Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

This article develops a welfare theoretic framework for interpreting evidence on the impacts of public programs on housing markets. We extend Rosen's hedonic model to explain how housing prices capitalize exogenous shocks to public goods and externalities. The model predicts that trading between heterogeneous buyers and sellers will drive a wedge between these “capitalization effects” and welfare changes. We test this hypothesis in the context of changes in measures of school quality in five metropolitan areas. Results from boundary discontinuity designs suggest that capitalization effects understate parents’ willingness to pay for public school improvements by as much as 75%.

Using a natural experiment (Regulation SHO), we show that short selling pressure and consequent stock price behavior have a causal effect on managers’ voluntary disclosure choices. Specifically, we find that managers respond to a positive exogenous shock to short selling pressure and price sensitivity to bad news by reducing the precision of bad news forecasts. This finding on management forecasts appears to be generalizable to other corporate disclosures. In particular, we find that, in response to increased short selling pressure, managers also reduce the readability (or increase the fuzziness) of bad news annual reports. Overall, our results suggest that maintaining the current level of stock prices is an important consideration in managers’ strategic disclosure decisions.

Many municipal governments have adopted affordable housing policies to benefit people whose socio-economic status is not commensurate with the price of housing. However, the effects and the functions of these policies in the city on sustainable development and living remains limited. Using a comparative case study, this study explores the characteristics and effects of affordable housing policies in three metropolitan cities in China: Beijing, Tianjin, and Guangshou. This study finds that these cities have their unique affordable housing policies and have experienced various challenges in implementing those policies. Conclusions and implications for other cities in China are addressed.

Background: Despite improvements in maternity healthcare services over the last few decades, more than 2.7 million babies worldwide are stillborn each year. The global health agenda is silent about stillbirth, perhaps, in part, because its wider impact has not been systematically analysed or understood before now across the world. Our study aimed to systematically review, evaluate and summarise the current evidence regarding the psychosocial impact of stillbirth to parents and their families, with the aim of improving guidance in bereavement care worldwide.

Methods: Systematic review and meta-summary (quantitative aggregation of qualitative findings) of quantitative, qualitative, and mixed-methods studies. All languages and countries were included.

Results: Two thousand, six hundred and nineteen abstracts were identified; 144 studies were included. Frequency effect sizes (FES %) were calculated for each theme, as a measure of their prevalence in the literature. Themes ranged from negative psychological symptoms post bereavement (77 · 1) and in subsequent pregnancies (27 · 1), to disenfranchised grief (31 · 2), and incongruent grief (28 · 5), There was also impact on siblings (23 · 6) and on the wider family (2 · 8). They included mixed-feelings about decisions made when the baby died (12 · 5), avoidance of memories (13 · 2), anxiety over other children (7 · 6), chronic pain and fatigue (6 · 9), and a different approach to the use of healthcare services (6 · 9). Some themes were particularly prominent in studies of fathers; grief suppression (avoidance)(18 · 1), employment difficulties, financial debt (5 · 6), and increased substance use (4 · 2). Others found in studies specific to mothers included altered body image (3 · 5) and impact on quality of life (2 · 1). Counter-intuitively, Some themes had mixed connotations. These included parental pride in the baby (5 · 6), motivation for engagement in healthcare improvement (4 · 2) and changed approaches to life and death, self-esteem, and own identity (25 · 7). In studies from low/middle income countries, stigmatisation (13 · 2) and pressure to prioritise or delay conception (9) were especially prevalent.

Conclusion: Experiencing the birth of a stillborn child is a life-changing event. The focus of the consequences may vary with parent gender and country. Stillbirth can have devastating psychological, physical and social costs, with ongoing effects on interpersonal relationships and subsequently born children. However, parents who experience the tragedy of stillbirth can develop resilience and new life-skills and capacities. Future research should focus on developing interventions that may reduce the psychosocial cost of stillbirth.

Increasing levels of financial inequality prompt questions about the relationship between income and well-being. Using a twins sample from the Survey of Midlife Development in the U. S. and controlling for personality as core self-evaluations (CSE), we found that men, but not women, had higher subjective financial well-being (SFWB) when they had higher incomes. This relationship was due to ‘unshared environmental’ factors rather than genes, suggesting that the effect of income on SFWB is driven by unique experiences among men. Further, for women and men, we found that CSE influenced income and SFWB, and that both genetic and environmental factors explained this relationship. Given the relatively small and male-specific relationship between income and SFWB, and the determination of both income and SFWB by personality, we propose that policy makers focus on malleable factors beyond merely income in order to increase SFWB, including financial education and building self-regulatory capacity.

The debate about representation in the brain and the nature of the cognitive system has been going on for decades now. This paper examines the neurophysiological evidence, primarily from single cell recordings, to get a better perspective on both the issues. After an initial review of some basic concepts, the paper reviews the data from single cell recordings – in cortical columns and of category-selective and multisensory neurons. In neuroscience, columns in the neocortex (cortical columns) are understood to be a basic functional/computational unit. The paper reviews the fundamental discoveries about the columnar organization and finds that it reveals a massively parallel search mechanism. This columnar organization could be the most extensive neurophysiological evidence for the widespread use of localist representation in the brain. The paper also reviews studies of category-selective cells. The evidence for category-selective cells reveals that localist representation is also used to encode complex abstract concepts at the highest levels of processing in the brain. A third major issue is the nature of the cognitive system in the brain and whether there is a form that is purely abstract and encoded by single cells. To provide evidence for a single-cell based purely abstract cognitive system, the paper reviews some of the findings related to multisensory cells. It appears that there is widespread usage of multisensory cells in the brain in the same areas where sensory processing takes place. Plus there is evidence for abstract modality invariant cells at higher levels of cortical processing. Overall, that reveals the existence of a purely abstract cognitive system in the brain. The paper also argues that since there is no evidence for dense distributed representation and since sparse representation is actually used to encode memories, there is actually no evidence for distributed representation in the brain. Overall, it appears that, at an abstract level, the brain is a massively parallel, distributed computing system that is symbolic. The paper also explains how grounded cognition and other theories of the brain are fully compatible with localist representation and a purely abstract cognitive system.

Public health messaging about antimicrobial resistance (AMR) sometimes conveys the problem as an epidemic. We outline why AMR is a serious endemic problem manifested in hospital and community-acquired infections.

AMR is not an epidemic condition, but may complicate epidemics, which are characterized by sudden societal impact due to rapid rise in cases over a short timescale. Influenza, which causes direct viral effects, or secondary bacterial complications is the most likely cause of an epidemic or pandemic where AMR may be a problem. We discuss other possible causes of a pandemic with AMR, and present a risk assessment formula to estimate the impact of AMR during a pandemic. Finally, we flag the potential impact of genetic engineering of pathogens on global risk and how this could radically change the epidemiology of AMR as we know it.

Understanding the epidemiology of AMR is key to successfully addressing the problem. AMR is an endemic condition but can play a role in epidemics or pandemics, and we present a risk analysis method for assessing the impact of AMR in a pandemic.

Epidemics and emerging infectious diseases are becoming an increasing threat to global populations - challenging public health practitioners, decision makers and researchers to plan, prepare, identify and respond to outbreaks in near real-timeframes. The aim of this research is to evaluate the range of public domain and freely available software epidemic modelling tools. Twenty freely utilizable software tools underwent assessment of software usability, utility and key functionalities. Stochastic and agent based tools were found to be highly flexible, adaptable, had high utility and many features, but low usability. Deterministic tools were highly usable with average to good levels of utility.

Understanding the food-energy-water nexus is necessary to identify risks and inform strategies for nexus governance to support resilient, secure, and sustainable societies. To manage risks and realize efficiencies, we must understand not only how these systems are physically connected but also how they are institutionally linked. It is important to understand how actors who make planning, management, and policy decisions understand the relationships among components of the systems. Our question is: How do stakeholders involved in food, energy, and water governance in Phoenix, Arizona understand the nexus and what are the implications for integrated nexus governance? We employ a case study design, generate qualitative data through focus groups and interviews, and conduct a content analysis. While stakeholders in the Phoenix area who are actively engaged in food, energy, and water systems governance appreciate the rationale for nexus thinking, they recognize practical limitations to implementing these concepts. Concept maps of nexus interactions provide one view of system interconnections that be used to complement other ways of knowing the nexus, such as physical infrastructure system diagrams or actor-networks. Stakeholders believe nexus governance could be improved through awareness and education, consensus and collaboration, transparency, economic incentives, working across scales, and incremental reforms.