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Dual quaternions and dual quaternion matrices have found widespread applications in robotic research, with their spectral theory been extensively studied in recent years. This paper delves into the realm of eigenvalue computation and related problems specific to dual quaternion Hermitian matrices. We establish the connection between dual quaternion matrices and their dual complex adjoint matrices, concerning eigenvalue problems and matrix rank-k approximations. By integrating the dual complex adjoint matrix, we refine the power method for eigenvalue computation for dual quaternion Hermitian matrices, achieving greater numerical efficiency. Furthermore, leveraging the eigen-decomposition of dual complex adjoint matrices, we introduce a novel approach for calculating all eigenpairs of dual quaternion Hermitian matrices. This method surpasses the power method in terms of accuracy and speed and addresses its limitations, as exemplified by its application to the eigenvalue computation of Laplacian matrices, where our algorithm demonstrates significant advantages. Additionally, we apply the improved power method and optimal rank-k approximations to pose graph optimization problem, enhancing efficiency and success rates, especially under low observation conditions., Comment: arXiv admin note: text overlap with arXiv:2407.12635

Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex adjoint matrices for dual quaternion matrices. We delve into exploring the properties of this matrix, utilizing it to study eigenvalues of dual quaternion matrices and defining the concept of standard right eigenvalues. Notably, we leverage the properties of the dual complex adjoint matrix to devise a direct solution to the Hand-Eye calibration problem. Additionally, we apply this matrix to solve dual quaternion linear equations systems, thereby advancing the Rayleigh quotient iteration method for computing eigenvalues of dual quaternion Hermitian matrices, enhancing its computational efficiency. Numerical experiments have validated the correctness of our proposed method in solving the Hand-Eye calibration problem and demonstrated the effectiveness in improving the Rayleigh quotient iteration method, underscoring the promising potential of dual complex adjoint matrices in tackling dual quaternion-related challenges.

Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian matrices and establish its convergence. The improved version with elimination strategy is proposed to reduce the computational time. Especially, we present a novel three-step Jacobi method to compute such eigenvalues which have identical standard parts but different dual parts. We prove that the proposed three-step Jacobi method terminates after at most finite iterations and can provide $\epsilon$-approximation of eigenvalue. To the best of our knowledge, both the power method and the Rayleigh quotient iteration method can not handle such eigenvalue problem in this scenario. Numerical experiments illustrate the proposed Jacobi-type algorithms are effective and stable, and also outperform the power method and the Rayleigh quotient iteration method.

We present the results of our observations using the Giant Meterwave Radio Telescope (GMRT) to investigate the radio continuum and OH line emission of 10 OHM candidates from the Arecibo Legacy Fast ALFA (ALFALFA) survey. Among these candidates, we have identified two sources, AGC115713 and AGC249507, which display compact OH line emission that are spatially associated with radio continuum emission. These characteristics align with the typical properties of OHM galaxies. Furthermore, the infrared (IR) properties of these two galaxies are consistent with those of known OHM galaxies. %Importantly, these two sources have been independently confirmed by alternative methods. Of the two sources, AGC 249507 has been confirmed through optical redshift, whereas AGC 115713 meets a WISE color selection criterion in the literature, providing additional support for this source being an OHM galaxy rather than a nearby \HI galaxy. On the contrary, no significant spectral line emission were detected in the remaining eight OHM candidates using our full GMRT dataset. This suggests that the spectral line emission initially detected by the ALFALFA survey may have been significantly resolved in our high-resolution observations. Additionally, the absence of radio continuum emission in 6 candidates also distinguishes them from known OHM galaxies documented in the literature. These findings support the notion that OHM emission may be distributed on a subarcsecond scale, underscoring the utility of arcsecond-scale observations in confirming OHM candidates, particularly those lacking optical redshift data., Comment: Accepted by A&A

Very recently, Qi and Cui extended the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts and proved that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz method was also extended to find Perron eigenpair. Qi and Cui proposed two conjectures. One is the k-order power of a dual number matrix tends to zero if and only if the spectral radius of its standard part less than one, and another is the linear convergence of the Collatz method. In this paper, we confirm these conjectures and provide theoretical proof. The main contribution is to show that the Collatz method R-linearly converges with an explicit rate., Comment: arXiv admin note: text overlap with arXiv:2306.16140 by other authors

The Event Horizon Telescope (EHT) observed in 2017 the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz ($\lambda$=1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT datasets. The high observing frequency means that pulsars - which typically exhibit steep emission spectra - are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic Center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most-sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the Fast-Folding-Algorithm and single pulse search targeting both pulsars and burst-like transient emission; using the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction ($\lesssim$2.2%) of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region., Comment: 33 pages, 7 figures, 6 Tables. Accepted for publication in ApJ

Sequential recommendation models, models that learn from chronological user-item interactions, outperform traditional recommendation models in many settings. Despite the success of sequential recommendation models, their robustness has recently come into question. Two properties unique to the nature of sequential recommendation models may impair their robustness - the cascade effects induced during training and the model's tendency to rely too heavily on temporal information. To address these vulnerabilities, we propose Cascade-guided Adversarial training, a new adversarial training procedure that is specifically designed for sequential recommendation models. Our approach harnesses the intrinsic cascade effects present in sequential modeling to produce strategic adversarial perturbations to item embeddings during training. Experiments on training state-of-the-art sequential models on four public datasets from different domains show that our training approach produces superior model ranking accuracy and superior model robustness to real item replacement perturbations when compared to both standard model training and generic adversarial training., Comment: Accepted to present at SIAM International Conference on Data Mining (SDM24)

Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I, Q, U , and V respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties., Comment: Accepted for publication in ApJ

We present new upgraded Giant Metrewave Radio Telescope (uGMRT) HI 21-cm observations of the ultra-luminous infrared galaxy IRAS 10565+2448, previously reported to show blueshifted, broad, and shallow HI absorption indicating an outflow. Our higher spatial resolution observations have localised this blueshifted outflow, which is $\sim$ 1.36 kpc southwest of the radio centre and has a blueshifted velocity of $\sim 148\,\rm km\,s^{-1}$ and a full width at half maximum (FWHM) of $\sim 581\,\rm km\,s^{-1}$. The spatial extent and kinematic properties of the HI outflow are consistent with the previously detected cold molecular outflows in IRAS 10565+2448, suggesting that they likely have the same driving mechanism and are tracing the same outflow. By combining the multi-phase gas observations, we estimate a total outflowing mass rate of at least $140\, \rm M_\odot \,yr^{-1}$ and a total energy loss rate of at least $8.9\times10^{42}\,\rm erg\,s^{-1}$, where the contribution from the ionised outflow is negligible, emphasising the importance of including both cold neutral and molecular gas when quantifying the impact of outflows. We present evidence of the presence of a radio jet and argue that this may play a role in driving the observed outflows. The modest radio luminosity $L_{\rm1.4GHz}$ $\sim1.3\times10^{23}\,{\rm W\,Hz^{-1}}$ of the jet in IRAS 10565+2448 implies that the jet contribution to driving outflows should not be ignored in low radio luminosity AGN., Comment: 12 pages, 9 figures, accepted for publication in MNRAS

We present the study of arcsecond scale radio continuum and OH line emission of a sample of known OH megamaser galaxies with $z \geq$ 0.15 using archival Very Large Array (VLA) data. And also the results of our pilot Five hundred meter aperture spherical radio telescope (FAST) observations of 12 of these OHM galaxies. The arcsecond-scale resolution images show that the OH emission is distributed in one compact structure and spatially associated with radio continuum emission. Furthermore, nearly all the fitted components are likely smaller than the beam size ($\sim$ 1.4"), which indicates that the broad OH line profiles of these sources originated from one masing region or that more components are distributed in sub-arcsec scales. The radio parameters, including brightness temperature, spectral index, and q-index, show no significant differences with the low-redshift OHM galaxies, which have significantly lower OH line luminosities. Because these parameters are indicators of the central power sources (AGN, starburst, or both), our results indicate that the presence of radio AGN in the nuclei may not be essential for the formation of OH emission. Over 1/3 of OHMs in this sample (6/17) show possible variable features likely caused by interstellar scintillation due to small angular sizes. We might underestimate this value because these sources are associated with this sample's highest OH line flux densities. Those with low OH line flux densities might need higher sensitivity observations to study the variabilities. These results support the compact nature of OH maser emission and a starburst origin for the OHMs in our selected sample., Comment: 25 pages,7 figures,accepted by A&A

The $\gamma$-ray narrow-line Seyfert 1 (NLS1) galaxies can be considered to be the third class of $\gamma$-ray active galactic nuclei possessing relativistic jets. In this paper, we present multi-band high resolution Very Long Baseline Array (VLBA) images of the $\gamma$-ray NLS1, SDSS J211852.96$-$073227.5 (J2118$-$0732, $z=0.26$). We find a core-jet radio morphology and significant flux density variations in the radio core. The high brightness temperature estimated from VLBA images and core variability demonstrate that it exhibits substantial relativistic beaming effects. From considering radio emission in several bands, we find that the source has an inverted spectrum above 1 GHz but a steep spectrum at low frequencies from 74 MHz to 1 GHz; these may arise from the present activity and the old diffuse/extended emission, respectively. The core-jet morphology, significant flux density variations, and beaming effect make J2118$-$0732 resemble a blazar. Considering the low mass of its central black hole and ongoing merger environment, J2118$-$0732 may represent a low-mass, low-power counterpart of blazars, and may finally evolve to a blazar., Comment: 12 pages, 6 figures. Published in ApJ

We report measurements of the gravitationally lensed secondary image -- the first in an infinite series of so-called "photon rings" -- around the supermassive black hole M87* via simultaneous modeling and imaging of the 2017 Event Horizon Telescope (EHT) observations. The inferred ring size remains constant across the seven days of the 2017 EHT observing campaign and is consistent with theoretical expectations, providing clear evidence that such measurements probe spacetime and a striking confirmation of the models underlying the first set of EHT results. The residual diffuse emission evolves on timescales comparable to one week. We are able to detect with high significance a southwestern extension consistent with that expected from the base of a jet that is rapidly rotating in the clockwise direction. This result adds further support to the identification of the jet in M87* with a black hole spin-driven outflow, launched via the Blandford-Znajek process. We present three revised estimates for the mass of M87* based on identifying the modeled thin ring component with the bright ringlike features seen in simulated images, one of which is only weakly sensitive to the astrophysics of the emission region. All three estimates agree with each other and previously reported values. Our strongest mass constraint combines information from both the ring and the diffuse emission region, which together imply a mass-to-distance ratio of $4.20^{+0.12}_{-0.06}~\mu{\rm as}$ and a corresponding black hole mass of $(7.13\pm0.39)\times10^9M_\odot$, where the error on the latter is now dominated by the systematic uncertainty arising from the uncertain distance to M87*.

To make Sequential Recommendation (SR) successful, recent works focus on designing effective sequential encoders, fusing side information, and mining extra positive self-supervision signals. The strategy of sampling negative items at each time step is less explored. Due to the dynamics of users' interests and model updates during training, considering randomly sampled items from a user's non-interacted item set as negatives can be uninformative. As a result, the model will inaccurately learn user preferences toward items. Identifying informative negatives is challenging because informative negative items are tied with both dynamically changed interests and model parameters (and sampling process should also be efficient). To this end, we propose to Generate Negative Samples (items) for SR (GenNi). A negative item is sampled at each time step based on the current SR model's learned user preferences toward items. An efficient implementation is proposed to further accelerate the generation process, making it scalable to large-scale recommendation tasks. Extensive experiments on four public datasets verify the importance of providing high-quality negative samples for SR and demonstrate the effectiveness and efficiency of GenNi.

Sequential recommendation is often considered as a generative task, i.e., training a sequential encoder to generate the next item of a user's interests based on her historical interacted items. Despite their prevalence, these methods usually require training with more meaningful samples to be effective, which otherwise will lead to a poorly trained model. In this work, we propose to train the sequential recommenders as discriminators rather than generators. Instead of predicting the next item, our method trains a discriminator to distinguish if a sampled item is a 'real' target item or not. A generator, as an auxiliary model, is trained jointly with the discriminator to sample plausible alternative next items and will be thrown out after training. The trained discriminator is considered as the final SR model and denoted as \modelname. Experiments conducted on four datasets demonstrate the effectiveness and efficiency of the proposed approach., Comment: Accepted to SIGIR 2022

The sequential recommendation aims at predicting the next items in user behaviors, which can be solved by characterizing item relationships in sequences. Due to the data sparsity and noise issues in sequences, a new self-supervised learning (SSL) paradigm is proposed to improve the performance, which employs contrastive learning between positive and negative views of sequences. However, existing methods all construct views by adopting augmentation from data perspectives, while we argue that 1) optimal data augmentation methods are hard to devise, 2) data augmentation methods destroy sequential correlations, and 3) data augmentation fails to incorporate comprehensive self-supervised signals. Therefore, we investigate the possibility of model augmentation to construct view pairs. We propose three levels of model augmentation methods: neuron masking, layer dropping, and encoder complementing. This work opens up a novel direction in constructing views for contrastive SSL. Experiments verify the efficacy of model augmentation for the SSL in the sequential recommendation. Code is available\footnote{\url{https://github.com/salesforce/SRMA}}., Comment: Preprint. Still under reivew

Based on the two epochs EVN archive data from OH line observations of IIZw 096, we confirm that the high-resolution OH emission in this source mainly comes from two spots (OH1 and OH2) of comp D1 of this merging system. We found no significant variations in the OH line emission. The OH 1665 MHz line emission is detected at about 6 $\sigma$ level in the OH1 region by combining two epoch EVN observations. We found that the comp D1 shows the brightest CO, HCO+ line emission, as well as multi-band radio continuum emission. The environment around D1 shows no clear velocity structure associated with circular motions, making it different from most other OHMs in the literature, which might have been caused by an effect during the merger stage. Meanwhile, we found that the CO emission shows three velocity structures around D1, including the central broad FWHM region, the double peak region where the CO line profile shows two separated peaks, and the region of the high-velocity clouds where the CO line peaks at a high velocity ($\sim$ 11000 \kms). \HI in absorption also show high-velocity clouds around the D1 region, which might be due to inflows caused by the merging of two or more galaxy components. Based on the high-resolution K-band VLA and L-band VLBA observations of the radio continuum emission, we derived the brightness temperature in the range $10^{5}$ K to $10^{6}$ K, which is consistent with other starburst dominant OHM sources in the literature. The multi-band VLA observations show that the radio continuum emission of comp D might also have contributions from free-free emission, besides synchrotron emission. As a concenquence, these results support a starburst origin for the OHMs, without the presence of an AGN., Comment: 11 pages,9 figures, Accepted by A&A

Users' interactions with items are driven by various intents (e.g., preparing for holiday gifts, shopping for fishing equipment, etc.).However, users' underlying intents are often unobserved/latent, making it challenging to leverage such latent intents forSequentialrecommendation(SR). To investigate the benefits of latent intents and leverage them effectively for recommendation, we proposeIntentContrastiveLearning(ICL), a general learning paradigm that leverages a latent intent variable into SR. The core idea is to learn users' intent distribution functions from unlabeled user behavior sequences and optimize SR models with contrastive self-supervised learning (SSL) by considering the learned intents to improve recommendation. Specifically, we introduce a latent variable to represent users' intents and learn the distribution function of the latent variable via clustering. We propose to leverage the learned intents into SR models via contrastive SSL, which maximizes the agreement between a view of sequence and its corresponding intent. The training is alternated between intent representation learning and the SR model optimization steps within the generalized expectation-maximization (EM) framework. Fusing user intent information into SR also improves model robustness. Experiments conducted on four real-world datasets demonstrate the superiority of the proposed learning paradigm, which improves performance, and robustness against data sparsity and noisy interaction issues.

In the time domain, the radio sky in particular along the Galactic plane direction may vary significantly because of various energetic activities associated with stars, stellar and supermassive black holes. Using multi-epoch Very Large Array surveys of the Galactic plane at 5.0 GHz, Becker et al. (2010) presented a catalogue of 39 variable radio sources in the flux density range 1-70 mJy. To probe their radio structures and spectra, we observed 17 sources with the very-long-baseline interferometric (VLBI) imaging technique and collected additional multi-frequency data from the literature. We detected all of the sources at 5 GHz with the Westerbork Synthesis Radio Telescope, but only G23.6644-0.0372 with the European VLBI Network (EVN). Together with its decadal variability and multi-frequency radio spectrum, we interpret it as an extragalactic peaked-spectrum source with a size of <~10 pc. The remaining sources were resolved out by the long baselines of the EVN because of either strong scatter broadening at the Galactic latitude <1 deg or intrinsically very extended structures on centi-arcsec scales. According to their spectral and structural properties, we find that the sample has a diverse nature. We notice two young H II regions and spot a radio star and a candidate planetary nebula. The rest of the sources are very likely associated with radio active galactic nuclei (AGN). Two of them also displays arcsec-scale faint jet activity. The sample study indicates that AGN are commonplace even among variable radio sources in the Galactic plane., Comment: 15 pages, 18 figures, accepted for publication in MNRAS

Very-long-baseline interferometry (VLBI) observations of active galactic nuclei at millimeter wavelengths have the power to reveal the launching and initial collimation region of extragalactic radio jets, down to $10-100$ gravitational radii ($r_g=GM/c^2$) scales in nearby sources. Centaurus A is the closest radio-loud source to Earth. It bridges the gap in mass and accretion rate between the supermassive black holes (SMBHs) in Messier 87 and our galactic center. A large southern declination of $-43^{\circ}$ has however prevented VLBI imaging of Centaurus A below ${\lambda}1$cm thus far. Here, we show the millimeter VLBI image of the source, which we obtained with the Event Horizon Telescope at $228$GHz. Compared to previous observations, we image Centaurus A's jet at a tenfold higher frequency and sixteen times sharper resolution and thereby probe sub-lightday structures. We reveal a highly-collimated, asymmetrically edge-brightened jet as well as the fainter counterjet. We find that Centaurus A's source structure resembles the jet in Messier 87 on ${\sim}500r_g$ scales remarkably well. Furthermore, we identify the location of Centaurus A's SMBH with respect to its resolved jet core at ${\lambda}1.3$mm and conclude that the source's event horizon shadow should be visible at THz frequencies. This location further supports the universal scale invariance of black holes over a wide range of masses., Comment: 27 pages, 9 figures. This is a post-peer-review, pre-copyedit version of an article published in Nature Astronomy. The final authenticated version is available online at: https://doi.org/10.1038/s41550-021-01417-w

The black-hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5-61 days) is comparable to the 6-day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure phase measurements on all six linearly independent non-trivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of $\sim3-5^\circ$. The only triangles that exhibit substantially higher variability ($\sim90-180^\circ$) are the ones with baselines that cross visibility amplitude minima on the $u-v$ plane, as expected from theoretical modeling. We used two sets of General Relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black-hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black-hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas., Comment: Accepted for Publication in ApJ

Traditional approaches to next item and next basket recommendation typically extract users' interests based on their past interactions and associated static contextual information (e.g. a user id or item category). However, extracted interests can be inaccurate and become obsolete. Dynamic attributes, such as user income changes, item price changes (etc.), change over time. Such dynamics can intrinsically reflect the evolution of users' interests. We argue that modeling such dynamic attributes can boost recommendation performance. However, properly integrating them into user interest models is challenging since attribute dynamics can be diverse such as time-interval aware, periodic patterns (etc.), and they represent users' behaviors from different perspectives, which can happen asynchronously with interactions. Besides dynamic attributes, items in each basket contain complex interdependencies which might be beneficial but nontrivial to effectively capture. To address these challenges, we propose a novel Attentive network to model Dynamic attributes (named AnDa). AnDa separately encodes dynamic attributes and basket item sequences. We design a periodic aware encoder to allow the model to capture various temporal patterns from dynamic attributes. To effectively learn useful item relationships, intra-basket attention module is proposed. Experimental results on three real-world datasets demonstrate that our method consistently outperforms the state-of-the-art.

Sequential Recommendationdescribes a set of techniques to model dynamic user behavior in order to predict future interactions in sequential user data. At their core, such approaches model transition probabilities between items in a sequence, whether through Markov chains, recurrent networks, or more recently, Transformers. However both old and new issues remain, including data-sparsity and noisy data; such issues can impair the performance, especially in complex, parameter-hungry models. In this paper, we investigate the application of contrastive Self-Supervised Learning (SSL) to the sequential recommendation, as a way to alleviate some of these issues. Contrastive SSL constructs augmentations from unlabelled instances, where agreements among positive pairs are maximized. It is challenging to devise a contrastive SSL framework for a sequential recommendation, due to its discrete nature, correlations among items, and skewness of length distributions. To this end, we propose a novel framework, Contrastive Self-supervised Learning for sequential Recommendation (CoSeRec). We introduce two informative augmentation operators leveraging item correlations to create high-quality views for contrastive learning. Experimental results on three real-world datasets demonstrate the effectiveness of the proposed method on improving model performance and the robustness against sparse and noisy data. Our implementation is available online at \url{https://github.com/YChen1993/CoSeRec}, Comment: Under-review. Work done during Zhiwei's intern at Salesforce. Inc