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Flow-based models are widely used in generative tasks, including normalizing flow, where a neural network transports from a data distribution $P$ to a normal distribution. This work develops a flow-based model that transports from $P$ to an arbitrary $Q$ where both distributions are only accessible via finite samples. We propose to learn the dynamic optimal transport between $P$ and $Q$ by training a flow neural network. The model is trained to optimally find an invertible transport map between $P$ and $Q$ by minimizing the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and distribution interpolation in the latent space for generative models. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on high-dimensional DRE, OT baselines, and image-to-image translation.

We present an ultra-fast simulator to augment the MRI scan imaging of glioblastoma brain tumors with predictions of future evolution. We consider the glioblastoma tumor growth model based on the Fisher-Kolmogorov diffusion-reaction equation with logistic growth. For the discretization we employ finite differences in space coupled with a time integrator in time employing the routines from [Al-Mohy, et. al. Computing the action of the matrix exponential, with an application to exponential integrators, SIAM Journal on Scientific Computing, 2011] to compute the actions of the exponentials of the linear operator. By combining these methods, we can perform the prediction of the tumor evolution for several months forward within a couple of seconds on a modern laptop. This method does not require HPC supercomputing centers, and it can be performed on the fly using a laptop with Windows 10, Octave simulations, and ParaView visualization. We illustrate our simulations by predicting the tumor growth evolution based on three-dimensional MRI scan data.

A Gaussian process is proposed as a model for the posterior distribution of the local predictive ability of a model or expert, conditional on a vec- tor of covariates, from historical predictions in the form of log predictive scores. Assuming Gaussian expert predictions and a Gaussian data generat- ing process, a linear transformation of the predictive score follows a noncen- tral chi-squared distribution with one degree of freedom. Motivated by this we develop a non-central chi-squared Gaussian process regression to flexibly model local predictive ability, with the posterior distribution of the latent GP function and kernel hyperparameters sampled by Hamiltonian Monte Carlo. We show that a cube-root transformation of the log scores is approximately Gaussian with homoscedastic variance, which makes it possible to estimate the model much faster by marginalizing the latent GP function analytically. Linear pools based on learned local predictive ability are applied to predict daily bike usage in Washington DC.

From a non-central panorama, 3D lines can be recovered by geometric reasoning. However, their sensitivity to noise and the complex geometric modeling required has led these panoramas being very little investigated. In this work we present a novel approach for 3D layout recovery of indoor environments using single non-central panoramas. We obtain the boundaries of the structural lines of the room from a non-central panorama using deep learning and exploit the properties of non-central projection systems in a new geometrical processing to recover the scaled layout. We solve the problem for Manhattan environments, handling occlusions, and also for Atlanta environments in an unified method. The experiments performed improve the state-of-the-art methods for 3D layout recovery from a single panorama. Our approach is the first work using deep learning with non-central panoramas and recovering the scale of single panorama layouts.

We build on the theory of ontology logs (ologs) created by Spivak and Kent, and define a notion of wiring diagrams. In this article, a wiring diagram is a finite directed labelled graph. The labels correspond to types in an olog; they can also be interpreted as readings of sensors in an autonomous system. As such, wiring diagrams can be used as a framework for an autonomous system to form abstract concepts. We show that the graphs underlying skeleton wiring diagrams form a category. This allows skeleton wiring diagrams to be compared and manipulated using techniques from both graph theory and category theory. We also extend the usual definition of graph edit distance to the case of wiring diagrams by using operations only available to wiring diagrams, leading to a metric on the set of all skeleton wiring diagrams. In the end, we give an extended example on calculating the distance between two concepts represented by wiring diagrams, and explain how to apply our framework to any application domain.

We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high-frequency) using semiclassical defect measures. The paper [GGGLS] (Gong-Gander-Graham-Lafontaine-Spence, 2022) recently showed that the behaviour of these impedance-to-impedance maps (and their compositions) dictates the convergence of the parallel overlapping Schwarz domain-decomposition method with impedance boundary conditions on the subdomain boundaries. For a model decomposition with two subdomains and sufficiently-large overlap, the results of this paper combined with those in [GGGLS] show that the parallel Schwarz method is power contractive, independent of the wavenumber. For strip-type decompositions with many subdomains, the results of this paper show that the composite impedance-to-impedance maps, in general, behave "badly" with respect to the wavenumber; nevertheless, by proving results about the composite maps applied to a restricted class of data, we give insight into the wavenumber-robustness of the parallel Schwarz method observed in the numerical experiments in [GGGLS].

Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many scenarios. Here we present an approach to effectively modeling the dynamics of the stochastic data without trajectories based on the weak form of the Fokker-Planck (FP) equation, which governs the evolution of the density function in the Brownian process. Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data. With a dictionary representation of the unknown terms, a linear system is built and then solved by the regression, revealing the unknown dynamics of the data. Hence, we name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression. The numerical experiments show that our method is flexible and fast, which reveals the dynamics within seconds in multi-dimensional problems and can be easily extended to high-dimensional data such as 20 dimensions. WCR can also correctly identify the hidden dynamics of the complex tasks with variable-dependent diffusion and coupled drift, and the performance is robust, achieving high accuracy in the case with noise added.

Clusters of similar or dissimilar objects are encountered in many fields. Frequently used approaches treat the central object of each cluster as latent. Yet, often objects of one or more types cluster around objects of another type. Such arrangements are common in biomedical images of cells, in which nearby cell types likely interact. Quantifying spatial relationships may elucidate biological mechanisms. Parent-offspring statistical frameworks can be usefully applied even when central objects (parents) differ from peripheral ones (offspring). We propose the novel multivariate cluster point process (MCPP) to quantify multi-object (e.g., multi-cellular) arrangements. Unlike commonly used approaches, the MCPP exploits locations of the central parent object in clusters. It accounts for possibly multilayered, multivariate clustering. The model formulation requires specification of which object types function as cluster centers and which reside peripherally. If such information is unknown, the relative roles of object types may be explored by comparing fit of different models via the deviance information criterion (DIC). In simulated data, we compared DIC of a series of models; the MCPP correctly identified simulated relationships. It also produced more accurate and precise parameter estimates than the classical univariate Neyman-Scott process model. We also used the MCPP to quantify proposed configurations and explore new ones in human dental plaque biofilm image data. MCPP models quantified simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus and successfully captured hypothesized structures for all taxa. Further exploration suggested the presence of clustering between Fusobacterium and Leptotrichia, a previously unreported relationship.

Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-viewcontrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, two extensions of HeCo are designed to generate harder negative samples with high quality, which further boosts the performance of HeCo. Extensive experiments conducted on a variety of real-world networks show the superior performance of the proposed methods over the state-of-the-arts.

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.