Cidade é uma palavra plural [City is a manifold word]

This text elaborates on the city as cultural construct and representation and Lisbocópio, the installation by Pancho Guedes and Ricardo Jacinto in the context of the Official Representation of Portugal at the 10. Mostra Internazionale di Architettura-La Biennale di Venezia.

Robust clustering of multi-type relational data via a heterogeneous manifold ensemble

High-Order Co-Clustering (HOCC) methods have attracted high attention in recent years because of their ability to cluster multiple types of objects simultaneously using all available information. During the clustering process, HOCC methods exploit object co-occurrence information, i.e., inter-type relationships amongst different types of objects as well as object affinity information, i.e., intra-type relationships amongst the same types of objects. However, it is difficult to learn accurate intra-type relationships in the presence of noise and outliers. Existing HOCC methods consider the p nearest neighbours based on Euclidean distance for the intra-type relationships, which leads to incomplete and inaccurate intra-type relationships. In this paper, we propose a novel HOCC method that incorporates multiple subspace learning with a heterogeneous manifold ensemble to learn complete and accurate intra-type relationships. Multiple subspace learning reconstructs the similarity between any pair of objects that belong to the same subspace. The heterogeneous manifold ensemble is created based on two-types of intra-type relationships learnt using p-nearest-neighbour graph and multiple subspaces learning. Moreover, in order to make sure the robustness of clustering process, we introduce a sparse error matrix into matrix decomposition and develop a novel iterative algorithm. Empirical experiments show that the proposed method achieves improved results over the state-of-art HOCC methods for FScore and NMI.

Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Domain Adaptation on the Statistical Manifold

In this paper, we tackle the problem of unsupervised domain adaptation for classification. In the unsupervised scenario where no labeled samples from the target domain are provided, a popular approach consists in transforming the data such that the source and target distributions be- come similar. To compare the two distributions, existing approaches make use of the Maximum Mean Discrepancy (MMD). However, this does not exploit the fact that prob- ability distributions lie on a Riemannian manifold. Here, we propose to make better use of the structure of this man- ifold and rely on the distance on the manifold to compare the source and target distributions. In this framework, we introduce a sample selection method and a subspace-based method for unsupervised domain adaptation, and show that both these manifold-based techniques outperform the cor- responding approaches based on the MMD. Furthermore, we show that our subspace-based approach yields state-of- the-art results on a standard object recognition benchmark.

Beyond Gauss: Image-set matching on the Riemannian manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar´ f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifold, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods.

A note on the equivalence of shock manifold equations

The shock manifold equation is a first order nonlinear partial differential equation, which describes the kinematics of a shockfront in an ideal gas with constant specific heats. However, it was found that there was more than one of these shock manifold equations, and the shock surface could be embedded in a one parameter family of surfaces, obtained as a solution of any of these shock manifold equations. Associated with each shock manifold equation is a set of characteristic curves called lsquoshock raysrsquo. This paper investigates the nature of various associated shock ray equations.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called 'symplectic condition' (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Pressure induced manifold enhancement of Li-kinetics in FCC fullerene

The reduction of the diffusion energy barrier for Li in electrodes is one of the required criteria to achieve better performances in Li ion batteries. Using density functional theory based calculations, we report a pressure induced manifold enhancement of Li-kinetics in bulk FCC fullerene. Scanning of the potential energy surface reveals a diffusion path with a low energy barrier of 0.62 eV, which reduces further under the application of hydrostatic pressure. The pressure induced reduction in the diffusion barrier continues till a uniform volume strain of 17.7% is reached. Further enhancement of strain increases the barrier due to the repulsion caused by C-C bond formation between two neighbouring fullerenes. The decrease in the barrier is attributed to the combined effect of charge transfer triggered by the enhanced interaction of Li with the fullerene as well as the change in profile of the local potential, which becomes more attractive for Li. The lowering of the barrier leads to an enhancement of two orders of magnitude in Li diffusivity at room temperature making pressurized bulk fullerene a promising artificial solid electrolyte interface (SEI) for a faster rechargeable battery.