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We investigate theoretically equilibrium and dynamical properties of a Kondo impurity coupled to either 1D or 2D superconductors, modeled by the attractive Fermi-Hubbard model. By employing a non-Gaussian variational approach, we go beyond the approximation of a constant superconducting (SC) gap. We show that dynamical properties of the system can be modified qualitatively, when space and time dependent renormalization of the SC gap and electron-impurity hybridization are included. For the ground state, we find the singlet-doublet phase transition and $\pi$-phase shifts of the SC order parameter. For dynamics, first we consider spin dynamics following an abrupt connection of the polarized impurity to the 2D bath. We find rapid relaxation of impurity polarization and directional emission of a magnetization pulse, which becomes damped as it propagates into the bulk. Then we analyze transport between two SC leads coupled through the impurity at finite bias voltage. Here we go beyond analysis of the steady state to investigate full-time dynamics following an abrupt application of the bias voltage. We uncover four distinct regimes in the transient dynamics and transport properties: (I) the AC Josephson effect regime; (II) dynamical competition between charge-density-wave (CDW) and SC orders with transient Kondo correlations; (III) the coexistence of AC and DC currents facilitated by partial Kondo screening and dynamical stabilization of the SC order; (IV) DC Kondo transport regime modified by the SC order. Regime II exhibits a dynamical transition from SC to CDW order that locally restores the U(1) symmetry. We argue that our findings for regime IV provide a theoretical explanation for the experimentally observed anomalous enhancement of DC conductance and suppression of the AC Josephson current. Finally, we discuss the potential experimental realization with ultracold atoms., Comment: 27 pages, 13 figures. The abstract on the arXiv website is slightly shorter than the PDF version due to the length limit set by arXiv

The distributed recursion (DR) algorithm is an effective method for solving the pooling problem that arises in many applications. It is based on the well-known P-formulation of the pooling problem, which involves the flow and quality variables; and it can be seen as a variant of the successive linear programming (SLP) algorithm, where the linear programming (LP) approximation problem can be transformed from the LP approximation problem derived by using the first-order Taylor series expansion technique. In this paper, we first propose a new nonlinear programming (NLP) formulation for the pooling problem involving only the flow variables, and show that the DR algorithm can be seen as a direct application of the SLP algorithm to the newly proposed formulation. With this new useful theoretical insight, we then develop a new variant of DR algorithm, called penalty DR (PDR) algorithm, based on the proposed formulation. The proposed PDR algorithm is a penalty algorithm where violations of the (linearized) nonlinear constraints are penalized in the objective function of the LP approximation problem with the penalty terms increasing when the constraint violations tend to be large. Compared with the LP approximation problem in the classic DR algorithm, the LP approximation problem in the proposed PDR algorithm can return a solution with a better objective value, which makes it more suitable for finding high-quality solutions for the pooling problem. Numerical experiments on benchmark and randomly constructed instances show that the proposed PDR algorithm is more effective than the classic SLP and DR algorithms in terms of finding a better solution for the pooling problem., Comment: 22 pages, 2 figures, submitted for possible publication

Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity $l_1$-norm and relative entropy, we first derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not the vice-versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states., Comment: 9 pages, 4 figures

Autocorrelation measurement is theoretically demonstrated to characterize attosecond pulses by studying the two-photon double ionization (TPDI) process. An interferometric autocorrelation curve is presented in the change of TPDI probability with the time delay between two identical attosecond pulses, and its full width at half maximum (FWHM) $\tau_{e}$ has a relationship $\tau_{e}=1.77\tau+15$ with the FWHM $\tau$ of the attosecond pulse. The curve is also decoded to obtain the center frequency and FWHM of the attosecond pulse by fitting. In addition, the required peak intensity of the attosecond pulse is estimated to be on the order of $10^{16}\,\rm{Wcm^{-2}}$ in autocorrelation experiments. The findings pave the way for autocorrelation measurement of intense isolated attosecond pulses., Comment: 7 pages, 6 figures

We present a method for reconstructing a clear Neural Radiance Field (NeRF) even with fast camera motions. To address blur artifacts, we leverage both (blurry) RGB images and event camera data captured in a binocular configuration. Importantly, when reconstructing our clear NeRF, we consider the camera modeling imperfections that arise from the simple pinhole camera model as learned embeddings for each camera measurement, and further learn a mapper that connects event camera measurements with RGB data. As no previous dataset exists for our binocular setting, we introduce an event camera dataset with captures from a 3D-printed stereo configuration between RGB and event cameras. Empirically, we evaluate our introduced dataset and EVIMOv2 and show that our method leads to improved reconstructions. Our code and dataset are available at https://github.com/ubc-vision/LSENeRF.

Image super-resolution pursuits reconstructing high-fidelity high-resolution counterpart for low-resolution image. In recent years, diffusion-based models have garnered significant attention due to their capabilities with rich prior knowledge. The success of diffusion models based on general text prompts has validated the effectiveness of textual control in the field of text2image. However, given the severe degradation commonly presented in low-resolution images, coupled with the randomness characteristics of diffusion models, current models struggle to adequately discern semantic and degradation information within severely degraded images. This often leads to obstacles such as semantic loss, visual artifacts, and visual hallucinations, which pose substantial challenges for practical use. To address these challenges, this paper proposes to leverage degradation-aligned language prompt for accurate, fine-grained, and high-fidelity image restoration. Complementary priors including semantic content descriptions and degradation prompts are explored. Specifically, on one hand, image-restoration prompt alignment decoder is proposed to automatically discern the degradation degree of LR images, thereby generating beneficial degradation priors for image restoration. On the other hand, much richly tailored descriptions from pretrained multimodal large language model elicit high-level semantic priors closely aligned with human perception, ensuring fidelity control for image restoration. Comprehensive comparisons with state-of-the-art methods have been done on several popular synthetic and real-world benchmark datasets. The quantitative and qualitative analysis have demonstrated that the proposed method achieves a new state-of-the-art perceptual quality level. Related source codes and pre-trained parameters were public in https://github.com/puppy210/DaLPSR.

This study investigates the robustness of graph embedding methods for community detection in the face of network perturbations, specifically edge deletions. Graph embedding techniques, which represent nodes as low-dimensional vectors, are widely used for various graph machine learning tasks due to their ability to capture structural properties of networks effectively. However, the impact of perturbations on the performance of these methods remains relatively understudied. The research considers state-of-the-art graph embedding methods from two families: matrix factorization (e.g., LE, LLE, HOPE, M-NMF) and random walk-based (e.g., DeepWalk, LINE, node2vec). Through experiments conducted on both synthetic and real-world networks, the study reveals varying degrees of robustness within each family of graph embedding methods. The robustness is found to be influenced by factors such as network size, initial community partition strength, and the type of perturbation. Notably, node2vec and LLE consistently demonstrate higher robustness for community detection across different scenarios, including networks with degree and community size heterogeneity. These findings highlight the importance of selecting an appropriate graph embedding method based on the specific characteristics of the network and the task at hand, particularly in scenarios where robustness to perturbations is crucial., Comment: 17 pages, 26 figures, 3 tables. Comments are welcome

As a natural extension to the standard conformal prediction method, several conformal risk control methods have been recently developed and applied to various learning problems. In this work, we seek to control the conformal risk in expectation for ordinal classification tasks, which have broad applications to many real problems. For this purpose, we firstly formulated the ordinal classification task in the conformal risk control framework, and provided theoretic risk bounds of the risk control method. Then we proposed two types of loss functions specially designed for ordinal classification tasks, and developed corresponding algorithms to determine the prediction set for each case to control their risks at a desired level. We demonstrated the effectiveness of our proposed methods, and analyzed the difference between the two types of risks on three different datasets, including a simulated dataset, the UTKFace dataset and the diabetic retinopathy detection dataset., Comment: 17 pages, 8 figures, 2 table; 1 supplementary page

Practical machine learning systems often operate in multiple sequential stages, as seen in ranking and recommendation systems, which typically include a retrieval phase followed by a ranking phase. Effectively assessing prediction uncertainty and ensuring effective risk control in such systems pose significant challenges due to their inherent complexity. To address these challenges, we developed two-stage risk control methods based on the recently proposed learn-then-test (LTT) and conformal risk control (CRC) frameworks. Unlike the methods in prior work that address multiple risks, our approach leverages the sequential nature of the problem, resulting in reduced computational burden. We provide theoretical guarantees for our proposed methods and design novel loss functions tailored for ranked retrieval tasks. The effectiveness of our approach is validated through experiments on two large-scale, widely-used datasets: MSLR-Web and Yahoo LTRC., Comment: 20 pages, 3 figures, 2 tables; 7 supplementary pages

We have investigated the angle-resolved ATI spectrum of oriented molecules in the IR+XUV co-rotating circular laser fields. According to the different roles of IR and XUV laser in the ionization process, we purposefully adjust the photon energy of XUV and the intensity of IR laser to make the ionization spectrum of the molecule distributed in a suitable momentum region. Moreover, under the same laser conditions, the background fringes in the ionization spectrum of the molecule can be removed by using the ionization spectrum of the atom with the same ionization energy as the molecule, so that the molecular orbital density distribution in the suitable momentum region can be obtained. That is, for any unknown molecule, as long as the ionization energy of the molecule can be measured, the density distribution of the molecular orbital can be imaged in a definite momentum region by adjusting the laser field conditions, which may shed light on the experimental detection of molecular orbitals.

We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=\Omega(\log N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error $\epsilon$ in depth $T=O(\log (N/\epsilon))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(\log\log (N/\epsilon))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS.

We obtain the formulae for the numbers of 4-matchings and 5-matchings in terms of the number of hexagonal faces in (4, 6)-fullerene graphs by studying structural classification of 6-cycles and some local structural properties, which correct the corresponding wrong results published. Furthermore, we obtain a formula for the number of 6-matchings in tubular (4, 6)-fullerenes in terms of the number of hexagonal faces, and a formula for the number of 6-matchings in the other (4,6)-fullerenes in terms of the numbers of hexagonal faces and dual-squares., Comment: This article was already published in 2017 in MATCH Commun. Math. Comput. Chem. We are uploading it to arXiv for readers' convenience

We introduce $\Lambda$-moments with respect to any positive map $\Lambda$. We show that these $\Lambda$-moments can effectively characterize the entanglement of unknown quantum states without theirs prior reconstructions. Based on $\Lambda$-moments necessary and sufficient separability criteria, as well as necessary optimized criteria are presented, which include the ones in [\href{https://link.aps.org/doi/10.1103/PhysRevLett.127.060504}{Phys. Rev. Lett. \textbf{127}, 060504 (2021)}] as special cases. Detailed example is given to show that our criteria can detect bound entanglement that can not be identified by positive partial transpose criterion, with the explicit measurement operators to experimentally measure the corresponding $\Lambda$-moments., Comment: 6 pages, 1 figure