How to read probability distributions as statements about process

Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale of information, opportunities arise to understand the processes that generate the commonly observed patterns. Probability expressions may be parsed into four components: the dissipation of all information, except the preservation of average values, taken over the measurement scale that relates changes in observed values to changes in information, and the transformation from the underlying scale on which information dissipates to alternative scales on which probability pattern may be expressed. Information invariances set the commonly observed measurement scales and the relations between them. In particular, a measurement scale for information is defined by its invariance to specific transformations of underlying values into measurable outputs. Essentially all common distributions can be understood within this simple framework of information invariance and measurement scale.Comment: v2: added table of contents, adjusted section numbers v3: minor editing, updated referenc

An analysis of hurricane seasons in the pre-HURDAT era (1751-1850)

An extensive database of the tracks of tropical cyclones in the North Atlantic Ocean since 1851 is known as the North Atlantic Hurricane Database (HURDAT). While this database is valuable to public and private agencies, many of the deadliest hurricanes on record occurred prior to 1851. This study will address the research problem of the availability of historical information and the feasibility of collecting data and producing historical tropical cyclone tracks. This thesis describes a methodology for identifying tropical cyclones that existed during the one hundred year period from 1751-1850 referred to as the “pre-HURDAT era” in this study. Uncovering historical tropical cyclone tracks are important for researchers seeking long term patterns in the climate record. This study is a synthesis of all readily available historical data which can be used to identify the tracks of documented tropical cyclones that occurred during the pre-HURDAT era. To emphasize the applicability of historical hurricane tracks, a study comparing landfall patterns of landfalling east coast hurricanes was also done. These tracks were analyzed using historical chronologies, ship data, and other “regional literature”.Department of GeographyThesis (M.S.

Microbial metabolism: optimal control of uptake versus synthesis

Microbes require several complex organic molecules for growth. A species may obtain a required factor by taking up molecules released by other species or by synthesizing the molecule. The patterns of uptake and synthesis set a flow of resources through the multiple species that create a microbial community. This article analyzes a simple mathematical model of the tradeoff between uptake and synthesis. Key factors include the influx rate from external sources relative to the outflux rate, the rate of internal decay within cells, and the cost of synthesis. Aspects of demography also matter, such as cellular birth and death rates, the expected time course of a local resource flow, and the associated lifespan of the local population. Spatial patterns of genetic variability and differentiation between populations may also strongly influence the evolution of metabolic regulatory controls of individual species and thus the structuring of microbial communities. The widespread use of optimality approaches in recent work on microbial metabolism has ignored demography and genetic structure

Receptor uptake arrays for vitamin B12, siderophores and glycans shape bacterial communities

Molecular variants of vitamin B12, siderophores and glycans occur. To take up variant forms, bacteria may express an array of receptors. The gut microbe Bacteroides thetaiotaomicron has three different receptors to take up variants of vitamin B12 and 88 receptors to take up various glycans. The design of receptor arrays reflects key processes that shape cellular evolution. Competition may focus each species on a subset of the available nutrient diversity. Some gut bacteria can take up only a narrow range of carbohydrates, whereas species such as B.~thetaiotaomicron can digest many different complex glycans. Comparison of different nutrients, habitats, and genomes provide opportunity to test hypotheses about the breadth of receptor arrays. Another important process concerns fluctuations in nutrient availability. Such fluctuations enhance the value of cellular sensors, which gain information about environmental availability and adjust receptor deployment. Bacteria often adjust receptor expression in response to fluctuations of particular carbohydrate food sources. Some species may adjust expression of uptake receptors for specific siderophores. How do cells use sensor information to control the response to fluctuations? That question about regulatory wiring relates to problems that arise in control theory and artificial intelligence. Control theory clarifies how to analyze environmental fluctuations in relation to the design of sensors and response systems. Recent advances in deep learning studies of artificial intelligence focus on the architecture of regulatory wiring and the ways in which complex control networks represent and classify environmental states. I emphasize the similar design problems that arise in cellular evolution, control theory, and artificial intelligence. I connect those broad concepts to testable hypotheses for bacterial uptake of B12, siderophores and glycans.Comment: Added many new references, edited throughou