Prime and Semiprime Inner Functions

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

Telomeres: Linking stress and survival, ecology and evolution.

Telomeres are protective structures at the ends of eukaryotic chromosomes. The loss of telomeres through cell division and oxidative stress is related to cellular aging, organismal growth and disease. In this way, telomeres link molecular and cellular mechanisms with organismal processes, and may explain variation in a number of important life-history traits. Here, we discuss how telomere biology relates to the study of physiological ecology and life history evolution. We emphasize current knowledge on how telomeres may relate to growth, survival and lifespan in natural populations. We finish by examining interesting new connections between telomeres and the glucocorticoid stress response. Glucocorticoids are often employed as indices of physiological condition, and there is evidence that the glucocorticoid stress response is adaptive. We suggest that one way that glucocorticoids impact organismal survival is through elevated oxidative stress and telomere loss. Future work needs to establish and explore the link between the glucocorticoid stress response and telomere shortening in natural populations. If a link is found, it provides an explanatory mechanism by which environmental perturbation impacts life history trajectories.

Harry Potter and the Theory of Things

This thesis investigates the boundaries between body and object in J.K. Rowling’s Harry Potter series, seven children’s literature novels published between 1997 and 2007. Lord Voldemort, Rowling’s villain, creates Horcruxes—objects that contain fragments of his soul—in order to ensure his immortality. As vessels for human soul, these objects rupture the boundaries between body and object and become “things.” Using contemporary thing theorists including John Plotz and materialists Jean Baudrillard and Walter Benjamin, I look at Voldemort’s Horcruxes as transgressive, liminal, unclassifiable entities in the first chapter. If objects can occupy the juncture between body and object, then bodies can as well. Dementors and Inferi, dark creatures that Rowling introduces throughout the series, live devoid of soul. Voldemort, too, becomes a thing as he splits his soul and creates Horcruxes. These soulless bodies are uncanny entities, provoking fear, revulsion, nausea, and the loss of language. In the second chapter, I use Sigmund Freud’s theorization of the uncanny as well as literary critic Kelly Hurley to investigate how Dementors, Inferi, and Voldemort exist as body-turned-object things at the juncture between life and death. As Voldemort increasingly invests his immaterial soul into material objects, he physically and spiritually degenerates, transforming from the young, handsome Tom Marvolo Riddle into the snake-like villain that murdered Harry’s parents and countless others. During his quest to find and destroy Voldemort’s Horcruxes, Harry encounters a different type of object, the Deathly Hallows. Although similarly accessing boundaries between body/object, life/death, and materiality/immateriality, the three Deathly Hallows do not transgress these boundaries. Through the Deathly Hallows, Rowling provides an alternative to thingification: objects that enable boundaries to fluctuate, but not breakdown. In the third chapter, I return to thing theorists, Baudrillard, and Benjamin to study how the Deathly Hallows resist thingification by not transgressing the boundaries between body and object.

Measuring Correlation Between HIV Sequence Variation and Disease Stage of HIV-Infected Individuals

With a virus such as Human Immunodeficiency Virus (HIV) that has infected millions of people worldwide, and with many unaware that they are infected, it becomes vital to understand how the virus works and how it functions at the molecular level. Because there currently is no vaccine and no way to eradicate the virus from an infected person, any information about how the virus interacts with its host greatly increases the chances of understanding how HIV works and brings scientists one step closer to being able to combat such a destructive virus. Thousands of HIV viruses have been sequenced and are available in many online databases for public use. Attributes that are linked to each sequence include the viral load within the host and how sick the patient is currently. Being able to predict the stage of infection for someone is a valuable resource, as it could potentially aid in treatment options and proper medication use. Our approach of analyzing region-specific amino acid composition for select genes has been able to predict patient disease state up to an accuracy of 85.4%. Moreover, we output a set of classification rules based on the sequence that may prove useful for diagnosing the expected clinical outcome of the infected patient.