Lyubeznik numbers of monomial ideals

We study Bass numbers of local cohomology modules supported on squarefree monomial ideals paying special attention to Lyubeznik numbers. We build a dictionary between local cohomology modules and minimal free resolutions that allow us to interpret Lyubeznik numbers as the obstruction to the acyclicity of the linear strands of the Alexander dual ideals. The methods we develop also help us to give a bound for the injective dimension of the local cohomology modules in terms of the dimension of the small support.Comment: 28 page

Strong amenability and the infinite conjugacy class property

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.Comment: 20 pages, 3 figures. Some minor corrections to the proof

Adaptive model predictive control for co-ordination of compression and friction brakes in heavy duty vehicles

In this paper, an adaptive model predictive control scheme is designed for speed control of heavy vehicles. The controller co-ordinates use of compression brakes and friction brakes on downhill slopes. Moreover, the model predictive controller takes the actuator constraints into account. A recursive least square scheme with forgetting is used in parallel with the controller to update the estimates of vehicle mass and road grade. The adaptation improved the model predictive controller. Also online estimation of the road grade enhanced the closed-loop performance further by contributing through feedforward control. Simulations of realistic driving scenarios with a validated longitudinal vehicle model are used throughout this paper to illustrate the benefits of co-ordinating the two braking mechanisms and influence of unknown vehicle mass and road grade. Copyright © 2006 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55894/1/917_ftp.pd

Artinian and non-artinian local cohomology modules

Let $M$ be a finite module over a commutative noetherian ring $R$. For ideals \fa and \fb of $R$, the relations between cohomological dimensions of $M$ with respect to \fa, \fb, \fa\cap\fb and \fa+ \fb are studied. When $R$ is local, it is shown that $M$ is generalized Cohen-Macaulay if there exists an ideal \fa such that all local cohomology modules of $M$ with respect to \fa have finite lengths. Also, when $r$ is an integer such that $0\leq r< \dim_R(M)$, any maximal element \fq of the non-empty set of ideals \{\fa : \H_\fa^i(M) is not artinian for some $i$, $i\geq r$$\}$ is a prime ideal and that all Bass numbers of \H_\fq^i(M) are finite for all $i\geq r$.Comment: 10 pages, to appear in Canadian Mathematical Bulleti

Complementary Mass Spectrometry Methods for Characterizing Protein Folding, Structure, and Dynamics

Proteins are involved in virtually every biochemical process. A comprehensive characterization of factors that govern protein function is essential for understanding the biomedical aspects of human health. This dissertation aims to develop complementary mass spectrometry-based methods and apply them to solve problems pertaining to the area of protein structure, folding and dynamics. ‎Chapter 1 uses fast photochemical oxidation of proteins (FPOP) to characterize partially disordered conformers populated under semi-denaturing conditions. In FPOP, ·OH generated by laser photolysis of H2O2 introduces oxidative modifications at solvent accessible side chains. By contrast, buried sites are protected from radical attack. Using apomyoglobin (aMb), it was demonstrated that under optimized conditions undesired can be almost completely eliminated and detailed structural information can be obtained. ‎Chapter 3 combines FPOP with submillisecond mixing to enable studying early events in protein folding. aMb served as a model system for these measurements. Spatially-resolved changes in solvent accessibility follow the folding process. Data revealed that early aMb folding events are driven by both local and sequence-remote docking of hydrophobic side chains. Assembly of a partially formed scaffold after 0.2 ms is followed by stepwise consolidation that ultimately yields the native state. The submillisecond mixer used improved the time resolution by a factor of 50 compared to earlier FPOP experiments. Submillisecond mixing in conjunction with slower mixing techniques help monitor completes folding pathways, from fractions of a millisecond all the way to minutes. ‎Chapter 4 uses ion mobility mass spectrometry (IM-MS) to explore the structural relationship between semi folded solution and gas phase protein conformers. Collision cross sections (CCSs) provide a measure of analyte size. Mb was used as model system because it follows a sequential unfolding pathway that comprises two partially disordered states. IM-MS data showed that the degree of gas phase unfolding is not strongly correlated with the corresponding solution. Gas phase unfolding as well as collapse events can lead to disparities between gaseous and solution structures for partially unfolded proteins. IM-MS data on non-native conformers should therefore be interpreted with caution. ‎Chapter 5 uses HDX-MS to examine the role of conformational dynamics for the function of multi-protein molecular machines such as FoF1 ATP synthase. HDX-MS monitors backbone deuteration kinetics in the presence of D2O. Disordered segments exchange more rapidly than those in tightly folded regions. Measurements of spatially-resolved deuterium are performed using LC-MS. It was found that the H-bonding network of key power transmission elements is insensitive to PMF-induced mechanical stress. Unexpectedly, HDX-MS reveals a pronounced destabilization of the g C-terminus during rotational catalysis under PMF. The behavior of g is attributed to kinetic friction within the apical rotor bearing