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This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed recently using a suitable metric to define the gradient flow of the phase field approximate energy. We generalize this approach to arbitrary nonnegative mobilities using a decomposition as sums of harmonically additive mobilities. We establish the consistency of the resulting method by analyzing the sharp interface limit of the flow: a formal expansion of the phase field shows that the method is of second order. We propose a simple numerical scheme to approximate the solutions to our new model. Finally, we present some numerical experiments in dimensions 2 and 3 that illustrate the interest and effectiveness of our approach, in particular for approximating flows in which the mobility of some phases is zero.

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schr\"odinger-F\"ollmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process $\{X_t\}_{t\in [0,1]}$ on $\mathbb{R}^d$, $d\in \mathbb{N}_0$. This latter process is constructed such that, starting at $X_0=0$, one has $X_1\sim \pi$. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, \cite{sf_orig,jiao} consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t.~$\pi$. We show that for this methodology to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, for arbitrary $\epsilon>0$, the associated cost is $\mathcal{O}(\epsilon^{-5})$. We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t.~$\pi$, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, the associated cost is, with high probability, $\mathcal{O}(\epsilon^{-2}|\log(\epsilon)|^{2+\delta})$, for any $\delta>0$. We implement our method on several examples including Bayesian inverse problems.

In recent years, deep learning has been a topic of interest in almost all disciplines due to its impressive empirical success in analyzing complex data sets, such as imaging, genetics, climate, and medical data. While most of the developments are treated as black-box machines, there is an increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning is proven to be promising in this regard. However, the recent developments do not address the situations of ultra-high dimensional and highly correlated feature selection in addition to the high noise level. In this article, we propose a novel screening and cleaning strategy with the aid of deep learning for the cluster-level discovery of highly correlated predictors with a controlled error rate. A thorough empirical evaluation over a wide range of simulated scenarios demonstrates the effectiveness of the proposed method by achieving high power while having a minimal number of false discoveries. Furthermore, we implemented the algorithm in the riboflavin (vitamin $B_2$) production dataset in the context of understanding the possible genetic association with riboflavin production. The gain of the proposed methodology is illustrated by achieving lower prediction error compared to other state-of-the-art methods.

We give algorithms for approximating the partition function of the ferromagnetic Potts model on $d$-regular expanding graphs. We require much weaker expansion than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models, using extremal graph theory and applications of Karger's algorithm to counting cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We believe that these methods can shed more light on other important problems such as sub-exponential algorithms for approximate counting problems.

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and relative difficulty of interpretation. This paper introduces a novel infinite-order VAR model which, with only a little sacrifice of generality, inherits the essential temporal patterns of the VARMA model but avoids all of the above drawbacks. As another attractive feature, the temporal and cross-sectional dependence structures of this model can be interpreted separately, since they are characterized by different sets of parameters. For high-dimensional time series, this separation motivates us to impose sparsity on the parameters determining the cross-sectional dependence. As a result, greater statistical efficiency and interpretability can be achieved, while no loss of temporal information is incurred by the imposed sparsity. We introduce an $\ell_1$-regularized estimator for the proposed model and derive the corresponding nonasymptotic error bounds. An efficient block coordinate descent algorithm and a consistent model order selection method are developed. The merit of the proposed approach is supported by simulation studies and a real-world macroeconomic data analysis.

This work considers Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function (Stein, 1999, Section 6.7) with Fourier coefficients $\phi$($\alpha$^2 + j^2)^(--$\nu$--1/2). Convergence rates are studied for the joint maximum likelihood estimation of $\nu$ and $\phi$ when the data is sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a ''deterministic'' element of a continuous Sobolev space is also considered, suggesting that bounding assumptions on some parameters can lead to different estimates.

Emergency shelters, which reflect the city's ability to respond to and deal with major public emergencies to a certain extent, are essential to a modern urban emergency management system. This paper is based on spatial analysis methods, using Analytic Hierarchy Process to analyze the suitability of the 28 emergency shelters in Wuhan City. The Technique for Order Preference by Similarity to an Ideal Solution is further used to evaluate the accommodation capacity of emergency shelters in central urban areas, which provides a reference for the optimization of existing shelters and the site selection of new shelters, and provides a basis for improving the service capacity of shelters. The results show that the overall situation of emergency shelters in Wuhan is good, with 96\% of the places reaching the medium level or above, but the suitability level needs to be further improved, especially the effectiveness and accessibility. Among the seven central urban areas in Wuhan, Hongshan District has the strongest accommodation capacity while Jianghan District has the weakest, with noticeable differences.

Generative Adversarial Network (GAN) based art has proliferated in the past year, going from a shiny new tool to generate fake human faces to a stage where anyone can generate thousands of artistic images with minimal effort. Some of these images are now ``good'' enough to win accolades from qualified judges. In this paper, we explore how Generative Models have impacted artistry, not only from a qualitative point of view, but also from an angle of exploitation of artisans --both via plagiarism, where models are trained on their artwork without permission, and via profit shifting, where profits in the art market have shifted from art creators to model owners or to traders in the unregulated secondary crypto market. This confluence of factors risks completely detaching humans from the artistic process, devaluing the labor of artists and distorting the public perception of the value of art.

The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal strategy to commit to, in order to protect some asset. In many of these applications, the parameters of the follower utility model are not known with certainty. Distributionally-robust optimization addresses this issue by allowing a distribution over possible model parameters, where this distribution comes from a set of possible distributions. The goal is to maximize the expected utility with respect to the worst-case distribution. We initiate the study of distributionally-robust models for computing the optimal strategy to commit to. We consider the case of normal-form games with uncertainty about the follower utility model. Our main theoretical result is to show that a distributionally-robust Stackelberg equilibrium always exists across a wide array of uncertainty models. For the case of a finite set of possible follower utility functions we present two algorithms to compute a distributionally-robust strong Stackelberg equilibrium (DRSSE) using mathematical programs. Next, in the general case where there is an infinite number of possible follower utility functions and the uncertainty is represented by a Wasserstein ball around a finitely-supported nominal distribution, we give an incremental mixed-integer-programming-based algorithm for computing the optimal distributionally-robust strategy. Experiments substantiate the tractability of our algorithm on a classical Stackelberg game, showing that our approach scales to medium-sized games.

This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with complex geometries formed by a large number of particles. Inspired by recent works on gradient descent algorithms for sampling maximum-entropy models, we describe a model that allows for fast sampling of new configurations reproducing the statistics of the given observation. Starting from an initial random configuration, its particles are moved according to the gradient of an energy, in order to match a set of prescribed moments (functionals). Our moments are defined via a phase harmonic operator on the wavelet transform of point patterns. They allow one to capture multi-scale interactions between the particles, while controlling explicitly the number of moments by the scales of the structures to model. We present numerical experiments on point processes with various geometric structures, and assess the quality of the model by spectral and topological data analysis.