Comments on the Sign and Other Aspects of Semiclassical Casimir Energies

The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The so defined semiclassical Casimir energy coincides with that obtained using zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are related to non-universal subtractions in the spectral density. The sign of the Casimir energy of a scalar field on a smooth manifold is estimated by the sign of the contribution due to the shortest periodic rays only. Demanding continuity of the Casimir energy under small deformations of the manifold, the method is extended to integrable systems. The Casimir energy of a massless scalar field on a manifold with boundaries includes contributions due to periodic rays that lie entirely within the boundaries. These contributions in general depend on the boundary conditions. Although the Casimir energy due to a massless scalar field may be sensitive to the physical dimensions of manifolds with boundary, its sign can in favorable cases be inferred without explicit calculation of the Casimir energy.Comment: 39 pages, no figures, references added, some correction

A Non-Riemannian Metric on Space-Time Emergent From Scalar Quantum Field Theory

We show that the two-point function \sigma(x,x')=\sqrt{} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It is very different from the Euclidean metric |x-x'| at large distances, yet agrees with it at short distances. For example, space-time has finite diameter which is not universal. The Lipschitz equivalence class of the metric is independent of the cutoff. \sigma(x,x') is not the length of the geodesic in any Riemannian metric. Nevertheless, it is possible to embed space-time in a higher dimensional space so that \sigma(x,x') is the length of the geodesic in the ambient space. \sigma(x,x') should be useful in constructing the continuum limit of quantum field theory with fundamental scalar particles

Random manifolds in non-linear resistor networks: Applications to varistors and superconductors

We show that current localization in polycrystalline varistors occurs on paths which are, usually, in the universality class of the directed polymer in a random medium. We also show that in ceramic superconductors, voltage localizes on a surface which maps to an Ising domain wall. The emergence of these manifolds is explained and their structure is illustrated using direct solution of non-linear resistor networks

Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging.

We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and tensor calculus. In Diffusion Tensor Imaging (DTI), the diffusion of water is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric framework. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restricting the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract multiple relevant directions, and Finsler geometry provides the natural geometric generalization appropriate for multi-fiber analysis. In this paper we provide an exact criterion to determine whether a spherical function satisfies the strong convexity criterion essential for a Finsler norm. We also show a novel fiber tracking method in Finsler setting. Our model incorporates a scale parameter, which can be beneficial in view of the noisy nature of the data. We demonstrate our methods on analytic as well as simulated and real HARDI data

Development of a land use regression model for black carbon using mobile monitoring data and its application to pollution-avoiding routing

Black carbon is often used as an indicator for combustion-related air pollution. In urban environments, on-road black carbon concentrations have a large spatial variability, suggesting that the personal exposure of a cyclist to black carbon can heavily depend on the route that is chosen to reach a destination. In this paper, we describe the development of a cyclist routing procedure that minimizes personal exposure to black carbon. Firstly, a land use regression model for predicting black carbon concentrations in an urban environment is developed using mobile monitoring data, collected by cyclists. The optimal model is selected and validated using a spatially stratified cross-validation scheme. The resulting model is integrated in a dedicated routing procedure that minimizes personal exposure to black carbon during cycling. The best model obtains a coefficient of multiple correlation of R = 0.520. Simulations with the black carbon exposure minimizing routing procedure indicate that the inhaled amount of black carbon is reduced by 1.58% on average as compared to the shortest-path route, with extreme cases where a reduction of up to 13.35% is obtained. Moreover, we observed that the average exposure to black carbon and the exposure to local peak concentrations on a route are competing objectives, and propose a parametrized cost function for the routing problem that allows for a gradual transition from routes that minimize average exposure to routes that minimize peak exposure

Semi-classical Dynamical Triangulations

For non-critical string theory the partition function reduces to an integral over moduli space after integrating over matter fields. The moduli integrand is known analytically for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory and we show that even for very small triangulations it reproduces very well the continuum integrand when the central charge $c$ of the matter fields is large negative, thus providing a striking example of how the quantum fluctuations of geometry disappear when $c \to -\infty$.Comment: 11 pages, 5 figure

Learning Generative Models across Incomparable Spaces

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML

Modeling relation paths for knowledge base completion via joint adversarial training

Knowledge Base Completion (KBC), which aims at determining the missing relations between entity pairs, has received increasing attention in recent years. Most existing KBC methods focus on either embedding the Knowledge Base (KB) into a specific semantic space or leveraging the joint probability of Random Walks (RWs) on multi-hop paths. Only a few unified models take both semantic and path-related features into consideration with adequacy. In this paper, we propose a novel method to explore the intrinsic relationship between the single relation (i.e. 1-hop path) and multi-hop paths between paired entities. We use Hierarchical Attention Networks (HANs) to select important relations in multi-hop paths and encode them into low-dimensional vectors. By treating relations and multi-hop paths as two different input sources, we use a feature extractor, which is shared by two downstream components (i.e. relation classifier and source discriminator), to capture shared/similar information between them. By joint adversarial training, we encourage our model to extract features from the multi-hop paths which are representative for relation completion. We apply the trained model (except for the source discriminator) to several large-scale KBs for relation completion. Experimental results show that our method outperforms existing path information-based approaches. Since each sub-module of our model can be well interpreted, our model can be applied to a large number of relation learning tasks.Comment: Accepted by Knowledge-Based System