Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras

We consider finite W-algebras U(g,e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g,e)-modules with integral central character in terms of the highest weight theory for finite W-algebras. As a corollary, we obtain a parametrization of primitive ideals of U(g) with associated variety the closure of the adjoint orbit of e and integral central character.Comment: 38 Pages; made some minor correction

Highest weight theory for finite W-algebras

We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we then formulate some precise conjectures in the case of nilpotent orbits of standard Levi type.Comment: 38 page

03-03 "Reconciling Growth and Environment"

Macroeconomic theory and policy are strongly based on the assumption that economic growth is a fundamental goal. The environmental realities of the twenty- first century compel a reassessment of macro theory in terms of the impact of current growth patterns on planetary ecosystems.This paper examines the macroeconomic impacts of growth in terms of several major areas of conflict between economic demands and ecosystem capacities:

Beyond DNA repair: DNA-PK function in cancer.

UNLABELLED: The DNA-dependent protein kinase (DNA-PK) is a pivotal component of the DNA repair machinery that governs the response to DNA damage, serving to maintain genome integrity. However, the DNA-PK kinase component was initially isolated with transcriptional complexes, and recent findings have illuminated the impact of DNA-PK-mediated transcriptional regulation on tumor progression and therapeutic response. DNA-PK expression has also been correlated with poor outcome in selected tumor types, further underscoring the importance of understanding its role in disease. Herein, the molecular and cellular consequences of DNA-PK are considered, with an eye toward discerning the rationale for therapeutic targeting of DNA-PK. SIGNIFICANCE: Although DNA-PK is classically considered a component of damage response, recent findings illuminate damage-independent functions of DNA-PK that affect multiple tumor-associated pathways and provide a rationale for the development of novel therapeutic strategies

Multi-train trajectory planning

Although different parts of the rail industry may have different primary concerns, all are under increasing pressure to minimise their operational energy consumption. Advances in single-train trajectory optimisation have allowed punctuality and traction energy efficiency to be maximised for isolated trains. However, on a railway network safe separation of trains is ensured by signalling and interlocking systems, so the movement of one train will impact the movement of others. This thesis considers methodologies for multi-train trajectory planning. First, a genetic algorithm is implemented and two bespoke genetic operators proposed to improve specific aspects of the optimisation. Compared with published results, the new optimisation is shown to increase the quality of solutions found by an average of 27.6% and increase consistency by a factor of 28. This allows detailed investigation into the effect of the relative priority given to achieving time targets or increasing energy efficiency. Secondly, the performance of optimised control strategies is investigated in a system containing uncertainty. Solutions optimised for a system without uncertainty perform well in those conditions but their performance quickly degrades as the level of uncertainty increases. To address this, a new genetic algorithm-based optimisation procedure is introduced and shown to find robust solutions in a system with multiple different types of uncertainty. Trade-offs are explored between highly optimised trajectories that are unlikely to be achieved, and slightly less optimal trajectories that are robust to real world disturbances. Finally, a massively parallel multi-train simulator is developed to accelerate population-based heuristic optimisations using a graphical processing unit (GPU). Execution time is minimised by implementing all parts of the simulation and optimisation on the GPU, and by designing data structure and algorithms to work efficiently together. This yields a three orders of magnitude increase in rate at which candidate control strategies can be evaluated

NEUROMECHANICAL CONTRIBUTIONS TO LOWER EXTREMITY STIFFNESS DURING RUNNING AND HOPPING IN HEALTHY RUNNERS

Lower extremity stiffness (KLeg) describes how subjects attenuate load during ground contact while completing dynamic tasks. Alterations in KLeg are associated with increased risk for lower extremity injury. Previous data suggests that lesser mobility during a clinical exam is associated with greater KLeg in healthy runners. The purpose of our study was to analyze the neuromechanical contributions to KLeg during running and hopping in healthy runners. Additionally we analyzed the relationship between running and hopping while also examining the feasibility of utilizing a waist-mounted accelerometer to estimate KLeg in a clinical setting. We analyzed 70 healthy runners with a 2 session cross-sectional study. We collected musculotendinous stiffness of the ankle plantarflexors and knee extensors in session 1. In session 2, we collected KLeg during self-selected running as well as single leg hopping at 3 frequencies (1.5 Hz, self-selected, 3.0 Hz). We also collected waist-mounted accelerations as well as muscle activation of the ankle plantarflexors and knee extensors. We found that at self-selected frequencies and higher, greater KLeg during single leg hopping is significantly associated with greater ankle plantarflexor musculotendinous stiffness, greater ankle plantarflexor muscle activation and greater hopping frequency. Greater KLeg during running is significantly associated with greater knee extensor musculotendinous stiffness, lesser hip internal range of motion and greater running velocity. We found that subjects who demonstrated greater KLeg during single leg hopping also demonstrated greater KLeg during running however this significant relationship was only minimal. Finally, our waist-mounted accelerometer significantly overestimated KLeg across all hopping frequencies. Out study found that active muscle contraction and greater musculotendinous stiffness of the ankle plantflexors and knee extensors are associated with greater KLeg during hopping and running, respectively. These may serve as rehabilitative targets to alter KLeg in the clinical setting. Additionally, assessing KLeg via hopping and with a waist-mounted accelerometer does not accurately reflect KLeg during running determine via motion capture. Additional studies should be completed to improve the clinical assessment of KLeg to reduce the occurrence of lower extremity injuries.Doctor of Philosoph