1,721,132 research outputs found
Closed geodesics on compact Lorentzian manifolds of splitting type
No full textIn this paper, we consider the problem of the existence of a spacelike closed geodesic on compact Lorentzian manifolds. Tipler and Galloway proved that, under suitable topological properties of the manifold, there exists a closed timelike geodesic. In their proofs, they use the hypothesis that the time coordinate of one timelike geodesic has derivative always different from zero. This clearly fails for spacelike geodesics. Using variational methods and applying the relative category theory, we prove the existence of a closed spacelike geodesic on a compact manifold script M sign of splitting type. Observe that, thanks to the previous results, the existence of at least two geometrically distinct closed geodesics on script M sign follows
Interpreting End-to-End Deep Learning Models for Speech Source Localization Using Layer-wise Relevance Propagation
No full textDeep learning models are widely applied in the signal processing community, yet their inner working procedure is often treated as a black box. In this paper, we investigate the use of eXplainable Artificial Intelligence (XAI) techniques to analyze learning-based end-to-end speech source localization models. We consider the Layer-wise Relevance Propagation (LRP) technique, which aims to determine which parts of the input are more important for the output prediction. Using LRP we analyze two state-of-the-art models, of differing architectural complexity that map audio signals acquired by the microphones to the cartesian coordinates of the source. Specifically, we inspect the relevance associated with the input features of the two models and discover that both networks seem to denoise and de-reverberate the microphone signals in order to compute more accurate statistical correlations between them and consequently localize the sources. To further demonstrate this fact, we estimate the Time-Difference of Arrivals (TDoAs) via the Generalized Cross Correlation with Phase Transform (GCC-PHAT) using both microphone signals and relevance signals extracted from the two networks and show that through the latter we obtain more accurate time-delay estimation results
A Deep Learning-Based Pressure Matching Approach To Soundfield Synthesis
No full textIn this paper we propose a technique for soundfield synthesis based on the combination of the Pressure Matching (PM) approach and of deep learning-based methods. The pressure matching approach retrieves the driving signals for soundfield reproduction by minimizing the reproduction error at discrete control points through least squares. In this paper we follow a similar approach, but we perform the minimization by applying a Convolutional Neural Network (CNN). Through simulations, we compare the performance of the original pressure matching approach with the proposed technique and demonstrate how the latter is able to overcome spatial aliasing issues
Synthesis of soundfields through irregular loudspeaker arrays based on convolutional neural networks
Full text linkMost soundfield synthesis approaches deal with extensive and regular loudspeaker arrays, which are often not suitable for home audio systems, due to physical space constraints. In this article, we propose a technique for soundfield synthesis through more easily deployable irregular loudspeaker arrays, i.e., where the spacing between loudspeakers is not constant, based on deep learning. The input are the driving signals obtained through a plane wave decomposition-based technique. While the considered driving signals are able to correctly reproduce the soundfield with a regular array, they show degraded performances when using irregular setups. Through a complex-valued convolutional neural network (CNN), we modify the driving signals in order to compensate the errors in the reproduction of the desired soundfield. Since no ground truth driving signals are available for the compensated ones, we train the model by calculating the loss between the desired soundfield at a number of control points and the one obtained through the driving signals estimated by the network. The proposed model must be retrained for each irregular loudspeaker array configuration. Numerical results show better reproduction accuracy with respect to the plane wave decomposition-based technique, pressure-matching approach, and linear optimizers for driving signal compensation
Special Issue: A Tale of Genes and Genomes
Full text linkVariability is the source on which selective pressure acts, allowing genome evolution and adaptation [...
Some results about geodesics on lorentzian manifolds of splitting type
No full textLet us consider a Lorentzian manifold (M,g), that is a smooth, connected, finite-dimensional manifold M endowed with a smooth symmetric second order metric tensor field g, having index 1. For any z in M, it induces on T,M a nondegenerate bilinear form g(z)[., .] having exactly one negative eigenvalue. In order to study the geometry of (M,g) geodesic curves play an important role. We recall that a geodesic is a smooth curve 7: [0, l] + M which satisfies the equation:
v,j-0,
where V,+(s) denotes the covariant derivative of 7(s) with respect to the Levi-Civita connection of the metric tensor g. A closed geodesic is a geodesic 7 such that
r(O) = 7(l) and %O) = ?(I).
It is well known that if 7 is a geodesic, there exists a constant E-, such that E-, = g(7(s))[j(s),j(s)]
for all s E [0, l] . Then 7 is said timelike, lightlike or spacelike respectively when E, is negative, null or positive.
The aim of this paper is to review some recent results concerning some properties of geodesics on a Lorentzian manifold. Particularly we will analyse two questions: the existence of closed geodesics and the geodesical connectedness for some classes of Lorentzian manifolds. We recall (M, g) is said geodesicallyconnectedif every couple of its points can be joined by a geodesic.
The results here reported are obtained by means of global variational methods and relative category theory and they refer to [l], [2], [4], [5], [6], [12], [13], [15].
The paper will be divided into two sections, dealing separately with the previous problems
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