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Consider words of length $n$. The set of all periods of a word of length $n$ is a subset of $\{0,1,2,\ldots,n-1\}$. However, any subset of $\{0,1,2,\ldots,n-1\}$ is not necessarily a valid set of periods. In a seminal paper in 1981, Guibas and Odlyzko have proposed to encode the set of periods of a word into an $n$ long binary string, called an autocorrelation, where a one at position $i$ denotes a period of $i$. They considered the question of recognizing a valid period set, and also studied the number of valid period sets for length $n$, denoted $\kappa_n$. They conjectured that $\ln(\kappa_n)$ asymptotically converges to a constant times $\ln^2(n)$. If improved lower bounds for $\ln(\kappa_n)/\ln^2(n)$ were proposed in 2001, the question of a tight upper bound has remained opened since Guibas and Odlyzko's paper. Here, we exhibit an upper bound for this fraction, which implies its convergence and closes this long standing conjecture. Moreover, we extend our result to find similar bounds for the number of correlations: a generalization of autocorrelations which encodes the overlaps between two strings.

Sparse code multiple access (SCMA) is the most concerning scheme among non-orthogonal multiple access (NOMA) technologies for 5G wireless communication new interface. Another efficient technique in 5G aimed to improve spectral efficiency for local communications is device-to-device (D2D) communications. Therefore, we utilize the SCMA cellular network coexisting with D2D communications for the connection demand of the Internet of things (IOT), and improve the system sum rate performance of the hybrid network. We first derive the information-theoretic expression of the capacity for all users and find the capacity bound of cellular users based on the mutual interference between cellular users and D2D users. Then we consider the power optimization problem for the cellular users and D2D users jointly to maximize the system sum rate. To tackle the non-convex optimization problem, we propose a geometric programming (GP) based iterative power allocation algorithm. Simulation results demonstrate that the proposed algorithm converges fast and well improves the sum rate performance.

Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more practical constraints, i.e., non-Gaussian signaling, non-IID channel, and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate capacity analysis for GMU-MIMO. In addition, it is unclear how to achieve the capacity optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the GMU-MIMO capacity and design a capacity optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to make a tradeoff between user rate allocation and implementation complexity. Specifically, the capacity region of group asymmetric GMU-MIMO is characterized by using the celebrated mutual information and minimum mean-square error (MMSE) lemma and the MMSE optimality of orthogonal approximate message passing (OAMP)/vector AMP (VAMP). Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the capacity region of group asymmetric GMU-MIMO. Numerical results verify that the gaps between theoretical detection thresholds of the proposed framework with optimized MU-LDPC codes and QPSK modulation and the sum capacity of GMU-MIMO are about 0.2 dB. Moreover, their finite-length performances are about 1~2 dB away from the associated sum capacity.

The use of 1-bit analog-to-digital converters (ADCs) is seen as a promising approach to significantly reduce the power consumption and hardware cost of multiple-input multiple-output (MIMO) receivers. However, the nonlinear distortion due to 1-bit quantization fundamentally changes the optimal communication strategy and also imposes a capacity penalty to the system. In this paper, the capacity of a Gaussian MIMO channel in which the antenna outputs are processed by an analog linear combiner and then quantized by a set of zero threshold ADCs is studied. A new capacity upper bound for the zero threshold case is established that is tighter than the bounds available in the literature. In addition, we propose an achievability scheme which configures the analog combiner to create parallel Gaussian channels with phase quantization at the output. Under this class of analog combiners, an algorithm is presented that identifies the analog combiner and input distribution that maximize the achievable rate. Numerical results are provided showing that the rate of the achievability scheme is tight in the low signal-to-noise ratio (SNR) regime. Finally, a new 1-bit MIMO receiver architecture which employs analog temporal and spatial processing is proposed. The proposed receiver attains the capacity in the high SNR regime.

Magnetic Resonance Fingerprinting (MRF) is a novel technique that simultaneously estimates multiple tissue-related parameters, such as the longitudinal relaxation time T1, the transverse relaxation time T2, off resonance frequency B0 and proton density, from a scanned object in just tens of seconds. However, the MRF method suffers from aliasing artifacts because it significantly undersamples the k-space data. In this work, we propose a compressed sensing (CS) framework for simultaneously estimating multiple tissue-related parameters based on the MRF method. It is more robust to low sampling ratio and is therefore more efficient in estimating MR parameters for all voxels of an object. Furthermore, the MRF method requires identifying the nearest atoms of the query fingerprints from the MR-signal-evolution dictionary with the L2 distance. However, we observed that the L2 distance is not always a proper metric to measure the similarities between MR Fingerprints. Adaptively learning a distance metric from the undersampled training data can significantly improve the matching accuracy of the query fingerprints. Numerical results on extensive simulated cases show that our method substantially outperforms stateof-the-art methods in terms of accuracy of parameter estimation.

Well-designed simultaneously transmitting and reflecting RIS (STAR-RIS), which extends the half-space coverage to full-space coverage, incurs wireless communication environments to be smart and reconfigurable. In this paper, we survey how STAR-RIS affects the performance of full-duplex communication systems with the presence of full-duplex users, wherein the base station (BS) and the uplink users are subject to maximum transmission power constraints. Firstly, the weighted sum-rate (WSR) is derived as a system performance metric. Then, we formulate the resource allocation design into an equivalent weighted minimum mean-square-error form and then transform it into several convex sub-problems to maximize the WSR as an optimization problem which jointly optimizes the beamforming and the combining vectors at the BS, the transmit powers of the uplink users, and phase shifts of STAR-RIS. Although the WSR optimization is non-convex, an efficient iterative alternating procedure is proposed to achieve a sub-optimal solution for the optimization problem. Secondly, the STAR-RIS's phase shifts are optimized via the successive convex approximation technique. Finally, numerical results are provided to explain how STAR-RIS improves the performance metric with the presence of full-duplex users.

Deep learning algorithms for predicting neuroimaging data have shown considerable promise in various applications. Prior work has demonstrated that deep learning models that take advantage of the data's 3D structure can outperform standard machine learning on several learning tasks. However, most prior research in this area has focused on neuroimaging data from adults. Within the Adolescent Brain and Cognitive Development (ABCD) dataset, a large longitudinal development study, we examine structural MRI data to predict gender and identify gender-related changes in brain structure. Results demonstrate that gender prediction accuracy is exceptionally high (>97%) with training epochs >200 and that this accuracy increases with age. Brain regions identified as the most discriminative in the task under study include predominantly frontal areas and the temporal lobe. When evaluating gender predictive changes specific to a two-year increase in age, a broader set of visual, cingulate, and insular regions are revealed. Our findings show a robust gender-related structural brain change pattern, even over a small age range. This suggests that it might be possible to study how the brain changes during adolescence by looking at how these changes are related to different behavioral and environmental factors.

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.

Multimodal learning helps to comprehensively understand the world, by integrating different senses. Accordingly, multiple input modalities are expected to boost model performance, but we actually find that they are not fully exploited even when the multimodal model outperforms its uni-modal counterpart. Specifically, in this paper we point out that existing multimodal discriminative models, in which uniform objective is designed for all modalities, could remain under-optimized uni-modal representations, caused by another dominated modality in some scenarios, e.g., sound in blowing wind event, vision in drawing picture event, etc. To alleviate this optimization imbalance, we propose on-the-fly gradient modulation to adaptively control the optimization of each modality, via monitoring the discrepancy of their contribution towards the learning objective. Further, an extra Gaussian noise that changes dynamically is introduced to avoid possible generalization drop caused by gradient modulation. As a result, we achieve considerable improvement over common fusion methods on different multimodal tasks, and this simple strategy can also boost existing multimodal methods, which illustrates its efficacy and versatility. The source code is available at \url{//github.com/GeWu-Lab/OGM-GE_CVPR2022}.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.