Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using Compound Poisson Processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.Comment: 23 pages, 8 figures, 21 reference

Exploring pure quantum states with maximally mixed reductions

We investigate multipartite entanglement for composite quantum systems in a pure state. Using the generalized Bloch representation for n-qubit states, we express the condition that all k-qubit reductions of the whole system are maximally mixed, reflecting maximum bipartite entanglement across all k vs. n-k bipartitions. As a special case, we examine the class of balanced pure states, which are constructed from a subset of the Pauli group P_n that is isomorphic to Z_2^n. This makes a connection with the theory of quantum error-correcting codes and provides bounds on the largest allowed k for fixed n. In particular, the ratio k/n can be lower and upper bounded in the asymptotic regime, implying that there must exist multipartite entangled states with at least k=0.189 n when $n\to \infty$. We also analyze symmetric states as another natural class of states with high multipartite entanglement and prove that, surprisingly, they cannot have all maximally mixed k-qubit reductions with k>1. Thus, measured through bipartite entanglement across all bipartitions, symmetric states cannot exhibit large entanglement. However, we show that the permutation symmetry only constrains some components of the generalized Bloch vector, so that very specific patterns in this vector may be allowed even though k>1 is forbidden. This is illustrated numerically for a few symmetric states that maximize geometric entanglement, revealing some interesting structures.Comment: 10 pages, 2 figure

Coordinate Bethe Ansatz for Spin s XXX Model

We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for spin 1/2 and spin 1 chains

A bisector line field approach to interpolation of orientation fields

We propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively generalizing the notion of doubling phase vector fields. Endowed with a well chosen energy minimization problem, we provide a polynomial interpolation of a target orientation field while bypassing the doubling phase step. The procedure is then illustrated with examples from fingerprint analysis

Sequentially Generated Instance-Dependent Image Representations for Classification

In this paper, we investigate a new framework for image classification that adaptively generates spatial representations. Our strategy is based on a sequential process that learns to explore the different regions of any image in order to infer its category. In particular, the choice of regions is specific to each image, directed by the actual content of previously selected regions.The capacity of the system to handle incomplete image information as well as its adaptive region selection allow the system to perform well in budgeted classification tasks by exploiting a dynamicly generated representation of each image. We demonstrate the system's abilities in a series of image-based exploration and classification tasks that highlight its learned exploration and inference abilities

Fader Networks: Manipulating Images by Sliding Attributes

This paper introduces a new encoder-decoder architecture that is trained to reconstruct images by disentangling the salient information of the image and the values of attributes directly in the latent space. As a result, after training, our model can generate different realistic versions of an input image by varying the attribute values. By using continuous attribute values, we can choose how much a specific attribute is perceivable in the generated image. This property could allow for applications where users can modify an image using sliding knobs, like faders on a mixing console, to change the facial expression of a portrait, or to update the color of some objects. Compared to the state-of-the-art which mostly relies on training adversarial networks in pixel space by altering attribute values at train time, our approach results in much simpler training schemes and nicely scales to multiple attributes. We present evidence that our model can significantly change the perceived value of the attributes while preserving the naturalness of images.Comment: NIPS 201

A probabilistic model to predict the formation and propagation of crack networks in thermal fatigue

International audienceA probabilistic model is presented to predict the formation and propagation of crack networks in thermal fatigue. It is based on a random distribution of sites where cracks initiate and on the shielding phenomenon corresponding to the relaxed stress field created around cracks. Currently, the model considers only heterogeneous uniaxial stress loading even if thermal fatigue is multiaxial. However, the first simulations on a uniaxial mechanical loading representative of the stress gradient that appears in thermal fatigue shocks are in qualitative agreement with experimental results. The larger the stress amplitude, the denser the crack network and the smaller the crack sizes