Basis Criteria for Generalized Spline Modules via Determinant

Given a graph whose edges are labeled by ideals of a commutative ring R with identity, a generalized spline is a vertex labeling by the elements of R such that the difference of the labels on adjacent vertices lies in the ideal associated to the edge. The set of generalized splines has a ring and an R-module structure. We study the module structure of generalized splines where the base ring is a greatest common divisor domain. We give basis criteria for generalized splines on cycles, diamond graphs and trees by using determinantal techniques. In the last section of the paper, we define a graded module structure for generalized splines and give some applications of the basis criteria for cycles, diamond graphs and trees.Comment: 20 pages, 10 figure

Dymamical Casimir emission from polariton condensates

We study theoretically the dynamical Casimir effect in an exciton-polariton condensate that is suddenly created by an ultrashort laser pulse at normal incidence. As a consequence of the abrupt change of the quantum vacuum, Bogoliubov excitations are generated. The subsequent evolution, governed by polariton interactions and losses, is studied within a linearized truncted Wigner approximation. We focus in particular on the momentum distribution and spatial coherence. The limiting behavior at large and small momenta is determined analytically. A simple scaling relation for the final condensate depletion as a function of the system parameters is found and the correlation length is shown to depend linearly on the condensate depletion.Comment: 5 pages, 4 figure

An Adaptive Policy Management Approach to BGP Convergence

The Border Gateway Protocol (BGP) is the current inter-domain routing protocol used to exchange reachability information between Autonomous Systems (ASes) in the Internet. BGP supports policy-based routing which allows each AS to independently adopt a set of local policies that specify which routes it accepts and advertises from/to other networks, as well as which route it prefers when more than one route becomes available. However, independently chosen local policies may cause global conflicts, which result in protocol divergence. In this paper, we propose a new algorithm, called Adaptive Policy Management Scheme (APMS), to resolve policy conflicts in a distributed manner. Akin to distributed feedback control systems, each AS independently classifies the state of the network as either conflict-free or potentially-conflicting by observing its local history only (namely, route flaps). Based on the degree of measured conflicts (policy conflict-avoidance vs. -control mode), each AS dynamically adjusts its own path preferences—increasing its preference for observably stable paths over flapping paths. APMS also includes a mechanism to distinguish route flaps due to topology changes, so as not to confuse them with those due to policy conflicts. A correctness and convergence analysis of APMS based on the substability property of chosen paths is presented. Implementation in the SSF network simulator is performed, and simulation results for different performance metrics are presented. The metrics capture the dynamic performance (in terms of instantaneous throughput, delay, routing load, etc.) of APMS and other competing solutions, thus exposing the often neglected aspects of performance.National Science Foundation (ANI-0095988, EIA-0202067, ITR ANI-0205294

When It’s Okay That I Don’t Play: Social Norms and the Situated Construal of Social Exclusion

Being excluded and ignored has been shown to threaten fundamental human needs and cause pain. Such reflexive reactions to social exclusion have been conceptualized as direct and unmoderated (temporal need threat model of ostracism). Here, we propose an extension and argue that reflexive reactions depend on how social exclusion situations are construed. If being excluded is understood as a violation of an inclusion norm, individuals will react with pain and threat. In contrast, if being excluded is consistent with the prevailing norm, the exclusion situation is interpreted as less threatening, and negative reflexive reactions to ostracism should be attenuated. Four studies empirically support this conceptual model. Studies 3 and 4 further show that to guide situated construal, the norm has to be endorsed by the individual. In both Studies 1 and 3, the effect of the norm is mediated by the objective situation’s subjective construal

Variations of selective separability and tightness in function spaces with set open topologies

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.Comment: 19 page

The nursing history of Ngala since 1890: An early parenting organisation in Western Australia

Background: This study was the first phase of a larger study which explored the past, present and future of nursing in early parenting services in Australia. Aim: The aim of this paper is to describe the history of nursing within an early parenting service in Western Australia (WA). Methods: Triangulation of multiple data sources was used to summarise the nursing role over 120 years. The history was discovered through a document analysis of archives, including oral histories, organisational documents, focus groups, nurses’ diaries and interviews with nurses. Findings: The nursing role and context is described over three time periods: 1890–1960; 1960–1990 and 1990–2010. Nursing during the 20th century was influenced by societal and policy changes, but the essence of nursing remained the same with a focus on providing support and education to parents during pregnancy and caring for their babies and young children. Nursing within early parenting up to the 1980s was reasonably static until the move from hospital-based training to the university sector, which was the turning point of change to a new era of professionalisation and ultimately working within an interdisciplinary team. Conclusion: This description of nursing history within one early parenting service has provided insight into this specialist area of nursing

Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries

We explore a newly proposed channel to create binary black holes of stellar origin. This scenario applies to massive, tight binaries where mixing induced by rotation and tides transports the products of hydrogen burning throughout the stellar envelopes. This slowly enriches the entire star with helium, preventing the build-up of an internal chemical gradient. The stars remain compact as they evolve nearly chemically homogeneously, eventually forming two black holes, which, we estimate, typically merge 4--11 Gyr after formation. Like other proposed channels, this evolutionary pathway suffers from significant theoretical uncertainties, but could be constrained in the near future by data from advanced ground-based gravitational-wave detectors. We perform Monte Carlo simulations of the expected merger rate over cosmic time to explore the implications and uncertainties. Our default model for this channel yields a local binary black hole merger rate of about $10$ Gpc$^{-3}$ yr$^{-1}$ at redshift $z=0$, peaking at twice this rate at $z=0.5$. This means that this channel is competitive, in terms of expected rates, with the conventional formation scenarios that involve a common-envelope phase during isolated binary evolution or dynamical interaction in a dense cluster. The events from this channel may be distinguished by the preference for nearly equal-mass components and high masses, with typical total masses between 50 and 110 $\textrm{M}_\odot$. Unlike the conventional isolated binary evolution scenario that involves shrinkage of the orbit during a common-envelope phase, short time delays are unlikely for this channel, implying that we do not expect mergers at high redshift.Comment: Minor update to match the version published in MNRAS; 15 pages 10 figure