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Dysarthria is a motor speech disorder often characterized by reduced speech intelligibility through slow, uncoordinated control of speech production muscles. Automatic Speech recognition (ASR) systems can help dysarthric talkers communicate more effectively. However, robust dysarthria-specific ASR requires a significant amount of training speech, which is not readily available for dysarthric talkers. This paper presents a new dysarthric speech synthesis method for the purpose of ASR training data augmentation. Differences in prosodic and acoustic characteristics of dysarthric spontaneous speech at varying severity levels are important components for dysarthric speech modeling, synthesis, and augmentation. For dysarthric speech synthesis, a modified neural multi-talker TTS is implemented by adding a dysarthria severity level coefficient and a pause insertion model to synthesize dysarthric speech for varying severity levels. To evaluate the effectiveness for synthesis of training data for ASR, dysarthria-specific speech recognition was used. Results show that a DNN-HMM model trained on additional synthetic dysarthric speech achieves WER improvement of 12.2% compared to the baseline, and that the addition of the severity level and pause insertion controls decrease WER by 6.5%, showing the effectiveness of adding these parameters. Overall results on the TORGO database demonstrate that using dysarthric synthetic speech to increase the amount of dysarthric-patterned speech for training has significant impact on the dysarthric ASR systems. In addition, we have conducted a subjective evaluation to evaluate the dysarthric-ness and similarity of synthesized speech. Our subjective evaluation shows that the perceived dysartrhic-ness of synthesized speech is similar to that of true dysarthric speech, especially for higher levels of dysarthria

We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare logic, and the axioms and rules of the logic ensure that the assertions about the state compose in the correct way. The main result of the paper is a realizability interpretation of our logic that extracts programs into a mixed functional/imperative language. All programs expressible in this language act on the state in a sequential manner, and we make this intuition precise by interpreting them in a semantic metatheory using the state monad. Our basic framework is very general, and our intention is that it can be instantiated and extended in a variety of different ways. We outline in detail one such extension: A monadic version of Heyting arithmetic with a wellfounded while rule, and conclude by outlining several other directions for future work.

We consider the fundamental task of optimizing a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in statistical inference. We use the warped Riemannian geometry notions to redefine the optimisation problem of a function on Euclidean space to a Riemannian manifold with a warped metric, and then find the function's optimum along this manifold. The warped metric chosen for the search domain induces a computational friendly metric-tensor for which optimal search directions associate with geodesic curves on the manifold becomes easier to compute. Performing optimization along geodesics is known to be generally infeasible, yet we show that in this specific manifold we can analytically derive Taylor approximations up to third-order. In general these approximations to the geodesic curve will not lie on the manifold, however we construct suitable retraction maps to pull them back onto the manifold. Therefore, we can efficiently optimize along the approximate geodesic curves. We cover the related theory, describe a practical optimization algorithm and empirically evaluate it on a collection of challenging optimisation benchmarks. Our proposed algorithm, using third-order approximation of geodesics, outperforms standard Euclidean gradient-based counterparts in term of number of iterations until convergence and an alternative method for Hessian-based optimisation routines.

We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.

We present a novel way to model diffusion magnetic resonance imaging (dMRI) datasets, that benefits from the structural coherence of the human brain while only using data from a single subject. Current methods model the dMRI signal in individual voxels, disregarding the intervoxel coherence that is present. We use a neural network to parameterize a spherical harmonics series (NeSH) to represent the dMRI signal of a single subject from the Human Connectome Project dataset, continuous in both the angular and spatial domain. The reconstructed dMRI signal using this method shows a more structurally coherent representation of the data. Noise in gradient images is removed and the fiber orientation distribution functions show a smooth change in direction along a fiber tract. We showcase how the reconstruction can be used to calculate mean diffusivity, fractional anisotropy, and total apparent fiber density. These results can be achieved with a single model architecture, tuning only one hyperparameter. In this paper we also demonstrate how upsampling in both the angular and spatial domain yields reconstructions that are on par or better than existing methods.

The identification of primal variables and adjoint variables is usually done via indices in operator overloading algorithmic differentiation tools. One approach is a linear management scheme, which is easy to implement and supports memory optimization for copy statements. An alternative approach performs a reuse of indices, which requires more implementation effort but results in much smaller adjoint vectors. Therefore, the vector mode of algorithmic differentiation scales better with the reuse management scheme. In this paper, we present a novel approach that reuses the indices and allows the copy optimization, thus combining the advantages of the two aforementioned schemes. The new approach is compared to the known approaches on a simple synthetic test case and a real-world example using the computational fluid dynamics solver SU2.

Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that encode censoring information in the neural network architecture. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (PM2.5) concentration over the whole of Saudi Arabia.

The simulation of supersonic or hypersonic flows often suffers from numerical shock instabilities if the flow field contains strong shocks, limiting the further application of shock-capturing schemes. In this paper, we develop the unified matrix stability analysis method for schemes with three-point stencils and present MSAT, an open-source tool to quantitatively analyze the shock instability problem. Based on the finite-volume approach on the structured grid, MSAT can be employed to investigate the mechanism of the shock instability problem, evaluate the robustness of numerical schemes, and then help to develop robust schemes. Also, MSAT has the ability to analyze the practical simulation of supersonic or hypersonic flows, evaluate whether it will suffer from shock instabilities, and then assist in selecting appropriate numerical schemes accordingly. As a result, MSAT is a helpful tool that can investigate the shock instability problem and help to cure it.

Aperiodic autocorrelation measures the similarity between a finite-length sequence of complex numbers and translates of itself. Autocorrelation is important in communications, remote sensing, and scientific instrumentation. The autocorrelation function reports the aperiodic autocorrelation at every possible translation. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform. Resolving the lack of phase information is called the phase problem. We say that two sequences are isospectral to mean that they have the same aperiodic autocorrelation function. Sequences used in technological applications often have restrictions on their terms: they are not arbitrary complex numbers, but come from an alphabet that may reside in a proper subring of the complex field or may come from a finite set of values. For example, binary sequences involve terms equal to only $+1$ and $-1$. In this paper, we investigate the necessary and sufficient conditions for two sequences to be isospectral, where we take their alphabet into consideration. There are trivial forms of isospectrality arising from modifications that predictably preserve the autocorrelation, for example, negating sequences or both conjugating their terms and writing them in reverse order. By an exhaustive search of binary sequences up to length $34$, we find that nontrivial isospectrality among binary sequences does occur, but is rare. We say that a positive integer $n$ is barren to mean that there are no nontrivially isospectral binary sequences of length $n$. For integers $n \leq 34$, we found that the barren ones are $1$--$8$, $10$, $11$, $13$, $14$, $19$, $22$, $23$, $26$, and $29$. We prove that any multiple of a non-barren number is also not barren, and pose an open question as to whether there are finitely or infinitely many barren numbers.

One of the ultimate goals of e-commerce platforms is to satisfy various shopping needs for their customers. Much efforts are devoted to creating taxonomies or ontologies in e-commerce towards this goal. However, user needs in e-commerce are still not well defined, and none of the existing ontologies has the enough depth and breadth for universal user needs understanding. The semantic gap in-between prevents shopping experience from being more intelligent. In this paper, we propose to construct a large-scale e-commerce cognitive concept net named "AliCoCo", which is practiced in Alibaba, the largest Chinese e-commerce platform in the world. We formally define user needs in e-commerce, then conceptualize them as nodes in the net. We present details on how AliCoCo is constructed semi-automatically and its successful, ongoing and potential applications in e-commerce.