Treatments of the exchange energy in density-functional theory

Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn-Sham equations, the Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn-Sham formulation of the Hartree-Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N=1,2,...), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors corrected, plus an additional summarizing figure (Appendix B) include

Message Passing and Metabolism

Active inference is an increasingly prominent paradigm in theoretical biology. It frames the dynamics of living systems as if they were solving an inference problem. This rests upon their flow towards some (non-equilibrium) steady state—or equivalently, their maximisation of the Bayesian model evidence for an implicit probabilistic model. For many models, these self-evidencing dynamics manifest as messages passed among elements of a system. Such messages resemble synaptic communication at a neuronal network level but could also apply to other network structures. This paper attempts to apply the same formulation to biochemical networks. The chemical computation that occurs in regulation of metabolism relies upon sparse interactions between coupled reactions, where enzymes induce conditional dependencies between reactants. We will see that these reactions may be viewed as the movement of probability mass between alternative categorical states. When framed in this way, the master equations describing such systems can be reformulated in terms of their steady-state distribution. This distribution plays the role of a generative model, affording an inferential interpretation of the underlying biochemistry. Finally, we see that—in analogy with computational neurology and psychiatry—metabolic disorders may be characterized as false inference under aberrant prior beliefs

Spin-independent v-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Electrons in one-dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derive from uncharged spin-1/2 electrons, can travel at different velocities when compared with the second, built from charged spinless electrons. Predicted theoretically in the early sixties, the spin-charge separation has attracted renewed attention since the first evidences of experimental observation, with usual mentions as a possible explanation for high-temperature superconductivity. In one-dimensional (1D) model systems, the spin-charge separation leads the frequencies of Friedel oscillations to suffer a 2k_F -- 4k_F crossover, mainly when dealing with strong correlations, where they are referred to as Wigner crystal oscillations. In non-magnetized systems, the current density functionals which are applied to the 1D Hubbard model are not seen to reproduce this crossover, referring to a more fundamental question: Are the Wigner crystal oscillations in 1D systems non-interacting v-representable? Or, is there a spin-independent Kohn-Sham potential which is able to yield spin-charge separation? Finding an appropriate answer to both questions is our main task here. By means of exact and DMRG solutions, as well as, a new approach of exchange-correlation potential, we show the answer to be positive. Specifically, the v-representable 4k_F oscillations emerge from attractive interactions mediated by positively charged spinless holes -- the holons -- as an additional contribution to the repulsive on-site Hubbard interaction

A comparison of the physiological consequences of head-loading and back-loading for African and European women

The aim is to quantify the physiological cost of head-load carriage and to examine the ‘free ride’ hypothesis for head-load carriage in groups of women differing in their experience of head-loading. Twenty-four Xhosa women [13 experienced head-loaders (EXP), 11 with no experience of head-loading (NON)] attempted to carry loads of up to 70% of body mass on both their heads and backs whilst walking on a treadmill at a self-selected walking speed. Expired air was collected throughout. In a second study nine women, members of the British Territorial Army, carried similar loads, again at a self-selected speed. Maximum load carried was greater for the back than the head (54.7 ± 15.1 vs. 40.8 ± 13.2% BM, P <0.0005). Considering study one, head-loading required a greater oxygen rate than back-loading (10.1 ± 2.6 vs. 8.8 ± 2.3 ml kg bodymass−1 min−1, P = 0.043, for loads 10–25% BM) regardless of previous head-loading experience (P = 0.333). Percentage changes in oxygen consumption associated with head-loading were greater than the proportional load added in both studies but were smaller than the added load for the lighter loads carried on the back in study 1. All other physiological variables were consistent with changes in oxygen consumption. The data provides no support for the ‘free ride’ hypothesis for head-loading although there is some evidence of energy saving mechanisms for back-loading at low speed/load combinations. Investigating the large individual variation in response may help in identifying combinations of factors that contribute to improved economy

Hadron-quark mixed phase in neutron stars

Possibility of structured mixed phase at first order phase transitions is examined by taking into account of charge screening and surface effects. Hadron-quark phase transition in dense neutron star interiors is considered as a concrete example.Comment: Talk given at the 7th International Symposium on "Nuclei in the Cosmos", July 8-12,200

The Computational Anatomy of Visual Neglect

Visual neglect is a debilitating neuropsychological phenomenon that has many clinical implications and—in cognitive neuroscience—offers an important lesion deficit model. In this article, we describe a computational model of visual neglect based upon active inference. Our objective is to establish a computational and neurophysiological process theory that can be used to disambiguate among the various causes of this important syndrome; namely, a computational neuropsychology of visual neglect. We introduce a Bayes optimal model based upon Markov decision processes that reproduces the visual searches induced by the line cancellation task (used to characterize visual neglect at the bedside). We then consider 3 distinct ways in which the model could be lesioned to reproduce neuropsychological (visual search) deficits. Crucially, these 3 levels of pathology map nicely onto the neuroanatomy of saccadic eye movements and the systems implicated in visual neglect

Active inference and the anatomy of oculomotion

Given that eye movement control can be framed as an inferential process, how are the requisite forces generated to produce anticipated or desired fixation? Starting from a generative model based on simple Newtonian equations of motion, we derive a variational solution to this problem and illustrate the plausibility of its implementation in the oculomotor brainstem. We show, through simulation, that the Bayesian filtering equations that implement ‘planning as inference’ can generate both saccadic and smooth pursuit eye movements. Crucially, the associated message passing maps well onto the known connectivity and neuroanatomy of the brainstem – and the changes in these messages over time are strikingly similar to single unit recordings of neurons in the corresponding nuclei. Furthermore, we show that simulated lesions to axonal pathways reproduce eye movement patterns of neurological patients with damage to these tracts

Local softness, softness dipole and polarizabilities of functional groups: application to the side chains of the twenty amino acids

The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the softness of the side chain of the twenty amino acid are clustered in groups reflecting their biochemical classification, namely: aliphatic, basic, acidic, sulfur containing, and aromatic amino acids . The present findings are in agreement with previous results using different approximations and partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126,145105 (2007)]. In addition, we show that the polarizability of the side chain of an amino acid depends mainly on its number of electrons (reflecting its size) and consequently cannot be used to cluster the amino acids in different biochemical groups, in contrast to the local softness. Our results also demonstrate that the global softness is not simply proportional to the global polarizability in disagreement with the intuition that "a softer moiety is also more polarizable". Amino acids with the same softness may have a polarizability differing by a factor as large as 1.7. This discrepancy can be understood from first principles as we show that the molecular polarizability depends on a "softness dipole vector" and not simply on the global softness

Bayesian Filtering with Multiple Internal Models: Toward a Theory of Social Intelligence

To exhibit social intelligence, animals have to recognize whom they are communicating with. One way to make this inference is to select among internal generative models of each conspecific who may be encountered. However, these models also have to be learned via some form of Bayesian belief updating. This induces an interesting problem: When receiving sensory input generated by a particular conspecific, how does an animal know which internal model to update? We consider a theoretical and neurobiologically plausible solution that enables inference and learning of the processes that generate sensory inputs (e.g., listening and understanding) and reproduction of those inputs (e.g., talking or singing), under multiple generative models. This is based on recent advances in theoretical neurobiology—namely, active inference and post hoc (online) Bayesian model selection. In brief, this scheme fits sensory inputs under each generative model. Model parameters are then updated in proportion to the probability that each model could have generated the input (i.e., model evidence). The proposed scheme is demonstrated using a series of (real zebra finch) birdsongs, where each song is generated by several different birds. The scheme is implemented using physiologically plausible models of birdsong production. We show that generalized Bayesian filtering, combined with model selection, leads to successful learning across generative models, each possessing different parameters. These results highlight the utility of having multiple internal models when making inferences in social environments with multiple sources of sensory information