Phenotypic plasticity and developmental instability in leaf traits are common in oak species but the role of environmental factors is not well understood. To decipher possible correlations between different leaf traits and effects of the position of leaves within the tree canopy, we quantified the plasticity of three leaf traits of 30 trees of Quercus alba L., Quercus palustris Muench and Quercus velutina Lam. We hypothesized that trees could modify the shape of their leaves for better adaptation to the variable microclimate within the canopy. Our results demonstrated that the south and north outer leaves were significantly smaller, more lobed and denser than those situated in the inner canopy. The order of leaves on the branch accounted for the plasticity of leaf traits in Q. alba only. Plasticity of lobing in Q. alba and Q. velutina depended on the height of the trees. We detected fluctuating asymmetry (FA) in all three species, but the source of variation depended on branch position in Q. velutina only. FA was more pronounced in north-facing leaves. Plasticity of the leaf traits ranged from small to medium. Plasticity of leaf area and leaf mass per area (LMA) depended on the branch position. However, the plasticity of lobation was not affected by the location of a branch within the tree canopy. Quercus alba and Q. palustris had similar plastic responses but the plasticity of Q. velutina was significantly smaller. We concluded that individual plants detect and cope with environmental stress through vegetative organ modification.

<p>In this thesis, we devise a new finite branch-and-bound algorithm for disjoint bilinear programs. In these problems, there are two vectors of variables, $\b{x}$ and $\b{y}$, and two polytopes $P_{\b{x}}$ and $P_{\b{y}}$ such that $\b{x}$ (resp. $\b{y}$) is chosen from $P_{\b{x}}$ (resp. $P_{\b{y}}$) so that a bilinear objective function is minimized. By a bilinear objective, we mean that the objective becomes linear when either one of $\b{x}$ or $\b{y}$ is fixed. </p> <p>  This branch-and-bound scheme uses a relaxation that is derived using the reformulation-linearization technique (RLT). The RLT relaxation is constructed by taking products of constraints and linearizing the bilinear terms using introduced variables. The quality of this relaxation improves as higher order products and the corresponding monomial terms are linearized. Although it is known that, as RLT relaxations are constructed with increasingly higher order linearizations, the relaxation eventually converges to the true optimal value. However, no finite convergence properties are known. In contrast, we show that the first level of the RLT hierarchy suffices to convexify the problem when one of the polytopes is a simplex. Then, using this insight we devise a new class of relaxations by combining RLT with a variant of the double description procedure, where the latter lifts a polytope into a simplex in a finite number of steps.  This leads us to a finite hierarchy of relaxations that converges to the optimal value. Although this hierarchy is finite, from a computational perspective, we find that the relaxations grow rapidly in size. However, we utilize the insight to derive a simplicial branch-and-bound scheme, that expresses each polytope as a union of simplices allowing us to converge finitely to the optimal solution for the problem. We perform preliminary numerical experiments to show that this approach holds promise and competes favorably with state-of-the-art methods on larger instances.</p>

Available as part of the thesis.

STUDY OBJECTIVE: To investigate the exit point of the motor branch of the nerve to vastus medialis (mNVM) from the posterior division of the femoral nerve. An enhanced understanding of the origin and course of the mNVM will minimize the risk of anesthetizing it when performing a local anesthetic adductor canal nerve block for postoperative analgesia following total knee arthroplasty. METHODS: Anatomical donors, obtained through generous donation to the Anatomical Gift Program at Boston University School of Medicine (BUSM), were used in this study. Dissection of the mNVM was performed in 22 body donors (44 lower limbs). Before the dissection, the thigh length, from the anterior superior iliac spine (ASIS) to the base of the patella was measured. Additionally, following the dissection, the distance from the exit point of the mNVM to the base of the patella was measured. Then, the ratio between the two distances was calculated to provide a straightforward and efficient estimate of the mNVM branch point. SUMMARY OF RESULTS: The mean ± SD thigh length in the 44 lower limbs was 43 cm ± 2.9cm. The mNVM exited the posterior division of the femoral nerve 19.2 cm ± 1.90 cm superior to the base of the patella. The exit point of the mNVM from the posterior division of the femoral nerve was 0.56 ± 0.04 of the distance from the ASIS to the patella base. Pearson correlation was performed in order to examine the relationship between the distance of mNVM from the base of the patella to the total length of the thigh in the 44 limbs. This relationship was significant with P = 0.003. The One-Way Anova revealed no significant difference between male and female body donors in the ratio of the exit point of the mNVM relative to the length of the thigh. CONCLUSION: The mNVM emerges from the posterior division of the femoral nerve at 0.56 ± 0.04 of the thigh lengths as measured from the ASIS to the base of the patella. This finding provides clinicians with a practical and useful guide for determining the injection point for an adductor canal nerve block, a procedure utilized for postoperative analgesia following total knee arthroplasty. Protecting the mNVM during the block will avoid weakening the vastus medialis muscle and may result in greater patient participation in postoperative physical therapy, safer gait and may reduce the risk of falls.

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The formation of axon collateral branches from the pre-existing shafts of axons is an important aspect of neurodevelopment and the response of the nervous system to injury. Both the actin filament and microtubule components of the cytoskeleton are required for the formation of axon branches. Recent work has begun to shed light on how these two elements of the cytoskeleton are integrated by proteins that functionally or physically link the cytoskeleton. While a number of signaling pathways have been determined as having a role in the formation of axon branches, the complexity of the downstream mechanisms and links to specific signaling pathways remain to be fully determined. Neurotrophins are growth factors that have a multitude of roles in the nervous system. In sensory neurons nerve growth factor (NGF) induces branching through activation of phosphoinositide 3-kinase (PI3K). Recently, mitochondria have emerged as major determinants of the sites of axon branching. In this work we reveal a new role of neurotrophins in mitochondria fission. We report that NGF promote a rapid burst of mitochondria fission, followed by a new steady state of mitochondria length and density. Mek- Erk and PI3k pathways are required for NGF-induced fission. Mek-Erk controls fission through Drp1 activation, while we suggest that PI3K may contributes to the actin dependent aspect of fission. Drp1 mediated fission is required for NGF- induced branching in sensory neurons in vitro and the branching of sensory axons along the developing spinal cord. We reveal that fission is also required for the intra-axonal translation of the actin regulatory proteins Cortactin and Arp2 subunit from the Arp2/3 complex, an important aspect of NGF induced branching. Collectively, these observations reveal a novel role of neurotrophins in mitochondria fission and the formation of collateral branching / Neuroscience