This paper studies a hierarchical over-the-air computation (AirComp) network over a large area, in which multiple relays are exploited to facilitate data aggregation from massive WDs. We present a two-phase amplify-and-forward (AF) relaying protocol. In the first phase, the WDs simultaneously send their data to the relays, while in the second phase, the relays amplify the respectively received signals and concurrently forward them to the fusion center (FC) for aggregation. Our objective is to minimize the computational mean squared error (MSE) at the FC, by jointly optimizing the WD transmit coefficients, the relay AF coefficients, and the FC de-noising factor, subject to their individual transmit power constraints. First, we consider the centralized design with global channel state information (CSI), in which the inter-relay signals can be exploited beneficially for data aggregation. In this case, we develop an alternating-optimization-based algorithm to obtain a high-quality solution to the computational MSE minimization problem. Next, to reduce the signaling overhead caused by the centralized design, we consider an alternative decentralized design with partial CSI, in which the relays and the FC make their own decisions by only requiring the channel power gain information across different relays. In this case, the relays and FC need to treat the inter-relay signals as harmful interference or noise. Accordingly, we optimize the transmit coefficients of the WDs associated with each relay, and the relay AF coefficients (together with the FC de-noising factor) in an iterative manner, which can be implemented efficiently in a decentralized way.
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This paper investigates a new downlink nonorthogonal multiple access (NOMA) system, where a multiantenna unmanned aerial vehicle (UAV) is powered by wireless power transfer (WPT) and serves as the base station for multiple pairs of ground users (GUs) running NOMA in each pair. An energy efficiency (EE) maximization problem is formulated to jointly optimize the WPT time and the placement for the UAV, and the allocation of the UAV's transmit power between different NOMA user pairs and within each pair. To efficiently solve this nonconvex problem, we decompose the problem into three subproblems using block coordinate descent. For the subproblem of intra-pair power allocation within each NOMA user pair, we construct a supermodular game with confirmed convergence to a Nash equilibrium. Given the intra-pair power allocation, successive convex approximation is applied to convexify and solve the subproblem of WPT time allocation and inter-pair power allocation between the user pairs. Finally, we solve the subproblem of UAV placement by using the Lagrange multiplier method. Simulations show that our approach can substantially outperform its alternatives that do not use NOMA and WPT techniques or that do not optimize the UAV location.
Vision Transformers (ViT) serve as powerful vision models. Unlike convolutional neural networks, which dominated vision research in previous years, vision transformers enjoy the ability to capture long-range dependencies in the data. Nonetheless, an integral part of any transformer architecture, the self-attention mechanism, suffers from high latency and inefficient memory utilization, making it less suitable for high-resolution input images. To alleviate these shortcomings, hierarchical vision models locally employ self-attention on non-interleaving windows. This relaxation reduces the complexity to be linear in the input size; however, it limits the cross-window interaction, hurting the model performance. In this paper, we propose a new shift-invariant local attention layer, called query and attend (QnA), that aggregates the input locally in an overlapping manner, much like convolutions. The key idea behind QnA is to introduce learned queries, which allow fast and efficient implementation. We verify the effectiveness of our layer by incorporating it into a hierarchical vision transformer model. We show improvements in speed and memory complexity while achieving comparable accuracy with state-of-the-art models. Finally, our layer scales especially well with window size, requiring up-to x10 less memory while being up-to x5 faster than existing methods. The code is publicly available at \url{//github.com/moabarar/qna}.
We consider the question of adaptive data analysis within the framework of convex optimization. We ask how many samples are needed in order to compute $\epsilon$-accurate estimates of $O(1/\epsilon^2)$ gradients queried by gradient descent, and we provide two intermediate answers to this question. First, we show that for a general analyst (not necessarily gradient descent) $\Omega(1/\epsilon^3)$ samples are required. This rules out the possibility of a foolproof mechanism. Our construction builds upon a new lower bound (that may be of interest of its own right) for an analyst that may ask several non adaptive questions in a batch of fixed and known $T$ rounds of adaptivity and requires a fraction of true discoveries. We show that for such an analyst $\Omega (\sqrt{T}/\epsilon^2)$ samples are necessary. Second, we show that, under certain assumptions on the oracle, in an interaction with gradient descent $\tilde \Omega(1/\epsilon^{2.5})$ samples are necessary. Our assumptions are that the oracle has only \emph{first order access} and is \emph{post-hoc generalizing}. First order access means that it can only compute the gradients of the sampled function at points queried by the algorithm. Our assumption of \emph{post-hoc generalization} follows from existing lower bounds for statistical queries. More generally then, we provide a generic reduction from the standard setting of statistical queries to the problem of estimating gradients queried by gradient descent. These results are in contrast with classical bounds that show that with $O(1/\epsilon^2)$ samples one can optimize the population risk to accuracy of $O(\epsilon)$ but, as it turns out, with spurious gradients.
Given a set $P$ of $n$ points in the plane, the $k$-center problem is to find $k$ congruent disks of minimum possible radius such that their union covers all the points in $P$. The $2$-center problem is a special case of the $k$-center problem that has been extensively studied in the recent past \cite{CAHN,HT,SH}. In this paper, we consider a generalized version of the $2$-center problem called \textit{proximity connected} $2$-center (PCTC) problem. In this problem, we are also given a parameter $\delta\geq 0$ and we have the additional constraint that the distance between the centers of the disks should be at most $\delta$. Note that when $\delta=0$, the PCTC problem is reduced to the $1$-center(minimum enclosing disk) problem and when $\delta$ tends to infinity, it is reduced to the $2$-center problem. The PCTC problem first appeared in the context of wireless networks in 1992 \cite{ACN0}, but obtaining a nontrivial deterministic algorithm for the problem remained open. In this paper, we resolve this open problem by providing a deterministic $O(n^2\log n)$ time algorithm for the problem.
This paper considers the problem of inference in cluster randomized experiments when cluster sizes are non-ignorable. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the cluster; by non-ignorable cluster sizes we mean that "large" clusters and "small" clusters may be heterogeneous, and, in particular, the effects of the treatment may vary across clusters of differing sizes. In order to permit this sort of flexibility, we consider a sampling framework in which cluster sizes themselves are random. In this way, our analysis departs from earlier analyses of cluster randomized experiments in which cluster sizes are treated as non-random. We distinguish between two different parameters of interest: the equally-weighted cluster-level average treatment effect, and the size-weighted cluster-level average treatment effect. For each parameter, we provide methods for inference in an asymptotic framework where the number of clusters tends to infinity and treatment is assigned using simple random sampling. We additionally permit the experimenter to sample only a subset of the units within each cluster rather than the entire cluster and demonstrate the implications of such sampling for some commonly used estimators. A small simulation study shows the practical relevance of our theoretical results.
Spectral efficiency improvement is a key focus in most wireless communication systems and achieved by various means such as using large antenna arrays and/or advanced modulation schemes and signal formats. This work proposes to further improve spectral efficiency through combining non-orthogonal spectrally efficient frequency division multiplexing (SEFDM) systems with index modulation (IM), which can efficiently make use of the indices of activated subcarriers as communication information. Recent research has verified that IM may be used with SEFDM to alleviate inter-carrier interference (ICI) and improve error performance. This work proposes new SEFDM signal formats based on novel activation pattern designs, which limit the locations of activated subcarriers and enable a variable number of activated subcarriers in each SEFDM subblock. SEFDM-IM system designs are developed by jointly considering activation patterns, modulation schemes and signal waveform formats, with a set of solutions evaluated under different spectral efficiency scenarios. Detailed modelling of coded systems and simulation studies reveal that the proposed designs not only lead to better bit error rate (BER) but also lower peak-to-average power ratio (PAPR) and reduced computational complexity relative to other reported index-modulated systems.
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.
The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.
We introduce a fast solver for the phase field crystal (PFC) and functionalized Cahn-Hilliard (FCH) equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov accelerated gradient descent (PAGD) method. We discretize these problems with a Fourier collocation method in space, and employ various second-order schemes in time. We observe a significant speedup with this solver when compared to the preconditioned gradient descent (PGD) method. With the PAGD solver, fully implicit, second-order-in-time schemes are not only feasible to solve the PFC and FCH equations, but also do so more efficiently than some semi-implicit schemes in some cases where accuracy issues are taken into account. Benchmark computations of five different schemes for the PFC and FCH equations are conducted and the results indicate that, for the FCH experiments, the fully implicit schemes (midpoint rule and BDF2 equipped with the PAGD as a nonlinear time marching solver) perform better than their IMEX versions in terms of computational cost needed to achieve a certain precision. For the PFC, the results are not as conclusive as in the FCH experiments, which, we believe, is due to the fact that the nonlinearity in the PFC is milder nature compared to the FCH equation. We also discuss some practical matters in applying the PAGD. We introduce an averaged Newton preconditioner and a sweeping-friction strategy as heuristic ways to choose good preconditioner parameters. The sweeping-friction strategy exhibits almost as good a performance as the case of the best manually tuned parameters.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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