Voting games with incomplete information

We examine voting situations in which individuals have incomplete information over each others' true preferences. In many respects, this work is motivated by a desire to provide a more complete understanding of so-called probabilistic voting.

Chapter 2 examines the similarities and differences between the incentives faced by politicians who seek to maximize expected vote share, expected plurality, or probability of victory in single member: single vote, simple plurality electoral systems. We find that, in general, the candidates' optimal policies in such an electoral system vary greatly depending on their objective function. We provide several examples, as well as a genericity result which states that almost all such electoral systems (with respect to the distributions of voter behavior) will exhibit different incentives for candidates who seek to maximize expected vote share and those who seek to maximize probability of victory.

In Chapter 3, we adopt a random utility maximizing framework in which individuals' preferences are subject to action-specific exogenous shocks. We show that Nash equilibria exist in voting games possessing such an information structure and in which voters and candidates are each aware that every voter's preferences are subject to such shocks. A special case of our framework is that in which voters are playing a Quantal Response Equilibrium (McKelvey and Palfrey (1995), (1998)). We then examine candidate competition in such games and show that, for sufficiently large electorates, regardless of the dimensionality of the policy space or the number of candidates, there exists a strict equilibrium at the social welfare optimum (i.e., the point which maximizes the sum of voters' utility functions). In two candidate contests we find that this equilibrium is unique.

Finally, in Chapter 4, we attempt the first steps towards a theory of equilibrium in games possessing both continuous action spaces and action-specific preference shocks. Our notion of equilibrium, Variational Response Equilibrium, is shown to exist in all games with continuous payoff functions. We discuss the similarities and differences between this notion of equilibrium and the notion of Quantal Response Equilibrium and offer possible extensions of our framework.

Chemical studies of viral entry mechanisms: I. Hydrophobic protein-lipid interactions during sendai virus membrane fusion. II. Kinetics of bacteriophage λ DNA injection.

Viruses possess very specific methods of targeting and entering cells. These methods would be extremely useful if they could also be applied to drug delivery, but little is known about the molecular mechanisms of the viral entry process. In order to gain further insight into mechanisms of viral entry, chemical and spectroscopic studies in two systems were conducted, examining hydrophobic protein-lipid interactions during Sendai virus membrane fusion, and the kinetics of bacteriophage λ DNA injection.

Sendai virus glycoprotein interactions with target membranes during the early stages of fusion were examined using time-resolved hydrophobic photoaffinity labeling with the lipid-soluble carbene generator3-(trifluoromethyl)-3-(m-^(125 )I] iodophenyl)diazirine (TID). The probe was incorporated in target membranes prior to virus addition and photolysis. During Sendai virus fusion with liposomes composed of cardiolipin (CL) or phosphatidylserine (PS), the viral fusion (F) protein is preferentially labeled at early time points, supporting the hypothesis that hydrophobic interaction of the fusion peptide at the N-terminus of the F_1 subunit with the target membrane is an initiating event in fusion. Correlation of the hydrophobic interactions with independently monitored fusion kinetics further supports this conclusion. Separation of proteins after labeling shows that the F_1 subunit, containing the putative hydrophobic fusion sequence, is exclusively labeled, and that the F_2 subunit does not participate in fusion. Labeling shows temperature and pH dependence consistent with a need for protein conformational mobility and fusion at neutral pH. Higher amounts of labeling during fusion with CL vesicles than during virus-PS vesicle fusion reflects membrane packing regulation of peptide insertion into target membranes. Labeling of the viral hemagglutinin/neuraminidase (HN) at low pH indicates that HN-mediated fusion is triggered by hydrophobic interactions, after titration of acidic amino acids. HN labeling under nonfusogenic conditions reveals that viral binding may involve hydrophobic as well as electrostatic interactions. Controls for diffusional labeling exclude a major contribution from this source. Labeling during reconstituted Sendai virus envelope-liposome fusion shows that functional reconstitution involves protein retention of the ability to undergo hydrophobic interactions.

Examination of Sendai virus fusion with erythrocyte membranes indicates that hydrophobic interactions also trigger fusion between biological membranes, and that HN binding may involve hydrophobic interactions as well. Labeling of the erythrocyte membranes revealed close membrane association of spectrin, which may play a role in regulating membrane fusion. The data show that hydrophobic fusion protein interaction with both artificial and biological membranes is a triggering event in fusion. Correlation of these results with earlier studies of membrane hydration and fusion kinetics provides a more detailed view of the mechanism of fusion.

The kinetics of DNA injection by bacteriophage λ. into liposomes bearing reconstituted receptors were measured using fluorescence spectroscopy. LamB, the bacteriophage receptor, was extracted from bacteria and reconstituted into liposomes by detergent removal dialysis. The DNA binding fluorophore ethidium bromide was encapsulated in the liposomes during dialysis. Enhanced fluorescence of ethidium bromide upon binding to injected DNA was monitored, and showed that injection is a rapid, one-step process. The bimolecular rate law, determined by the method of initial rates, revealed that injection occurs several times faster than indicated by earlier studies employing indirect assays.

It is hoped that these studies will increase the understanding of the mechanisms of virus entry into cells, and to facilitate the development of virus-mimetic drug delivery strategies.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Multilayer Active Shell Mirrors

This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.

Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.

Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.

The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.

Death or taxes? The political economy of sanitation expenditure in nineteenth-century Britain

This thesis consists of three papers studying the relationship between democratic reform, expenditure on sanitation public goods and mortality in Britain in the second half of the nineteenth century. During this period decisions over spending on critical public goods such as water supply and sewer systems were made by locally elected town councils, leading to extensive variation in the level of spending across the country. This dissertation uses new historical data to examine the political factors determining that variation, and the consequences for mortality rates.

The first substantive chapter describes the spread of government sanitation expenditure, and analyzes the factors that determined towns' willingness to invest. The results show the importance of towns' financial constraints, both in terms of the available tax base and access to borrowing, in limiting the level of expenditure. This suggests that greater involvement by Westminster could have been very effective in expediting sanitary investment. There is little evidence, however, that democratic reform was an important driver of greater expenditure.

Chapter 3 analyzes the effect of extending voting rights to the poor on government public goods spending. A simple model predicts that the rich and the poor will desire lower levels of public goods expenditure than the middle class, and so extensions of the right to vote to the poor will be associated with lower spending. This prediction is tested using plausibly exogenous variation in the extent of the franchise. The results strongly support the theoretical prediction: expenditure increased following relatively small extensions of the franchise, but fell once more than approximately 50% of the adult male population held the right to vote.

Chapter 4 tests whether the sanitary expenditure was effective in combating the high mortality rates following the Industrial Revolution. The results show that increases in urban expenditure on sanitation-water supply, sewer systems and streets-was extremely effective in reducing mortality from cholera and diarrhea.