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Non-probability sampling is prevailing in survey sampling, but ignoring its selection bias leads to erroneous inferences. We offer a unified nonparametric calibration method to estimate the sampling weights for a non-probability sample by calibrating functions of auxiliary variables in a reproducing kernel Hilbert space. The consistency and the limiting distribution of the proposed estimator are established, and the corresponding variance estimator is also investigated. Compared with existing works, the proposed method is more robust since no parametric assumption is made for the selection mechanism of the non-probability sample. Numerical results demonstrate that the proposed method outperforms its competitors, especially when the model is misspecified. The proposed method is applied to analyze the average total cholesterol of Korean citizens based on a non-probability sample from the National Health Insurance Sharing Service and a reference probability sample from the Korea National Health and Nutrition Examination Survey.

A directed graph is oriented if it can be obtained by orienting the edges of a simple, undirected graph. For an oriented graph $G$, let $\beta(G)$ denote the size of a minimum feedback arc set, a smallest subset of edges whose deletion leaves an acyclic subgraph. A simple consequence of a result of Berger and Shor is that any oriented graph $G$ with $m$ edges satisfies $\beta(G) = m/2 - \Omega(m^{3/4})$. We observe that if an oriented graph $G$ has a fixed forbidden subgraph $B$, the upper bound of $\beta(G) = m/2 - \Omega(m^{3/4})$ is best possible as a function of the number of edges if $B$ is not bipartite, but the exponent $3/4$ in the lower order term can be improved if $B$ is bipartite. We also show that for every rational number $r$ between $3/4$ and $1$, there is a finite collection of digraphs $\mathcal{B}$ such that every $\mathcal{B}$-free digraph $G$ with $m$ edges satisfies $\beta(G) = m/2 - \Omega(m^r)$, and this bound is best possible up to the implied constant factor. The proof uses a connection to Tur\'an numbers and a result of Bukh and Conlon. Both of our upper bounds come equipped with randomized linear-time algorithms that construct feedback arc sets achieving those bounds. Finally, we give a characterization of quasirandom directed graphs via minimum feedback arc sets.

In this paper, we consider a resilient consensus problem for the multi-agent network where some of the agents are subject to Byzantine attacks and may transmit erroneous state values to their neighbors. In particular, we develop an event-triggered update rule to tackle this problem as well as reduce the communication for each agent. Our approach is based on the mean subsequence reduced (MSR) algorithm with agents being capable to communicate with multi-hop neighbors. Since delays are critical in such an environment, we provide necessary graph conditions for the proposed algorithm to perform well with delays in the communication. We highlight that through multi-hop communication, the network connectivity can be reduced especially in comparison with the common onehop communication case. Lastly, we show the effectiveness of the proposed algorithm by a numerical example.

Integrated sensing and communication (ISAC) creates a platform to exploit the synergy between two powerful functionalities that have been developing separately. However, the interference management and resource allocation between sensing and communication have not been fully studied. In this paper, we consider the design of perceptive mobile networks (PMNs) by adding sensing capability to current cellular networks. To avoid the full-duplex operation, we propose the PMN with distributed target monitoring terminals (TMTs) where passive TMTs are deployed over wireless networks to locate the sensing target (ST). We jointly optimize the transmit and receive beamformers towards the communication user terminals (UEs) and the ST by alternating-optimization (AO) and prove its convergence. To reduce computation complexity and obtain physical insights, we further investigate the use of linear transceivers, including zero forcing and beam synthesis (B-syn). Our analysis revealed interesting physical insights regarding interference management and resource allocation between sensing and communication: 1) instead of forming dedicated sensing signals, it is more efficient to redesign the communication signals for both communication and sensing purposes and "leak" communication energy for sensing; 2) the amount of energy leakage from one UE to the ST depends on their relative locations.

We study the performance of a phase-noise impaired double reconfigurable intelligent surface (RIS)-aided multiuser (MU) multiple-input single-output (MISO) system under spatial correlation at both RISs and base-station (BS). The downlink achievable rate is derived in closed-form under maximum ratio transmission (MRT) precoding. In addition, we obtain the optimal phase-shift design at both RISs in closed-form for the considered channel and phase-noise models. Numerical results validate the analytical expressions, and highlight the effects of different system parameters on the achievable rate. Our analysis shows that phase-noise can severely degrade the performance when users do not have direct links to both RISs, and can only be served via the double-reflection link. Also, we show that high spatial correlation at RISs is essential for high achievable rates.

Federated learning (FL) has been recognized as a viable distributed learning paradigm which trains a machine learning model collaboratively with massive mobile devices in the wireless edge while protecting user privacy. Although various communication schemes have been proposed to expedite the FL process, most of them have assumed ideal wireless channels which provide reliable and lossless communication links between the server and mobile clients. Unfortunately, in practical systems with limited radio resources such as constraint on the training latency and constraints on the transmission power and bandwidth, transmission of a large number of model parameters inevitably suffers from quantization errors (QE) and transmission outage (TO). In this paper, we consider such non-ideal wireless channels, and carry out the first analysis showing that the FL convergence can be severely jeopardized by TO and QE, but intriguingly can be alleviated if the clients have uniform outage probabilities. These insightful results motivate us to propose a robust FL scheme, named FedTOE, which performs joint allocation of wireless resources and quantization bits across the clients to minimize the QE while making the clients have the same TO probability. Extensive experimental results are presented to show the superior performance of FedTOE for deep learning-based classification tasks with transmission latency constraints.

Universal coding of integers~(UCI) is a class of variable-length code, such that the ratio of the expected codeword length to $\max\{1,H(P)\}$ is within a constant factor, where $H(P)$ is the Shannon entropy of the decreasing probability distribution $P$. However, if we consider the ratio of the expected codeword length to $H(P)$, the ratio tends to infinity by using UCI, when $H(P)$ tends to zero. To solve this issue, this paper introduces a class of codes, termed generalized universal coding of integers~(GUCI), such that the ratio of the expected codeword length to $H(P)$ is within a constant factor $K$. First, the definition of GUCI is proposed and the coding structure of GUCI is introduced. Next, we propose a class of GUCI $\mathcal{C}$ to achieve the expansion factor $K_{\mathcal{C}}=2$ and show that the optimal GUCI is in the range $1\leq K_{\mathcal{C}}^{*}\leq 2$. Then, by comparing UCI and GUCI, we show that when the entropy is very large or $P(0)$ is not large, there are also cases where the average codeword length of GUCI is shorter. Finally, the asymptotically optimal GUCI is presented.

The success of deep learning attracted interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using a learning rule fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.

White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that, grounded on combinatorial considerations, contributes to give new interesting insights both for modelling and theoretical purposes. To this aim, we incorporate the ordinal pattern analysis approach which allows us to abstract a time series as a sequence of patterns and their associated permutations, and introduce a simple functional over permutations that partitions them into classes encoding their level of asymmetry. We compute the exact probability mass function (p.m.f.) of this functional over the symmetric group of degree $n$, thus providing the description for the case of an infinite white noise realization. This p.m.f. can be conveniently approximated by a continuous probability density from an exponential family, the Gaussian, hence providing natural sufficient statistics that render a convenient and simple statistical analysis through ordinal patterns. Such analysis is exemplified on experimental data for the spatial increments from tracks of gold nanoparticles in 3D diffusion.

The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While recent works have focused on forward reachability as a strategy for safety certification of NFLs, backward reachability offers advantages over the forward strategy, particularly in obstacle avoidance scenarios. Prior works have developed techniques for backward reachability analysis for systems without NNs, but the presence of NNs in the feedback loop presents a unique set of problems due to the nonlinearities in their activation functions and because NN models are generally not invertible. To overcome these challenges, we use existing forward NN analysis tools to find affine bounds on the control inputs and solve a series of linear programs (LPs) to efficiently find an approximation of the backprojection (BP) set, i.e., the set of states for which the NN control policy will drive the system to a given target set. We present an algorithm to iteratively find BP set estimates over a given time horizon and demonstrate the ability to reduce conservativeness in the BP set estimates by up to 88% with low additional computational cost. We use numerical results from a double integrator model to verify the efficacy of these algorithms and demonstrate the ability to certify safety for a linearized ground robot model in a collision avoidance scenario where forward reachability fails.