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Hybrid quantum-classical computing algorithms offer significant potential for accelerating the calculation of the electronic structure of strongly correlated molecules. In this work, we present the first quantum simulation of conical intersections (CIs) in a biomolecule, cytosine, using a superconducting quantum computer. We apply the Contracted Quantum Eigensolver (CQE) -- with comparisons to conventional Variational Quantum Deflation (VQD) -- to compute the near-degenerate ground and excited states associated with the conical intersection, a key feature governing the photostability of DNA and RNA. The CQE is based on an exact ansatz for many-electron molecules in the absence of noise -- a critically important property for resolving strongly correlated states at CIs. Both methods demonstrate promising accuracy when compared with exact diagonalization, even on noisy intermediate-scale quantum computers, highlighting their potential for advancing the understanding of photochemical and photobiological processes. The ability to simulate these intersections is critical for advancing our knowledge of biological processes like DNA repair and mutation, with potential implications for molecular biology and medical research.

Seismic phase picking, which aims to determine the arrival time of P- and S-waves according to seismic waveforms, is fundamental to earthquake monitoring. Generally, manual phase picking is trustworthy, but with the increasing number of worldwide stations and seismic monitors, it becomes more challenging for human to complete the task comprehensively. In this work, we explore multiple ways to do automatic phase picking, including traditional and learning-based methods.

The advancements in cloud-based Large Languages Models (LLMs) have revolutionized AI-assisted programming. However, their integration into certain local development environments like ones within the Apple software ecosystem (e.g., iOS apps, macOS) remains challenging due to computational demands and sandboxed constraints. This paper presents CAMP, a multi-model AI-assisted programming framework that consists of a local model that employs Retrieval-Augmented Generation (RAG) to retrieve contextual information from the codebase to facilitate context-aware prompt construction thus optimizing the performance of the cloud model, empowering LLMs' capabilities in local Integrated Development Environments (IDEs). The methodology is actualized in Copilot for Xcode, an AI-assisted programming tool crafted for Xcode that employs the RAG module to address software constraints and enables diverse generative programming tasks, including automatic code completion, documentation, error detection, and intelligent user-agent interaction. The results from objective experiments on generated code quality and subjective experiments on user adoption collectively demonstrate the pilot success of the proposed system and mark its significant contributions to the realm of AI-assisted programming., Comment: 12 pages, 3 figures, 4 tables

Here we show that shadow tomography can generate an efficient and exact ansatz for the many-fermion wave function on quantum devices. We derive the shadow ansatz -- a product of transformations applied to the mean-field wave function -- by exploiting a critical link between measurement and preparation. Each transformation is obtained by measuring a classical shadow of the residual of the contracted Schr\"odinger equation (CSE), the many-electron Schr\"odinger equation (SE) projected onto the space of two electrons. We show that the classical shadows of the CSE vanish if and only if the wave function satisfies the SE and, hence, that randomly sampling only the two-electron space yields an exact ansatz regardless of the total number of electrons. We demonstrate the ansatz's advantages for scalable simulations -- fewer measurements and shallower circuits -- by computing H$_{3}$ on simulators and a quantum device.

The annotation of polarimetric synthetic aperture radar (PolSAR) images is a labor-intensive and time-consuming process. Therefore, classifying PolSAR images with limited labels is a challenging task in remote sensing domain. In recent years, self-supervised learning approaches have proven effective in PolSAR image classification with sparse labels. However, we observe a lack of research on generative selfsupervised learning in the studied task. Motivated by this, we propose a dual-branch classification model based on generative self-supervised learning in this paper. The first branch is a superpixel-branch, which learns superpixel-level polarimetric representations using a generative self-supervised graph masked autoencoder. To acquire finer classification results, a convolutional neural networks-based pixel-branch is further incorporated to learn pixel-level features. Classification with fused dual-branch features is finally performed to obtain the predictions. Experimental results on the benchmark Flevoland dataset demonstrate that our approach yields promising classification results.

Thanks to Deep Neural Networks (DNNs), the accuracy of Keyword Spotting (KWS) has made substantial progress. However, as KWS systems are usually implemented on edge devices, energy efficiency becomes a critical requirement besides performance. Here, we take advantage of spiking neural networks' energy efficiency and propose an end-to-end lightweight KWS model. The model consists of two innovative modules: 1) Global-Local Spiking Convolution (GLSC) module and 2) Bottleneck-PLIF module. Compared to the hand-crafted feature extraction methods, the GLSC module achieves speech feature extraction that is sparser, more energy-efficient, and yields better performance. The Bottleneck-PLIF module further processes the signals from GLSC with the aim to achieve higher accuracy with fewer parameters. Extensive experiments are conducted on the Google Speech Commands Dataset (V1 and V2). The results show our method achieves competitive performance among SNN-based KWS models with fewer parameters.

Live streaming services are becoming increasingly popular due to real-time interactions and entertainment. Viewers can chat and send comments or virtual gifts to express their preferences for the streamers. Accurately modeling the gifting interaction not only enhances users' experience but also increases streamers' revenue. Previous studies on live streaming gifting prediction treat this task as a conventional recommendation problem, and model users' preferences using categorical data and observed historical behaviors. However, it is challenging to precisely describe the real-time content changes in live streaming using limited categorical information. Moreover, due to the sparsity of gifting behaviors, capturing the preferences and intentions of users is quite difficult. In this work, we propose MMBee based on real-time Multi-Modal Fusion and Behaviour Expansion to address these issues. Specifically, we first present a Multi-modal Fusion Module with Learnable Query (MFQ) to perceive the dynamic content of streaming segments and process complex multi-modal interactions, including images, text comments and speech. To alleviate the sparsity issue of gifting behaviors, we present a novel Graph-guided Interest Expansion (GIE) approach that learns both user and streamer representations on large-scale gifting graphs with multi-modal attributes. Comprehensive experiment results show that MMBee achieves significant performance improvements on both public datasets and Kuaishou real-world streaming datasets and the effectiveness has been further validated through online A/B experiments. MMBee has been deployed and is serving hundreds of millions of users at Kuaishou., Comment: Accepted at KDD 2024

This paper begins with a theoretical exploration of the rise of large language models (LLMs) in Human-Computer Interaction (HCI), their impact on user experience (HX), and related challenges. It then discusses the benefits of Human-Centered Design (HCD) principles and the possibility of their application within LLMs, subsequently deriving six specific HCD guidelines for LLMs. Following this, a preliminary experiment is presented as an example to demonstrate how HCD principles can be employed to enhance user experience within GPT by using a single document input to GPT's Knowledge base as a new knowledge resource to control the interactions between GPT and users, aiming to meet the diverse needs of hypothetical software learners as much as possible. The experimental results demonstrate the effect of different elements' forms and organizational methods in the document, as well as GPT's relevant configurations, on the interaction effectiveness between GPT and software learners. A series of trials are conducted to explore better methods to realize text and image displaying, and jump action. Two template documents are compared in the aspects of the performances of the four interaction modes. Through continuous optimization, an improved version of the document was obtained to serve as a template for future use and research.

DNN-based watermarking methods are rapidly developing and delivering impressive performances. Recent advances achieve resolution-agnostic image watermarking by reducing the variant resolution watermarking problem to a fixed resolution watermarking problem. However, such a reduction process can potentially introduce artifacts and low robustness. To address this issue, we propose the first, to the best of our knowledge, Resolution-Agnostic Image WaterMarking (RAIMark) framework by watermarking the implicit neural representation (INR) of image. Unlike previous methods, our method does not rely on the previous reduction process by directly watermarking the continuous signal instead of image pixels, thus achieving resolution-agnostic watermarking. Precisely, given an arbitrary-resolution image, we fit an INR for the target image. As a continuous signal, such an INR can be sampled to obtain images with variant resolutions. Then, we quickly fine-tune the fitted INR to get a watermarked INR conditioned on a binary secret message. A pre-trained watermark decoder extracts the hidden message from any sampled images with arbitrary resolutions. By directly watermarking INR, we achieve resolution-agnostic watermarking with increased robustness. Extensive experiments show that our method outperforms previous methods with significant improvements: averagely improved bit accuracy by 7%$\sim$29%. Notably, we observe that previous methods are vulnerable to at least one watermarking attack (e.g. JPEG, crop, resize), while ours are robust against all watermarking attacks., Comment: Accepted by ACM MM'24

Distinct from human cognitive processing, deep neural networks trained by backpropagation can be easily fooled by adversarial examples. To design a semantically meaningful representation learning, we discard backpropagation, and instead, propose a local contrastive learning, where the representation for the inputs bearing the same label shrink (akin to boson) in hidden layers, while those of different labels repel (akin to fermion). This layer-wise learning is local in nature, being biological plausible. A statistical mechanics analysis shows that the target fermion-pair-distance is a key parameter. Moreover, the application of this local contrastive learning to MNIST benchmark dataset demonstrates that the adversarial vulnerability of standard perceptron can be greatly mitigated by tuning the target distance, i.e., controlling the geometric separation of prototype manifolds., Comment: 32 pages, 6 figures, a physics inspired machine without backpropagation yet with enhanced adversarial robustness

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure., Comment: 40 pages including references, 13 figures, revised

Nickel-based layered double hydroxides (LDHs) are promising electrode materials in the fields of energy storage (supercapacitors) and conversion (urea oxidation). The rational construction of atomic and electronic structure is crucial for nickel-based LDHs to realize their satisfactory electrochemical performance. Herein, we report a facile, ecofriendly, one-step synthesis process to construct petal-like oxygen-deficient NiAl-LDH nanosheets for hybrid super-capacitors (HSCs) and urea oxidation reaction (UOR). The asprepared NiAl-LDH nanosheets with rich oxygen vacancies possess a large specific surface area of 216.6 m2 g-1 and a desirable electronic conductivity of 3.45 * 10-4 S cm-1 to deliver an ultra-high specific capacitance of 2801 F g-1 (700 C g-1) at 1 A g-1. Furthermore, high specific energy of 50.0 W h kg-1 at 400 W kg-1 and excellent cycle stability with 91% capacitance retention after 10,000 cycles are achieved by the NiAl-LDHs/CFP (carbon fiber paper) (+)//YP-80F (a commercial activated carbon) (-) HSC. Besides, NiAl-LDH nanosheets also work as an efficient electrocatalyst for UOR, which only requires 1.42 V vs. reversible hydrogen electrode to drive 10 mA cm-2 in 1 mol L-1 KOH with 0.33 mol L-1 urea. This remarkable performance is superior to most reported values of previous candidates owing to the thin structure of NiAl-LDH nanosheets for exposing more active sites and abundant oxygen vacancies. In addition, various reaction parameters are investigated to optimize the electrochemical performance. In general, this work paves a new way for the architecture of multifunctional nanostructured energy materials.

Effective regulation of the morphology of transition metal spinel structures is crucial for creating efficient and stable bifunctional catalysts for electrocatalysis of water. In this work, micro-flower NiCo2O4 (F-NCO) assembled by nanosheets via a chemical template method for the simultaneous promotion of hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). Electronic microscope analysis revealed that the thickness of the F-NCO catalyst was only 2.7% of that of the NiCo2O4 bulk (B-NCO), and this ultrathin lamellar structure was conducive to further exposure of the active site and improved reaction kinetics. The F-NCO catalyst exhibited superior HER and OER performance (10 = 236 and 310 mV) and robust long-term stability over the B-NCO catalyst in 1.0 M KOH, with a 2.68-fold and 4.16-fold increase in active surface area and a 0.42-fold and 0.61-fold decrease in charge transfer resistance values, respectively. This micro-flower-structured electrode has remarkable electrocatalytic property and long-term durability, providing a novel insight for characterizing cost-effective and high-performance bifunctional electrocatalysts.

Rational design and cost-effective fabrication of layered double hydroxides (LDHs) nanosheets with extraordinary electrochemical performance is a key challenge for hybrid supercapacitors (HSCs). Herein, we report a facile in situ growth methodology to eco-friendly synthesize hydrophilic NiCo-LDHs nanosheets on biomass waste-derived porous carbon (BC) for robust high-performance HSC cathode. The in situ growth process under ultrasonication realizes the rational arrangement of NiCo-LDHs nanosheets on the surface of BC, which effectively increases the specific surface area, promotes the electronic conductivity and enhances the wettability of NiCo-LDHs nanosheets without affecting their thickness values. With the beneficial effects of ultrathin thickness of LDHs nanosheets (6.20 nm), large specific surface area (2324.1 m2 g-1), low charge transfer resistance (1.65 ohm), and high wettability with electrolyte (34-35 degree), the obtained Ni2Co1-LDHs/BC50 electrode possesses an ultra-high specific capacitance of 2390 F g-1 (956 C g-1) at 1 A g-1, which is superior to most reported values. Furthermore, an assembled Ni2Co1-LDHs/BC50//YP-80F HSC delivers a maximum specific energy of 52.47 Wh kg-1 at 375 W kg-1, and maintains a high capacitance retention of 75.9% even after 4000 cycles. This work provides a facile approach to fabricate LDHs nanosheets based cathode materials for high-performance HSCs.

Rational synthesis of robust layered double hydroxides (LDHs) nanosheets for high-energy supercapacitors is full of challenges. Herein, we reported an ultrasonication-assisted strategy to eco-friendly fabricate NiFe-LDHs nanosheets for the enhanced capacitive behavior. The experimental results combined with different advanced characterization tools document that the utilization of ultrasonication has a profound effect on the morphology and thickness of the as-obtained NiFe-LDHs, alternatively affecting the capacitive behavior. It shows that NiFe-LDHs nanosheets prepared with 2-h ultrasonic treatments display the exceptional capacitive performance because of the synergetic effect of ultrathin thickness, large specific surface area, and high mesoporous volume. The maximum specific capacitance of Ni3Fe1-LDHs nanosheets with the thickness of 7.39 nm and the specific surface area of 77.16 m2 g-1 reached 1923 F g-1, which is competitive with most previously reported values. In addition, the maximum specific energy of the assembled NiFe-LDHs//AC asymmetric supercapacitor achieved 49.13 Wh kg-1 at 400 W kg-1. This work provides a green technology to fabricate LDHs nanosheets, and offers deep insights for understanding the relationship between the morphology/structure and capacitive behavior of LDHs nanosheets, which is helpful for achieving high-performance LDHs-based electrode materials.

Transition-metal-based layered double hydroxides (TM-LDHs) nanosheets are promising electrocatalysts in the renewable electrochemical energy conversion system, which are regarded as alternatives to noble metal-based materials. In this review, recent advances on effective and facile strategies to rationally design TM-LDHs nanosheets as electrocatalysts, such as increasing the number of active sties, improving the utilization of active sites (atomic-scale catalysts), modulating the electron configurations, and controlling the lattice facets, are summarized and compared. Then, the utilization of these fabricated TM-LDHs nanosheets for oxygen evolution reaction, hydrogen evolution reaction, urea oxidation reaction, nitrogen reduction reaction, small molecule oxidations, and biomass derivatives upgrading is articulated through systematically discussing the corresponding fundamental design principles and reaction mechanism. Finally, the existing challenges in increasing the density of catalytically active sites and future prospects of TM-LDHs nanosheets-based electrocatalysts in each application are also commented.

Electrocatalytic hydrogenation of nitrobenzene (Ph-NO2) reaction (EHNR) has been considered as a potential alternative to the traditional thermocatalytic process in the production of high-value aniline (Ph-NH2). However, due to the absence of robust catalyst and low surface H* coverage, the EHNR faces the challenges of undesired performance and indetermined mechanism. Herein, we construct a type of noble-metal free topological FeSi (M-FeSi) materials through a solvent-free microwave strategy for efficient EHNR in neutral medium. Impressively, benefiting from abundant active H* intermediates on the surface of M-FeSi catalyst, the topological M-FeSi catalyst exhibits 99.7% conversion of Ph-NO2 and 93.8% yield of Ph-NH2 after 200 C in neutral medium, which are superior to previous candidates and FeSi catalyst synthesized via the traditional arc-melting method under same conditions. Besides, theoretical calculations validate that high surface H* coverage over M-FeSi catalyst is conducive to switching the rate-determining step from Ph-NO2* Ph-NO* to Ph-NO* Ph-NHOH*, and thus decreasing the total energy barrier of electrocatalytic Ph-NH2 production.

Adaptive Variational Quantum Dynamics (AVQD) algorithms offer a promising approach to providing quantum-enabled solutions for systems treated within the purview of open quantum dynamical evolution. In this study, we employ the unrestricted vectorization variant of AVQD to simulate and benchmark various non-unitarily evolving systems. We exemplify how construction of an expressible ansatz unitary and the associated operator pool can be implemented to analyze examples such as the Fenna Matthews Olson complex (FMO) and even the permutational invariant Dicke model of quantum optics. We furthermore show an efficient decomposition scheme for the ansatz used, which can extend its applications to a wide range of other open quantum system scenarios in near future. In all cases the results obtained are in excellent agreement with exact numerical computations which bolsters the effectiveness of this technique. Our successful demonstrations pave the way for utilizing this adaptive variational technique to study complex systems in chemistry and physics, like light harvesting devices, thermal, and opto mechanical switches, to name a few., Comment: 14 pages, 6 figures

We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schr\"odinger equation (CSE), our approach guides a trial wave function to the ground state of any arbitrary mixed Hamiltonian by directly measuring residuals of the mixed CSE on a quantum device. Unlike density-functional and coupled-cluster theories applied to electron-phonon or electron-photon systems, the accuracy of our approach is not limited by the unknown exchange-correlation functional or the uncontrolled form of the exponential ansatz. To test the performance of the method, we study the Tavis-Cummings model, commonly used in polaritonic quantum chemistry. Our results demonstrate that the CSE is a powerful tool in the development of quantum algorithms for solving general fermion-boson many-body problems.

The opioid epidemic, referring to the growing hospitalizations and deaths because of overdose of opioid usage and addiction, has become a severe health problem in the United States. Many strategies have been developed by the federal and local governments and health communities to combat this crisis. Among them, improving our understanding of the epidemic through better health surveillance is one of the top priorities. In addition to direct testing, machine learning approaches may also allow us to detect opioid users by analyzing data from social media because many opioid users may choose not to do the tests but may share their experiences on social media anonymously. In this paper, we take advantage of recent advances in machine learning, collect and analyze user posts from a popular social network Reddit with the goal to identify opioid users. Posts from more than 1,000 users who have posted on three sub-reddits over a period of one month have been collected. In addition to the ones that contain keywords such as opioid, opiate, or heroin, we have also collected posts that contain slang words of opioid such as black or chocolate. We apply an attention-based bidirectional long short memory model to identify opioid users. Experimental results show that the approaches significantly outperform competitive algorithms in terms of F1-score. Furthermore, the model allows us to extract most informative words, such as opiate, opioid, and black, from posts via the attention layer, which provides more insights on how the machine learning algorithm works in distinguishing drug users from non-drug users.

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H$_{3}^{+}$ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schr{\"o}dinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

Let $M=S^n/ \Gamma$ and $h \in \pi_1(M)$ be a non-trivial element of finite order $p$, where the integers $n, p\geq2$ and $\Gamma$ is a finite abelian group which acts on the sphere freely and isometrically, therefore $M$ is diffeomorphic to a compact space form which is typical a non-simply connected manifold. We prove there exist at least two non-contractible closed geodesics on $\mathbb{R}P^2$ and obtain the upper bounds on their lengths. Moreover, we prove there exist at least $n$ prime non-contractible simple closed geodesics on $(M,F)$ of prescribed class $[h]$, provided \[ F^2 <(\frac{\lambda+1}{\lambda})^2 g_0 \;\; \text{ and } \;\; (\frac{\lambda}{\lambda+1})^2 < K \leq 1 \text{ for $n$ is odd or }\; 0

We present Ego-Exo4D, a diverse, large-scale multimodal multiview video dataset and benchmark challenge. Ego-Exo4D centers around simultaneously-captured egocentric and exocentric video of skilled human activities (e.g., sports, music, dance, bike repair). 740 participants from 13 cities worldwide performed these activities in 123 different natural scene contexts, yielding long-form captures from 1 to 42 minutes each and 1,286 hours of video combined. The multimodal nature of the dataset is unprecedented: the video is accompanied by multichannel audio, eye gaze, 3D point clouds, camera poses, IMU, and multiple paired language descriptions -- including a novel "expert commentary" done by coaches and teachers and tailored to the skilled-activity domain. To push the frontier of first-person video understanding of skilled human activity, we also present a suite of benchmark tasks and their annotations, including fine-grained activity understanding, proficiency estimation, cross-view translation, and 3D hand/body pose. All resources are open sourced to fuel new research in the community. Project page: http://ego-exo4d-data.org/, Comment: Expanded manuscript (compared to arxiv v1 from Nov 2023 and CVPR 2024 paper from June 2024) for more comprehensive dataset and benchmark presentation, plus new results on v2 data release

Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schr\"odinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh-Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

Uplift modeling has shown very promising results in online marketing. However, most existing works are prone to the robustness challenge in some practical applications. In this paper, we first present a possible explanation for the above phenomenon. We verify that there is a feature sensitivity problem in online marketing using different real-world datasets, where the perturbation of some key features will seriously affect the performance of the uplift model and even cause the opposite trend. To solve the above problem, we propose a novel robustness-enhanced uplift modeling framework with adversarial feature desensitization (RUAD). Specifically, our RUAD can more effectively alleviate the feature sensitivity of the uplift model through two customized modules, including a feature selection module with joint multi-label modeling to identify a key subset from the input features and an adversarial feature desensitization module using adversarial training and soft interpolation operations to enhance the robustness of the model against this selected subset of features. Finally, we conduct extensive experiments on a public dataset and a real product dataset to verify the effectiveness of our RUAD in online marketing. In addition, we also demonstrate the robustness of our RUAD to the feature sensitivity, as well as the compatibility with different uplift models.

Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model entangled many-boson system with the contracted quantum eigensolver (CQE). We generalize the CQE to many-boson systems by encoding the bosonic wavefunction on qubits. The CQE provides a compact ansatz for the bosonic wave function whose gradient is proportional to the residual of a contracted Schr\"odinger equation. We apply the CQE to a bosonic system, where $N$ quantum harmonic oscillators are coupled through a pairwise quadratic repulsion. The model is relevant to the study of coupled vibrations in molecular systems on quantum devices. Results demonstrate the potential efficiency of the CQE in simulating bosonic processes such as molecular vibrations with good accuracy and convergence even in the presence of noise.

We consider rigidity properties of steady Euler flows in two-dimensional bounded domains. We prove that steady Euler flows in a disk with exactly one interior stagnation point and tangential boundary conditions must be circular flows, which confirms a conjecture proposed by F. Hamel and N. Nadirashvili in [J. Eur. Math. Soc., 25 (2023), no. 1, 323-368]. Moreover, for steady Euler flows on annuli with tangential boundary conditions, we prove that they must be circular flows provided there is no stagnation point inside, which answers another open problem proposed by F. Hamel and N. Nadirashvili in the same paper. We secondly show that the no-slip boundary conditions would result in absolute rigidity in the sense that except for the disks (\emph{resp}. annuli), there is no other smooth simply (\emph{resp}. doubly) connected bounded domain on which there exists a steady flow with only one (\emph{resp}. no) interior stagnation point and no-slip boundary conditions, and if present on the other hand, the flow must be circular. The arguments are based on the geometry of streamlines and 'local' symmetry properties for the non-negative solutions of semi-linear elliptic problems.

We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which addresses an open question proposed by F. Hamel and N. Nadirashvili in [J. Eur. Math. Soc., 25 (2023), no. 1, 323-368]. The proof is based on the study of the geometric properties of the streamlines of the flow and on `local' symmetry properties for the non-negative solutions of semi-linear elliptic equations with a continuous nonlinearity., Comment: arXiv admin note: substantial text overlap with arXiv:2306.00302

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to program a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.

In this paper, we consider a sign-changing free boundary problem that comes from the boundary regularity of rotating vortex patches of the two-dimensional incompressible Euler equations. The complete classification of singular points has been obtained through establishing a new Weiss-type monotonicity formula. Upon these results, we prove that only $90^\circ$ corner type of singularity could happen at the boundary of a Lipschitz rotating vortex patch, while the other parts are $C^\infty$ smooth.