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Triggerless Data Acquisition Systems (DAQs) require transmitting the data stream from multiple links to the processing node. The short input data words must be concentrated and packed into the longer bit vectors the output interface (e.g., PCI Express) uses. In that process, the unneeded data must be eliminated, and a dense stream of useful DAQ data must be created. Additionally, the time order of the data should be preserved. This paper presents a new solution using the Baseline Network with Reversed Outputs (BNRO) for high-speed data routing. A thorough analysis of the network's operation enabled increased scalability compared to the previously published concentrator based on an 8x8 network. The solution may be scaled by adding additional layers to the BNRO network while minimizing resource consumption. Simulations were done for 4 and 5 layers (16 and 32 inputs). The FPGA implementation and tests in the actual hardware have been successfully performed for 16 inputs. The pipeline registers may be added in each layer independently, shortening the critical path and increasing the maximum acceptable clock frequency.

This tutorial shows how various Bayesian survival models can be fitted using the integrated nested Laplace approximation in a clear, legible, and comprehensible manner using the INLA and INLAjoint R-packages. Such models include accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data, originally presented in the article "Bayesian survival analysis with BUGS" (Alvares et al., 2021). In addition, we illustrate the implementation of a new joint model for a longitudinal semicontinuous marker, recurrent events, and a terminal event. Our proposal aims to provide the reader with syntax examples for implementing survival models using a fast and accurate approximate Bayesian inferential approach.

A closed electromagnetic resonant chamber (RC) is a highly favorable artificial environment for wireless communication. A pair of antennas within the chamber constitutes a two-port network described by an impedance matrix. We analyze communication between the two antennas when the RC has perfectly conducting walls and the impedance matrix is imaginary-valued. The transmit antenna is driven by a current source, and the receive antenna is connected to a load resistor whose voltage is measured by an infinite-impedance amplifier. There are a countably infinite number of poles in the channel, associated with resonance in the RC, which migrate towards the real frequency axis as the load resistance increases. There are two sources of receiver noise: the Johnson noise of the load resistor, and the internal amplifier noise. An application of Shannon theory yields the capacity of the link, subject to bandwidth and power constraints on the transmit current. For a constant transmit power, capacity increases without bound as the load resistance increases. Surprisingly, the capacity-attaining allocation of transmit power versus frequency avoids placing power close to the resonant frequencies.

We investigate how shallow ReLU networks interpolate between known regions. Our analysis shows that empirical risk minimizers converge to a minimum norm interpolant as the number of data points and parameters tends to infinity when a weight decay regularizer is penalized with a coefficient which vanishes at a precise rate as the network width and the number of data points grow. With and without explicit regularization, we numerically study the implicit bias of common optimization algorithms towards known minimum norm interpolants.

The core is a strong fairness notion in multiwinner voting and participatory budgeting (PB). It is known that the core can be empty if we consider cardinal utilities, but it is not known whether it is always satisfiable with approval-ballots. In this short note, I show that in approval-based PB the core can be empty for nearly all satisfaction functions that are based on the cost of a project. In particular, I show that the core can be empty for the cost satisfaction function, satisfaction functions based on diminishing marginal returns and the share. However, it remains open whether the core can be empty for the cardinality satisfaction function.

We investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of the numerical simulators have inconsistent dimensions across the multilevel hierarchy. This requires the introduction of grid transfer operators borrowed from multigrid methods. Starting from a simple 1D illustration, we demonstrate numerically that the resulting MLMC estimator deteriorates the estimation of high-frequency components of the discretized expectation field compared to a Monte Carlo (MC) estimator. By adapting mathematical tools initially developed for multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. This analysis provides a spectral decomposition of the variance into contributions associated with each scale component of the discretized field. We then propose improved MLMC estimators using a filtering mechanism similar to the smoothing process of multigrid methods. The filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. These improvements are quantified for the specific class of simulators considered in our spectral analysis. The resulting filtered MLMC (F-MLMC) estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the proposed F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator.

The Business Process Modeling Notation (BPMN) is a widely used standard notation for defining intra- and inter-organizational workflows. However, the informal description of the BPMN execution semantics leads to different interpretations of BPMN elements and difficulties in checking behavioral properties. In this article, we propose a formalization of the execution semantics of BPMN that, compared to existing approaches, covers more BPMN elements while also facilitating property checking. Our approach is based on a higher-order transformation from BPMN models to graph transformation systems. To show the capabilities of our approach, we implemented it as an open-source web-based tool.

In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true autocovariance sequence with respect to an $\ell_2$ distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.

Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the Weisfeiler--Lehman (WL) test. However, these results suffer from some limitations, both because they were derived using the Stone--Weierstrass theorem -- which is existential in nature, -- and because they assume that the target function to be approximated must be continuous. Furthermore, all current results are dedicated to graph classification/regression tasks, where the GNN must produce a single output for the whole graph, while also node classification/regression problems, in which an output is returned for each node, are very common. In this paper, we propose an alternative way to demonstrate the approximation capability of GNNs that overcomes these limitations. Indeed, we show that GNNs are universal approximators in probability for node classification/regression tasks, as they can approximate any measurable function that satisfies the 1--WL equivalence on nodes. The proposed theoretical framework allows the approximation of generic discontinuous target functions and also suggests the GNN architecture that can reach a desired approximation. In addition, we provide a bound on the number of the GNN layers required to achieve the desired degree of approximation, namely $2r-1$, where $r$ is the maximum number of nodes for the graphs in the domain.

Occluded person re-identification (re-ID) presents a challenging task due to occlusion perturbations. Although great efforts have been made to prevent the model from being disturbed by occlusion noise, most current solutions only capture information from a single image, disregarding the rich complementary information available in multiple images depicting the same pedestrian. In this paper, we propose a novel framework called Multi-view Information Integration and Propagation (MVI$^{2}$P). Specifically, realizing the potential of multi-view images in effectively characterizing the occluded target pedestrian, we integrate feature maps of which to create a comprehensive representation. During this process, to avoid introducing occlusion noise, we develop a CAMs-aware Localization module that selectively integrates information contributing to the identification. Additionally, considering the divergence in the discriminative nature of different images, we design a probability-aware Quantification module to emphatically integrate highly reliable information. Moreover, as multiple images with the same identity are not accessible in the testing stage, we devise an Information Propagation (IP) mechanism to distill knowledge from the comprehensive representation to that of a single occluded image. Extensive experiments and analyses have unequivocally demonstrated the effectiveness and superiority of the proposed MVI$^{2}$P. The code will be released at \url{//github.com/nengdong96/MVIIP}.