Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

Structural phase transitions in low-dimensional ion crystals

A chain of singly charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the particle number. This structural change is a phase transition of second order, whose order parameter is the crystal displacement from the chain axis. We study analytically the transition using Landau theory and find full agreement with numerical predictions by Schiffer [Phys. Rev. Lett. 70, 818 (1993)] and Piacente [Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine analytically the system's behavior at the transition point.

Human pose tracking in low dimensional space enhanced by limb correction

This paper proposes a two-level 3D human pose tracking method for a specific action captured by several cameras. The generation of pose estimates relies on fitting a 3D articulated model on a Visual Hull generated from the input images. First, an initial pose estimate is constrained by a low dimensional manifold learnt by Temporal Laplacian Eigenmaps. Then, an improved global pose is calculated by refining individual limb poses. The validation of our method uses a public standard dataset and demonstrates its accurate and computational efficiency. © 2011 IEEE.

Structural and electronic properties of Ce overlayers and low-dimensional Pt-Ce alloys on Pt{111}

The structural, thermal, chemisorptive, and electronic properties of Ce on Pt{111} are studied by photoemission, Auger spectroscopy, scanning tunnel microscope (STM), and low-energy electron diffraction (LEED). Stranski-Krastanov-like growth of low-density Ce layers is accompanied by substantial valence charge transfer from Ce to Pt: in line with this, the measured dipole moment and polarizability of adsorbed Ce at low coverages are 7.2 x 10(-30) C m and similar to 1.3x10(-29) m(3), respectively. Pt-Ce intermixing commences at similar to 400 K and with increasing temperature a sequence of five different ordered surface alloys evolves. The symmetry, periodicities, and rotational epitaxy observed by LEED are in good accord with the STM data which reveal the true complexity of the system. The Various bimetallic surface phases are based on growth of crystalline Pt5Ce, a hexagonal layer structure consisting of alternating layers of Pt2Ce and Kagome nets of Pt atoms. This characteristic ABAB layered arrangement of the surface alloys is clearly imaged, and chemisorption data permit a distinction to be made between the more reactive Pt2Ce layer and the less reactive Pt Kagome net. Either type of layer can appear at the surface as the terminating structure, thicker films exhibiting unit mesh parameters characteristic of the bulk alloy.

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

Tools for analysing configuration interaction wavefunctions

The configuration interaction (CI) approach to quantum chemical calculations is a well-established means of calculating accurately the solution to the Schrodinger equation for many-electron systems. It represents the many-body electron wavefunction as a sum of spin-projected Slater determinants of orthogonal one-body spin-orbitals. The CI wavefunction becomes the exact solution of the Schrodinger equation as the length of the expansion becomes infinite, however, it is a difficult quantity to visualise and analyse for many-electron problems. We describe a method for efficiently calculating the spin-averaged one- and two-body reduced density matrices rho(psi)((r) over bar; (r) over bar' ) and Gamma(psi)((r) over bar (1), (r) over bar (2); (r) over bar'(1), (r) over bar'(2)) of an arbitrary CI wavefunction Psi. These low-dimensional functions are helpful tools for analysing many-body wavefunctions; we illustrate this for the case of the electron-electron cusp. From rho and Gamma one can calculate the matrix elements of any one- or two-body spin-free operator (O) over cap. For example, if (O) over cap is an applied electric field, this field can be included into the CI Hamiltonian and polarisation or gating effects may be studied for finite electron systems. (C) 2003 Elsevier B.V. All rights reserved.

How trophic interaction strength depends on traits

A key problem in community ecology is to understand how individual-level traits give rise to population-level trophic interactions. Here, we propose a synthetic framework based on ecological considerations to address this question systematically. We derive a general functional form for the dependence of trophic interaction coefficients on trophically relevant quantitative traits of consumers and resources. The derived expression encompasses-and thus allows a unified comparison of-several functional forms previously proposed in the literature. Furthermore, we show how a community's, potentially low-dimensional, effective trophic niche space is related to its higher-dimensional phenotypic trait space. In this manner, we give ecological meaning to the notion of the "dimensionality of trophic niche space." Our framework implies a method for directly measuring this dimensionality. We suggest a procedure for estimating the relevant parameters from empirical data and for verifying that such data matches the assumptions underlying our derivation. © Springer Science+Business Media B.V. 2009.


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Temporal extension of Laplacian Eigenmaps for unsupervised dimensionality reduction of time series

A novel non-linear dimensionality reduction method, called Temporal Laplacian Eigenmaps, is introduced to process efficiently time series data. In this embedded-based approach, temporal information is intrinsic to the objective function, which produces description of low dimensional spaces with time coherence between data points. Since the proposed scheme also includes bidirectional mapping between data and embedded spaces and automatic tuning of key parameters, it offers the same benefits as mapping-based approaches. Experiments on a couple of computer vision applications demonstrate the superiority of the new approach to other dimensionality reduction method in term of accuracy. Moreover, its lower computational cost and generalisation abilities suggest it is scalable to larger datasets. © 2010 IEEE.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

Simplifying the representation of complex free-energy landscapes using sketch-map

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.

Generalized Laplacian Eigenmaps for Modeling and Tracking Human Motions

This paper presents generalized Laplacian eigenmaps, a novel dimensionality reduction approach designed to address stylistic variations in time series. It generates compact and coherent continuous spaces whose geometry is data-driven. This paper also introduces graph-based particle filter, a novel methodology conceived for efficient tracking in low dimensional space derived from a spectral dimensionality reduction method. Its strengths are a propagation scheme, which facilitates the prediction in time and style, and a noise model coherent with the manifold, which prevents divergence, and increases robustness. Experiments show that a combination of both techniques achieves state-of-the-art performance for human pose tracking in underconstrained scenarios.

Efficient tracking of human poses using a manifold hierarchy

In this paper a 3D human pose tracking framework is presented. A new dimensionality reduction method (Hierarchical Temporal Laplacian Eigenmaps) is introduced to represent activities in hierarchies of low dimensional spaces. Such a hierarchy provides increasing independence between limbs, allowing higher flexibility and adaptability that result in improved accuracy. Moreover, a novel deterministic optimisation method (Hierarchical Manifold Search) is applied to estimate efficiently the position of the corresponding body parts. Finally, evaluation on public datasets such as HumanEva demonstrates that our approach achieves a 62.5mm-65mm average joint error for the walking activity and outperforms state-of-the-art methods in terms of accuracy and computational cost.

Perception and Automatic Recognition of Laughter from Whole-Body Motion: Continuous and Categorical Perspectives

Despite its importance in social interactions, laughter remains little studied in affective computing. Intelligent virtual agents are often blind to users’ laughter and unable to produce convincing laughter themselves. Respiratory, auditory, and facial laughter signals have been investigated but laughter-related body movements have received less attention. The aim of this study is threefold. First, to probe human laughter perception by analyzing patterns of categorisations of natural laughter animated on a minimal avatar. Results reveal that a low dimensional space can describe perception of laughter “types”. Second, to investigate observers’ perception of laughter (hilarious, social, awkward, fake, and non-laughter) based on animated avatars generated from natural and acted motion-capture data. Significant differences in torso and limb movements are found between animations perceived as laughter and those perceived as non-laughter. Hilarious laughter also differs from social laughter. Different body movement features were indicative of laughter in sitting and standing avatar postures. Third, to investigate automatic recognition of laughter to the same level of certainty as observers’ perceptions. Results show recognition rates of the Random Forest model approach human rating levels. Classification comparisons and feature importance analyses indicate an improvement in recognition of social laughter when localized features and nonlinear models are used.

General, PDB-based collective variables for protein folding

New, automated forms of data-analysis are required in order to understand the high-dimensional trajectories that are obtained from molecular dynamics simulations on proteins. Dimensionality reduction algorithms are particularly appealing in this regard as they allow one to construct unbiased, low-dimensional representations of the trajectory using only the information encoded in the trajectory. The downside of this approach is that different sets of coordinates are required for each different chemical systems under study precisely because the coordinates are constructed using information from the trajectory. In this paper we show how one can resolve this problem by using the sketch-map algorithm that we recently proposed to construct a low-dimensional representation of the structures contained in the protein data bank (PDB). We show that the resulting coordinates are as useful for analysing trajectory data as coordinates constructed using landmark configurations taken from the trajectory and that these coordinates can thus be used for understanding protein folding across a range of systems.

Person Re-Identification using Deep Convnets with Multi-task Learning

Person re-identification involves recognizing a person across non-overlapping camera views, with different pose, illumination, and camera characteristics. We propose to tackle this problem by training a deep convolutional network to represent a person’s appearance as a low-dimensional feature vector that is invariant to common appearance variations encountered in the re-identification problem. Specifically, a Siamese-network architecture is used to train a feature extraction network using pairs of similar and dissimilar images. We show that use of a novel multi-task learning objective is crucial for regularizing the network parameters in order to prevent over-fitting due to the small size the training dataset. We complement the verification task, which is at the heart of re-identification, by training the network to jointly perform verification, identification, and to recognise attributes related to the clothing and pose of the person in each image. Additionally, we show that our proposed approach performs well even in the challenging cross-dataset scenario, which may better reflect real-world expected performance.