Higher Dimensional Lattice Chains and Delannoy Numbers

Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new proof of a recent result of Duichi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

In vivo pharmacological activity and biodistribution of S-nitrosophytochelatins after intravenous and intranasal administration in mice

AbstractS-nitrosophytochelatins (SNOPCs) are novel analogues of S-nitrosoglutathione (GSNO) with the advantage of carrying varying ratios of S-nitrosothiol (SNO) moieties per molecule. Our aim was to investigate the in vivo pharmacological potency and biodistribution of these new GSNO analogues after intravenous (i.v.) and intranasal (i.n.) administration in mice. SNOPCs with either two or six SNO groups and GSNO were synthesized and characterized for purity. Compounds were administered i.v. or i.n. at 1 μmol NO/kg body weight to CD-1 mice. Blood pressure was measured and biodistribution studies of total nitrate and nitrite species (NOx) and phytochelatins were performed after i.v. administration. At equivalent doses of NO, it was observed that SNOPC-6 generated a rapid and significantly greater reduction in blood pressure (∼60% reduction compared to saline) whereas GSNO and SNOPC-2 only achieved a 30–35% decrease. The reduction in blood pressure was transient and recovered to baseline levels within ∼2 min for all compounds. NOx species were transiently elevated (over 5 min) in the plasma, lung, heart and liver. Interestingly, a size-dependent phytochelatin accumulation was observed in several tissues including the heart, lungs, kidney, brain and liver. Biodistribution profiles of NOx were also obtained after i.n. administration, showing significant lung retention of NOx over 15 min with minor systemic increases observed from 5 to 15 min. In summary, this study has revealed interesting in vivo pharmacological properties of SNOPCs, with regard to their dramatic hypotensive effects and differing biodistribution patterns following two different routes of administration

Counting lattice chains and Delannoy paths in higher dimensions

AbstractLattice chains and Delannoy paths represent two different ways to progress through a lattice. We use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in a lattice of arbitrary finite dimension. Specifically, fix nonnegative integers n1,…,nd, and let L denote the lattice of points (a1,…,ad)∈Zd that satisfy 0≤ai≤ni for 1≤i≤d. We prove that the number of chains in L is given by 2nd+1∑k=1kmax′∑i=1k(−1)i+kk−1i−1nd+k−1nd∏j=1d−1nj+i−1nj, where kmax′=n1+⋯+nd−1+1. We also show that the number of Delannoy paths in L equals ∑k=1kmax′∑i=1k(−1)i+k(k−1i−1)(nd+k−1nd)∏j=1d−1(nd+i−1nj). Setting ni=n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

A comparison of Doctor of Physical Therapy students' self-reported empathy with standardized patients perceptions of empathy during a simulated telehealth encounter

Empathy is an important factor in developing a positive patient-provider relationship. It has been shown to lead to improved patient outcomes, well-being, and satisfaction. This study examines the relationship between first-year physical therapy students' self-reported empathy levels and a patient's perceptions of caregiver empathy during a standardized patient interview via telehealth. Forty-five students completed a self-reported empathy survey before the standardized patient encounter using telehealth. Following the experience, standardized patients rated the perceived empathy demonstrated by the students during that patient-provider encounter using 2 validated measures. The mean student self-reported empathy using the Jefferson Scale of Empathy-Health Care Provider Student (JSE-HPS) version was 123.93 (range 95-135 SD 7.328). The standardized Jefferson Scale of Patient Perception of Provider Empathy (JSPPPE) scores showed a mean of 23.8 (range 11-32 SD 3.951) and a mean of 3.16 (range 1-5 SD.85) on the Global Rating of Empathy (GRE). There was no significant correlation found between the JSE-HPS and the JSPPPE, r = -.47, P = .760, or the GRE r = -.166, P = .276. The artificial nature of a standardized patient interaction using the telehealth format for this encounter may have contributed to the students' inability to communicate empathy to the patient and may explain this discrepancy.Published versio

Area, perimeter, height, and width of rectangle visibility graphs

A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width)

A Collaborative Model for Implementing State Common Core School Standards

In this early part of the 21st century, education leaders are increasingly challenged to improve P-12 teaching and learning to increase student achievement and to prepare all students for college and career success. Education reforms such as the adoption of the Common Core Standards within existing policies and practices of state department, district and school bureaucracies requires the repurposing and refocusing of existing resources and structures. This article describes the efforts in one state to employ collaboration to meet the requirements of legislated mandates for implementation of the Common Core Standards in English language arts and mathematics and the implications of the legislated mandates for postsecondary education. Three education entities (a university, schools, and a state agency) collaborated to design and implement professional development to inform K-12 teachers, state agency personnel, and university faculty about legislated mandates for K-12 education (e.g., state implementation of the Common Core Standards for college- and career-readiness, increase in high school graduation rates, etc.). As the state was the first to adopt the Common Core Standards and the first to assess K-12 student learning in this education reform context, this early adopter model of professional development will be useful and informative for others embarking on such efforts

UNLV College of Education Multicultural & Diversity Newsletter

Each morning I wound my way up the steep hill along the deeply rutted dirt path, exchanging daily maaa\u27s with five bleating sheep and shouting out, ¡Hola! in response to the children who gleefully identified me as ¡Gringa! Women and children, colorful bowls of cooked maize balanced atop their heads, sauntered to and from Maria Elena\u27s where their maize would be ground; at home the dough would be shaped and flattened into tortillas, the mainstay of every meal in the small Guatemalan village of San Juan

Event Tracker: a Text Analytics Platform for Use During Disasters

Emergency management organisations currently rely on a wide range of disparate tools and technologies to support the monitoring and management of events during crisis situations. This has a number of disadvantages, in terms of training time for new staff members, reliance on external services, and a lack of integration (and hence poor transfer of information) between those services. On the other hand, Event Tracker is a new solution that aims to provide a unified view of an event, integrating information from emergency response officers, the public (via social media) and also volunteers from around the world. In particular, Event Tracker provides a series of novel functionalities to realise this unified view of the event, namely: real-time identification of critical information, automatic grouping of content by the information needs of response officers, as well as real-time volunteers management and communication. This is supported by an efficient and scalable back-end infrastructure designed to ingest and process high-volumes of real-time streaming data with low latency

Widespread Hydrogenation of the Moons South Polar Cold Traps

The study shows widespread evidence that the Moons permanently shadowed regions (PSR) are enhanced in hydrogen, likely in the form of water ice, as compared to non-permanently shadowed region locations (non-PSRs), to 79deg S. Results are consistent with the original findings of Watson et al, 1961. We use a novel method to aggregate the hydrogen response from all PSR, greater than 2 km wide pixels. Poleward of 79deg S, the PSR have a consistent hydrogen spatial response, which is enhanced in PSR (where the PSRs area density is highest) and diminishes with distance from any PSR (where the PSR area density is lowest). A correlation between the PSRs diameters and their observed hydrogen, is induced by the instrumental blurring of relatively hydrogenated PSR areas. An anomalously enhanced hydrogen concentration observed at Cabeus-1 PSR suggests a second hydrogen budget process at that location. Linear correlations, derived from the PSRs hydrogen observations, from two independent latitude bands, closely predict the hydrogen observation at Shoemaker, the largest area PSR, 1) 75deg to 83deg S, 2) 83deg to 90deg S. Results are consistent with ongoing processes that introduce volatiles to the surface including outgassing, solar wind production with regolith silicates, and mixing from small-scale meteor impacts and diurnal temperature variation. Results are derived from the Collimated Sensor for EpiThermal Neutrons (CSETN), which part of the Lunar Exploration Neutron Detector (LEND), onboard the Lunar Reconnaissance Orbiter (LRO).Comment: 27 pages, 14 Figure