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We derive the Alternating-Direction Implicit (ADI) method based on a commuting operator split and apply the results to the continuous time algebraic Lyapunov equation with low-rank constant term and approximate solution. Previously, it has been mandatory to start the low-rank ADI (LR-ADI) with an all-zero initial value. Our approach retains the known efficient iteration schemes of low-rank increments and residual to arbitrary low-rank initial values for the LR-ADI method. We further generalize some of the known properties of the LR-ADI for Lyapunov equations to larger classes of algorithms or problems. We investigate the performance of arbitrary initial values using two outer iterations in which LR-ADI is typically called. First, we solve an algebraic Riccati equation with the Newton method. Second, we solve a differential Riccati equation with a first-order Rosenbrock method. Numerical experiments confirm that the proposed new initial value of the alternating-directions implicit (ADI) can lead to a significant reduction in the total number of ADI steps, while also showing a 17% and 8x speed-up over the zero initial value for the two equation types, respectively.

We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their promise variant. In this way, we establish a linear-level (and, thus, optimal) lower bound against the local-consistency algorithm applied to the class of aperiodic promise CSPs. The proof is based on a combination of the probabilistic method for random Erd\H{o}s-R\'enyi hypergraphs and a structural result on the number of fibers (i.e., long chains of hyperedges) in sparse hypergraphs of large girth. As a corollary, we completely classify the power of local consistency for the approximate graph homomorphism problem by establishing that, in the nontrivial cases, the problem has linear width.

Prediction of climate tipping is challenging due to the lack of recent observation of actual climate tipping. Despite many previous efforts to accurately predict the existence and timing of climate tippings under specific climate scenarios, the predictability of climate tipping, the necessary conditions under which climate tipping can be predicted, has yet to be explored. In this study, the predictability of climate tipping is analyzed by Observation System Simulation Experiment (OSSE), in which the value of observation for prediction is assessed through the idealized experiment of data assimilation, using a simplified dynamic vegetation model and an Atlantic Meridional Overturning Circulation (AMOC) two box model. We find that the ratio of internal variability to observation error, or signal-to-noise ratio, should be large enough to accurately predict climate tippings. When observation can accurately resolve the internal variability of the system, assimilating these observations into process-based models can effectively improve the skill of predicting climate tippings. Our quantitative estimation of required observation accuracy to predict climate tipping implies that the existing observation network is not always sufficient to accurately project climate tipping.

Weakly Supervised Semantic Segmentation (WSSS) employs weak supervision, such as image-level labels, to train the segmentation model. Despite the impressive achievement in recent WSSS methods, we identify that introducing weak labels with high mean Intersection of Union (mIoU) does not guarantee high segmentation performance. Existing studies have emphasized the importance of prioritizing precision and reducing noise to improve overall performance. In the same vein, we propose ORANDNet, an advanced ensemble approach tailored for WSSS. ORANDNet combines Class Activation Maps (CAMs) from two different classifiers to increase the precision of pseudo-masks (PMs). To further mitigate small noise in the PMs, we incorporate curriculum learning. This involves training the segmentation model initially with pairs of smaller-sized images and corresponding PMs, gradually transitioning to the original-sized pairs. By combining the original CAMs of ResNet-50 and ViT, we significantly improve the segmentation performance over the single-best model and the naive ensemble model, respectively. We further extend our ensemble method to CAMs from AMN (ResNet-like) and MCTformer (ViT-like) models, achieving performance benefits in advanced WSSS models. It highlights the potential of our ORANDNet as a final add-on module for WSSS models.

Multimodal intent recognition poses significant challenges, requiring the incorporation of non-verbal modalities from real-world contexts to enhance the comprehension of human intentions. Existing benchmark datasets are limited in scale and suffer from difficulties in handling out-of-scope samples that arise in multi-turn conversational interactions. We introduce MIntRec2.0, a large-scale benchmark dataset for multimodal intent recognition in multi-party conversations. It contains 1,245 dialogues with 15,040 samples, each annotated within a new intent taxonomy of 30 fine-grained classes. Besides 9,304 in-scope samples, it also includes 5,736 out-of-scope samples appearing in multi-turn contexts, which naturally occur in real-world scenarios. Furthermore, we provide comprehensive information on the speakers in each utterance, enriching its utility for multi-party conversational research. We establish a general framework supporting the organization of single-turn and multi-turn dialogue data, modality feature extraction, multimodal fusion, as well as in-scope classification and out-of-scope detection. Evaluation benchmarks are built using classic multimodal fusion methods, ChatGPT, and human evaluators. While existing methods incorporating nonverbal information yield improvements, effectively leveraging context information and detecting out-of-scope samples remains a substantial challenge. Notably, large language models exhibit a significant performance gap compared to humans, highlighting the limitations of machine learning methods in the cognitive intent understanding task. We believe that MIntRec2.0 will serve as a valuable resource, providing a pioneering foundation for research in human-machine conversational interactions, and significantly facilitating related applications. The full dataset and codes are available at //github.com/thuiar/MIntRec2.0.

In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of joint occurrence of extremes in higher dimensions. In this paper, we propose a notion of mutual asymptotic independence to capture the behavior of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence. Furthermore, we define $k$-wise asymptotic independence which lies in between pairwise and mutual asymptotic independence. The concepts are compared using examples of Archimedean, Gaussian and Marshall-Olkin copulas among others. Notably, for the popular Gaussian copula, we provide explicit conditions on the correlation matrix for mutual asymptotic independence to hold; moreover, we are able to compute exact tail orders for various tail events.

This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes feasible the inference on this computationally efficient model, especially for economic and financial time series. An efficient block coordinate descent algorithm is further introduced to search for estimates, and a Bayesian information criterion with selection consistency is suggested for model selection. Simulation experiments are conducted to illustrate their finite sample performance, and a real application on six macroeconomic indicators illustrates the usefulness of the proposed methodology.

A non-linear complex system governed by multi-spatial and multi-temporal physics scales cannot be fully understood with a single diagnostic, as each provides only a partial view and much information is lost during data extraction. Combining multiple diagnostics also results in imperfect projections of the system's physics. By identifying hidden inter-correlations between diagnostics, we can leverage mutual support to fill in these gaps, but uncovering these inter-correlations analytically is too complex. We introduce a groundbreaking machine learning methodology to address this issue. Our multimodal approach generates super resolution data encompassing multiple physics phenomena, capturing detailed structural evolution and responses to perturbations previously unobservable. This methodology addresses a critical problem in fusion plasmas: the Edge Localized Mode (ELM), a plasma instability that can severely damage reactor walls. One method to stabilize ELM is using resonant magnetic perturbation to trigger magnetic islands. However, low spatial and temporal resolution of measurements limits the analysis of these magnetic islands due to their small size, rapid dynamics, and complex interactions within the plasma. With super-resolution diagnostics, we can experimentally verify theoretical models of magnetic islands for the first time, providing unprecedented insights into their role in ELM stabilization. This advancement aids in developing effective ELM suppression strategies for future fusion reactors like ITER and has broader applications, potentially revolutionizing diagnostics in fields such as astronomy, astrophysics, and medical imaging.

Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.

Assessment of the performance of a player in any sport is very much needed to determine the ranking of players and make a solid team with the best players. Besides these, fans, journalists, sports persons, and sports councils often analyse the performances of current and retired players to identify the best players of all time. Here, we study the performance of all-time top batters in one-day cricket using physics-based statistical methods. The batters are selected in this study who possess either higher total runs or a high number of centuries. It is found that the total runs increases linearly with the innings number at the later stage of the batter carrier, and the runs rate estimated from the linear regression analysis also increases linearly with the average runs. The probability of non-scoring innings is found to be a negligibly small number (i.e., $\leq 0.1$ ) for each batter. Furthermore, based on innings-wise runs, we have computed the six-dimensional probability distribution vector for each player. Two components of the probability distribution vector vary linearly with average runs. The component representing the probability of scoring runs less than 50 linearly decreases with the average runs. In contrast, the probability of scoring runs greater than or equal to 100 and less than 150 linearly increases with the average runs. We have also estimated the entropy to assess the diversity of a player. Interestingly, the entropy varies linearly with the average runs, giving rise to two clusters corresponding to the old and recent players. Furthermore, the angle between two probability vectors is calculated for each pair of players to measure the similarities among the players. It is found that some of the players are almost identical to each other.