Identifying areas in a landscape where individuals have higher probability of becoming infected with a pathogen is a crucial step towards disease management. We perform a novel epidemiological tomography for the estimation of landscape propensity to disease infection, using GPS animal tracks in a manner analogous to tomographic techniques in Positron Emission Tomography. Our study data consists of individual tracks of white-tailed deer (Odocoileus virginianus) and three exotic Cervidae species moving freely in a high-fenced game preserve over given time periods. A serological test was performed on each individual to measure antibody concentration of epizootic hemorrhagic disease viruses (EHDV) at the beginning and at the end of each tracking period. EHDV is a vector-borne viral disease indirectly transmitted between ruminant hosts by biting midges. We model the data as a binomial linear inverse problem, where spatial coherence is enforced with a total variation regularization. The smoothness of the reconstructed propensity map is selected by the quantile universal threshold, which can also test the null hypothesis that the propensity map is spatially constant. We apply our method to simulated and real data, showing good statistical properties during simulations and consistent results and interpretations compared to intensive field estimations.
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Computational models of syntax are predominantly text-based. Here we propose that the most basic syntactic operations can be modeled directly from raw speech in a fully unsupervised way. We focus on one of the most ubiquitous and elementary properties of syntax -- concatenation. We introduce spontaneous concatenation: a phenomenon where convolutional neural networks (CNNs) trained on acoustic recordings of individual words start generating outputs with two or even three words concatenated without ever accessing data with multiple words in the input. We replicate this finding in several independently trained models with different hyperparameters and training data. Additionally, networks trained on two words learn to embed words into novel unobserved word combinations. To our knowledge, this is a previously unreported property of CNNs trained in the ciwGAN/fiwGAN setting on raw speech and has implications both for our understanding of how these architectures learn as well as for modeling syntax and its evolution from raw acoustic inputs.
Motivated by the application of saddlepoint approximations to resampling-based statistical tests, we prove that a Lugananni-Rice style approximation for conditional tail probabilities of averages of conditionally independent random variables has vanishing relative error. We also provide a general condition on the existence and uniqueness of the solution to the corresponding saddlepoint equation. The results are valid under a broad class of distributions involving no restrictions on the smoothness of the distribution function. The derived saddlepoint approximation formula can be directly applied to resampling-based hypothesis tests, including bootstrap, sign-flipping and conditional randomization tests. Our results extend and connect several classical saddlepoint approximation results. On the way to proving our main results, we prove a new conditional Berry-Esseen inequality for the sum of conditionally independent random variables, which may be of independent interest.
Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed to suppress nonphysical oscillations. However, the application of such limiters can reduce accuracy. It is important to identify the weakest set of sufficient conditions required on the limiter as to allow the development of successful numerical algorithms. The main goal of this paper is to identify new less restrictive sufficient conditions for flux form in-compressible advection to remain monotonic. We identify additional necessary conditions for incompressible flux form advection to be monotonic, demonstrating that the Spekreijse limiter region is not sufficient for incompressible flux form advection to remain monotonic. Then a convex combination argument is used to derive new sufficient conditions that are less restrictive than the Sweby region for a discrete maximum principle. This allows the introduction of two new more general limiter regions suitable for flux form incompressible advection.
Electromagnetic stimulation probes and modulates the neural systems that control movement. Key to understanding their effects is the muscle recruitment curve, which maps evoked potential size against stimulation intensity. Current methods to estimate curve parameters require large samples; however, obtaining these is often impractical due to experimental constraints. Here, we present a hierarchical Bayesian framework that accounts for small samples, handles outliers, simulates high-fidelity data, and returns a posterior distribution over curve parameters that quantify estimation uncertainty. It uses a rectified-logistic function that estimates motor threshold and outperforms conventionally used sigmoidal alternatives in predictive performance, as demonstrated through cross-validation. In simulations, our method outperforms non-hierarchical models by reducing threshold estimation error on sparse data and requires fewer participants to detect shifts in threshold compared to frequentist testing. We present two common use cases involving electrical and electromagnetic stimulation data and provide an open-source library for Python, called hbMEP, for diverse applications.
The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization which results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading therefore to a corrective advective term which cancels out non-reciprocity at the leading order but not at the second order.
A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in complex manifolds with boundaries and nonuniform sampling. Rigorous theoretical guarantees of its asymptotic behavior have been lacking. We show that, under mild conditions, this estimator asymptotically converges to the Hessian operator, with nonuniform sampling and curvature effects proving negligible, even near boundaries. Our analysis framework simplifies the intensive computations required for direct analysis.
Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using convolutional neural networks (CNNs) on graph images to predict the cardinality of combinatorial properties of random graphs and networks. Specifically, we use image representations of modified adjacency matrices of random graphs as training samples for a CNN model to predict the stability number of random graphs; where the stability number is the cardinality of a maximum set of vertices containing no pairwise adjacency. Our approach demonstrates the potential for applying deep learning in combinatorial optimization problems.
We present a Bayesian method for multivariate changepoint detection that allows for simultaneous inference on the location of a changepoint and the coefficients of a logistic regression model for distinguishing pre-changepoint data from post-changepoint data. In contrast to many methods for multivariate changepoint detection, the proposed method is applicable to data of mixed type and avoids strict assumptions regarding the distribution of the data and the nature of the change. The regression coefficients provide an interpretable description of a potentially complex change. For posterior inference, the model admits a simple Gibbs sampling algorithm based on P\'olya-gamma data augmentation. We establish conditions under which the proposed method is guaranteed to recover the true underlying changepoint. As a testing ground for our method, we consider the problem of detecting topological changes in time series of images. We demonstrate that our proposed method $\mathtt{bclr}$, combined with a topological feature embedding, performs well on both simulated and real image data. The method also successfully recovers the location and nature of changes in more traditional changepoint tasks.
In the literature on spatial point processes, there is an emerging challenge in studying marked point processes with points being labelled by functions. In this paper, we focus on point processes living on linear networks and, from distinct points of view, propose several marked summary characteristics that are of great use in studying the average association and dispersion of the function-valued marks. Through a simulation study, we evaluate the performance of our proposed marked summary characteristics, both when marks are independent and when some sort of spatial dependence is evident among them. Finally, we employ our proposed mark summary characteristics to study the spatial structure of urban cycling profiles in Vancouver, Canada.
Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster relations, be computationally efficient, and identify smaller communities. We address these challenges by integrating coarsening and modularity maximization, effectively leveraging both adjacency and node features to enhance clustering accuracy. We propose a loss function incorporating log-determinant, smoothness, and modularity components using a block majorization-minimization technique, resulting in superior clustering outcomes. The method is theoretically consistent under the Degree-Corrected Stochastic Block Model (DC-SBM), ensuring asymptotic error-free performance and complete label recovery. Our provably convergent and time-efficient algorithm seamlessly integrates with graph neural networks (GNNs) and variational graph autoencoders (VGAEs) to learn enhanced node features and deliver exceptional clustering performance. Extensive experiments on benchmark datasets demonstrate its superiority over existing state-of-the-art methods for both attributed and non-attributed graphs.
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