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Recently, Sato et al. proposed an public verifiable blind quantum computation (BQC) protocol by inserting a third-party arbiter. However, it is not true public verifiable in a sense, because the arbiter is determined in advance and participates in the whole process. In this paper, a public verifiable protocol for measurement-only BQC is proposed. The fidelity between arbitrary states and the graph states of 2-colorable graphs is estimated by measuring the entanglement witnesses of the graph states,so as to verify the correctness of the prepared graph states. Compared with the previous protocol, our protocol is public verifiable in the true sense by allowing other random clients to execute the public verification. It also has greater advantages in the efficiency, where the number of local measurements is O(n^3*log {n}) and graph states' copies is O(n^2*log{n}).

eXplainable Artificial Intelligence (XAI) has emerged as an essential requirement when dealing with mission-critical applications, ensuring transparency and interpretability of the employed black box AI models. The significance of XAI spans various domains, from healthcare to finance, where understanding the decision-making process of deep learning algorithms is essential. Most AI-based computer vision models are often black boxes; hence, providing explainability of deep neural networks in image processing is crucial for their wide adoption and deployment in medical image analysis, autonomous driving, and remote sensing applications. Recently, several XAI methods for image classification tasks have been introduced. On the contrary, image segmentation has received comparatively less attention in the context of explainability, although it is a fundamental task in computer vision applications, especially in remote sensing. Only some research proposes gradient-based XAI algorithms for image segmentation. This paper adapts the recent gradient-free Sobol XAI method for semantic segmentation. To measure the performance of the Sobol method for segmentation, we propose a quantitative XAI evaluation method based on a learnable noise model. The main objective of this model is to induce noise on the explanation maps, where higher induced noise signifies low accuracy and vice versa. A benchmark analysis is conducted to evaluate and compare performance of three XAI methods, including Seg-Grad-CAM, Seg-Grad-CAM++ and Seg-Sobol using the proposed noise-based evaluation technique. This constitutes the first attempt to run and evaluate XAI methods using high-resolution satellite images.

Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction that involves an additional scalar correction (in an additive sense) based on degrees of freedom adjusted training errors from each ensemble component. The proposed estimator (termed CGCV) maintains the computational advantages of GCV and requires neither sample splitting, model refitting, or out-of-bag risk estimation. The estimator stems from a finer inspection of ensemble risk decomposition and two intermediate risk estimators for the components in this decomposition. We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model. In the special case of ridge regression, we extend the analysis to general feature and response distributions using random matrix theory, which establishes model-free uniform consistency of CGCV.

Graphics Processing Unit, or GPUs, have been successfully adopted both for graphic computation in 3D applications, and for general purpose application (GP-GPUs), thank to their tremendous performance-per-watt. Recently, there is a big interest in adopting them also within automotive and avionic industrial settings, imposing for the first time real-time constraints on the design of such devices. Unfortunately, it is extremely hard to extract timing guarantees from modern GPU designs, and current approaches rely on a model where the GPU is treated as a unique monolithic execution device. Unlike state-of-the-art of research, we try to open the box of modern GPU architectures, providing a clean way to exploit intra-GPU predictable execution.

We propose a new method to compare survival data based on Higher Criticism (HC) of P-values obtained from many exact hypergeometric tests. The method can accommodate censorship and is sensitive to moderate differences in some unknown and relatively few time intervals, attaining much better power against such differences than the log-rank test and other tests that are popular under non-proportional hazard alternatives. We demonstrate the usefulness of the HC-based test in detecting rare differences compared to existing tests using simulated data and using actual gene expression data. Additionally, we analyze the asymptotic power of our method under a piece-wise homogeneous exponential decay model with rare and weak departures, describing two groups experiencing failure rates that are usually identical over time except in a few unknown instances in which the second group's failure rate is higher. Under an asymptotic calibration of the model's parameters, the HC-based test's power experiences a phase transition across the plane involving the rarity and intensity parameters that mirrors the phase transition in a two-sample rare and weak normal means setting. In particular, the phase transition curve of our test indicates a larger region in which it is fully powered than the corresponding region of the log-rank test. %The latter attains a phase transition curve that is analogous to a test based on Fisher's combination statistic of the hypergeometric P-values. %To our knowledge, this is the first analysis of a rare and weak signal detection model that involves individually dependent effects in a non-Gaussian setting.

Graph Neural Networks (GNNs) have emerged as formidable resources for processing graph-based information across diverse applications. While the expressive power of GNNs has traditionally been examined in the context of graph-level tasks, their potential for node-level tasks, such as node classification, where the goal is to interpolate missing node labels from the observed ones, remains relatively unexplored. In this study, we investigate the proficiency of GNNs for such classifications, which can also be cast as a function interpolation problem. Explicitly, we focus on ascertaining the optimal configuration of weights and layers required for a GNN to successfully interpolate a band-limited function over Euclidean cubes. Our findings highlight a pronounced efficiency in utilizing GNNs to generalize a bandlimited function within an $\varepsilon$-error margin. Remarkably, achieving this task necessitates only $O_d((\log\varepsilon^{-1})^d)$ weights and $O_d((\log\varepsilon^{-1})^d)$ training samples. We explore how this criterion stacks up against the explicit constructions of currently available Neural Networks (NNs) designed for similar tasks. Significantly, our result is obtained by drawing an innovative connection between the GNN structures and classical sampling theorems. In essence, our pioneering work marks a meaningful contribution to the research domain, advancing our understanding of the practical GNN applications.

We propose a method to construct a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional equation defining the model has a unique solution under fairly weak conditions. The model is characterized by two orthogonal parameters: the dependence parameter and the marginal parameter. To estimate the dependence parameter, a conditional inference together with a sampling procedure is proposed and is shown to provide a consistent estimator. Illustrative examples of data analyses involving penguins and earthquakes are presented.

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to predict solutions to $strongly\,\,degenerate\,\,parabolic\,\,problems\,\,with\,\,asymptotic\,\,structure\,\,of\,\,Laplacian\,\,type$. To the best of our knowledge, this is one of the first papers demonstrating the efficacy of the PINN framework for solving such kind of problems. In particular, we estimate an appropriate approximation error for some test problems whose analytical solutions are fortunately known. The numerical experiments discussed include two and three-dimensional spatial domains, emphasizing the effectiveness of this approach in predicting accurate solutions.

Problems from metric graph theory such as Metric Dimension, Geodetic Set, and Strong Metric Dimension have recently had a strong impact on the field of parameterized complexity by being the first problems in NP to admit double-exponential lower bounds in the treewidth, and even in the vertex cover number for the latter. We initiate the study of enumerating minimal solution sets for these problems and show that they are also of great interest in enumeration. More specifically, we show that enumerating minimal resolving sets in graphs and minimal geodetic sets in split graphs are equivalent to hypergraph dualization, arguably one of the most important open problems in algorithmic enumeration. This provides two new natural examples to a question that emerged in different works this last decade: for which vertex (or edge) set graph property $\Pi$ is the enumeration of minimal (or maximal) subsets satisfying $\Pi$ equivalent to hypergraph dualization? As only very few properties are known to fit within this context -- namely, properties related to minimal domination -- our results make significant progress in characterizing such properties, and provide new angles of approach for tackling hypergraph dualization. In a second step, we consider cases where our reductions do not apply, namely graphs with no long induced paths, and show these cases to be mainly tractable.

In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.