Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles

It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. This is proved directly for the two body problem and for the three body problem by using the Garnier equations for isomonodromic transformations. For a number of particles greater than three the existence of the hamiltonian is shown to be a consequence of a conjecture by Polyakov which connects the auxiliary parameters of the fuchsian differential equation which solves the SU(1,1) Riemann-Hilbert problem, to the Liouville action of the conformal factor which describes the space-metric. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics. The quantum mechanical Green's function for the two body problem is given.Comment: 34 pages LaTe

Fighting Authorship Linkability with Crowdsourcing

Massive amounts of contributed content -- including traditional literature, blogs, music, videos, reviews and tweets -- are available on the Internet today, with authors numbering in many millions. Textual information, such as product or service reviews, is an important and increasingly popular type of content that is being used as a foundation of many trendy community-based reviewing sites, such as TripAdvisor and Yelp. Some recent results have shown that, due partly to their specialized/topical nature, sets of reviews authored by the same person are readily linkable based on simple stylometric features. In practice, this means that individuals who author more than a few reviews under different accounts (whether within one site or across multiple sites) can be linked, which represents a significant loss of privacy. In this paper, we start by showing that the problem is actually worse than previously believed. We then explore ways to mitigate authorship linkability in community-based reviewing. We first attempt to harness the global power of crowdsourcing by engaging random strangers into the process of re-writing reviews. As our empirical results (obtained from Amazon Mechanical Turk) clearly demonstrate, crowdsourcing yields impressively sensible reviews that reflect sufficiently different stylometric characteristics such that prior stylometric linkability techniques become largely ineffective. We also consider using machine translation to automatically re-write reviews. Contrary to what was previously believed, our results show that translation decreases authorship linkability as the number of intermediate languages grows. Finally, we explore the combination of crowdsourcing and machine translation and report on the results

Controllable Image-to-Video Translation: A Case Study on Facial Expression Generation

The recent advances in deep learning have made it possible to generate photo-realistic images by using neural networks and even to extrapolate video frames from an input video clip. In this paper, for the sake of both furthering this exploration and our own interest in a realistic application, we study image-to-video translation and particularly focus on the videos of facial expressions. This problem challenges the deep neural networks by another temporal dimension comparing to the image-to-image translation. Moreover, its single input image fails most existing video generation methods that rely on recurrent models. We propose a user-controllable approach so as to generate video clips of various lengths from a single face image. The lengths and types of the expressions are controlled by users. To this end, we design a novel neural network architecture that can incorporate the user input into its skip connections and propose several improvements to the adversarial training method for the neural network. Experiments and user studies verify the effectiveness of our approach. Especially, we would like to highlight that even for the face images in the wild (downloaded from the Web and the authors' own photos), our model can generate high-quality facial expression videos of which about 50\% are labeled as real by Amazon Mechanical Turk workers.Comment: 10 page

Massive Dimensionality Reduction for the Left Ventricular Mesh

Statistical emulation is a promising approach for the translation of cardio-mechanical modelling into the clinical practice. However, a key challenge is to find a low-dimensional representation of the heart, or, for the specific purpose of diagnosing the risk of heart attacks, the left-ventricle of the heart. We consider the problem of dimensionality reduction of the left ventricular mesh, in which we investigate three classes of techniques: principal component analysis (PCA), deep learning (DL) methods based on auto-encoders, and a parametric model from the cardio-mechanical literature. Our finding is that PCA performs as well as the computationally more expensive DL methods, and both outperform the state-of-the-art parametric model

Massive Dimensionality Reduction for the Left Ventricular Mesh

Statistical emulation is a promising approach for the translation of cardio-mechanical modelling into the clinical practice. However, a key challenge is to find a low-dimensional representation of the heart, or, for the specific purpose of diagnosing the risk of heart attacks, the left-ventricle of the heart. We consider the problem of dimensionality reduction of the left ventricular mesh, in which we investigate three classes of techniques: principal component analysis (PCA), deep learning (DL) methods based on auto-encoders, and a parametric model from the cardio-mechanical literature. Our finding is that PCA performs as well as the computationally more expensive DL methods, and both outperform the state-of-the-art parametric model

Stable and Unstable Crack Growth in Viscoelastic Media

The failure of load-bearing structures by fracture is generally important in all phases of our society. It may concern small household items as well as expensive structures of civil or space applications and accordingly may cause varying degrees of economic distress. While the state of failure is usually easily determined as either "not failed" or "completely failed," the estimation of how close to either state a structure is, poses a much more difficult problem. It is important to recognize, however, that from an engineering point of view, the latter problem is the important one because it would allow, in principle, the prediction of the conditions leading to fracture and thus to a close estimate of the service life of a structure. Inasmuch as failures by fracture involve the growth of cracks it appears that keeping track of the size of a crack in a particular structure provides a means of assessing *quantitatively* the strength prior to complete failure. If one agrees that the description of structural strength is rationalized in terms of the size of the defects, it foll0ws that one must attempt to understand the laws that govern the growth of such defects in order to predict complete failure. Fracture of materials is a complicated process which encompasses atomistic aspects, as well as microscopic and large-scale continuum mechanical considerations. Although one of these aspects should not be considered without the other we shall be concerned with the continuum-mechanical formulation of the problem of fracture growth in viscoelastic materials. From this viewpoint the prediction of failure comprises three phases: first an examination of the physical situation presented by a static or growing defect in a material, second the translation of this physically observable situation into a mathematical model which is amenable to analysis by currently available or extendable tools of mathematics, third the theoretical exploitation of the mathematical model in an attempt to predict the behavior of defects under load and the comparison of these results with experimentally observable phenomena to assess the validity of the modelling process as given from phase one and phase two. While there are many important details that have bearing on such a development we shall be concerned more with the principles of the analysis and show how the various considerations of the three phases enter into the overall structure of the crack propagation problem. In keeping analytic work as simple as possible it is intended to emphasize what type of results may be obtained with the aid of continuum mechanics and where continuum mechanics requires support by microscopic considerations