Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

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.

Deep near-infrared spectroscopy of high-redshift galaxies: the physical growth of passive systems

The assembly history of massive galaxies is one of the most important aspects of galaxy formation and evolution. Although we have a broad idea of what physical processes govern the early phases of galaxy evolution, there are still many open questions. In this thesis I demonstrate the crucial role that spectroscopy can play in a physical understanding of galaxy evolution. I present deep near-infrared spectroscopy for a sample of high-redshift galaxies, from which I derive important physical properties and their evolution with cosmic time. I take advantage of the recent arrival of efficient near-infrared detectors to target the rest-frame optical spectra of z > 1 galaxies, from which many physical quantities can be derived. After illustrating the applications of near-infrared deep spectroscopy with a study of star-forming galaxies, I focus on the evolution of massive quiescent systems.

Most of this thesis is based on two samples collected at the W. M. Keck Observatory that represent a significant step forward in the spectroscopic study of z > 1 quiescent galaxies. All previous spectroscopic samples at this redshift were either limited to a few objects, or much shallower in terms of depth. Our first sample is composed of 56 quiescent galaxies at 1 < z < 1.6 collected using the upgraded red arm of the Low Resolution Imaging Spectrometer (LRIS). The second consists of 24 deep spectra of 1.5 < z < 2.5 quiescent objects observed with the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE). Together, these spectra span the critical epoch 1 < z < 2.5, where most of the red sequence is formed, and where the sizes of quiescent systems are observed to increase significantly.

We measure stellar velocity dispersions and dynamical masses for the largest number of z > 1 quiescent galaxies to date. By assuming that the velocity dispersion of a massive galaxy does not change throughout its lifetime, as suggested by theoretical studies, we match galaxies in the local universe with their high-redshift progenitors. This allows us to derive the physical growth in mass and size experienced by individual systems, which represents a substantial advance over photometric inferences based on the overall galaxy population. We find a significant physical growth among quiescent galaxies over 0 < z < 2.5 and, by comparing the slope of growth in the mass-size plane dlogR_e/dlogM_∗ with the results of numerical simulations, we can constrain the physical process responsible for the evolution. Our results show that the slope of growth becomes steeper at higher redshifts, yet is broadly consistent with minor mergers being the main process by which individual objects evolve in mass and size.

By fitting stellar population models to the observed spectroscopy and photometry we derive reliable ages and other stellar population properties. We show that the addition of the spectroscopic data helps break the degeneracy between age and dust extinction, and yields significantly more robust results compared to fitting models to the photometry alone. We detect a clear relation between size and age, where larger galaxies are younger. Therefore, over time the average size of the quiescent population will increase because of the contribution of large galaxies recently arrived to the red sequence. This effect, called progenitor bias, is different from the physical size growth discussed above, but represents another contribution to the observed difference between the typical sizes of low- and high-redshift quiescent galaxies. By reconstructing the evolution of the red sequence starting at z ∼ 1.25 and using our stellar population histories to infer the past behavior to z ∼ 2, we demonstrate that progenitor bias accounts for only half of the observed growth of the population. The remaining size evolution must be due to physical growth of individual systems, in agreement with our dynamical study.

Finally, we use the stellar population properties to explore the earliest periods which led to the formation of massive quiescent galaxies. We find tentative evidence for two channels of star formation quenching, which suggests the existence of two independent physical mechanisms. We also detect a mass downsizing, where more massive galaxies form at higher redshift, and then evolve passively. By analyzing in depth the star formation history of the brightest object at z > 2 in our sample, we are able to put constraints on the quenching timescale and on the properties of its progenitor.

A consistent picture emerges from our analyses: massive galaxies form at very early epochs, are quenched on short timescales, and then evolve passively. The evolution is passive in the sense that no new stars are formed, but significant mass and size growth is achieved by accreting smaller, gas-poor systems. At the same time the population of quiescent galaxies grows in number due to the quenching of larger star-forming galaxies. This picture is in agreement with other observational studies, such as measurements of the merger rate and analyses of galaxy evolution at fixed number density.