Beckermann models. It is found that for dilute succinonitrile-acetone alloys, the measured dendrite tip Péclet numbers agree well with previous theories of free dendritic growth, if the effects of melt convection are taken into account. The tip selection parameter deviates significantly from the pure succinonitrile value and is inversely related to the applied undercooling. Besides, the selection parameter shows no dependence on the solute concentration. These results are consistent with phase-field simulations and preceding experimental investigations. In addition, scaling relationships for the sidebranching shape were obtained in terms of the dendritic envelope, projection area and contour length. These new scaling relations agree well with previous measurements in pure succinonitrile dendrites by Li and Beckermann.

During the critical period of CNS development, dendritic architecture is shaped, in part, by activity-dependent stabilization and elimination of branches. This restructuring is partly dependent on the subunit composition of glutamate receptors in a manner that is both regionally specific and temporally regulated. We used primary cultures of rodent hippocampal neurons to investigate the consequences for hippocampal dendrite development when the glutamate ?-amino-3-hydroxy-5-methyl-4-isoxazoleproprionic acid receptor (AMPAR) subunit composition was altered. Overexpression of the AMPAR subunits GluR1 or GluR2 differentially modified hippocampal dendrite architecture. We investigated signaling pathways known to be involved in activity-dependent circuit development as possible downstream effectors of AMPA-mediated morphogenesis. We identified extracellular signal regulated kinase (ERK) 1/2 as a potential candidate of GluR1-mediated dendrite outgrowth. We found that levels of docosahexaenoic acid (DHA) and a DHA-derived bioactive metabolite, neuroprotectin D1 (NPD1) are differentially regulated by GluR1 and GluR2. DHA, but not NPD1, induced extensive dendritic branching and outgrowth. Overexpression of 15 lipoxygenase 1 (15LOX1), the enzyme responsible for conversion of DHA to NPD1, interrupted outgrowth mediated by GluR1 overexpression. In order to investigate molecular mechanisms that regulated neural circuitry outside of the critical period of CNS development, we examined dendrite morphology across the CNS in response to chronic variable stress (CVS). We found wide-spread changes in circuits implicated in neurocognitive dysfunctions associated with chronic stress, and observed substantial dendritic plasticity in the adult brain. / acase@tulane.edu

Le dispositif d'imagerie X synchrotron, combinant radiographie et diffraction, développé au cours de ma thèse permet une étude in situ et en temps réel des phénomènes dynamiques complexes impliqués dans la solidification des alliages métalliques. Grace à ce dispositif, nous avons pu mettre en évidence le processus de TGZM (Temperature Gradient Zone Melting) et ses effets sur la microstructure de solidification.<br />Nous avons également pu quantifier l'évolution de la composition de l'alliage tout au long du processus de solidification. Nous avons montré comment à partir des images 2D obtenues en diffraction, il est possible – en utilisant la théorie dynamique de la diffraction - de reconstruire une représentation 3D des dendrites avant leur mûrissement. Nous avons pu observer et quantifier des phénomènes mécaniques réversibles (rotation) ou irréversibles (fléchissement) au sein de la microstructure dendritique.<br />Enfin, nous avons étudié les déformations apparues suite à la solidification de la phase eutectique.

Aluminum alloys are widely used in many manufacturing areas due to good castability, lightness and mechanical properties. The purpose of this research is to investigate copper’s influence on an Al-Si-Mg alloy (A356). Copper in the range of 0.6 – 1.6 wt. % has been used in an A356 aluminum based alloy. In this work a simulation of three different casting processes, sand-, die- and high pressure die-casting has been employed with the help of gradient solidification equipment. The microstructure of the samples has been studied by optical and scanning electron microscopy. Materials in both as-cast and heat treated states have been investigated through tensile test bars  to get the mechanical properties of the different conditions.   Questions that have been subjected to answer are what influence does copper have on the plastic deformation and on fracture behavior and whether there is a relationship between the content of copper and increased porosity or not; and in that case explore this relationship  between the amount of copper and the mechanical behaviour.   It has been analyzed that a peak of mechanical properties is obtained with a content about 1.6 wt. % copper. The increment of copper seems to have a remarkable impact on the mechanical properties and especially after the aging process showing a large raise on the ultimate tensile strength and yield strength. Relationship between the copper content and increased porosity could not be found.

This thesis presents a body of work in the field of reconfigurable and neuromorphic circuits and systems. Three main projects were undertaken. The first was using a Field-Programmable Analog Array (FPAA) to model the cable behavior of dendrites using analog circuits. The second was to design, lay out, and test part of a new FPAA, the RASP 2.9v. The final project was to use floating-gate programming to remove offsets in a neuromorphic FPAA, the RASP Neuron 1D.

The size and morphology of the dendrite growth patterns are simulated for laser powder deposition of Ti-Nb alloys under steady-state and transient growth conditions. A phase field model using an adaptive grid technique was employed to simulate the steady-state growth of dendrites on rather small domains, in which fixed local solidification conditions are present. For simulation of dendrite growth patterns at transient conditions, a cellular automaton model was used along with a virtual front tracking technique on larger domains, containing various initial orientations of the solid-liquid (SL) interface. To obtain the required input thermal data, i.e., the temporal distribution of temperature, a finite element analysis was performed along with a novel numerical approach for the real-time addition of new deposition material in each time step, thus building the deposition geometry momentarily. Using the output of the thermal model, the motion and morphology of the SL interface was determined through tracking the isotherm of the solidification temperature. First, in this study, the appropriate set of processing parameters was found through an optimization process using a new concept, laser supplied energy Es, which combines the effects of the energy and powder density in the process. With the developed analytical/experimental procedure, crack and pore-free coatings of Ti-Nb with continuous beads were produced by examining the effects of a few sets of processing parameters, including laser power, laser scan velocity, laser beam diameter and powder feed rate. The results of the thermal model for the optimized set of parameters matched with the thermocouple temperature measurements with only ~5% deviation. The thermal model was able to predict realistic profiles for the temporal development of deposition geometry, thus predicting meaningful morphologies of the SL interface. The model output was easily treated for extraction of local processing parameters, such as the temperature gradient and solidification velocity. These data are very useful when simulating the dendrite growth patterns at steady-state conditions in directional solidification of selected regions in the microstructure. In order to define transient growth conditions, the simulated distribution of temperature can be also directly fed into the microstructure model at each solution time step. Phase field simulations of steady-state growth of dendrites during directional solidification showed a remarkable agreement with the experimental observations for the local dendrite arm spacing across the microstructure. Also qualitatively agreeing with the experiment, the simulated dendrite spacing exhibited a minimum around the mid-height region of the microstructure, which is explained by the counter effect of the temperature gradient and solidification velocity along the height of the sample. On a large domain containing different initial orientations of the SL interface, cellular automaton simulations for transient growth patterns of dendrites could reproduce most qualitative features observed in the microstructure. The dendrite arm spacing gradually decreased from the top of the microstructure. The competition was won by the dendrites growing in areas with higher cooling rates, i.e., in the regions closer to the top of the microstructure. The secondary arms of the primary dendrites, which are initially inclined on the vertical axis, grew extensively only along the overall growth direction and eventually became primary arms in some cases.

The growth of a neuronal dendritic tree depends on the neuron’s internal state and the environment within which it is situated. Different types of neuron develop dendritic trees with specific characteristics, such as the average number of terminal branches and the average length of terminal and intermediate segments. A key aspect of the growth process is the construction of the microtubule cytoskeleton within the dendritic tree. Neurite elongation requires assembly of microtubules from free tubulin at the growth cone. The stability of microtubule bundles is an important factor in determining how likely it is for a growth cone to split to form new daughter branches. Microtubule assembly rates and bundle stability are controlled by microtubule-associated proteins, principally MAP2 in dendrites. Extending previous work (Hely et al, J. Theor. Biol. 210:375-384, 2001) I have developed a mathematical model of neurite outgrowth in which elongation and branching rates are determined by the phosphorylation state of MAP2 at the tips of each terminal branch. Tubulin and MAP2 are produced in the cell body and transported along the neurite by a combination of diffusion and active transport. Microtubule (dis)assembly at neurite tips is a function of tubulin concentration. The rate of assembly depends on the amount of unphosphorylated MAP2 bound to the microtubules and linking them together. Phosphorylation of MAP2 destroys its linking capability and destabilises the microtubule bundles. Each terminal has a probability of branching that depends on the phosphorylation of MAP2 which, in turn, is a function of calcium concentration. Results from this model show that changes in the (de)phosphorylation rates of MAP2 affect the topology of the final dendritic tree. Higher phosphorylation promotes branching and results in trees with many short terminal branches and relatively long intermediate segments. Reducing phosphorylation promotes elongation and inhibits branching.

In this master thesis we investigate, from a topological point of view and without applying Thurston´s Theorem, why the mating of the so called basilica polynomial <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D(z)=z%5E%7B2%7D-1" /> and the dendrite <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7Bi%7D(z)=z%5E%7B2%7D+i" /> is shared with the mating of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D" /> and the dendrite <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-i%7D(z)=z%5E%7B2%7D-i" />. Both these matings equal the rational map <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?R_%7B3%7D(z)=%5Cfrac%7B3%7D%7Bz%5E%7B2%7D+2z%7D" />. Defined in the thesis are for both matings homeomorphic changes of coordinates<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cpsi_%7B-1%7D%5E%7B%5Cpm%7D" /> from the set <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?L=%5Coverset%7B%5Ccirc%7D%7BK%7D%5Cleft(f_%7B-1%7D%20%5Cright)%5Ccup%5Cleft(%5Ccup_%7Bn=0%7D%5E%7B%5Cinfty%7Df_%7B-1%7D%5E%7B%5Ccirc(-n)%7D(z_%7B%5Calpha%7D)%5Cright)" /> to the Fatou and Julia set of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?R_%7B3%7D" />. Here <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?K%5Cleft(f_%7B-1%7D%20%5Cright)" /> is the filled Julia set of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D" /> and <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?z_%7B%5Calpha%7D" /> is the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" />-fixed point of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?K%5Cleft(f_%7B-1%7D%20%5Cright)" />. / I detta examensarbete undersöker vi, från en topologisk synvinkel och utan applicering av Thurstons teorem, varför matchningen av det så kallade basilikapolynomet <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D(z)=z%5E%7B2%7D-1" /> och dendriten <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7Bi%7D(z)=z%5E%7B2%7D+i" /> är delad med matchningen av <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D" /> och dendriten <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-i%7D(z)=z%5E%7B2%7D-i" />. Båda dessa matchningar är lika med den rationella avbildningen  <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?R_%7B3%7D(z)=%5Cfrac%7B3%7D%7Bz%5E%7B2%7D+2z%7D" />. Definierat i examensarbetet är för båda matchningarna homoemorfa koordinatbyten<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cpsi_%7B-1%7D%5E%7B%5Cpm%7D" /> från mängden<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?L=%5Coverset%7B%5Ccirc%7D%7BK%7D%5Cleft(f_%7B-1%7D%20%5Cright)%5Ccup%5Cleft(%5Ccup_%7Bn=0%7D%5E%7B%5Cinfty%7Df_%7B-1%7D%5E%7B%5Ccirc(-n)%7D(z_%7B%5Calpha%7D)%5Cright)" /> till Fatou- och Juliamängden av <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?R_%7B3%7D" />. Här är <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?K%5Cleft(f_%7B-1%7D%20%5Cright)" /> den ifyllda Juliamängden av avbildningen <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?f_%7B-1%7D" /> och <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?z_%7B%5Calpha%7D" /> är den <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" />-fixerade punkten i <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?K%5Cleft(f_%7B-1%7D%20%5Cright)" />.

The size and morphology of the dendrite growth patterns are simulated for laser powder deposition of Ti-Nb alloys under steady-state and transient growth conditions. A phase field model using an adaptive grid technique was employed to simulate the steady-state growth of dendrites on rather small domains, in which fixed local solidification conditions are present. For simulation of dendrite growth patterns at transient conditions, a cellular automaton model was used along with a virtual front tracking technique on larger domains, containing various initial orientations of the solid-liquid (SL) interface. To obtain the required input thermal data, i.e., the temporal distribution of temperature, a finite element analysis was performed along with a novel numerical approach for the real-time addition of new deposition material in each time step, thus building the deposition geometry momentarily. Using the output of the thermal model, the motion and morphology of the SL interface was determined through tracking the isotherm of the solidification temperature. First, in this study, the appropriate set of processing parameters was found through an optimization process using a new concept, laser supplied energy Es, which combines the effects of the energy and powder density in the process. With the developed analytical/experimental procedure, crack and pore-free coatings of Ti-Nb with continuous beads were produced by examining the effects of a few sets of processing parameters, including laser power, laser scan velocity, laser beam diameter and powder feed rate. The results of the thermal model for the optimized set of parameters matched with the thermocouple temperature measurements with only ~5% deviation. The thermal model was able to predict realistic profiles for the temporal development of deposition geometry, thus predicting meaningful morphologies of the SL interface. The model output was easily treated for extraction of local processing parameters, such as the temperature gradient and solidification velocity. These data are very useful when simulating the dendrite growth patterns at steady-state conditions in directional solidification of selected regions in the microstructure. In order to define transient growth conditions, the simulated distribution of temperature can be also directly fed into the microstructure model at each solution time step. Phase field simulations of steady-state growth of dendrites during directional solidification showed a remarkable agreement with the experimental observations for the local dendrite arm spacing across the microstructure. Also qualitatively agreeing with the experiment, the simulated dendrite spacing exhibited a minimum around the mid-height region of the microstructure, which is explained by the counter effect of the temperature gradient and solidification velocity along the height of the sample. On a large domain containing different initial orientations of the SL interface, cellular automaton simulations for transient growth patterns of dendrites could reproduce most qualitative features observed in the microstructure. The dendrite arm spacing gradually decreased from the top of the microstructure. The competition was won by the dendrites growing in areas with higher cooling rates, i.e., in the regions closer to the top of the microstructure. The secondary arms of the primary dendrites, which are initially inclined on the vertical axis, grew extensively only along the overall growth direction and eventually became primary arms in some cases.