Fractional spins and static correlation error in density functional theory

Electronic states with fractional spins arise in systems with large static correlation (strongly correlated systems). Such fractional-spin states are shown to be ensembles of degenerate ground states with normal spins. It is proven here that the energy of the exact functional for fractional-spin states is a constant, equal to the energy of the comprising degenerate pure spin states. Dramatic deviations from this exact constancy condition exist with all approximate functionals, leading to large static correlation errors for strongly correlated systems, such as chemical bond dissociation and band structure of Mott insulators. This is demonstrated with numerical calculations for several molecular systems. Approximating the constancy behavior for fractional spins should be a major aim in functional constructions and should open the frontier for DFT to describe strongly correlated systems. The key results are also shown to apply in reduced density-matrix functional theory.Comment: 6 pages, 4 figure

A guide to nestling development and aging in altricial passerines

Nestling growth and development studies have been a topic of interest for a greater part of the last century (Sutton 1935, Walkinshaw 1948) and continue to be of interest today. This is not surprising since studies on nestling growth can provide a wealth of biological information that has larger implications for avian management and conservation. Despite this history of studying nestling development, basic information is still limited or absent for many species. Many questions remain unanswered, and contradictory conclusions are often found in the literature (Starck and Ricklefs 1998a). Therefore, much information on aging and development can still be gained from studying the development patterns of similar species and from comparative studies, across avian orders (Minea et al. 1982, Saunders and Hansen 1989, Carsson and Hörnfeldt 1993). Additionally, nestling growth studies can yield insight into the effects of different nesting strategies on productivity (O’Connor 1978), as well as the impacts of parental effort and environmental variables on fitness (Ross 1980, Ricklefs and Peters 1981, Magrath 1991). Since low reproductive success may play a significant role in the declines of many North American passerines (Sherry and Holmes 1992, Ballard et al. 2003), a better understanding of the factors that influence reproductive success is a vital component of avian conservation (Martin 1992). Data on nestling aging can be used to improve nest survival estimates (Dinsmore 2002, Nur et al. 2004), providing information that can be used to more precisely age nests (Pinkowski 1975, Podlesack and Blem 2002), (Jones and Geupel 2007). Indeed, the relatively short time period young spend developing in the nest is a critical part of a bird’s life cycle and a nestling’s developmental path can affect its survival to independence, its survival as an adult, and its future reproductive success

Fractional charge perspective on the band-gap in density-functional theory

The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems with fractional charges. Formulas for the energy derivatives with respect to number of electrons are derived which clarify the role of optimized effective potentials in prediction of the band-gap. Calculations with a recent functional that has much improved behavior for fractional charges give a good prediction of the energy gap and also $\epsilon_{{\rm homo}}\simeq-I$ for finite systems. Our results indicate it is possible, within DFT, to have a functional whose eigenvalues or derivatives accurately predict the band-gap

Barro's fertility equations: the robustness of the role of female education and income

Barro and Lee (1994) and Barro and Sala-i-Martin (1995) find that real per-capita GDP and both male and female education have important effects on fertility in their cross-country empirical studies. In order to assess the robustness of their results, their estimated models are subjected to specification and diagnostic testing, the effects on the model of using the improved Barro and Lee (1996) cross-country data on educational attainment of the population aged 15 and over are examined, and the different specifications used by Barro and Lee and by Barro and Sala-i-Martin compared. The results obtained suggest that their fertility equations do not perform well in terms of diagnostic testing, and are very sensitive to the use of different vintages of the educational attainment proxies and of the Summers-Heston cross-country income data. A robust explanation of fertility, to link with empirical growth equations, has, therefore, not yet been found; further work is required in this area

Geometric classical and total correlations via trace distance

We introduce the concepts of geometric classical and total correlations through Schatten 1-norm (trace norm), which is the only Schatten p-norm able to ensure a well-defined geometric measure of correlations. In particular, we derive the analytical expressions for the case of two-qubit Bell-diagonal states, discussing the superadditivity of geometric correlations. As an illustration, we compare our results with the entropic correlations, discussing both their hierarchy and monotonicity properties. Moreover, we apply the geometric correlations to investigate the ground state of spin chains in the thermodynamic limit. In contrast to the entropic quantifiers, we show that the classical correlation is the only source of 1-norm geometric correlation that is able to signaling an infinite-order quantum phase transition.Comment: v2: published versio

Body Composition Measurement in Children with Cerebral Palsy, Spina Bifida and Spinal Cord Injury: A Systematic Review of the Literature

Pediatric obesity is a major health concern that has an increased prevalence in children with special needs. In order to categorize a child’s weight, an assessment of body composition is needed. Obtaining an accurate body composition measurement in children with special needs has many challenges associated with it. This perplexing scenario limits the provider’s ability to screen, prevent and treat an abnormal weight status in this vulnerable population. This systematic review summarizes common methods of body composition measurements, their strengths and limitations and reviews the literature when measurements were used in children with cerebral palsy, spina bifida and spinal cord injury. Following PRISMA guidelines, 222 studies were identified. The application of the inclusion and exclusion criteria yielded a final sample of nine studies included in this review. Overall, articles reinforced the inconsistencies of body composition measurement and methodology when used with children with special needs. Concerns include small sample sizes, the need to validate prediction equations for this population, and the lack of controlled trials and reporting of measurement methodology. Healthcare providers need to be aware of the complexities associated with measuring body composition in children with special needs and advocate for further testing of these measurements. Additional studies addressing the reliability and validity of these measures are needed to facilitate appropriate health promotion in children

Book Review: The Entry Level Occupational Therapy Doctorate Capstone: A Framework for the Experience and Project

This paper is a book review of The Entry Level Occupational Therapy Doctorate Capstone: A Framework for the Experience and Project (DeIuliis & Bednarski, 2019). This review includes a description of the book, content summary, and critical analysis of its educational value. Overall, this book is recommended as a resource for doctoral capstone coordinators

Periodic Neural Activity Induced by Network Complexity

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barab\'asi and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with chaotic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.Comment: 4 pages, 5 figure