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The hypergraph unreliability problem asks for the probability that a hypergraph gets disconnected when every hyperedge fails independently with a given probability. For graphs, the unreliability problem has been studied over many decades, and multiple fully polynomial-time approximation schemes are known starting with the work of Karger (STOC 1995). In contrast, prior to this work, no non-trivial result was known for hypergraphs (of arbitrary rank). In this paper, we give quasi-polynomial time approximation schemes for the hypergraph unreliability problem. For any fixed $\varepsilon \in (0, 1)$, we first give a $(1+\varepsilon)$-approximation algorithm that runs in $m^{O(\log n)}$ time on an $m$-hyperedge, $n$-vertex hypergraph. Then, we improve the running time to $m\cdot n^{O(\log^2 n)}$ with an additional exponentially small additive term in the approximation.

The rise of new video modalities like virtual reality or autonomous driving has increased the demand for efficient multi-view video compression methods, both in terms of rate-distortion (R-D) performance and in terms of delay and runtime. While most recent stereo video compression approaches have shown promising performance, they compress left and right views sequentially, leading to poor parallelization and runtime performance. This work presents Low-Latency neural codec for Stereo video Streaming (LLSS), a novel parallel stereo video coding method designed for fast and efficient low-latency stereo video streaming. Instead of using a sequential cross-view motion compensation like existing methods, LLSS introduces a bidirectional feature shifting module to directly exploit mutual information among views and encode them effectively with a joint cross-view prior model for entropy coding. Thanks to this design, LLSS processes left and right views in parallel, minimizing latency; all while substantially improving R-D performance compared to both existing neural and conventional codecs.

Audit logs are one of the most important tools for transparently tracking system events and maintaining continuous oversight in corporate organizations and enterprise business systems. There are many cases where the audit logs contain sensitive data, or the audit logs are enormous. In these situations, dealing with a subset of the data is more practical than the entire data set. To provide a secure solution to handle these issues, a sanitizable signature scheme (SSS) is a viable cryptographic primitive. Herein, we first present the first post-quantum secure multivariate-based SSS, namely Mul-SAN. Our proposed design provides unforgeability, privacy, immutability, signer accountability, and sanitizer accountability under the assumption that the MQ problem is NP-hard. Mul-SAN is very efficient and only requires computing field multiplications and additions over a finite field for its implementation. Mul-SAN presents itself as a practical method to partially delegate control of the authenticated data in avenues like the healthcare industry and government organizations. We also explore using Blockchain to provide a tamper-proof and robust audit log mechanism.

Spatial autoregressive (SAR) models are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement privacy protection measures that make classical SAR models inapplicable. In this study, we introduce a privacy-protected SAR model with noise-added response and covariates to meet privacy-protection requirements. However, in this scenario, the traditional quasi-maximum likelihood estimator becomes infeasible because the likelihood function cannot be formulated. To address this issue, we first consider an explicit expression for the likelihood function with only noise-added responses. However, the derivatives are biased owing to the noise in the covariates. Therefore, we develop techniques that can correct the biases introduced by noise. Correspondingly, a Newton-Raphson-type algorithm is proposed to obtain the estimator, leading to a corrected likelihood estimator. To further enhance computational efficiency, we introduce a corrected least squares estimator based on the idea of bias correction. These two estimation methods ensure both data security and the attainment of statistically valid estimators. Theoretical analysis of both estimators is carefully conducted, and statistical inference methods are discussed. The finite sample performances of different methods are demonstrated through extensive simulations and the analysis of a real dataset.

Despite their unprecedented success, DNNs are notoriously fragile to small shifts in data distribution, demanding effective testing techniques that can assess their dependability. Despite recent advances in DNN testing, there is a lack of systematic testing approaches that assess the DNN's capability to generalise and operate comparably beyond data in their training distribution. We address this gap with DeepKnowledge, a systematic testing methodology for DNN-based systems founded on the theory of knowledge generalisation, which aims to enhance DNN robustness and reduce the residual risk of 'black box' models. Conforming to this theory, DeepKnowledge posits that core computational DNN units, termed Transfer Knowledge neurons, can generalise under domain shift. DeepKnowledge provides an objective confidence measurement on testing activities of DNN given data distribution shifts and uses this information to instrument a generalisation-informed test adequacy criterion to check the transfer knowledge capacity of a test set. Our empirical evaluation of several DNNs, across multiple datasets and state-of-the-art adversarial generation techniques demonstrates the usefulness and effectiveness of DeepKnowledge and its ability to support the engineering of more dependable DNNs. We report improvements of up to 10 percentage points over state-of-the-art coverage criteria for detecting adversarial attacks on several benchmarks, including MNIST, SVHN, and CIFAR.

For doubly-selective channels, delay-Doppler (DD) modulation, mostly known as orthogonal time frequency space (OTFS) modulation, enables simultaneous compensation of delay and Doppler shifts. However, OTFS modulated signal has high peak-to-average power ratio (PAPR) because of its precoding operation performed over the DD domain. In order to deal with this problem, we propose a single-carrier transmission with delay-Doppler domain equalization (SC-DDE). In this system, the discretized time-domain SC signal is converted to the DD domain by discrete Zak transform (DZT) at the receiver side, followed by delay-Doppler domain equalization (DDE). Since equalization is performed in the DD domain, the SC-DDE receiver should acquire the channel delay-Doppler response. To this end, we introduce an embedded pilot-aided channel estimation scheme designed for SC-DDE, which does not affect the peak power property of transmitted signals. Through computer simulation, distribution of PAPR and bit error rate (BER) performance of the proposed system are compared with those of the conventional OTFS and SC with frequency-domain equalization (SC-FDE). As a result, our proposed SC-DDE significantly outperforms SC-FDE in terms of BER at the expense of additional computational complexity at the receiver. Furthermore, SC-DDE shows much lower PAPR than OTFS even though they achieve comparable coded BER performance.

The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling is attractive and is well developed. But a fundamental requirement in almost all applications is stability of the fitted model. And this has not been addressed in the rank reduced case. Here, we develop, for the first time, a closed-form formula for an estimator of a rank reduced transition matrix which is guaranteed to be stable. We show that our estimator is consistent and asymptotically statistically efficient and illustrate it in comparative simulations.

Traditional machine learning methods heavily rely on the independent and identically distribution assumption, which imposes limitations when the test distribution deviates from the training distribution. To address this crucial issue, out-of-distribution (OOD) generalization, which aims to achieve satisfactory generalization performance when faced with unknown distribution shifts, has made a significant process. However, the OOD method for graph-structured data currently lacks clarity and remains relatively unexplored due to two primary challenges. Firstly, distribution shifts on graphs often occur simultaneously on node attributes and graph topology. Secondly, capturing invariant information amidst diverse distribution shifts proves to be a formidable challenge. To overcome these obstacles, in this paper, we introduce a novel framework, namely Graph Learning Invariant Domain genERation (GLIDER). The goal is to (1) diversify variations across domains by modeling the potential seen or unseen variations of attribute distribution and topological structure and (2) minimize the discrepancy of the variation in a representation space where the target is to predict semantic labels. Extensive experiment results indicate that our model outperforms baseline methods on node-level OOD generalization across domains in distribution shift on node features and topological structures simultaneously.

Exoskeleton locomotion must be robust while being adaptive to different users with and without payloads. To address these challenges, this work introduces a data-driven predictive control (DDPC) framework to synthesize walking gaits for lower-body exoskeletons, employing Hankel matrices and a state transition matrix for its data-driven model. The proposed approach leverages DDPC through a multi-layer architecture. At the top layer, DDPC serves as a planner employing Hankel matrices and a state transition matrix to generate a data-driven model that can learn and adapt to varying users and payloads. At the lower layer, our method incorporates inverse kinematics and passivity-based control to map the planned trajectory from DDPC into the full-order states of the lower-body exoskeleton. We validate the effectiveness of this approach through numerical simulations and hardware experiments conducted on the Atalante lower-body exoskeleton with different payloads. Moreover, we conducted a comparative analysis against the model predictive control (MPC) framework based on the reduced-order linear inverted pendulum (LIP) model. Through this comparison, the paper demonstrates that DDPC enables robust bipedal walking at various velocities while accounting for model uncertainties and unknown perturbations.

The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.