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This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale gradient descent approach for the efficient resolution of the corresponding minimization problem, which interleaves the optimization of the barycenter weights with the optimization of the atom diagrams. Our approach leverages the analytic expressions for the gradient of both sub-problems to ensure fast iterations and it additionally exploits shared-memory parallelism. Extensive experiments on public ensembles demonstrate the efficiency of our approach, with Wasserstein dictionary computations in the orders of minutes for the largest examples. We show the utility of our contributions in two applications. First, we apply Wassserstein dictionaries to data reduction and reliably compress persistence diagrams by concisely representing them with their weights in the dictionary. Second, we present a dimensionality reduction framework based on a Wasserstein dictionary defined with a small number of atoms (typically three) and encode the dictionary as a low dimensional simplex embedded in a visual space (typically in 2D). In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used to reproduce our results.

This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that undecidability, a principle traditionally associated with theoretical computer science, extends its relevance to the music industry. The study adopts a multidimensional approach, focusing on five key areas: (1) the Turing completeness of Ableton, a widely used digital audio workstation, (2) the undecidability of satisfiability in sound creation utilizing an array of effects, (3) the undecidability of constraints on polymeters in musical compositions, (4) the undecidability of satisfiability in just intonation harmony constraints, and (5) the undecidability of "new ordering systems". In addition to providing theoretical proof for these assertions, the paper elucidates the practical relevance of these concepts for practitioners outside the field of theoretical computer science. The ultimate aim is to foster a new understanding of undecidability in music, highlighting its broader applicability and potential to influence contemporary computer-assisted (and traditional) music making.

Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes use of the symplectic form on phase space and allows a precise study of the covariance matrix of a density operator. The latter is a fundamental object in quantum information theory., The second variant is a symplectically covariant version of the usual polar duality highlighting the role played by Lagrangian planes. It allows us to define the notion of "geometric quantum states" with are in bijection with generalized Gaussians.

Estimating the head pose of a person is a crucial problem for numerous applications that is yet mainly addressed as a subtask of frontal pose prediction. We present a novel method for unconstrained end-to-end head pose estimation to tackle the challenging task of full range of orientation head pose prediction. We address the issue of ambiguous rotation labels by introducing the rotation matrix formalism for our ground truth data and propose a continuous 6D rotation matrix representation for efficient and robust direct regression. This allows to efficiently learn full rotation appearance and to overcome the limitations of the current state-of-the-art. Together with new accumulated training data that provides full head pose rotation data and a geodesic loss approach for stable learning, we design an advanced model that is able to predict an extended range of head orientations. An extensive evaluation on public datasets demonstrates that our method significantly outperforms other state-of-the-art methods in an efficient and robust manner, while its advanced prediction range allows the expansion of the application area. We open-source our training and testing code along with our trained models: //github.com/thohemp/6DRepNet360.

In this paper, we present methodologies for optimal selection for renewable energy sites under a different set of constraints and objectives. We consider two different models for the site-selection problem - coarse-grained and fine-grained, and analyze them to find solutions. We consider multiple different ways to measure the benefits of setting up a site. We provide approximation algorithms with a guaranteed performance bound for two different benefit metrics with the coarse-grained model. For the fine-grained model, we provide a technique utilizing Integer Linear Program to find the optimal solution. We present the results of our extensive experimentation with synthetic data generated from sparsely available real data from solar farms in Arizona.

This paper investigates the performance of a singleuser fluid antenna system (FAS), by exploiting a class of elliptical copulas to describe the structure of dependency amongst the fluid antenna ports. By expressing Jakes' model in terms of the Gaussian copula, we consider two cases: (i) the general case, i.e., any arbitrary correlated fading distribution; and (ii) the specific case, i.e., correlated Nakagami-m fading. For both scenarios, we first derive analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the equivalent channel in terms of multivariate normal distribution. Then, we obtain the outage probability (OP) and the delay outage rate (DOR) to analyze the performance of the FAS. By employing the popular rank correlation coefficients such as Spearman's \{rho} and Kendall's {\tau}, we measure the degree of dependency in correlated arbitrary fading channels and illustrate how the Gaussian copula can be accurately connected to Jakes' model in FAS without complicated mathematical analysis. Numerical results show that increasing the fluid antenna size provides lower OP and DOR, but the system performance saturates as the number of antenna ports increases. In addition, our results indicate that FAS provides better performance compared to conventional single-fixed antenna systems even when the size of fluid antenna is small.

In this paper a new optical-computational method is introduced to unveil images of targets whose visibility is severely obscured by light scattering in dense, turbid media. The targets of interest are taken to be dynamic in that their optical properties are time-varying whether stationary in space or moving. The scheme, to our knowledge the first of its kind, is human vision inspired whereby diffuse photons collected from the turbid medium are first transformed to spike trains by a dynamic vision sensor as in the retina, and image reconstruction is then performed by a neuromorphic computing approach mimicking the brain. We combine benchtop experimental data in both reflection (backscattering) and transmission geometries with support from physics-based simulations to develop a neuromorphic computational model and then apply this for image reconstruction of different MNIST characters and image sets by a dedicated deep spiking neural network algorithm. Image reconstruction is achieved under conditions of turbidity where an original image is unintelligible to the human eye or a digital video camera, yet clearly and quantifiable identifiable when using the new neuromorphic computational approach.

In this paper, we study the shape reconstruction problem, when the shape we wish to reconstruct is an orientable smooth d-dimensional submanifold of the Euclidean space. Assuming we have as input a simplicial complex K that approximates the submanifold (such as the Cech complex or the Rips complex), we recast the problem of reconstucting the submanifold from K as a L1-norm minimization problem in which the optimization variable is a d-chain of K. Providing that K satisfies certain reasonable conditions, we prove that the considered minimization problem has a unique solution which triangulates the submanifold and coincides with the flat Delaunay complex introduced and studied in a companion paper. Since the objective is a weighted L1-norm and the contraints are linear, the triangulation process can thus be implemented by linear programming.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.