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We study the problem of density estimation for a random vector ${\boldsymbol X}$ in $\mathbb R^d$ with probability density $f(\boldsymbol x)$. For a spanning tree $T$ defined on the vertex set $\{1,\dots ,d\}$, the tree density $f_{T}$ is a product of bivariate conditional densities. The optimal spanning tree $T^*$ is the spanning tree $T$, for which the Kullback-Leibler divergence of $f$ and $f_{T}$ is the smallest. From i.i.d. data we identify the optimal tree $T^*$ and computationally efficiently construct a tree density estimate $f_n$ such that, without any regularity conditions on the density $f$, one has that $\lim_{n\to \infty} \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x=0$ a.s. For Lipschitz continuous $f$ with bounded support, $\mathbb E\{ \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x\}=O(n^{-1/4})$.

Next-generation communication technology will be fueled on the cooperation of terrestrial networks with nonterrestrial networks (NTNs) that contain mega-constellations of high-altitude platform stations and low-Earth orbit satellites. On the other hand, humanity has embarked on a long road to establish new habitats on other planets. This deems the cooperation of NTNs with deep space networks (DSNs) necessary. In this regard, we propose the use of reconfigurable intelligent surfaces (RISs) to improve and escalate this collaboration owing to the fact that they perfectly match with the size, weight, and power restrictions of the operational environment of space. A comprehensive framework of RIS-assisted non-terrestrial and interplanetary communications is presented by pinpointing challenges, use cases, and open issues. Furthermore, the performance of RIS-assisted NTNs under environmental effects such as solar scintillation and satellite drag is discussed through simulation results.

In this letter, we investigate the performance of reconfigurable intelligent surface (RIS)-assisted communications, under the assumption of generalized Gaussian noise (GGN), over Rayleigh fading channels. Specifically, we consider an RIS, equipped with $N$ reflecting elements, and derive a novel closed-form expression for the symbol error rate (SER) of arbitrary modulation schemes. The usefulness of the derived new expression is that it can be used to capture the SER performance in the presence of special additive noise distributions such as Gamma, Laplacian, and Gaussian noise. These special cases are also considered and their associated asymptotic SER expressions are derived, and then employed to quantify the achievable diversity order of the system. The theoretical framework is corroborated by numerical results, which reveal that the shaping parameter of the GGN ($\alpha$) has a negligible effect on the diversity order of RIS-assisted systems, particularly for large $\alpha$ values. Accordingly, the maximum achievable diversity order is determined by $N$.

A reconfigurable intelligent surface (RIS) employs an array of individually-controllable elements to scatter incident signals in a desirable way; for example, to facilitate links between base stations and mobile stations that would otherwise be blocked. A principal consideration in the study of RIS-enabled propagation channels is path loss. This paper presents a simple yet broadly-applicable method for calculating the path loss of a channel consisting of a passive reflectarray-type RIS. This model is then used to characterize path loss as a function of RIS size, link geometry, and the method used to set the element states. Whereas previous work presumes either (1) an array of parameterizable element patterns and spacings (most useful for analysis of specific designs) or (2) a continuous electromagnetic surface (most useful for determining scaling laws and theoretical limits), this work begins with (1) and is then shown to be consistent with (2), making it possible to identify specific practical designs and scenarios that exhibit the performance predicted using (2). This model is used to further elucidate the matter of path loss of the RIS-enabled channel relative to that of the free space direct and specular reflection channels, which is an important consideration in the design of networks employing RIS technology.

Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian single and multiple change-point detection procedures for the rapid detection of propagating spatial events. It is assumed that the spatial event propagates across a network of sensors according to the physical properties of the source causing the event. The multi-sensor system configuration is arbitrary and sensors may be mobile. We begin by considering a single spatial event and are interested in detecting this event as quickly as possible, while controlling the probability of false alarm. Using a dynamic programming framework we derive the structure of the optimal procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation pattern of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting attenuating random signals. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel. A method that provides false discovery rate (FDR) control is proposed. In the simulation section, it is clearly demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.

Content caching at the network edge has been considered an effective way of mitigating backhaul load and improving user experience. Caching efficiency can be enhanced by content recommendation and by keeping the information fresh. To the best of our knowledge, there is no work that jointly takes into account these aspects. By content recommendation, a requested content that is not in the cache can be alternatively satisfied by a related cached content recommended by the system. Information freshness can be quantified by age of information (AoI). We address, optimal scheduling of cache updates for a time-slotted system accounting for content recommendation and AoI. For each content, there are requests that need to be satisfied, and there is a cost function capturing the freshness of information. We present the following contributions. First, we prove that the problem is NP-hard. Second, we derive an integer linear formulation, by which the optimal solution can be obtained for small-scale scenarios. Third, we develop an algorithm based on Lagrangian decomposition. Fourth, we develop efficient algorithms for solving the resulting subproblems. Our algorithm computes a bound that can be used to evaluate the performance of any suboptimal solution. Finally, we conduct simulations to show the effectiveness of our algorithm in comparison to a greedy schedule.

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.

Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.

We present a generalization of the Cauchy/Lorentzian, Geman-McClure, Welsch/Leclerc, generalized Charbonnier, Charbonnier/pseudo-Huber/L1-L2, and L2 loss functions. By introducing robustness as a continous parameter, our loss function allows algorithms built around robust loss minimization to be generalized, which improves performance on basic vision tasks such as registration and clustering. Interpreting our loss as the negative log of a univariate density yields a general probability distribution that includes normal and Cauchy distributions as special cases. This probabilistic interpretation enables the training of neural networks in which the robustness of the loss automatically adapts itself during training, which improves performance on learning-based tasks such as generative image synthesis and unsupervised monocular depth estimation, without requiring any manual parameter tuning.

The ever-growing interest witnessed in the acquisition and development of unmanned aerial vehicles (UAVs), commonly known as drones in the past few years, has brought generation of a very promising and effective technology. Because of their characteristic of small size and fast deployment, UAVs have shown their effectiveness in collecting data over unreachable areas and restricted coverage zones. Moreover, their flexible-defined capacity enables them to collect information with a very high level of detail, leading to high resolution images. UAVs mainly served in military scenario. However, in the last decade, they have being broadly adopted in civilian applications as well. The task of aerial surveillance and situation awareness is usually completed by integrating intelligence, surveillance, observation, and navigation systems, all interacting in the same operational framework. To build this capability, UAV's are well suited tools that can be equipped with a wide variety of sensors, such as cameras or radars. Deep learning has been widely recognized as a prominent approach in different computer vision applications. Specifically, one-stage object detector and two-stage object detector are regarded as the most important two groups of Convolutional Neural Network based object detection methods. One-stage object detector could usually outperform two-stage object detector in speed; however, it normally trails in detection accuracy, compared with two-stage object detectors. In this study, focal loss based RetinaNet, which works as one-stage object detector, is utilized to be able to well match the speed of regular one-stage detectors and also defeat two-stage detectors in accuracy, for UAV based object detection. State-of-the-art performance result has been showed on the UAV captured image dataset-Stanford Drone Dataset (SDD).