The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Identifying rate-limiting nodes in large-scale cortical networks for visuospatial processing: an illustration using fMRI

With the advent of functional neuroimaging techniques, in particular functional magnetic resonance imaging (fMRI), we have gained greater insight into the neural correlates of visuospatial function. However, it may not always be easy to identify the cerebral regions most specifically associated with performance on a given task. One approach is to examine the quantitative relationships between regional activation and behavioral performance measures. In the present study, we investigated the functional neuroanatomy of two different visuospatial processing tasks, judgement of line orientation and mental rotation. Twenty-four normal participants were scanned with fMRI using blocked periodic designs for experimental task presentation. Accuracy and reaction time (RT) to each trial of both activation and baseline conditions in each experiment was recorded. Both experiments activated dorsal and ventral visual cortical areas as well as dorsolateral prefrontal cortex. More regionally specific associations with task performance were identified by estimating the association between (sinusoidal) power of functional response and mean RT to the activation condition; a permutation test based on spatial statistics was used for inference. There was significant behavioral-physiological association in right ventral extrastriate cortex for the line orientation task and in bilateral (predominantly right) superior parietal lobule for the mental rotation task. Comparable associations were not found between power of response and RT to the baseline conditions of the tasks. These data suggest that one region in a neurocognitive network may be most strongly associated with behavioral performance and this may be regarded as the computationally least efficient or rate-limiting node of the network.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

Visualization of learning in multilayer perceptron networks using principal component analysis

This paper is concerned with the use of scientific visualization methods for the analysis of feedforward neural networks (NNs). Inevitably, the kinds of data associated with the design and implementation of neural networks are of very high dimensionality, presenting a major challenge for visualization. A method is described using the well-known statistical technique of principal component analysis (PCA). This is found to be an effective and useful method of visualizing the learning trajectories of many learning algorithms such as back-propagation and can also be used to provide insight into the learning process and the nature of the error surface.

Synthesis and Characterization of Semi-Interpenetrating Networks Based on Poly(dimethylsiloxane) and Poly(vinyl alcohol)

Semi-interpenetrating networks (Semi-IPNs) with different compositions were prepared from poly(dimethylsiloxane) (PDMS), tetraethylorthosilicate (TEOS), and poly (vinyl alcohol) (PVA) by the sol-gel process in this study. The characterization of the PDMS/PVA semi-IPN was carried out using Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and swelling measurements. The presence of PVA domains dispersed in the PDMS network disrupted the network and allowed PDMS to crystallize, as observed by the crystallization and melting peaks in the DSC analyses. Because of the presence of hydrophilic (-OH) and hydrophobic (Si-(CH(3))(2)) domains, there was an appropriate hydrophylic/hydrophobic balance in the semi-IPNs prepared, which led to a maximum equilibrium water content of similar to 14 wt % without a loss in the ability to swell less polar solvents. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 115: 158-166, 2010

Intergeneric phylogenetic relationships in catfishes of the Loricariinae (Siluriformes: Loricariidae), with the description of Fonchiiloricaria nanodon: a new genus and species from Peru

Recent investigations in the upper Rio Huallaga in Peru revealed the presence of an intriguing species of the Loricariinae. To characterize and place this species within the evolutionary tree of the subfamily, a molecular phylogeny of this group was inferred based on the 12S and 16S mitochondrial genes and the nuclear gene F-reticulon4. The phylogeny indicated that this distinctive species was a member of the subtribe Loricariina. Given its phylogenetic placement, and its unusual morphology, this species is described as a new genus and new species of Loricariinae: Fonchiiloricaria nanodon. This new taxon is diagnosed by usually possessing one to three premaxillary teeth that are greatly reduced; lips with globular papillae on the surface; the distal margin of lower lip bearing short, triangular filaments; the premaxilla greatly reduced; the abdomen completely covered by plates, with the plates between lateral abdominal plates small and rhombic; a caudal fin with 14 rays; the orbital notch absent; five lateral series of plates; dorsal-fin spinelet absent; preanal plate present, large and solid, and of irregular, polygonal shape, the caudal peduncle becoming more compressed posteriorly for the last seven to 10 plates. (C) 2011 The Authors Journal of Fish Biology (C) 2011 The Fisheries Society of the British Isles

Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice

Motivated by the unconventional properties and rich phase diagram of NaxCoO2 we consider the electronic and magnetic properties of a two-dimensional Hubbard model on an isotropic triangular lattice doped with electrons away from half-filling. Dynamical mean-field theory (DMFT) calculations predict that for negative intersite hopping amplitudes (t < 0) and an on-site Coulomb repulsion, U, comparable to the bandwidth, the system displays properties typical of a weakly correlated metal. In contrast, for t > 0 a large enhancement of the effective mass, itinerant ferromagnetism, and a metallic phase with a Curie-Weiss magnetic susceptibility are found in a broad electron doping range. The different behavior encountered is a consequence of the larger noninteracting density of states (DOS) at the Fermi level for t > 0 than for t < 0, which effectively enhances the mass and the scattering amplitude of the quasiparticles. The shape of the DOS is crucial for the occurrence of ferromagnetism as for t > 0 the energy cost of polarizing the system is much smaller than for t < 0. Our observation of Nagaoka ferromagnetism is consistent with the A-type antiferromagnetism (i.e., ferromagnetic layers stacked antiferromagnetically) observed in neutron scattering experiments on NaxCoO2. The transport and magnetic properties measured in NaxCoO2 are consistent with DMFT predictions of a metal close to the Mott insulator and we discuss the role of Na ordering in driving the system towards the Mott transition. We propose that the Curie-Weiss metal phase observed in NaxCoO2 is a consequence of the crossover from a bad metal with incoherent quasiparticles at temperatures T > T-* and Fermi liquid behavior with enhanced parameters below T-*, where T-* is a low energy coherence scale induced by strong local Coulomb electron correlations. Our analysis also shows that the one band Hubbard model on a triangular lattice is not enough to describe the unusual properties of NaxCoO2 and is used to identify the simplest relevant model that captures the essential physics in NaxCoO2. We propose a model which allows for the Na ordering phenomena observed in the system which, we propose, drives the system close to the Mott insulating phase even at large dopings.

Visuospatial processing and the function of prefrontal-parietal networks in autism spectrum disorders: a functional MRI study

Objective: Individuals with autism spectrum disorders typically have normal visuospatial abilities but impaired executive functioning, particularly in abilities related to working memory and attention. The aim of this study was to elucidate the functioning of frontoparietal networks underlying spatial working memory processes during mental rotation in persons with autism spectrum disorders. Method: Seven adolescent males with normal IQ with an autism spectrum disorder and nine age- and IQ-matched male comparison subjects underwent functional magnetic resonance imaging scans while performing a mental rotation task. Results: The autism spectrum disorders group showed less activation in lateral and medial premotor cortex, dorsolateral prefrontal cortex, anterior cingulate gyrus, and caudate nucleus. Conclusions: The finding of less activation in prefrontal regions but not in parietal regions supports a model of dysfunction of frontostriatal networks in autism spectrum disorders.

An fMRI Normative Database for Connectivity Networks Using One-Class Support Vector Machines

The application of functional magnetic resonance imaging (fMRI) in neuroscience studies has increased enormously in the last decade. Although primarily used to map brain regions activated by specific stimuli, many studies have shown that fMRI can also be useful in identifying interactions between brain regions (functional and effective connectivity). Despite the widespread use of fMRI as a research tool, clinical applications of brain connectivity as studied by fMRI are not well established. One possible explanation is the lack of normal pattern, and intersubject variability-two variables that are still largely uncharacterized in most patient populations of interest. In the current study, we combine the identification of functional connectivity networks extracted by using Spearman partial correlation with the use of a one-class support vector machine in order construct a normative database. An application of this approach is illustrated using an fMRI dataset of 43 healthy Subjects performing a visual working memory task. In addition, the relationships between the results obtained and behavioral data are explored. Hum Brain Mapp 30:1068-1076, 2009. (C) 2008 Wiley-Liss. Inc.