The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Urban Scale Modeling of Atmospheric Carbon Dioxide and Validation of Emission Inventories

There exists a pressing need for high resolution emissions inventories for cities. For greenhouse gases, cities and regions need a careful analysis of their carbon footprint to design effective policies to control and mitigate emissions. High resolution emissions inventories can be used in conjunction with meteorology models and atmospheric measurements to place top-down constraints on emissions. High resolution emissions inventories for criteria pollutants like NOx, CO, and O3 enable urban-scale air pollution modeling down to the neighborhood level. For example, the Vulcan project estimates CO2 using county-scale vehicle miles traveled (VMT) from the National Mobile Inventory Model (NMIM) County Database (NCD). The Hestia Project similarly allocates CO2 from Vulcan’s county-level inventory down to the building scale using eQUEST and building footprints. On-road transport is the most important sector for anthropogenic CO2, 38% in Portland, 32% nationally. Here we show a new model of CO2 emissions for the Portland, OR metropolitan region. The backbone is traffic counter recordings made by the Portland Bureau of Transportation at 9,352 sites over 21 years (1986-2006), augmented with PORTAL (The Portland Regional Transportation Archive Listing) freeway data. We constructed a regression model to fill in traffic network gaps using GIS data such as road class and population density. EPA MOVES was used to estimate transportation CO2 emissions. Our transportation emissions served as input into WRF meteorological modeling to simulate atmospheric CO2 at sites where frequent CO2 measurements are made. We show preliminary model results

Supply-side approaches to the economic valuation of coastal and marine habitat in the Red Sea

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of King Saud University - Science 25 (2013): 217–228, doi:10.1016/j.jksus.2013.02.006.The degradation of natural fish habitat in the ocean implies lost economic benefits. These value losses often are not measured or anticipated fully, and therefore they are mainly ignored in decisions to develop the coast for industrial or residential purposes. In such circumstances, the ocean habitat and its associated ecosystem are treated as if they are worthless. Measures of actual or potential economic values generated by fisheries in commercial markets can be used to assess a conservative (lower-bound) value of ocean habitat. With this information, one can begin to compare the values of coastal developments to the values of foregone ocean habitat in order to help understand whether development would be justified economically. In this paper, we focus on the economic value associated with the harvesting of commercial fish stocks as a relevant case for the Saudi Arabian portion of the Red Sea. We describe first the conceptual basis behind supply-side approaches to economic valuation. Next we review the literature on the use of these methods for valuing ocean habitat. We provide an example based on recent research assessing the bioeconomic status of the traditional fisheries of the Red Sea in the Kingdom of Saudi Arabia (KSA). We estimate the economic value of ecosystem services provided by the KSA Red Sea coral reefs, finding that annual per-unit values supporting the traditional fisheries only are on the order of $7000/km2. Finally, we develop some recommendations for refining future applications of these methods to the Red Sea environment and for further research.This research is based on work supported by Award Nos. USA 00002 and KSA 00011 made by the King Abdullah University of Science and Technology (KAUST)

Sudden unexpected death in epilepsy: mechanisms, risk factors and the role of the nurse

Epilepsy is a disease which can have significant effects upon a person’s life. A subject discussed less frequently is sudden unexpected death in epilepsy (SUDEP). This article summarises the main risk factors for its occurrence; notably, seizure types, medications management and sleeping position. It discusses potential pathophysiological mechanisms, including the emerging research on laryngospasm and the role that genetics may play in increasing risk. Finally, it identifies several nursing responsibilities within the structure of a SUDEP checklist that has been shown to improve patient outcomes. It discusses how these responsibilities are underpinned by patient education and the need for all nurses to develop their own knowledge of epilepsy and SUDEP to facilitate this

Integrated Clinical and Magnetic Resonance Imaging Assessments Late After Fontan Operation

BACKGROUND Several clinical and cardiac magnetic resonance (CMR)-derived parameters have been shown to be associated with death or heart transplant late after the Fontan operation. OBJECTIVES The objective of this study was to identify the relative importance and interactions of clinical and CMR-based parameters for risk stratification after the Fontan operation. METHODS Fontan patients were retrospectively reviewed. Clinical and CMR parameters were analyzed using univariable Cox regression. The primary endpoint was time to death or (listing for) heart transplant. To identify the patients at highest risk for the endpoint, classification and regression tree survival analysis was performed, including all significant variables from Cox regression. RESULTS The cohort consisted of 416 patients (62% male) with a median age of 16 years (25th, 75th percentiles: 11, 23 years). Over a median follow-up of 5.4 years (25th, 75th percentiles: 2.4, 10.0 years) after CMR, 57 patients (14%) reached the endpoint (46 deaths, 7 heart transplants, 4 heart transplant listings). Lower total indexed end-diastolic volume (EDVi) was the strongest predictor of transplant-free survival. Among patients with dilated ventricles (EDVi >= 156 ml/BSA(1.3)), worse global circumferential strain (GCS) was the next most important predictor (73% vs. 44%). In patients with smaller ventricles (EDVi = II was the next most important predictor (30% vs. 4%). CONCLUSIONS In this cohort of patients late after Fontan operation, increased ventricular dilation was the strongest independent predictor of death or transplant (listing). Patients with both ventricular dilation and worse GCS were at highest risk. These data highlight the value of integrating CMR and clinical parameters for risk stratification in this population. (C) 2021 by the American College of Cardiology Foundation

The rat retrosplenial cortex as a link for frontal functions: a lesion analysis

Cohorts of rats with excitotoxic retrosplenial cortex lesions were tested on four behavioural tasks sensitive to dysfunctions in prelimbic cortex, anterior cingulate cortex, or both. In this way the study tested whether retrosplenial cortex has nonspatial functions that reflect its anatomical interactions with these frontal cortical areas. In Experiment 1, retrosplenial cortex lesions had no apparent effect on a set-shifting digging task that taxed intradimensional and extradimensional attention, as well as reversal learning. Likewise, retrosplenial cortex lesions did not impair a strategy shift task in an automated chamber, which involved switching from visual-based to response-based discriminations and, again, included a reversal (Experiment 2). Indeed, there was evidence that the retrosplenial lesions aided the initial switch to response-based selection. No lesion deficit was found on an automated cost-benefit task that pitted size of reward against effort to achieve that reward (Experiment 3). Finally, while retrosplenial cortex lesions affected matching-to-place task in a T-maze, the profile of deficits differed from that associated with prelimbic cortex damage (Experiment 4). When the task was switched to a nonmatching design, retrosplenial cortex lesions had no apparent effect on performance. The results from the four experiments show that many frontal tasks do not require the retrosplenial cortex, highlighting the specificity of their functional interactions. The results show how retrosplenial cortex lesions spare those learning tasks in which there is no mismatch between the internal and external representations used to guide behavioural choice. In addition, these experiments further highlight the importance of the retrosplenial cortex in solving tasks with a spatial component

Pilot study of a social network intervention for heroin users in opiate substitution treatment: study protocol for a randomized controlled trial

Background: Research indicates that 3% of people receiving opiate substitution treatment (OST) in the UK manage to achieve abstinence from all prescribed and illicit drugs within 3 years of commencing treatment, and there is concern that treatment services have become skilled at engaging people but not at helping them to enter a stage of recovery and drug abstinence. The National Treatment Agency for Substance Misuse recommends the involvement of families and wider social networks in supporting drug users' psychological treatment, and this pilot randomized controlled trial aims to evaluate the impact of a social network-focused intervention for patients receiving OST.Methods and design: In this two-site, early phase, randomized controlled trial, a total of 120 patients receiving OST will be recruited and randomized to receive one of three treatments: 1) Brief Social Behavior and Network Therapy (B-SBNT), 2) Personal Goal Setting (PGS) or 3) treatment as usual. Randomization will take place following baseline assessment. Participants allocated to receive B-SBNT or PGS will continue to receive the same treatment that is routinely provided by drug treatment services, plus four additional sessions of either intervention. Outcomes will be assessed at baseline, 3 and 12 months. The primary outcome will be assessment of illicit heroin use, measured by both urinary analysis and self-report. Secondary outcomes involve assessment of dependence, psychological symptoms, social satisfaction, motivation to change, quality of life and therapeutic engagement. Family members (n = 120) of patients involved in the trial will also be assessed to measure the level of symptoms, coping and the impact of the addiction problem on the family member at baseline, 3 and 12 months.Discussion: This study will provide experimental data regarding the feasibility and efficacy of implementing a social network intervention within routine drug treatment services in the UK National Health Service. The study will explore the impact of the intervention on both patients receiving drug treatment and their family members.Trial registration: Trial Registration Number: ISRCTN22608399. ISRCTN22608399 registration: 27/04/2012. Date of first randomisation: 14/08/2012. © 2013 Day et al.; licensee BioMed Central Ltd

Two‐species, 3D, MHD simulation of Europa's interaction with Jupiter's magnetosphere

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95391/1/grl12120.pd