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

Active Inference, Novelty and Neglect

In this chapter, we provide an overview of the principles of active inference. We illustrate how different forms of short-term memory are expressed formally (mathematically) through appealing to beliefs about the causes of our sensations and about the actions we pursue. This is used to motivate an approach to active vision that depends upon inferences about the causes of 'what I have seen' and learning about 'what I would see if I were to look there'. The former could manifest as persistent 'delay-period' activity - of the sort associated with working memory, while the latter is better suited to changes in synaptic efficacy - of the sort that underlies short-term learning and adaptation. We review formulations of these ideas in terms of active inference, their role in directing visual exploration and the consequences - for active vision - of their failures. To illustrate the latter, we draw upon some of our recent work on the computational anatomy of visual neglect

Comment on “The extent of forest in dryland biomes”

This is the author accepted manuscript. The final version is available from American Association for the Advancement of Science via the DOI in this record.Bastin et al. (Reports, 12 May 2017, p. 635) infer forest as more globally extensive than previously estimated using tree cover data. However, their forest definition does not reflect ecosystem function or biotic composition. These structural and climatic definitions inflate forest estimates across the tropics and undermine conservation goals, leading to inappropriate management policies and practices in tropical grassy ecosystems

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

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

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

Peer reviewedPublisher PD

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

The impact of out-of-hospital models of care on paediatric emergency department presentations

OBJECTIVE: To estimate the potential impact of enhanced primary care and new out-of-hospital models (OOHMs) on emergency department (ED) presentations by children and young people (CYP). DESIGN: Observational study. PATIENTS AND SETTING: Data collected prospectively on 3020 CYP 0–17.9 years from 6 London EDs during 14 days by 25 supernumerary clinicians. CYP with transient acute illness, exacerbation of long-term condition (LTC), complex LTC/disability and injury/trauma were considered manageable within OOHM. OOHMs assessed included nurse-led services, multispecialty community provider (MCP), primary and acute care system (PACS) plus current and enhanced primary care. MEASURES: Diagnosis, severity; record of investigations, management and outcome that occurred; objective assessment of clinical need and potential alternative management options/destinations. RESULTS: Of the patients 95.6% had diagnoses appropriate for OOHM. Most presentations required assessment by a clinician with skills in assessing illness (39.6%) or injuries (30.9%). One thousand two hundred and ninety-one (42.75%) required no investigations and 1007 (33.3%) were provided only with reassurance. Of the presentations 42.2% were judged to have been totally avoidable if the family had had better health education. Of the patients 26.1% were judged appropriate for current primary care (community pharmacy or general practice) with 31.5% appropriate for the combination of enhanced general practice and community pharmacy. Proportions suitable for new models were 14.1% for the nurse-led acute illness team, MCP 25.7%, GP federation CYP service 44.6%, comprehensive walk-in centre for CYP 64.3% and 75.5% for a PACS. CONCLUSIONS: High proportions of ED presentations by CYP could potentially be managed in new OOHMs or by enhancement of existing primary care

Rhesus Monkeys See Who They Hear: Spontaneous Cross-Modal Memory for Familiar Conspecifics

Rhesus monkeys gather much of their knowledge of the social world through visual input and may preferentially represent this knowledge in the visual modality. Recognition of familiar faces is clearly advantageous, and the flexibility and utility of primate social memory would be greatly enhanced if visual memories could be accessed cross-modally either by visual or auditory stimulation. Such cross-modal access to visual memory would facilitate flexible retrieval of the knowledge necessary for adaptive social behavior. We tested whether rhesus monkeys have cross-modal access to visual memory for familiar conspecifics using a delayed matching-to-sample procedure. Monkeys learned visual matching of video clips of familiar individuals to photographs of those individuals, and generalized performance to novel videos. In crossmodal probe trials, coo-calls were played during the memory interval. The calls were either from the monkey just seen in the sample video clip or from a different familiar monkey. Even though the monkeys were trained exclusively in visual matching, the calls influenced choice by causing an increase in the proportion of errors to the picture of the monkey whose voice was heard on incongruent trials. This result demonstrates spontaneous cross-modal recognition. It also shows that viewing videos of familiar monkeys activates naturally formed memories of real monkeys, validating the use of video stimuli in studies of social cognition in monkeys