Generalized Collatz Functions: Cycle Lengths and Statistics

Consider the function T (n) defined on the positive integers as follows. If n is even, T (n) = n/2. If n is odd, T (n) = 3n + 1. The Collatz Conjecture states that for any integer n, the sequence n, T (n), T (T (n)), . . . will eventually reach 1. We consider several generalizations of this function, focusing on functions which replace 3n + 1 with 3n + b for odd b. We show that for all odd b \u3c 400, and all integers n ≤ 106, iterating this function always results in a finite cycle of values. Furthermore, we empirically observe several interesting patterns in the lengths of these cycles for several classes of values of b.Faculty Sponsor: Dr. Dominic Klyv

Radiation osteitis of the clavicle

The bone alterations in the region of the clavicle (3 cases) are similar to those we have observed and described elsewhere in the skeleton i.e., the mandible, maxillary and ethmoid bones. Rarefaction is the result of three different types of bone destruction: osteoclasia, a kind of osteocytic osteolysis only observed after irradiation and obviously related with infection, and a pure demineralization of the osseous tissue by contact with pus. Reconstruction processes, although unable to prevent spontaneous fracture, are also present and correspond to islets of chondroid tissue surrounded by lamellar bone. However, these recently deposited calcified tissues are already necrotic since most of their lacunae are empty.Les modifications osseuses dans la région de la clavicule (3 observations) sont semblables à celles observées ailleurs dans le squelette, par exemple la mandibule, le maxillaire et l’os ethmoïde. La raréfaction osseuse est le résultat de trois types différents de destruction: l’ostéoclasie, une espèce d’ostéolyse ostéocytaire observée après irradiation, en rapport certain avec une infection et une déminéralisation pure du tissu osseux en contact avec du pus. Les phénomènes de reconstruction, bien qu’incapables d’éviter une fracture spontanée, sont également présents et ils correspondent à des îlots de tissu chondroïde au sein de travées d’os lamellaire. Cependant ces tissus calcifiés récemment déposés sont déjà nécrosés puisque les ostéoplastes sont vides

‘Stick that knife in me’: Shane Meadows’ children

This article brings Shane Meadows’ Dead Man's Shoes (2004) into dialogue with the history of the depiction of the child on film. Exploring Meadows’ work for its complex investment in the figure of the child on screen, it traces the limits of the liberal ideology of the child in his cinema and the structures of feeling mobilised by its uses – at once aesthetic and sociological – of technologies of vision

Defect Level Switching for Highly-Nonlinear and Hysteretic Electronic Devices

Nonlinear and hysteretic electrical devices are needed for applications from circuit protection to next-generation computing. Widely-studied devices for resistive switching are based on mass transport, such as the drift of ions in an electric field, and on collective phenomena, such as insulator-metal transitions. We ask whether the large photoconductive response known in many semiconductors can be stimulated in the dark and harnessed to design electrical devices. We design and test devices based on photoconductive CdS, and our results are consistent with the hypothesis that resistive switching arises from point defects that switch between deep- and shallow-donor configurations: defect level switching (DLS). This new electronic device design principle - photoconductivity without photons - leverages decades of research on photoconductivity and defect spectroscopy. It is easily generalized and will enable the rational design of new nonlinear, hysteretic devices for future electronics.Comment: Text and supplemental merged into one fil

Small bowel stromal tumour revealed by a lower gastrointestinal bleeding

Small bowel stromal tumour must be systematically researched in the presence of obscure and persistent low gastrointestinal bleeding despite a normal endoscopic examination (OGDF and colonoscopy). Video capsule endoscopy is the best diagnosis examination; if it is not available a CT enterography could be useful. Surgical treatment is effective on localized and weak malignancy small bowel stromal tumours

Nonlinear Seebeck Effect in a Model Granular Superconductor

The change of the Josephson supercurrent density of a weakly-connected granular superconductor in response to externally applied arbitrary thermal gradient dT/dx (nonlinear Seebeck effect) is considered within a model of 3D Josephson junction arrays. For dT/dx>(dT/dx)_c, where (dT/dx)_c is estimated to be of the order of 10^4 K/m for YBCO ceramics with an average grain's size of 10 microns, the weak-links-dominated thermopower S (Seebeck coefficient) is predicted to become strongly dT/dx-dependent.Comment: REVTEX, no figure

Cannabis Withdrawal Among Detained Adolscents: Exploring the Impact of Nicotine and Race

Rates of marijuana use among detained youths are exceptionally high. Research suggests a cannabis withdrawal syndrome is valid and clinically significant; however, these studies have mostly been conducted in highly controlled laboratory settings with treatment-seeking, White adults. The present study analyzed archival data to explore the magnitude of cannabis withdrawal symptoms within a diverse sample of detained adolescents while controlling for tobacco use and investigating the impact of race on symptom reports. Adolescents recruited from a juvenile correctional facility (N=93) completed a background questionnaire and the Marijuana Withdrawal Checklist. Analyses revealed a significant main effect for level of tobacco use on severity of irritability, and for level of marijuana use on severity of craving to smoke marijuana and strange/wild dreams. Furthermore, a significant main effect for race was found with Black adolescents reporting lower withdrawal discomfort scores and experiencing less severe depressed mood, difficulty sleeping, nervousness/anxiety, and strange/wild dreams. Although exploratory, these findings may have significant clinical implications for providers in juvenile detention facilities, allowing the execution of proper medical and/or behavioral interventions to assist adolescents presenting with problematic cannabis and/or tobacco withdrawal