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The flexoelectric effect, coupling polarization and strain gradient as well as strain and electric field gradients, is universal to dielectrics, but, as compared to piezoelectricity, it is more difficult to harness as it requires field gradients and it is a small-scale effect. These drawbacks can be overcome by suitably designing metamaterials made of a non-piezoelectric base material but exhibiting apparent piezoelectricity. We develop a theoretical and computational framework to perform topology optimization of the representative volume element of such metamaterials by accurately modeling the governing equations of flexoelectricity using a Cartesian B-spline method, describing geometry with a level set, and resorting to genetic algorithms for optimization. We consider a multi-objective optimization problem where area fraction competes with four fundamental piezoelectric functionalities (stress/strain sensor/ actuator). We computationally obtain Pareto fronts, and discuss the different geometries depending on the apparent piezoelectric coefficient being optimized. In general, we find competitive estimations of apparent piezoelectricity as compared to reference materials such as quartz and PZT ceramics. This opens the possibility to design devices for sensing, actuation and energy harvesting from a much wider, cheaper and effective class of materials.

Quantifying the difference between two probability density functions, $p$ and $q$, using available data, is a fundamental problem in Statistics and Machine Learning. A usual approach for addressing this problem is the likelihood-ratio estimation (LRE) between $p$ and $q$, which -- to our best knowledge -- has been investigated mainly for the offline case. This paper contributes by introducing a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t \sim p, x'_t \sim q)$ are observed over time. The non-parametric nature of our approach has the advantage of being agnostic to the forms of $p$ and $q$. Moreover, we capitalize on the recent advances in Kernel Methods and functional minimization to develop an estimator that can be efficiently updated online. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.

The synthesis of information deriving from complex networks is a topic receiving increasing relevance in ecology and environmental sciences. In particular, the aggregation of multilayer networks, i.e. network structures formed by multiple interacting networks (the layers), constitutes a fast-growing field. In several environmental applications, the layers of a multilayer network are modelled as a collection of similarity matrices describing how similar pairs of biological entities are, based on different types of features (e.g. biological traits). The present paper first discusses two main techniques for combining the multi-layered information into a single network (the so-called monoplex), i.e. Similarity Network Fusion (SNF) and Similarity Matrix Average (SMA). Then, the effectiveness of the two methods is tested on a real-world dataset of the relative abundance of microbial species in the ecosystems of nine glaciers (four glaciers in the Alps and five in the Andes). A preliminary clustering analysis on the monoplexes obtained with different methods shows the emergence of a tightly connected community formed by species that are typical of cryoconite holes worldwide. Moreover, the weights assigned to different layers by the SMA algorithm suggest that two large South American glaciers (Exploradores and Perito Moreno) are structurally different from the smaller glaciers in both Europe and South America. Overall, these results highlight the importance of integration methods in the discovery of the underlying organizational structure of biological entities in multilayer ecological networks.

We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics utilizing the monotone rearrangement and the nonparametric estimation. We capitalize the Gaussian approximation for the nonparametric monotone estimator and construct the asymptotically correct simultaneous confidence bands (SCBs) by carefully designed bootstrap methods. We investigate two general and practical scenarios. The first is the simultaneous inference of monotone smooth trends from moderately high-dimensional time series, and the proposed algorithm has been employed for the joint inference of temperature curves from multiple areas. Specifically, most existing methods are designed for a single monotone smooth trend. In such cases, our proposed SCB empirically exhibits the narrowest width among existing approaches while maintaining confidence levels, and has been used for testing several hypotheses tailored to global warming. The second scenario involves simultaneous inference of monotone and smoothly time-varying regression coefficients in time-varying coefficient linear models. The proposed algorithm has been utilized for testing the impact of sunshine duration on temperature which is believed to be increasing by the increasingly severe greenhouse effect. The validity of the proposed methods has been justified in theory as well as by extensive simulations.

In prediction settings where data are collected over time, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories. These measures can be estimated and the same approaches for inference can be applied regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics, and we illustrate their use by investigating the longitudinal importance of risk factors for suicide attempt.

At least two, different approaches to define and solve statistical models for the analysis of economic systems exist: the typical, econometric one, interpreting the Gravity Model specification as the expected link weight of an arbitrary probability distribution, and the one rooted into statistical physics, constructing maximum-entropy distributions constrained to satisfy certain network properties. In a couple of recent, companion papers they have been successfully integrated within the framework induced by the constrained minimisation of the Kullback-Leibler divergence: specifically, two, broad classes of models have been devised, i.e. the integrated and the conditional ones, defined by different, probabilistic rules to place links, load them with weights and turn them into proper, econometric prescriptions. Still, the recipes adopted by the two approaches to estimate the parameters entering into the definition of each model differ. In econometrics, a likelihood that decouples the binary and weighted parts of a model, treating a network as deterministic, is typically maximised; to restore its random character, two alternatives exist: either solving the likelihood maximisation on each configuration of the ensemble and taking the average of the parameters afterwards or taking the average of the likelihood function and maximising the latter one. The difference between these approaches lies in the order in which the operations of averaging and maximisation are taken - a difference that is reminiscent of the quenched and annealed ways of averaging out the disorder in spin glasses. The results of the present contribution, devoted to comparing these recipes in the case of continuous, conditional network models, indicate that the annealed estimation recipe represents the best alternative to the deterministic one.

We consider the estimation of the cumulative hazard function, and equivalently the distribution function, with censored data under a setup that preserves the privacy of the survival database. This is done through a $\alpha$-locally differentially private mechanism for the failure indicators and by proposing a non-parametric kernel estimator for the cumulative hazard function that remains consistent under the privatization. Under mild conditions, we also prove lowers bounds for the minimax rates of convergence and show that estimator is minimax optimal under a well-chosen bandwidth.

We propose to approximate a (possibly discontinuous) multivariate function f (x) on a compact set by the partial minimizer arg miny p(x, y) of an appropriate polynomial p whose construction can be cast in a univariate sum of squares (SOS) framework, resulting in a highly structured convex semidefinite program. In a number of non-trivial cases (e.g. when f is a piecewise polynomial) we prove that the approximation is exact with a low-degree polynomial p. Our approach has three distinguishing features: (i) It is mesh-free and does not require the knowledge of the discontinuity locations. (ii) It is model-free in the sense that we only assume that the function to be approximated is available through samples (point evaluations). (iii) The size of the semidefinite program is independent of the ambient dimension and depends linearly on the number of samples. We also analyze the sample complexity of the approach, proving a generalization error bound in a probabilistic setting. This allows for a comparison with machine learning approaches.

Exploring the semantic context in scene images is essential for indoor scene recognition. However, due to the diverse intra-class spatial layouts and the coexisting inter-class objects, modeling contextual relationships to adapt various image characteristics is a great challenge. Existing contextual modeling methods for indoor scene recognition exhibit two limitations: 1) During training, space-independent information, such as color, may hinder optimizing the network's capacity to represent the spatial context. 2) These methods often overlook the differences in coexisting objects across different scenes, suppressing scene recognition performance. To address these limitations, we propose SpaCoNet, which simultaneously models the Spatial relation and Co-occurrence of objects based on semantic segmentation. Firstly, the semantic spatial relation module (SSRM) is designed to explore the spatial relation among objects within a scene. With the help of semantic segmentation, this module decouples the spatial information from the image, effectively avoiding the influence of irrelevant features. Secondly, both spatial context features from the SSRM and deep features from the Image Feature Extraction Module are used to distinguish the coexisting object across different scenes. Finally, utilizing the discriminative features mentioned above, we employ the self-attention mechanism to explore the long-range co-occurrence among objects, and further generate a semantic-guided feature representation for indoor scene recognition. Experimental results on three widely used scene datasets demonstrate the effectiveness and generality of the proposed method. The code will be made publicly available after the blind review process is completed.

Reliable quantification of epistemic and aleatoric uncertainty is of crucial importance in applications where models are trained in one environment but applied to multiple different environments, often seen in real-world applications for example, in climate science or mobility analysis. We propose a simple approach using surjective normalizing flows to identify out-of-distribution data sets in deep neural network models that can be computed in a single forward pass. The method builds on recent developments in deep uncertainty quantification and generative modeling with normalizing flows. We apply our method to a synthetic data set that has been simulated using a mechanistic model from the mobility literature and several data sets simulated from interventional distributions induced by soft and atomic interventions on that model, and demonstrate that our method can reliably discern out-of-distribution data from in-distribution data. We compare the surjective flow model to a Dirichlet process mixture model and a bijective flow and find that the surjections are a crucial component to reliably distinguish in-distribution from out-of-distribution data.