Splitting Behavior of SnS_n-Polynomials

We analyze the probability that, for a fixed finite set of primes S, a random, monic, degree n polynomial f(x) with integer coefficients in a box of side B around 0 satisfies: (i) f(x) is irreducible over the rationals, with splitting field over the rationals having Galois group $S_n$; (ii) the polynomial discriminant Disc(f) is relatively prime to all primes in S; (iii) f(x) has a prescribed splitting type at each prime p in S. The limit probabilities as $B \to \infty$ are described in terms of values of a one-parameter family of measures on $S_n$, called splitting measures, with parameter $z$ evaluated at the primes p in S. We study properties of these measures. We deduce that there exist degree n extensions of the rationals with Galois closure having Galois group $S_n$ with a given finite set of primes S having given Artin symbols, with some restrictions on allowed Artin symbols for p<n. We compare the distributions of these measures with distributions formulated by Bhargava for splitting probabilities for a fixed prime $p$ in such degree $n$ extensions ordered by size of discriminant, conditioned to be relatively prime to $p$.Comment: 33 pages, v2 34 pages, introduction revise

The Cultivation Theory and Reality Television: An Old Theory With a Modern Twist

George Gerbner, a Hungarian-born professor of communication, founded the cultivation theory, one of the most popular and regarded theories in the communications world. Developed in the mid 20th century, the theory focus on the long-term effects of television on people. Longer exposure to signs, images and people on television cultivates their perception of reality in the real world. The television became a household staple during this time. Families often spent time together watching programming together, however, it played out different effects for each person. Television\u27s constant visual and auditory stimulation on a person made it easier to cultivate certain messages, thoughts and feelings into a person, making it a powerful media source. The theory\u27s perception of violence shown on television was a main focal point. Violence associated with different races, genders and sexualities cultivated different perceptions of people. Not everyone\u27s perceptions of society, and some demographics are portrayed very negatively. The theory can still be felt today in the 21st century. Television has continued to cultivate new perceptions of society on more generations. New forms of television programming, such as reality television, have ushered in a new way of cultivating messages, thoughts and feelings. I have taken the cultivation theory, and applied it to a popular television show titled, Below Deck. I have analyzed viewers perception of gender, race, relationships, wealth, workplace drama and behavior. I also touched on the cast\u27s interactions and perceptions of the wealthy too. These topics are not new to television, and have found their way into today\u27s television programming for viewers to perceive

Development and characterization of an intracortical closed-loop brain-computer interface

Intracortical brain-computer interfaces (BCI) have the potential to restore motor function to people with paralysis by extracting movement intent signals directly from motor cortex. While current technology has allowed individuals to perform simple object interactions with robotic arms, such demonstrations have depended exclusively on visual feedback. Additional forms of sensory feedback may lessen the dependence on vision and allow for more dexterous control. Intracortical microstimulation (ICMS) has been proposed as a method of adding somatosensory feedback to BCI by directly stimulating somatosensory cortex to evoke tactile sensations referred to the hand. Our lab recently demonstrated that ICMS can elicit graded and focal tactile sensations in an individual with spinal cord injury (SCI). However, several challenges must be resolved to demonstrate the viability of ICMS as a technique for incorporating sensory feedback in a closed-loop BCI. First, microstimulation generates large voltage transients that appear as artifacts in the neural recordings used for BCI control. These artifacts can corrupt the recorded signal throughout the entire stimulus train, and must be eliminated to allow for continuous BCI decoding. Second, it is unknown whether the sensations elicited by ICMS can be perceived quickly enough for use as a feedback signal. Here, I present several aspects of the development of a closed-loop BCI system, including a method for artifact rejection and the characterization of simple reaction times to ICMS of human somatosensory cortex. A human participant with tetraplegia due to SCI was implanted with four microelectrode arrays in primary motor and somatosensory cortices. I implemented a robust method of artifact rejection that preserves neural data as soon as 750 microseconds after each stimulus pulse by applying signal blanking and an appropriate digital filter. I validated this method by comparing BCI performance with and without ICMS and found that performance was maintained with ICMS and artifact rejection. Next, I characterized simple reaction times to single-channel ICMS, and found that responses to ICMS were comparable, and often faster, than responses to electrical stimulation on the hand. These findings suggest that ICMS is a viable method to provide feedback in a closed-loop BCI

Circadian patterns in postvoid residual and voided percentage among older women with urinary incontinence

Background: Women with urinary incontinence incur an increased risk of elevated postvoid residual (PVR) volume and impaired voiding efficiency (i.e., voided percentage (Void%)), but the clinical significance of these parameters remains poorly described. Further characterization of PVR and voiding efficiency may thus be useful in refining the evaluation and management of urinary incontinence. This study aims to explore possible circadian variations in PVR and Void% in older women with stress (SUI), urge (UUI) and mixed urinary incontinence (MUI). Methods: A single center prospective study which enrolled a convenience sample of 90 older women who consulted a tertiary referral hospital for urinary incontinence. Participants underwent an extensive medical interview and were hospitalized to complete a 24-h frequency-volume chart (FVC) with PVR measurement after each void (FVCPVR). Results: FVCPVR analysis demonstrated no differences in mean PVR and Void% between patients with SUI, UUI and MUI. Likewise, no daytime or nighttime differences were observed in mean PVR or Void% within or between groups. Conclusions: No evidence of circadian variation in PVR or Void% was observed in older women with SUI, UUI or MUI