Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Lower N-Acetyl-Aspartate Levels in Prefrontal Cortices in Pediatric Bipolar Disorder: A (1)H Magnetic Resonance Spectroscopy Study

Objective: The few studies applying single-voxel(1)H spectroscopy in children and adolescents with bipolar disorder (BD) have reported low N-acetyl-aspartate (NAA) levels in the dorsolateral prefrontal cortex (DLPFC), and high myo-inositol / phosphocreatine plus creatine (PCr+Cr) ratios in the anterior cingulate. The aim of this study was to evaluate NAA, glycerophosphocholine plus phosphocholine (GPC+PC) and PCr+Cr in various frontal cortical areas in children and adolescents with BD. We hypothesized that NAA levels within the prefrontal cortex are lower in BD patients than in healthy controls, indicating neurodevelopmental alterations in the former. Method: We studied 43 pediatric patients with DSM-IV BD (19 female, mean age 13.2 +/- 2.9 years) and 38 healthy controls (79 female, mean age 13.9 +/- 2.7 years). We conducted multivoxel in vivo (1)H spectroscopy measurements at 1.5 Tesla using a long echo time of 272 ms to obtain bilateral metabolite levels from the medial prefrontal cortex (MPFC), DLPFC (white and gray matter), cingulate (anterior and posterior), and occipital lobes. We used the nonparametric Mann-Whitney U test to compare neurochemical levels between groups. Results: In pediatric BD patients, NAA and GPC+PC levels in the bilateral MPFC, and PCr+Cr levels in the left MPFC were lower than those seen in the controls. In the left DLPFC white matter, levels of NAA and PCr+Cr were also lower in BD patients than in controls. Conclusions: Lower NAA and PCr+Cr levels in the PFC of children and adolescents with BD may be indicative of abnormal dendritic arborization and neuropil, suggesting neurodevelopmental abnormalities. J. Am. Acad. Child Adolesc. Psychiatry, 2011;50(1):85-94.

Temporal lobe epilepsy and social behavior: An animal model

Social behavior depends on the integrity of social brain circuitry. The temporal lobe is an important part of the social brain, and manifests morphological and functional alterations in autism spectrum disorders (ASD). Rats with temporal lobe epilepsy (TLE), induced with pilocarpine, were subjected to a social discrimination test that has been used to investigate potential animal models of ASD, and the results were compared with those for the control group. Rats with TLE exhibited fewer social behaviors than controls. No differences were observed in nonsocial behavior between groups. The results suggest an important role for the temporal lobe in regulating social behaviors. This animal model might be used to explore some questions about ASD pathophysiology. (c) 2008 Elsevier Inc. All rights reserved.

The non-coding RNA BC1 is down-regulated in the hippocampus of Wistar Audiogenic Rat (WAR) strain after audiogenic kindling

The aim of this study was to identify molecular pathways involved in audiogenic seizures in the epilepsy-prone Wistar Audiogenic Rat (WAR). For this, we used a suppression-subtractive hybridization (SSH) library from the hippocampus of WARs coupled to microarray comparative gene expression analysis, followed by Northern blot validation of individual genes. We discovered that the levels of the non-protein coding (npc) RNA BC1 were significantly reduced in the hippocampus of WARs submitted to repeated audiogenic seizures (audiogenic kindling) when compared to Wistar resistant rats and to both naive WARs and Wistars. By quantitative in situ hybridization, we verified lower levels of BC1 RNA in the GD-hilus and significant signal ratio reduction in the stratum radiatum and stratum pyramidale of hippocampal CA3 subfield of audiogenic kindled animals. Functional results recently obtained in a BC1-/- mouse model and our current data are supportive of a potential disruption in signaling pathways, upstream of BC1, associated with the seizure susceptibility of WARs. (C) 2010 Elsevier B.V. All rights reserved.

Cognitive control associated with irritability induction: an autobiographical recall fMRI study

OBJECTIVE: Despite the relevance of irritability emotions to the treatment, prognosis and classification of psychiatric disorders, the neurobiological basis of this emotional state has been rarely investigated to date. We assessed the brain circuitry underlying personal script-driven irritability in healthy subjects (n = 11) using functional magnetic resonance imaging. METHOD: Blood oxygen level-dependent signal changes were recorded during auditory presentation of personal scripts of irritability in contrast to scripts of happiness or neutral emotional content. Self-rated emotional measurements and skin conductance recordings were also obtained. Images were acquired using a 1,5T magnetic resonance scanner. Brain activation maps were constructed from individual images, and between-condition differences in the mean power of experimental response were identified by using cluster-wise nonparametric tests. RESULTS: Compared to neutral scripts, increased blood oxygen level-dependent signal during irritability scripts was detected in the left subgenual anterior cingulate cortex, and in the left medial, anterolateral and posterolateral dorsal prefrontal cortex (cluster-wise p-value < 0.05). While the involvement of the subgenual cingulate and dorsal anterolateral prefrontal cortices was unique to the irritability state, increased blood oxygen level-dependent signal in dorsomedial and dorsal posterolateral prefrontal regions were also present during happiness induction. CONCLUSION: Irritability induction is associated with functional changes in a limited set of brain regions previously implicated in the mediation of emotional states. Changes in prefrontal and cingulate areas may be related to effortful cognitive control aspects that gain salience during the emergence of irritability.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Density functional theory study of Fe(3)Ga

First-principles scalar relativistic calculations in supercells of 16 atoms are used to represent disordered B2 ordering of Fe(3)Ga in order to observe the effect of Ga-Ga pairs on the electronic structure of this alloy. From a comparison with pure bcc Fe it is observed that the energy position and occupation of e(g) and t(2g) states are largely affected by the Ga-Ga pairs and strengthened intraplane interactions takes place. The results show that a larger hybridization of the conduction band is in the source of the magnetostriction enhancement experimentally observed in Galfenol. (C) 2011 American Institute of Physics. [doi:10.1063/1.3525609]

Combining Monte Carlo simulation and density-functional theory to describe the spectral changes of Na(2) in liquid helium

Spectral changes of Na(2) in liquid helium were studied using the sequential Monte Carlo-quantum mechanics method. Configurations composed by Na(2) surrounded by explicit helium atoms sampled from the Monte Carlo simulation were submitted to time-dependent density-functional theory calculations of the electronic absorption spectrum using different functionals. Attention is given to both line shift and line broadening. The Perdew, Burke, and Ernzerhof (PBE1PBE, also known as PBE0) functional, with the PBE1PBE/6-311++G(2d,2p) basis set, gives the spectral shift, compared to gas phase, of 500 cm(-1) for the allowed X (1)Sigma(+)(g) -> B (1)Pi(u) transition, in very good agreement with the experimental value (700 cm(-1)). For comparison, cluster calculations were also performed and the first X (1)Sigma(+)(g) -> A (1)Sigma(+)(u) transition was also considered.

Edge effects in bilayer graphene nanoribbons: Ab initio total-energy density functional theory calculations

We show that the ground state of zigzag bilayer graphene nanoribbons is nonmagnetic. It also possesses a finite gap, which has a nonmonotonic dependence with the width as a consequence of the competition between bulk and strongly attractive edge interactions. All results were obtained using ab initio total-energy density functional theory calculations with the inclusion of parametrized van der Waals interactions.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

Density functional theory and ab initio molecular dynamics study of NO adsorption on Pd(111) and Pt(111) surfaces

The origin of the unique geometry for nitric oxide (NO) adsorption on Pd(111) and Pt(111) surfaces as well as the effect of temperature were studied by density functional theory calculations and ab initio molecular dynamics at finite temperature. We found that at low coverage, the adsorption geometry is determined by electronic interactions, depending sensitively on the adsorption sites and coverages, and the effect of temperature on geometries is significant. At coverage of 0.25 monolayer (ML), adsorbed NO at hollow sites prefer an upright configuration, while NO adsorbed at top sites prefer a tilting configuration. With increase in the coverage up to 0.50 ML, the enhanced steric repulsion lead to the tilting of hollow NO. We found that the tilting was enhanced by the thermal effects. At coverage of 0.75 ML with p(2 x 2)-3NO(fcc+hcp+top) structure, we found that there was no preferential orientation for tilted top NO. The interplay of the orbital hybridization, thermal effects, steric repulsion, and their effects on the adsorption geometries were highlighted at the end.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Abnormally increased effective connectivity between parahippocampal gyrus and ventromedial prefrontal regions during emotion labeling in bipolar disorder

Emotional liability and mood dysregulation characterize bipolar disorder (BID), yet no study has examined effective connectivity between parahippocampal gyrus and prefrontal cortical regions in ventromedial and dorsal/lateral neural systems subserving mood regulation in BD. Participants comprised 46 individuals (age range: 18-56 years): 21 with a DSM-IV diagnosis of BID, type I currently remitted; and 25 age- and gender-matched healthy controls (HC). Participants performed an event-related functional magnetic resonance imaging paradigm, viewing mild and intense happy and neutral faces. We employed dynamic causal modeling (I)CM) to identify significant alterations in effective connectivity between BD and HC. Bayes model selection was used to determine the best model. The right parahippocampal gyrus (PHG) and right subgenual cingulate gyrus (sgCG) were included as representative regions of the ventromedial neural system. The right dorsolateral prefrontal cortex (DLPFC) region was included as representative of the dorsal/lateral neural system. Right PHG-sgCG effective connectivity was significantly greater in BD than HC, reflecting more rapid, forward PHG-sgCG signaling in BD than HC. There was no between-group difference in sgCG-DLPFC effective connectivity. In BD, abnormally increased right PHG-sgCG effective connectivity and reduced right PHG activity to emotional stimuli suggest a dysfunctional ventromedial neural system implicated in early stimulus appraisal, encoding and automatic regulation of emotion that may represent a pathophysiological functional neural mechanism for mood dysregulation in BD. (C) 2009 Elsevier Ireland Ltd. All rights reserved.