An efficient and accurate decomposition of the Fermi operator

We present a method to compute the Fermi function of the Hamiltonian for a system of independent fermions, based on an exact decomposition of the grand-canonical potential. This scheme does not rely on the localization of the orbitals and is insensitive to ill-conditioned Hamiltonians. It lends itself naturally to linear scaling, as soon as the sparsity of the system's density matrix is exploited. By using a combination of polynomial expansion and Newton-like iterative techniques, an arbitrarily large number of terms can be employed in the expansion, overcoming some of the difficulties encountered in previous papers. Moreover, this hybrid approach allows us to obtain a very favorable scaling of the computational cost with increasing inverse temperature, which makes the method competitive with other Fermi operator expansion techniques. After performing an in-depth theoretical analysis of computational cost and accuracy, we test our approach on the DFT Hamiltonian for the metallic phase of the LiAl alloy.Comment: 8 pages, 7 figure

Action Sets: Weakly Supervised Action Segmentation without Ordering Constraints

Action detection and temporal segmentation of actions in videos are topics of increasing interest. While fully supervised systems have gained much attention lately, full annotation of each action within the video is costly and impractical for large amounts of video data. Thus, weakly supervised action detection and temporal segmentation methods are of great importance. While most works in this area assume an ordered sequence of occurring actions to be given, our approach only uses a set of actions. Such action sets provide much less supervision since neither action ordering nor the number of action occurrences are known. In exchange, they can be easily obtained, for instance, from meta-tags, while ordered sequences still require human annotation. We introduce a system that automatically learns to temporally segment and label actions in a video, where the only supervision that is used are action sets. An evaluation on three datasets shows that our method still achieves good results although the amount of supervision is significantly smaller than for other related methods.Comment: CVPR 201

Weakly Supervised Action Learning with RNN based Fine-to-coarse Modeling

We present an approach for weakly supervised learning of human actions. Given a set of videos and an ordered list of the occurring actions, the goal is to infer start and end frames of the related action classes within the video and to train the respective action classifiers without any need for hand labeled frame boundaries. To address this task, we propose a combination of a discriminative representation of subactions, modeled by a recurrent neural network, and a coarse probabilistic model to allow for a temporal alignment and inference over long sequences. While this system alone already generates good results, we show that the performance can be further improved by approximating the number of subactions to the characteristics of the different action classes. To this end, we adapt the number of subaction classes by iterating realignment and reestimation during training. The proposed system is evaluated on two benchmark datasets, the Breakfast and the Hollywood extended dataset, showing a competitive performance on various weak learning tasks such as temporal action segmentation and action alignment

Quantum Monte Carlo Study of High Pressure Solid Molecular Hydrogen

We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {\bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {\bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules

A Visual Notation for Declarative Behaviour Specification

Logical programming has many merits that should appeal to modellers. It enables declarative specifications that are free from implementation details and even (mostly) abstracts away from control flow specification. However, the textual syntax of, for example PROLOG, most likely represents a barrier to the adoption of such languages in the modelling community. The visual notation presented in this paper aims to facilitate the understanding of behaviour specifications based on logic programming. I anticipate that the dataflow-like nature of the resulting diagrams will appeal to modellers. I believe the visual notation to be an improvement over the traditional textual syntax for the purpose of specifying PROLOG programs as such, but the ultimate hope is to have found a vehicle to make declarative logic programming a commonplace activity in multi-paradigm modelling