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We present a novel laboratory experiment, boiling stratified flow, as an analogy for atmospheric moist convection. A layer of diluted syrup is placed below freshwater in a beaker and heated from below. The vertical temperature profile in the experiment is analogous to the vapor mixing ratio in the atmosphere while the vertical profile of freshwater concentration in the experiment is analogous to the potential temperature profile in the atmosphere. Boiling starts when the bottom of the syrup layer reaches the boiling point, producing bubbles and vortex rings that stir the two-layer density interface and bring colder fresh water into the syrup layer. When the syrup layer at the beginning of the experiment is sufficiently thin and diluted, the vortex rings entrain more cold water than needed to remove superheating in the syrup layer, ending the boiling. When the syrup layer is deep and concentrated, the boiling is steady since the entrained colder water instantaneously removes the superheating in the bottom syrup layer. A theory is derived to predict the entrainment rate and the transition between the intermittent and steady boiling regimes, validated by experimental data. We suggest that these dynamics may share similarities with the mixing and lifecycle of cumulus convection.

In a hierarchical, dark matter-dominated Universe, stellar mass functions (SMFs), galaxy merger rates, star formation histories (SFHs), satellite abundances, and intracluster light, should all be intimately connected observables. However, the systematics affecting observations still prevent universal and uniform measurements of, for example, the SMF and the SFHs, inevitably preventing theoretical models to compare with multiple data sets robustly and simultaneously. We here present our holistic semi-empirical model DECODE (Discrete statistical sEmi-empiriCal mODEl) that converts via abundance matching dark matter merger trees into galaxy assembly histories, using different SMFs in input and predicting all other observables in output in a fully data-driven and self-consistent fashion with minimal assumptions. We find that: 1) weakly evolving or nearly constant SMFs below the knee ($M_\star \lesssim 10^{11} \, M_\odot$) are the best suited to generate star formation histories aligned with those inferred from MaNGA, SDSS, GAMA, and, more recently, JWST; 2) the evolution of satellites after infall only affects the satellite abundances and star formation histories of massive central galaxies but not their merger histories; 3) the resulting SFR-$M_\star$ relation is lower in normalization by a factor of $\sim 2$ with respect to observations, with a flattening at high masses more pronounced in the presence of mergers; 4) the latest data on intracluster light can be reproduced if mass loss from mergers is included in the models. Our findings are pivotal in acting as pathfinder to test the self-consistency of the high-quality data from, e.g., JWST and Euclid., Comment: 21 pages, 12 figures, MNRAS accepted

Recent advances in Out-of-Distribution (OOD) Detection is the driving force behind safe and reliable deployment of Convolutional Neural Networks (CNNs) in real world applications. However, existing studies focus on OOD detection through confidence score and deep generative model-based methods, without considering the impact of DNN structures, especially dense connectivity in architecture fabrications. In addition, existing outlier detection approaches exhibit high variance in generalization performance, lacking stability and confidence in evaluating and ranking different outlier detectors. In this work, we propose a novel paradigm, Dense Connectivity Search of Outlier Detector (DCSOD), that automatically explore the dense connectivity of CNN architectures on near-OOD detection task using Neural Architecture Search (NAS). We introduce a hierarchical search space containing versatile convolution operators and dense connectivity, allowing a flexible exploration of CNN architectures with diverse connectivity patterns. To improve the quality of evaluation on OOD detection during search, we propose evolving distillation based on our multi-view feature learning explanation. Evolving distillation stabilizes training for OOD detection evaluation, thus improves the quality of search. We thoroughly examine DCSOD on CIFAR benchmarks under OOD detection protocol. Experimental results show that DCSOD achieve remarkable performance over widely used architectures and previous NAS baselines. Notably, DCSOD achieves state-of-the-art (SOTA) performance on CIFAR benchmark, with AUROC improvement of $\sim$1.0%.

Detection of out-of-distribution (OOD) samples is crucial for safe real-world deployment of machine learning models. Recent advances in vision language foundation models have made them capable of detecting OOD samples without requiring in-distribution (ID) images. However, these zero-shot methods often underperform as they do not adequately consider ID class likelihoods in their detection confidence scoring. Hence, we introduce CLIPScope, a zero-shot OOD detection approach that normalizes the confidence score of a sample by class likelihoods, akin to a Bayesian posterior update. Furthermore, CLIPScope incorporates a novel strategy to mine OOD classes from a large lexical database. It selects class labels that are farthest and nearest to ID classes in terms of CLIP embedding distance to maximize coverage of OOD samples. We conduct extensive ablation studies and empirical evaluations, demonstrating state of the art performance of CLIPScope across various OOD detection benchmarks.

The ambiguous appearance, tiny scale, and fine-grained classes of objects in remote sensing imagery inevitably lead to the noisy annotations in category labels of detection dataset. However, the effects and treatments of the label noises are underexplored in modern oriented remote sensing object detectors. To address this issue, we propose a robust oriented remote sensing object detection method through dynamic loss decay (DLD) mechanism, inspired by the two phase ``early-learning'' and ``memorization'' learning dynamics of deep neural networks on clean and noisy samples. To be specific, we first observe the end point of early learning phase termed as EL, after which the models begin to memorize the false labels that significantly degrade the detection accuracy. Secondly, under the guidance of the training indicator, the losses of each sample are ranked in descending order, and we adaptively decay the losses of the top K largest ones (bad samples) in the following epochs. Because these large losses are of high confidence to be calculated with wrong labels. Experimental results show that the method achieves excellent noise resistance performance tested on multiple public datasets such as HRSC2016 and DOTA-v1.0/v2.0 with synthetic category label noise. Our solution also has won the 2st place in the "fine-grained object detection based on sub-meter remote sensing imagery" track with noisy labels of 2023 National Big Data and Computing Intelligence Challenge.

Localizing text in low-light environments is challenging due to visual degradations. Although a straightforward solution involves a two-stage pipeline with low-light image enhancement (LLE) as the initial step followed by detector, LLE is primarily designed for human vision instead of machine and can accumulate errors. In this work, we propose an efficient and effective single-stage approach for localizing text in dark that circumvents the need for LLE. We introduce a constrained learning module as an auxiliary mechanism during the training stage of the text detector. This module is designed to guide the text detector in preserving textual spatial features amidst feature map resizing, thus minimizing the loss of spatial information in texts under low-light visual degradations. Specifically, we incorporate spatial reconstruction and spatial semantic constraints within this module to ensure the text detector acquires essential positional and contextual range knowledge. Our approach enhances the original text detector's ability to identify text's local topological features using a dynamic snake feature pyramid network and adopts a bottom-up contour shaping strategy with a novel rectangular accumulation technique for accurate delineation of streamlined text features. In addition, we present a comprehensive low-light dataset for arbitrary-shaped text, encompassing diverse scenes and languages. Notably, our method achieves state-of-the-art results on this low-light dataset and exhibits comparable performance on standard normal light datasets. The code and dataset will be released.

In the one-class recommendation problem, it's required to make recommendations basing on users' implicit feedback, which is inferred from their action and inaction. Existing works obtain representations of users and items by encoding positive and negative interactions observed from training data. However, these efforts assume that all positive signals from implicit feedback reflect a fixed preference intensity, which is not realistic. Consequently, representations learned with these methods usually fail to capture informative entity features that reflect various preference intensities. In this paper, we propose a multi-tasking framework taking various preference intensities of each signal from implicit feedback into consideration. Representations of entities are required to satisfy the objective of each subtask simultaneously, making them more robust and generalizable. Furthermore, we incorporate attentive graph convolutional layers to explore high-order relationships in the user-item bipartite graph and dynamically capture the latent tendencies of users toward the items they interact with. Experimental results show that our method performs better than state-of-the-art methods by a large margin on three large-scale real-world benchmark datasets., Comment: RecSys 2020 (ACM Conference on Recommender Systems 2020)

Document representation is the core of many NLP tasks on machine understanding. A general representation learned in an unsupervised manner reserves generality and can be used for various applications. In practice, sentiment analysis (SA) has been a challenging task that is regarded to be deeply semantic-related and is often used to assess general representations. Existing methods on unsupervised document representation learning can be separated into two families: sequential ones, which explicitly take the ordering of words into consideration, and non-sequential ones, which do not explicitly do so. However, both of them suffer from their own weaknesses. In this paper, we propose a model that overcomes difficulties encountered by both families of methods. Experiments show that our model outperforms state-of-the-art methods on popular SA datasets and a fine-grained aspect-based SA by a large margin., Comment: International ACM SIGIR Conference 2019

We investigate the quantum phase transition in the alternating XY chain with the XZX+YZY type of three-spin interactions. We present the exact solution derived by means of the Jordan-Wigner transformation and study the average magnetization, spin correlations, and von Neumann entropy to establish the phase diagram. The phase diagram consists of the ferromagnetic phases, the paramagnetic phases, and the phase with weak magnetization (WM). By examining the nearest-neighbor transverse spin correlation, we probe that in the WM phase, the spins within a supercell generate a cluster with a small total spin, but between the nearest-neighbor supercells are distributed randomly. Especially for the dimerized limit case, the spins within a supercell tend to point to opposite directions of the transverse field. In addition, we also investigate the influence of the three-site interaction, and find that the WM phase is absent as the strength of the three-site interaction increases. Our findings shed light on the complex behavior of the alternating XY chain and provide valuable insights for future studies., Comment: 10 pages,12 figures

As the leading candidate of quantum error correction codes, surface code suffers from significant overhead, such as execution time. Reducing the circuit's execution time not only enhances its execution efficiency but also improves fidelity. However, finding the shortest execution time is NP-hard. In this work, we study the surface code mapping and scheduling problem. To reduce the execution time of a quantum circuit, we first introduce two novel metrics: Circuit Parallelism Degree and Chip Communication Capacity to quantitatively characterize quantum circuits and chips. Then, we propose a resource-adaptive mapping and scheduling method, named Ecmas, with customized initialization of chip resources for each circuit. Ecmas can dramatically reduce the execution time in both double defect and lattice surgery models. Furthermore, we provide an additional version Ecmas-ReSu for sufficient qubits, which is performance-guaranteed and more efficient. Extensive numerical tests on practical datasets show that Ecmas outperforms the state-of-the-art methods by reducing the execution time by 51.5% on average for double defect model. Ecmas can reach the optimal result in most benchmarks, reducing the execution time by up to 13.9% for lattice surgery model., Comment: 12 pages, Accepted to IEEE/ACM International Symposium on Code Generation and Optimization

Robot crowd navigation has been gaining increasing attention and popularity in various practical applications. In existing research, deep reinforcement learning has been applied to robot crowd navigation by training policies in an online mode. However, this inevitably leads to unsafe exploration, and consequently causes low sampling efficiency during pedestrian-robot interaction. To this end, we propose an offline reinforcement learning based robot crowd navigation algorithm by utilizing pre-collected crowd navigation experience. Specifically, this algorithm integrates a spatial-temporal state into implicit Q-Learning to avoid querying out-of-distribution robot actions of the pre-collected experience, while capturing spatial-temporal features from the offline pedestrian-robot interactions. Experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art methods by means of qualitative and quantitative analysis.

We study the quantum phase transitions (QPTs) in extended Kitaev chains with long-range ($1/r^{\alpha}$) hopping. Formally, there are two QPT points at $\mu=\mu_0(\alpha)$ and $\mu_\pi(\alpha)$ ($\mu$ is the chemical potential) which correspond to the summations of $\sum_{m=1}^{\infty}m^{-\alpha}$ and $\sum_{m=1}^{\infty}(-1)^{m-1}m^{-\alpha}$, respectively. When $\alpha\leq0$, both the series are divergent and it is usually believed that no QPTs exist. However, we find that there are two QPTs at $\mu=\mu_0(0)$ and $\mu_\pi(0)$ for $\alpha=0$ and one QPT at $\mu=\mu_\pi(\alpha)$ for $\alpha<0$. These QPTs are second order. The $\mu_0(0)$ and $\mu_\pi(\alpha\leq0)$ correspond to the summations of the divergent series obtained by the analytic continuation of the Riemann $\zeta$ function and Dirichlet $\eta$ function. Moreover, it is found that the quasiparticle energy spectra are discontinue functions of the wave vector $k$ and divide into two branches. This is quite different from that in the case of $\alpha>0$ and induces topological phases with the winding number $\omega:=\pm1/2$. At the same time, the von Neumann entropy are power law of the subchain length $L$ no matter in the gapped region or not. In addition, we also study the QPTs, topological properties, and von Neumann entropy of the systems with $\alpha>0$.

In recent years, increasing attention has been devoted to semi empirical, data-driven models to tackle some aspects of the complex and still largely debated topic of galaxy formation and evolution. We here present a new semi empirical model whose marking feature is simplicity: it relies on solely two assumptions, one initial condition and two free parameters. Galaxies are connected to evolving dark matter haloes through abundance matching between specific halo accretion rate (sHAR) and specific star formation rate (sSFR). Quenching is treated separately, in a fully empirical way, to marginalize over quiescent galaxies and test our assumption on the sSFR evolution without contaminations from passive objects. Our flexible and transparent model is able to reproduce the observed stellar mass functions up to $z\sim 5$, giving support to our hypothesis of a monotonic relation between sHAR and sSFR. We then exploit the model to test a hypothesis on morphological evolution of galaxies. We attempt to explain the bulge/disk bimodality in terms of the two halo accretion modes: fast and slow accretion. Specifically, we speculate that bulge/spheroidal components might form during the early phase of fast halo growth, while disks form during the later phase of slow accretion. We find excellent agreement with both the observational bulge and elliptical mass functions., Comment: 22 pages, 13 Figures

Quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology. In this work, generalizing the ideas of classical and quantum autoencoder, we introduce the model of Quantum Circuit AutoEncoder (QCAE) to compress and encode information within quantum circuits. We provide a comprehensive protocol for QCAE and design a variational quantum algorithm, varQCAE, for its implementation. We theoretically analyze this model by deriving conditions for lossless compression and establishing both upper and lower bounds on its recovery fidelity. Finally, we apply varQCAE to three practical tasks and numerical results show that it can effectively (1) compress the information within quantum circuits, (2) detect anomalies in quantum circuits, and (3) mitigate the depolarizing noise in quantum devices. This suggests that our algorithm is potentially applicable to other information processing tasks for quantum circuits., Comment: 13 pages, 7 figures

This paper proposes a data-efficient detection method for deep neural networks against backdoor attacks under a black-box scenario. The proposed approach is motivated by the intuition that features corresponding to triggers have a higher influence in determining the backdoored network output than any other benign features. To quantitatively measure the effects of triggers and benign features on determining the backdoored network output, we introduce five metrics. To calculate the five-metric values for a given input, we first generate several synthetic samples by injecting the input's partial contents into clean validation samples. Then, the five metrics are computed by using the output labels of the corresponding synthetic samples. One contribution of this work is the use of a tiny clean validation dataset. Having the computed five metrics, five novelty detectors are trained from the validation dataset. A meta novelty detector fuses the output of the five trained novelty detectors to generate a meta confidence score. During online testing, our method determines if online samples are poisoned or not via assessing their meta confidence scores output by the meta novelty detector. We show the efficacy of our methodology through a broad range of backdoor attacks, including ablation studies and comparison to existing approaches. Our methodology is promising since the proposed five metrics quantify the inherent differences between clean and poisoned samples. Additionally, our detection method can be incrementally improved by appending more metrics that may be proposed to address future advanced attacks., Comment: Published in the IEEE Transactions on Information Forensics and Security

Discriminating the traversability of terrains is a crucial task for autonomous driving in off-road environments. However, it is challenging due to the diverse, ambiguous, and platform-specific nature of off-road traversability. In this paper, we propose a novel self-supervised terrain traversability learning framework, utilizing a contrastive label disambiguation mechanism. Firstly, weakly labeled training samples with pseudo labels are automatically generated by projecting actual driving experiences onto the terrain models constructed in real time. Subsequently, a prototype-based contrastive representation learning method is designed to learn distinguishable embeddings, facilitating the self-supervised updating of those pseudo labels. As the iterative interaction between representation learning and pseudo label updating, the ambiguities in those pseudo labels are gradually eliminated, enabling the learning of platform-specific and task-specific traversability without any human-provided annotations. Experimental results on the RELLIS-3D dataset and our Gobi Desert driving dataset demonstrate the effectiveness of the proposed method., Comment: 9 pages, 11 figures

For autonomous driving, traversability analysis is one of the most basic and essential tasks. In this paper, we propose a novel LiDAR-based terrain modeling approach, which could output stable, complete and accurate terrain models and traversability analysis results. As terrain is an inherent property of the environment that does not change with different view angles, our approach adopts a multi-frame information fusion strategy for terrain modeling. Specifically, a normal distributions transform mapping approach is adopted to accurately model the terrain by fusing information from consecutive LiDAR frames. Then the spatial-temporal Bayesian generalized kernel inference and bilateral filtering are utilized to promote the stability and completeness of the results while simultaneously retaining the sharp terrain edges. Based on the terrain modeling results, the traversability of each region is obtained by performing geometric connectivity analysis between neighboring terrain regions. Experimental results show that the proposed method could run in real-time and outperforms state-of-the-art approaches., Comment: accepted to Journal of Field Robotics

The social robot navigation is an open and challenging problem. In existing work, separate modules are used to capture spatial and temporal features, respectively. However, such methods lead to extra difficulties in improving the utilization of spatio-temporal features and reducing the conservative nature of navigation policy. In light of this, we present a spatio-temporal transformer-based policy optimization algorithm to enhance the utilization of spatio-temporal features, thereby facilitating the capture of human-robot interactions. Specifically, this paper introduces a gated embedding mechanism that effectively aligns the spatial and temporal representations by integrating both modalities at the feature level. Then Transformer is leveraged to encode the spatio-temporal semantic information, with hope of finding the optimal navigation policy. Finally, a combination of spatio-temporal Transformer and self-adjusting policy entropy significantly reduces the conservatism of navigation policies. Experimental results demonstrate the effectiveness of the proposed framework, where our method shows superior performance., Comment: The duplication rate is too high and the manuscript needs to be withdrawn

Embedding based retrieval has seen its usage in a variety of search applications like e-commerce, social networking search etc. While the approach has demonstrated its efficacy in tasks like semantic matching and contextual search, it is plagued by the problem of uncontrollable relevance. In this paper, we conduct an analysis of embedding-based retrieval launched in early 2021 on our social network search engine, and define two main categories of failures introduced by it, integrity and junkiness. The former refers to issues such as hate speech and offensive content that can severely harm user experience, while the latter includes irrelevant results like fuzzy text matching or language mismatches. Efficient methods during model inference are further proposed to resolve the issue, including indexing treatments and targeted user cohort treatments, etc. Though being simple, we show the methods have good offline NDCG and online A/B tests metrics gain in practice. We analyze the reasons for the improvements, pointing out that our methods are only preliminary attempts to this important but challenging problem. We put forward potential future directions to explore.

We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter $\epsilon>0$ that controls the magnitude of transaction costs. When $\epsilon$ is small, we can implement an NN algorithm based on the expansion of the solution in powers of $\epsilon$. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions without requiring any knowledge of the distribution models. The computation of our bound is time-efficient and memory-efficient and only requires finite samples. The proposed bound shows its value in one-class classification and domain shift analysis. Specifically, in one-class classification, we build a novel one-class classifier by converting the bound into a confidence score function. Unlike most one-class classifiers, the training process is not needed for our classifier. Additionally, the experimental results show that our classifier can be accurate with only a small number of in-class samples and outperform many state-of-the-art methods on various datasets in different one-class classification scenarios. In domain shift analysis, we propose a theorem based on our bound. The theorem is useful in detecting the existence of domain shift and inferring data information. The detection and inference processes are both computation-efficient and memory-efficient. Our work shows significant promise toward broadening the applications of overlap-based metrics.

We propose a framework in which multiple entities collaborate to build a machine learning model while preserving privacy of their data. The approach utilizes feature embeddings from shared/per-entity feature extractors transforming data into a feature space for cooperation between entities. We propose two specific methods and compare them with a baseline method. In Shared Feature Extractor (SFE) Learning, the entities use a shared feature extractor to compute feature embeddings of samples. In Locally Trained Feature Extractor (LTFE) Learning, each entity uses a separate feature extractor and models are trained using concatenated features from all entities. As a baseline, in Cooperatively Trained Feature Extractor (CTFE) Learning, the entities train models by sharing raw data. Secure multi-party algorithms are utilized to train models without revealing data or features in plain text. We investigate the trade-offs among SFE, LTFE, and CTFE in regard to performance, privacy leakage (using an off-the-shelf membership inference attack), and computational cost. LTFE provides the most privacy, followed by SFE, and then CTFE. Computational cost is lowest for SFE and the relative speed of CTFE and LTFE depends on network architecture. CTFE and LTFE provide the best accuracy. We use MNIST, a synthetic dataset, and a credit card fraud detection dataset for evaluations.

(Abridged) We study the galaxy mass-size relation in CARLA spectroscopically confirmed clusters at $1.410.5$ are systematically $\gtrsim 0.2-0.3~{\rm dex}$ larger than field ETGs. The passive ETG average size evolution is slower at $1

Mazur's principle gives a criterion under which an irreducible mod $\ell$ Galois representation arising from a modular form of level $Np$ (with $p$ prime to $N$) can also arise from a modular form of level $N.$ We prove an analogous result showing that a mod $\ell$ Galois representation arising from a stable cuspidal automorphic representation of the unitary similitude group $G=\mathrm{GU}(1,2)$ which is Steinberg at an inert prime $p$ can also arise from an automorphic representation of $G$ that is unramified at $p$., Comment: 44 pages; minor corrections. arXiv admin note: text overlap with arXiv:1912.11942 by other authors

Modeling the evolution of user preference is essential in recommender systems. Recently, dynamic graph-based methods have been studied and achieved SOTA for recommendation, majority of which focus on user's stable long-term preference. However, in real-world scenario, user's short-term preference evolves over time dynamically. Although there exists sequential methods that attempt to capture it, how to model the evolution of short-term preference with dynamic graph-based methods has not been well-addressed yet. In particular: 1) existing methods do not explicitly encode and capture the evolution of short-term preference as sequential methods do; 2) simply using last few interactions is not enough for modeling the changing trend. In this paper, we propose Long Short-Term Preference Modeling for Continuous-Time Sequential Recommendation (LSTSR) to capture the evolution of short-term preference under dynamic graph. Specifically, we explicitly encode short-term preference and optimize it via memory mechanism, which has three key operations: Message, Aggregate and Update. Our memory mechanism can not only store one-hop information, but also trigger with new interactions online. Extensive experiments conducted on five public datasets show that LSTSR consistently outperforms many state-of-the-art recommendation methods across various lines., Comment: 9 pages, 4 figures

The relative roles of mergers and star formation in regulating galaxy growth are still a matter of intense debate. We here present our DECODE, a new Discrete statistical sEmi-empiriCal mODEl specifically designed to predict rapidly and efficiently, in a full cosmological context, galaxy assembly and merger histories for any given input stellar mass-halo mass (SMHM) relation. DECODE generates object-by-object dark matter merger trees (hence discrete) from accurate subhalo mass and infall redshift probability functions (hence statistical) for all subhaloes, including those residing within other subhaloes, with virtually no resolution limits on mass or volume. Merger trees are then converted into galaxy assembly histories via an input, redshift dependent SMHM relation, which is highly sensitive to the significant systematics in the galaxy stellar mass function and on its evolution with cosmic time. DECODE can accurately reproduce the predicted mean galaxy merger rates and assembly histories of hydrodynamic simulations and semi-analytic models, when adopting in input their SMHM relations. In the present work we use DECODE to prove that only SMHM relations implied by stellar mass functions characterized by large abundances of massive galaxies and significant redshift evolution, at least at $M_\star \gtrsim 10^{11} \, M_\odot$, can simultaneously reproduce the local abundances of satellite galaxies, the galaxy (major merger) pairs since $z \sim 3$, and the growth of Brightest Cluster Galaxies. The same models can also reproduce the local fraction of elliptical galaxies, on the assumption that these are strictly formed by major mergers, but not the full bulge-to-disc ratio distributions, which require additional processes., Comment: MNRAS, accepted, 29 pages, 25 figures

This paper considers a formulation of the robust adaptive beamforming (RAB) problem based on worst-case signal-to-interference-plus-noise ratio (SINR) maximization with a nonconvex uncertainty set for the steering vectors. The uncertainty set consists of a similarity constraint and a (nonconvex) double-sided ball constraint. The worst-case SINR maximization problem is turned into a quadratic matrix inequality (QMI) problem using the strong duality of semidefinite programming. Then a linear matrix inequality (LMI) relaxation for the QMI problem is proposed, with an additional valid linear constraint. Necessary and sufficient conditions for the tightened LMI relaxation problem to have a rank-one solution are established. When the tightened LMI relaxation problem still has a high-rank solution, the LMI relaxation problem is further restricted to become a bilinear matrix inequality (BLMI) problem. We then propose an iterative algorithm to solve the BLMI problem that finds an optimal/suboptimal solution for the original RAB problem by solving the BLMI formulations. To validate our results, simulation examples are presented to demonstrate the improved array output SINR of the proposed robust beamformer.