Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter $F_0^a$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism --- negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at $F_0^a=-1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter $F_0^s$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to $F_0^a$ at $J<0$ it requires an attraction beyond a critical value $V_c$ to generate the divergence of the charge susceptibility at $F_0^s=-1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.Comment: 12 pages, 10 figure

Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems

An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class systems based on homological arguments is proposed. The general formalism is exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page

The effect of the range of interaction on the phase diagram of a globular protein

Thermodynamic perturbation theory is applied to the model of globular proteins studied by ten Wolde and Frenkel (Science 277, pg. 1976) using computer simulation. It is found that the reported phase diagrams are accurately reproduced. The calculations show how the phase diagram can be tuned as a function of the lengthscale of the potential.Comment: 20 pages, 5 figure

Onset of collective and cohesive motion

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. {\bf 75},1226 (1995)] for which a non-trivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.Comment: accepted for publication in Phys. Rev. Let

Boltzmann and hydrodynamic description for self-propelled particles

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.Comment: 4 pages, 3 figures, final versio

Triplectic Gauge Fixing for N=1 Super Yang-Mills Theory

The Sp(2)-gauge fixing of N = 1 super-Yang-Mills theory is considered here. We thereby apply the triplectic scheme, where two classes of gauge-fixing bosons are introduced. The first one depends only on the gauge field, whereas the second boson depends on this gauge field and also on a pair of Majorana fermions. In this sense, we build up the BRST extended (BRST plus antiBRST) algebras for the model, for which the nilpotency relations, s^2_1=s^2_2=s_1s_2+s_2s_1=0, hold.Comment: 10 pages, no figures, latex forma

Coordination of Foliar and Wood Anatomical Traits Contributes to Tropical Tree Distributions and Productivity along the Malay-Thai Peninsula

Drought is a critical factor in plant species distributions. Much research points to its relevance even in moist tropical regions. Recent studies have begun to elucidate mechanisms underlying the distributions of tropical tree species with respect to drought; however, how such desiccation tolerance mechanisms correspond with the coordination of hydraulic and photosynthetic traits in determining species distributions with respect to rainfall seasonality deserves attention. In the present study, we used a common garden approach to quantify inherent differences in wood anatomical and foliar physiological traits in 21 tropical tree species with either widespread (occupying both seasonal and aseasonal climates) or southern (restricted to aseasonal forests) distributions with respect to rainfall seasonality. Use of congeneric species pairs and phylogenetically independent contrast analyses allowed examination of this question in a phylogenetic framework. Widespread species opted for wood traits that provide biomechanical support and prevent xylem cavitation and showed associated reductions in canopy productivity and consequently growth rates compared with southern species. These data support the hypothesis that species having broader distributions with respect to climatic variability will be characterized by traits conducive to abiotic stress tolerance. This study highlights the importance of the well-established performance vs. stress tolerance trade-off as a contributor to species distributions at larger scales

Permutation-invariant distance between atomic configurations

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e. fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the Root Mean Square Distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e. their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity

Towards Interpretable Deep Learning Models for Knowledge Tracing

As an important technique for modeling the knowledge states of learners, the traditional knowledge tracing (KT) models have been widely used to support intelligent tutoring systems and MOOC platforms. Driven by the fast advancements of deep learning techniques, deep neural network has been recently adopted to design new KT models for achieving better prediction performance. However, the lack of interpretability of these models has painfully impeded their practical applications, as their outputs and working mechanisms suffer from the intransparent decision process and complex inner structures. We thus propose to adopt the post-hoc method to tackle the interpretability issue for deep learning based knowledge tracing (DLKT) models. Specifically, we focus on applying the layer-wise relevance propagation (LRP) method to interpret RNN-based DLKT model by backpropagating the relevance from the model's output layer to its input layer. The experiment results show the feasibility using the LRP method for interpreting the DLKT model's predictions, and partially validate the computed relevance scores from both question level and concept level. We believe it can be a solid step towards fully interpreting the DLKT models and promote their practical applications in the education domain