Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality

Bibliography: pages 93-101.The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory

Quantitative Assessment of the Anatomical Footprint of the C1 Pedicle Relative to the Lateral Mass: A Guide for C1 Lateral Mass Fixation

Study Design: Anatomic study. Objectives: To determine the relationship of the anatomical footprint of the C1 pedicle relative to the lateral mass (LM). Methods: Anatomic measurements were made on fresh frozen human cadaveric C1 specimens: pedicle width/height, LM width/height (minimum/maximum), LM depth, distance between LM’s medial aspect and pedicle’s medial border, distance between LM’s lateral aspect to pedicle’s lateral border, distance between pedicle’s inferior aspect and LM’s inferior border, distance between arch’s midline and pedicle’s medial border. The percentage of LM medial to the pedicle and the distance from the center of the LM to the pedicle’s medial wall were calculated. Results: A total of 42 LM were analyzed. The C1 pedicle’s lateral aspect was nearly confluent with the LM’s lateral border. Average pedicle width was 9.0 ± 1.1 mm, and average pedicle height was 5.0 ± 1.1 mm. Average LM width and depth were 17.0 ± 1.6 and 17.2 ± 1.6 mm, respectively. There was 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle, which constituted 41% ± 9% of the LM’s width. The distance from C1 arch’s midline to the medial pedicle was 13.5 ± 2.0 mm. The LM’s center was 1.6 ± 1 mm lateral to the medial pedicle wall. There was on average 3.5 ± 0.6 mm of the LM inferior to the pedicle inferior border. Conclusions: The center of the lateral mass is 1.6 ± 1 mm lateral to the medial wall of the C1 pedicle and approximately 15 mm from the midline. There is 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle. Thus, the medial aspect of C1 pedicle may be used as an anatomic reference for locating the center of the C1 LM for screw fixation

Clinical Outcomes After Four-Level Anterior Cervical Discectomy and Fusion.

Study Design: Retrospective cohort study. Objectives: Anterior cervical discectomy and fusion (ACDF) demonstrates reliable improvement in neurologic symptoms associated with anterior compression of the cervical spine. There is a paucity of data on outcomes following 4-level ACDFs. The purpose of this study was to evaluate clinical outcomes for patients undergoing 4-level ACDF. Methods: All 4-level ACDFs with at least 1-year clinical follow-up were identified. Clinical outcomes, including fusion rates, neurologic outcomes, and reoperation rates were determined. Results: Retrospective review of our institutional database revealed 25 patients who underwent 4-level ACDF with at least 1-year clinical follow-up. Average age was 57.5 years (range 38.2-75.0 years); 14 (56%) were male, and average body mass index was 30.2 kg/m Conclusions: Review of our institution\u27s experience demonstrated a low rate of revision cervical surgery for any reason of 8% at mean 19 months follow-up, and neurological examinations consistently improved, despite a high rate of radiographic nonunion (31%)

Using K-Means Clustering and Neural Net Analysis to Define and Predict Chicago Neighborhood Energy Consumption Trends

Energy markets worldwide are facing two primary issues: 1) meeting exponentially increasing demand and 2) satisfying external pressures to transition to clean energy sources. This report studies electricity consumption patterns in the City of Chicago through historical socioeconomic data. Using an unsupervised method of analysis (K-Means Cluster) together with a supervised method (Neural Net), our report provides three classifications of Chicago neighborhoods and identifies the strongest predictors of electricity consumption in each. Using this analysis framework, major cities can effectively devise long-term strategies for meeting energy demand while planning for a sustainable future

A New N-terminal Recognition Domain in Caveolin-1 Interacts with Sterol Carrier Protein-2 (SCP-2)

Although plasma membrane domains, such as caveolae, provide an organizing principle for signaling pathways and cholesterol homeostasis in the cell, relatively little is known regarding specific mechanisms, whereby intracellular lipid-binding proteins are targeted to caveolae. Therefore, the interaction between caveolin-1 and sterol carrier protein-2 (SCP-2), a protein that binds and transfers both cholesterol and signaling lipids (e.g., phosphatidylinositides and sphingolipids), was examined by yeast two-hybrid, in vitro binding and fluorescence resonance energy transfer (FRET) analyses. Results of the in vivo and in vitro assays identified for the first time the N-terminal amino acids (aa) 1−32 amphipathic α helix of SCP-2 functionally interacted with caveolin-1. This interaction was independent of the classic caveolin-1 scaffolding domain, in which many signaling proteins interact. Instead, SCP-2 bound caveolin-1 through a new domain identified in the N-terminal domain of caveolin-1 between aa 34−40. Modeling studies suggested that electrostatic interactions between the SCP-2 N-terminal aa 1−32 amphipathic α-helical domain (cationic, positively charged face) and the caveolin-1 N-terminal aa 33−59 α helix (anionic, negatively charged face) may significantly contribute to this interaction. These findings provide new insights on how SCP-2 enhances cholesterol retention within the cell as well as regulates the distribution of signaling lipids, such as phosphoinositides and sphingolipids, at plasma membrane caveolae

Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning

In many real-world settings, a team of agents must coordinate its behaviour while acting in a decentralised fashion. At the same time, it is often possible to train the agents in a centralised fashion where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a mixing network that estimates joint action-values as a monotonic combination of per-agent values. We structurally enforce that the joint-action value is monotonic in the per-agent values, through the use of non-negative weights in the mixing network, which guarantees consistency between the centralised and decentralised policies. To evaluate the performance of QMIX, we propose the StarCraft Multi-Agent Challenge (SMAC) as a new benchmark for deep multi-agent reinforcement learning. We evaluate QMIX on a challenging set of SMAC scenarios and show that it significantly outperforms existing multi-agent reinforcement learning methods.Comment: Extended version of the ICML 2018 conference paper (arXiv:1803.11485