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This paper proposes a novel method for computing bijective density-equalizing quasiconformal (DEQ) flattening maps for multiply-connected open surfaces. In conventional density-equalizing maps, shape deformations are solely driven by prescribed constraints on the density distribution, defined as the population per unit area, while the bijectivity and local geometric distortions of the mappings are uncontrolled. Also, prior methods have primarily focused on simply-connected open surfaces but not surfaces with more complicated topologies. Our proposed method overcomes these issues by formulating the density diffusion process as a quasiconformal flow, which allows us to effectively control the local geometric distortion and guarantee the bijectivity of the mapping by solving an energy minimization problem involving the Beltrami coefficient of the mapping. To achieve an optimal parameterization of multiply-connected surfaces, we develop an iterative scheme that optimizes both the shape of the target planar circular domain and the density-equalizing quasiconformal map onto it. In addition, landmark constraints can be incorporated into our proposed method for consistent feature alignment. The method can also be naturally applied to simply-connected open surfaces. By changing the prescribed population, a large variety of surface flattening maps with different desired properties can be achieved. The method is tested on both synthetic and real examples, demonstrating its efficacy in various applications in computer graphics and medical imaging.

In this paper, we propose a novel ROM stabilization strategy for under-resolved convection-dominated flows, the approximate deconvolution Leray ROM (ADL-ROM). The new ADL-ROM introduces AD as a new means to increase the accuracy of the classical Leray ROM (L-ROM) without degrading its numerical stability. We also introduce two new AD ROM strategies: the Tikhonov and van Cittert methods. Our numerical investigation for convection-dominated systems shows that, when the filter radius is relatively large, the new ADL-ROM is more accurate than the standard L-ROM. Furthermore, the new ADL-ROM is less sensitive with respect to model parameters than L-ROM.

This paper studies the joint digital self-interference (SI) cancellation and data detection in an orthogonal-frequency-division-multiplexing (OFDM) full-duplex (FD) system, considering the effect of phase noise introduced by the oscillators at both the local transmitter and receiver. In particular, an universal iterative two-stage joint SI cancellation and data detection framework is considered and its performance bound independent of any specific estimation and detection methods is derived. First, the channel and phase noise estimation mean square error (MSE) lower bounds in each iteration are derived by analyzing the Fisher information of the received signal. Then, by substituting the derived MSE lower bound into the SINR expression, which is related to the channel and phase noise estimation MSE, the SINR upper bound in each iteration is computed. Finally, by exploiting the SINR upper bound and the transition information of the detection errors between two adjacent iterations, the universal bit error rate (BER) lower bound for data detection is derived.

The classical ski-rental problem admits a textbook 2-competitive deterministic algorithm, and a simple randomized algorithm that is $\frac{e}{e-1}$-competitive in expectation. The randomized algorithm, while optimal in expectation, has a large variance in its performance: it has more than a 37% chance of competitive ratio exceeding 2, and a $\Theta(1/n)$ chance of the competitive ratio exceeding $n$! We ask what happens to the optimal solution if we insist that the tail risk, i.e., the chance of the competitive ratio exceeding a specific value, is bounded by some constant $\delta$. We find that this additional modification significantly changes the structure of the optimal solution. The probability of purchasing skis on a given day becomes non-monotone, discontinuous, and arbitrarily large (for sufficiently small tail risk $\delta$ and large purchase cost $n$).

We address the task of probabilistic anomaly attribution in the black-box regression setting, where the goal is to compute the probability distribution of the attribution score of each input variable, given an observed anomaly. The training dataset is assumed to be unavailable. This task differs from the standard XAI (explainable AI) scenario, since we wish to explain the anomalous deviation from a black-box prediction rather than the black-box model itself. We begin by showing that mainstream model-agnostic explanation methods, such as the Shapley values, are not suitable for this task because of their ``deviation-agnostic property.'' We then propose a novel framework for probabilistic anomaly attribution that allows us to not only compute attribution scores as the predictive mean but also quantify the uncertainty of those scores. This is done by considering a generative process for perturbations that counter-factually bring the observed anomalous observation back to normalcy. We introduce a variational Bayes algorithm for deriving the distributions of per variable attribution scores. To the best of our knowledge, this is the first probabilistic anomaly attribution framework that is free from being deviation-agnostic.

With the rise in popularity of digital Atlases to communicate spatial variation, there is an increasing need for robust small-area estimates. However, current small-area estimation methods suffer from various modelling problems when data are very sparse or when estimates are required for areas with very small populations. These issues are particularly heightened when modelling proportions. Additionally, recent work has shown significant benefits in modelling at both the individual and area levels. We propose a two-stage Bayesian hierarchical small area estimation model for proportions that can: account for survey design; use both individual-level survey-only covariates and area-level census covariates; reduce direct estimate instability; and generate prevalence estimates for small areas with no survey data. Using a simulation study we show that, compared with existing Bayesian small area estimation methods, our model can provide optimal predictive performance (Bayesian mean relative root mean squared error, mean absolute relative bias and coverage) of proportions under a variety of data conditions, including very sparse and unstable data. To assess the model in practice, we compare modeled estimates of current smoking prevalence for 1,630 small areas in Australia using the 2017-2018 National Health Survey data combined with 2016 census data.

The recently developed deep algorithms achieve promising progress in the field of image copy-move forgery detection (CMFD). However, they have limited generalizability in some practical scenarios, where the copy-move objects may not appear in the training images or cloned regions are from the background. To address the above issues, in this work, we propose a novel end-to-end CMFD framework by integrating merits from both conventional and deep methods. Specifically, we design a deep cross-scale patchmatch method tailored for CMFD to localize copy-move regions. In contrast to existing deep models, our scheme aims to seek explicit and reliable point-to-point matching between source and target regions using features extracted from high-resolution scales. Further, we develop a manipulation region location branch for source/target separation. The proposed CMFD framework is completely differentiable and can be trained in an end-to-end manner. Extensive experimental results demonstrate the high generalizability of our method to different copy-move contents, and the proposed scheme achieves significantly better performance than existing approaches.

We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored by the automatic differentiation algorithm. We begin by asking, "what is an implementation of AD?" and "what does it mean for an implementation of AD to be correct?" We answer these questions both at an informal level, in precise English prose, and at a formal level, using types and logical assertions. After answering these broad questions, we focus on a specific implementation of AD, which involves a number of subtle programming-language features, including dynamically allocated mutable state, first-class functions, and effect handlers. We present a machine-checked proof, expressed in a modern variant of Separation Logic, of its correctness. We view this result as an advanced exercise in program verification, with potential future applications to the verification of more realistic automatic differentiation systems and of other software components that exploit delimited-control effects.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.