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P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not violate any temporal constraints. In this paper, we solve the long-standing problem of characterizing the decidability of consistency by showing that, assuming unary encoding of the initial marking, this property can be verified in strongly polynomial time. The proof is based on a reduction to the problem of detecting paths with infinite weight in infinite weighted digraphs called N-periodic graphs.

Spatial data can come in a variety of different forms, but two of the most common generating models for such observations are random fields and point processes. Whilst it is known that spectral analysis can unify these two different data forms, specific methodology for the related estimation is yet to be developed. In this paper, we solve this problem by extending multitaper estimation, to estimate the spectral density matrix function for multivariate spatial data, where processes can be any combination of either point processes or random fields. We discuss finite sample and asymptotic theory for the proposed estimators, as well as specific details on the implementation, including how to perform estimation on non-rectangular domains and the correct implementation of multitapering for processes sampled in different ways, e.g. continuously vs on a regular grid.

Vegetation structure mapping is critical for understanding the global carbon cycle and monitoring nature-based approaches to climate adaptation and mitigation. Repeated measurements of these data allow for the observation of deforestation or degradation of existing forests, natural forest regeneration, and the implementation of sustainable agricultural practices like agroforestry. Assessments of tree canopy height and crown projected area at a high spatial resolution are also important for monitoring carbon fluxes and assessing tree-based land uses, since forest structures can be highly spatially heterogeneous, especially in agroforestry systems. Very high resolution satellite imagery (less than one meter (1m) Ground Sample Distance) makes it possible to extract information at the tree level while allowing monitoring at a very large scale. This paper presents the first high-resolution canopy height map concurrently produced for multiple sub-national jurisdictions. Specifically, we produce very high resolution canopy height maps for the states of California and Sao Paulo, a significant improvement in resolution over the ten meter (10m) resolution of previous Sentinel / GEDI based worldwide maps of canopy height. The maps are generated by the extraction of features from a self-supervised model trained on Maxar imagery from 2017 to 2020, and the training of a dense prediction decoder against aerial lidar maps. We also introduce a post-processing step using a convolutional network trained on GEDI observations. We evaluate the proposed maps with set-aside validation lidar data as well as by comparing with other remotely sensed maps and field-collected data, and find our model produces an average Mean Absolute Error (MAE) of 2.8 meters and Mean Error (ME) of 0.6 meters.

In this paper, we consider variational autoencoders (VAE) for general state space models. We consider a backward factorization of the variational distributions to analyze the excess risk associated with VAE. Such backward factorizations were recently proposed to perform online variational learning and to obtain upper bounds on the variational estimation error. When independent trajectories of sequences are observed and under strong mixing assumptions on the state space model and on the variational distribution, we provide an oracle inequality explicit in the number of samples and in the length of the observation sequences. We then derive consequences of this theoretical result. In particular, when the data distribution is given by a state space model, we provide an upper bound for the Kullback-Leibler divergence between the data distribution and its estimator and between the variational posterior and the estimated state space posterior distributions.Under classical assumptions, we prove that our results can be applied to Gaussian backward kernels built with dense and recurrent neural networks.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometric quantization, which yields a spatially discretized analogue of the MHD equations as a finite-dimensional Lie--Poisson system on the dual of the magnetic extension Lie algebra $\mathfrak{f}=\mathfrak{su}(N)\ltimes\mathfrak{su}(N)^{*}$. We also give accompanying structure preserving time discretizations for Lie--Poisson systems on the dual of semidirect product Lie algebras of the form $\mathfrak{f}=\mathfrak{g}\ltimes\mathfrak{g^{*}}$, where $\mathfrak{g}$ is a $J$-quadratic Lie algebra. Critically, the time integration method is free of computationally costly matrix exponentials. We prove that the full method preserves the underlying geometry, namely the Lie--Poisson structure and all the Casimirs. To showcase the method, we apply it to two models for magnetic fluids: incompressible magnetohydrodynamics and Hazeltine's model.

Discovering underlying structures of causal relations from observational studies poses a great challenge in scientific research where randomized trials or intervention-based studies are infeasible. This challenge pertains to the lack of knowledge on pre-specified roles of cause and effect in observations studies. Leveraging Shannon's seminal work on information theory, we propose a new conceptual framework of asymmetry where any causal link between putative cause and effect is captured by unequal information flows from one variable to another. We present an entropy-based asymmetry coefficient that not only enables us to assess for whether one variable is a stronger predictor of the other, but also detects an imprint of the underlying causal relation in observational studies. Our causal discovery analytics can accommodate low-dimensional confounders naturally. The proposed methodology relies on scalable non-parametric density estimation using fast Fourier transformation, making the resulting estimation method manyfold faster than the classical bandwidth-based density estimation while maintaining comparable mean integrated squared error rates. We investigate key asymptotic properties of our methodology and utilize a data-splitting and cross-fitting technique to facilitate inference for the direction of causal relations. We illustrate the performance of our methodology through simulation studies and real data examples.

In the study of the brain, there is a hypothesis that sparse coding is realized in information representation of external stimuli, which is experimentally confirmed for visual stimulus recently. However, unlike the specific functional region in the brain, sparse coding in information processing in the whole brain has not been clarified sufficiently. In this study, we investigate the validity of sparse coding in the whole human brain by applying various matrix factorization methods to functional magnetic resonance imaging data of neural activities in the whole human brain. The result suggests sparse coding hypothesis in information representation in the whole human brain, because extracted features from sparse MF method, SparsePCA or MOD under high sparsity setting, or approximate sparse MF method, FastICA, can classify external visual stimuli more accurately than non-sparse MF method or sparse MF method under low sparsity setting.

Owing to effective and flexible data acquisition, unmanned aerial vehicle (UAV) has recently become a hotspot across the fields of computer vision (CV) and remote sensing (RS). Inspired by recent success of deep learning (DL), many advanced object detection and tracking approaches have been widely applied to various UAV-related tasks, such as environmental monitoring, precision agriculture, traffic management. This paper provides a comprehensive survey on the research progress and prospects of DL-based UAV object detection and tracking methods. More specifically, we first outline the challenges, statistics of existing methods, and provide solutions from the perspectives of DL-based models in three research topics: object detection from the image, object detection from the video, and object tracking from the video. Open datasets related to UAV-dominated object detection and tracking are exhausted, and four benchmark datasets are employed for performance evaluation using some state-of-the-art methods. Finally, prospects and considerations for the future work are discussed and summarized. It is expected that this survey can facilitate those researchers who come from remote sensing field with an overview of DL-based UAV object detection and tracking methods, along with some thoughts on their further developments.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.