Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental limitations on DFT, as an efficient description of the associated universal functional would allow to solve any problem in the class QMA (the quantum version of NP) and thus particularly any problem in NP in polynomial time. This follows from the fact that finding the ground state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, while given the universal functional it can be computed efficiently using DFT. This provides a clear illustration how the field of quantum computing is useful even if quantum computers would never be built.Comment: 8 pages, 3 figures. v2: Version accepted at Nature Physics; differs significantly from v1 (including new title). Includes an extra appendix (not contained in the journal version) on the NP-completeness of Hartree-Fock, which is taken from v

Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner and Hartree--Fock orbitals are often very similar, any local exchange functional that works well with Hartree--Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle--Salvetti correlation-energy functional, and the LYP variant, are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: One is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy

Improving the delivery of care for patients with diabetes through understanding optimised team work and organisation in primary care

Peer reviewedPublisher PD

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

Preference for novel faces in male infant monkeys predicts cerebrospinal fluid oxytocin concentrations later in life

The ability to recognize individuals is a critical skill acquired early in life for group living species. In primates, individual recognition occurs predominantly through face discrimination. Despite the essential adaptive value of this ability, robust individual differences in conspecific face recognition exist, yet its associated biology remains unknown. Although pharmacological administration of oxytocin has implicated this neuropeptide in face perception and social memory, no prior research has tested the relationship between individual differences in face recognition and endogenous oxytocin concentrations. Here we show in a male rhesus monkey cohort (N = 60) that infant performance in a task used to determine face recognition ability (specifically, the ability of animals to show a preference for a novel face) robustly predicts cerebrospinal fluid, but not blood, oxytocin concentrations up to five years after behavioural assessment. These results argue that central oxytocin biology may be related to individual face perceptual abilities necessary for group living, and that these differences are stable traits

Threat-sensitive anti-predator defence in precocial wader, the northern lapwing Vanellus vanellus

Birds exhibit various forms of anti-predator behaviours to avoid reproductive failure, with mobbing—observation, approach and usually harassment of a predator—being one of the most commonly observed. Here, we investigate patterns of temporal variation in the mobbing response exhibited by a precocial species, the northern lapwing (Vanellus vanellus). We test whether brood age and self-reliance, or the perceived risk posed by various predators, affect mobbing response of lapwings. We quantified aggressive interactions between lapwings and their natural avian predators and used generalized additive models to test how timing and predator species identity are related to the mobbing response of lapwings. Lapwings diversified mobbing response within the breeding season and depending on predator species. Raven Corvus corax, hooded crow Corvus cornix and harriers evoked the strongest response, while common buzzard Buteo buteo, white stork Ciconia ciconia, black-headed gull Chroicocephalus ridibundus and rook Corvus frugilegus were less frequently attacked. Lapwings increased their mobbing response against raven, common buzzard, white stork and rook throughout the breeding season, while defence against hooded crow, harriers and black-headed gull did not exhibit clear temporal patterns. Mobbing behaviour of lapwings apparently constitutes a flexible anti-predator strategy. The anti-predator response depends on predator species, which may suggest that lapwings distinguish between predator types and match mobbing response to the perceived hazard at different stages of the breeding cycle. We conclude that a single species may exhibit various patterns of temporal variation in anti-predator defence, which may correspond with various hypotheses derived from parental investment theory

Views of addiction neuroscientists and clinicians on the clinical impact of a ‘Brain Disease Model of Addiction’

Addiction is increasingly described as a "chronic and relapsing brain disease". The potential impact of the brain disease model on the treatment of addiction or addicted individuals' treatment behaviour remains uncertain. We conducted a qualitative study to examine: (i) the extent to which leading Australian addiction neuroscientists and clinicians accept the brain disease view of addiction; and (ii) their views on the likely impacts of this view on addicted individuals' beliefs and behaviour. Thirty-one Australian addiction neuroscientists and clinicians (10 females and 21 males; 16 with clinical experience and 15 with no clinical experience) took part in 1 h semi-structured interviews. Most addiction neuroscientists and clinicians did not uncritically support the use of brain disease model of addiction. Most were cautious about the potential for adverse impacts on individuals' recovery and motivation to enter treatment. While some recognised the possibility that the brain disease model of addiction may provide a rationale for addicted persons to seek treatment and motivate behaviour change, Australian addiction neuroscientist and clinicians do not assume that messages about "diseased brains" will always lead to increased treatment-seeking and reduced drug use. Research is needed on how neuroscience research could be used in ways that optimise positive outcomes for addicted persons

Assessing the cost of global biodiversity and conservation knowledge

Knowledge products comprise assessments of authoritative information supported by standards, governance, quality control, data, tools, and capacity building mechanisms. Considerable resources are dedicated to developing and maintaining knowledge products for biodiversity conservation, and they are widely used to inform policy and advise decision makers and practitioners. However, the financial cost of delivering this information is largely undocumented. We evaluated the costs and funding sources for developing and maintaining four global biodiversity and conservation knowledge products: The IUCN Red List of Threatened Species, the IUCN Red List of Ecosystems, Protected Planet, and the World Database of Key Biodiversity Areas. These are secondary data sets, built on primary data collected by extensive networks of expert contributors worldwide. We estimate that US$160 million (range: US$116-204 million), plus 293 person-years of volunteer time (range: 278-308 person-years) valued at US$14 million (range US$12-16 million), were invested in these four knowledge products between 1979 and 2013. More than half of this financing was provided through philanthropy, and nearly three-quarters was spent on personnel costs. The estimated annual cost of maintaining data and platforms for three of these knowledge products (excluding the IUCN Red List of Ecosystems for which annual costs were not possible to estimate for 2013 ) is US$6.5 million in total (range: US$6.2-6.7 million). We estimated that an additional US$114 million will be needed to reach pre-defined baselines of data coverage for all the four knowledge products, and that once achieved, annual maintenance costs will be approximately US$12 million. These costs are much lower than those to maintain many other, similarly important, global knowledge products. Ensuring that biodiversity and conservation knowledge products are sufficiently up to date, comprehensive and accurate is fundamental to inform decision-making for biodiversity conservation and sustainable development. Thus, the development and implementation of plans for sustainable long-term financing for them is critical