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Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.

This paper introduces a novel framework called DTNet for 3D mesh reconstruction and generation via Disentangled Topology. Beyond previous works, we learn a topology-aware neural template specific to each input then deform the template to reconstruct a detailed mesh while preserving the learned topology. One key insight is to decouple the complex mesh reconstruction into two sub-tasks: topology formulation and shape deformation. Thanks to the decoupling, DT-Net implicitly learns a disentangled representation for the topology and shape in the latent space. Hence, it can enable novel disentangled controls for supporting various shape generation applications, e.g., remix the topologies of 3D objects, that are not achievable by previous reconstruction works. Extensive experimental results demonstrate that our method is able to produce high-quality meshes, particularly with diverse topologies, as compared with the state-of-the-art methods.

Reciprocity-based time-division duplex (TDD) Massive MIMO (multiple-input multiple-output) systems utilize channel estimates obtained in the uplink to perform precoding in the downlink. However, this method has been criticized of breaking down, in the sense that the channel estimates are not good enough to spatially separate multiple user terminals, at low uplink reference signal signal-to-noise ratios, due to insufficient channel estimation quality. Instead, codebook-based downlink precoding has been advocated for as an alternative solution in order to bypass this problem. We analyze this problem by considering a "grid-of-beams world" with a finite number of possible downlink channel realizations. Assuming that the terminal accurately can detect the downlink channel, we show that in the case where reciprocity holds, carefully designing a mapping between the downlink channel and the uplink reference signals will perform better than both the conventional TDD Massive MIMO and frequency-division duplex (FDD) Massive MIMO approach. We derive elegant metrics for designing this mapping, and further, we propose algorithms that find good sequence mappings.

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit to the training data. We prove that this is not the case for the linear model fit by ordinary least squares; rather it estimates the average prediction error of models fit on other unseen training sets drawn from the same population. We further show that this phenomenon occurs for most popular estimates of prediction error, including data splitting, bootstrapping, and Mallow's Cp. Next, the standard confidence intervals for prediction error derived from cross-validation may have coverage far below the desired level. Because each data point is used for both training and testing, there are correlations among the measured accuracies for each fold, and so the usual estimate of variance is too small. We introduce a nested cross-validation scheme to estimate this variance more accurately, and we show empirically that this modification leads to intervals with approximately correct coverage in many examples where traditional cross-validation intervals fail.

We develop a spectral method to solve the heat equation in a closed cylinder, achieving a near-optimal $\mathcal{O}(N\log N)$ complexity and high-order, \emph{spectral} accuracy. The algorithm relies on a novel Chebyshev--Chebyshev--Fourier (CCF) discretization of the cylinder, which is easily implemented and decouples the heat equation into a collection of smaller, sparse Sylvester equations. In turn, each of these equations is solved using the alternating direction implicit (ADI) method, which improves the complexity of each solve from cubic in the matrix size (in more traditional methods) to log-linear; overall, this represents an improvement in the heat equation solver from $\mathcal{O}(N^{7/3})$ (in traditional methods) to $\mathcal{O}(N\log N)$. Lastly, we provide numerical simulations demonstrating significant speed-ups over traditional spectral collocation methods and finite difference methods, and we provide a framework by which this heat equation solver could be applied to the incompressible Navier--Stokes equations. For the latter, we decompose the equations using a poloidal--toroidal (PT) decomposition, turning them into heat equations with nonlinear forcing from the advection term; by using implicit--explicit methods to integrate these, we can achieve the same $\mathcal{O}(N\log N)$ complexity and spectral accuracy achieved here in the heat equation.

Kernel Stein discrepancy (KSD) is a widely used kernel-based non-parametric measure of discrepancy between probability measures. It is often employed in the scenario where a user has a collection of samples from a candidate probability measure and wishes to compare them against a specified target probability measure. A useful property of KSD is that it may be calculated with samples from only the candidate measure and without knowledge of the normalising constant of the target measure. KSD has been employed in a range of settings including goodness-of-fit testing, parametric inference, MCMC output assessment and generative modelling. Two main issues with current KSD methodology are (i) the lack of applicability beyond the finite dimensional Euclidean setting and (ii) a lack of clarity on what influences KSD performance. This paper provides a novel spectral representation of KSD which remedies both of these, making KSD applicable to Hilbert-valued data and revealing the impact of kernel and Stein operator choice on the KSD. We demonstrate the efficacy of the proposed methodology by performing goodness-of-fit tests for various Gaussian and non-Gaussian functional models in a number of synthetic data experiments.

The massive multiple-input multiple-output (MIMO) transmission technology has recently attracted much attention in the non-geostationary, e.g., low earth orbit (LEO) satellite communication (SATCOM) systems since it can significantly improve the energy efficiency (EE) and spectral efficiency. In this work, we develop a hybrid analog/digital precoding technique in the massive MIMO LEO SATCOM downlink, which reduces the onboard hardware complexity and power consumption. In the proposed scheme, the analog precoder is implemented via a more practical twin-resolution phase shifting (TRPS) network to make a meticulous tradeoff between the power consumption and array gain. In addition, we consider and study the impact of the distortion effect of the nonlinear power amplifiers (NPAs) in the system design. By jointly considering all the above factors, we propose an efficient algorithmic approach for the TRPS-based hybrid precoding problem with NPAs. Numerical results show the EE gains considering the nonlinear distortion and the performance superiority of the proposed TRPS-based hybrid precoding scheme over the baselines.

Falsification is the basis for testing existing hypotheses, and a great danger is posed when results incorrectly reject our prior notions (false positives). Though nonparametric and nonlinear exploratory methods of uncovering coupling provide a flexible framework to study network configurations and discover causal graphs, multiple comparisons analyses make false positives more likely, exacerbating the need for their control. We aim to robustify the Gaussian Processes Convergent Cross-Mapping (GP-CCM) method through Variational Bayesian Gaussian Process modeling (VGP-CCM). We alleviate computational costs of integrating with conditional hyperparameter distributions through mean field approximations. This approximation model, in conjunction with permutation sampling of the null distribution, permits significance statistics that are more robust than permutation sampling with point hyperparameters. Simulated unidirectional Lorenz-Rossler systems as well as mechanistic models of neurovascular systems are used to evaluate the method. The results demonstrate that the proposed method yields improved specificity, showing promise to combat false positives

Image-to-image translation aims to learn the mapping between two visual domains. There are two main challenges for many applications: 1) the lack of aligned training pairs and 2) multiple possible outputs from a single input image. In this work, we present an approach based on disentangled representation for producing diverse outputs without paired training images. To achieve diversity, we propose to embed images onto two spaces: a domain-invariant content space capturing shared information across domains and a domain-specific attribute space. Our model takes the encoded content features extracted from a given input and the attribute vectors sampled from the attribute space to produce diverse outputs at test time. To handle unpaired training data, we introduce a novel cross-cycle consistency loss based on disentangled representations. Qualitative results show that our model can generate diverse and realistic images on a wide range of tasks without paired training data. For quantitative comparisons, we measure realism with user study and diversity with a perceptual distance metric. We apply the proposed model to domain adaptation and show competitive performance when compared to the state-of-the-art on the MNIST-M and the LineMod datasets.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.