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For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation, \begin{equation*} \partial_t\phi+\partial_{x_1}(\Delta \phi+\phi^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}, \end{equation*} we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel-Merle-Rapha\"el [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property., Comment: 20 pages

Understanding how the structured incident light interacts with the inherent properties of the manipulated particle and governs the optical force/torque exerted is a cornerstone in the design of optical manipulation techniques, apart from its theoretical significance. Based on the Cartesian multipole expansion theory, we establish a framework for optical force/torque exerted on an arbitrary sized bi-isotropic (chiral) spherical particle immersed in generic monochromatic optical fields. Rigorous expressions are thus derived which explicitly bridges such mechanical effects of light with particle-property-dependent coefficients and "force/torque source" quantities that characterize the incident light structures. Such quantities, totalled only 12, are quadratic in terms of electric and magnetic field vectors, among which are linear and angular momenta, gradient of energy density, spin density, and helicity. They are further organized into four categories based on their parity (P) and duality (D) symmetries and shown to couple with a particle with different P and D symmetries to induce optical force/torque. This classification specifies the symmetry-breaking criteria required to induce optical force/torque, offering a promising roadmap for engineering the optical manipulation.

Despite remarkable successes in unimodal learning tasks, backdoor attacks against cross-modal learning are still underexplored due to the limited generalization and inferior stealthiness when involving multiple modalities. Notably, since works in this area mainly inherit ideas from unimodal visual attacks, they struggle with dealing with diverse cross-modal attack circumstances and manipulating imperceptible trigger samples, which hinders their practicability in real-world applications. In this paper, we introduce a novel bilateral backdoor to fill in the missing pieces of the puzzle in the cross-modal backdoor and propose a generalized invisible backdoor framework against cross-modal learning (BadCM). Specifically, a cross-modal mining scheme is developed to capture the modality-invariant components as target poisoning areas, where well-designed trigger patterns injected into these regions can be efficiently recognized by the victim models. This strategy is adapted to different image-text cross-modal models, making our framework available to various attack scenarios. Furthermore, for generating poisoned samples of high stealthiness, we conceive modality-specific generators for visual and linguistic modalities that facilitate hiding explicit trigger patterns in modality-invariant regions. To the best of our knowledge, BadCM is the first invisible backdoor method deliberately designed for diverse cross-modal attacks within one unified framework. Comprehensive experimental evaluations on two typical applications, i.e., cross-modal retrieval and VQA, demonstrate the effectiveness and generalization of our method under multiple kinds of attack scenarios. Moreover, we show that BadCM can robustly evade existing backdoor defenses. Our code is available at https://github.com/xandery-geek/BadCM.

Large Multimodal Models (LMMs) have achieved significant progress by extending large language models. Building on this progress, the latest developments in LMMs demonstrate the ability to generate dense pixel-wise segmentation through the integration of segmentation models.Despite the innovations, the textual responses and segmentation masks of existing works remain at the instance level, showing limited ability to perform fine-grained understanding and segmentation even provided with detailed textual cues.To overcome this limitation, we introduce a Multi-Granularity Large Multimodal Model (MGLMM), which is capable of seamlessly adjusting the granularity of Segmentation and Captioning (SegCap) following user instructions, from panoptic SegCap to fine-grained SegCap. We name such a new task Multi-Granularity Segmentation and Captioning (MGSC). Observing the lack of a benchmark for model training and evaluation over the MGSC task, we establish a benchmark with aligned masks and captions in multi-granularity using our customized automated annotation pipeline. This benchmark comprises 10K images and more than 30K image-question pairs. We will release our dataset along with the implementation of our automated dataset annotation pipeline for further research.Besides, we propose a novel unified SegCap data format to unify heterogeneous segmentation datasets; it effectively facilitates learning to associate object concepts with visual features during multi-task training. Extensive experiments demonstrate that our MGLMM excels at tackling more than eight downstream tasks and achieves state-of-the-art performance in MGSC, GCG, image captioning, referring segmentation, multiple and empty segmentation, and reasoning segmentation tasks. The great performance and versatility of MGLMM underscore its potential impact on advancing multimodal research., Comment: Code and dataset will be released at https://github.com/lizhou-cs/mglmm. 7 pages, 4 figures with Supplementary Material

Adversarial training (AT) can help improve the robustness of Vision Transformers (ViT) against adversarial attacks by intentionally injecting adversarial examples into the training data. However, this way of adversarial injection inevitably incurs standard accuracy degradation to some extent, thereby calling for a trade-off between standard accuracy and robustness. Besides, the prominent AT solutions are still vulnerable to adaptive attacks. To tackle such shortcomings, this paper proposes a novel ViT architecture, including a detector and a classifier bridged by our newly developed adaptive ensemble. Specifically, we empirically discover that detecting adversarial examples can benefit from the Guided Backpropagation technique. Driven by this discovery, a novel Multi-head Self-Attention (MSA) mechanism is introduced to enhance our detector to sniff adversarial examples. Then, a classifier with two encoders is employed for extracting visual representations respectively from clean images and adversarial examples, with our adaptive ensemble to adaptively adjust the proportion of visual representations from the two encoders for accurate classification. This design enables our ViT architecture to achieve a better trade-off between standard accuracy and robustness. Besides, our adaptive ensemble technique allows us to mask off a random subset of image patches within input data, boosting our ViT's robustness against adaptive attacks, while maintaining high standard accuracy. Experimental results exhibit that our ViT architecture, on CIFAR-10, achieves the best standard accuracy and adversarial robustness of 90.3% and 49.8%, respectively., Comment: 9 pages

Federated learning (FL) is an emerging distributed machine learning paradigm that enables collaborative training of machine learning models over decentralized devices without exposing their local data. One of the major challenges in FL is the presence of uneven data distributions across client devices, violating the well-known assumption of independent-and-identically-distributed (IID) training samples in conventional machine learning. To address the performance degradation issue incurred by such data heterogeneity, clustered federated learning (CFL) shows its promise by grouping clients into separate learning clusters based on the similarity of their local data distributions. However, state-of-the-art CFL approaches require a large number of communication rounds to learn the distribution similarities during training until the formation of clusters is stabilized. Moreover, some of these algorithms heavily rely on a predefined number of clusters, thus limiting their flexibility and adaptability. In this paper, we propose {\em FedClust}, a novel approach for CFL that leverages the correlation between local model weights and the data distribution of clients. {\em FedClust} groups clients into clusters in a one-shot manner by measuring the similarity degrees among clients based on the strategically selected partial weights of locally trained models. We conduct extensive experiments on four benchmark datasets with different non-IID data settings. Experimental results demonstrate that {\em FedClust} achieves higher model accuracy up to $\sim$45\% as well as faster convergence with a significantly reduced communication cost up to 2.7$\times$ compared to its state-of-the-art counterparts.

In this article, we consider the Cauchy problem for the cubic (mass-critical) Zakharov-Kuznetsov equations in dimension two: $$\partial_t u+\partial_{x_1}(\Delta u+u^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}.$$ For initial data in $H^1$ close to the soliton with a suitable space-decay property, we fully describe the asymptotic behavior of the corresponding solution. More precisely, for such initial data, we show that only three possible behaviors can occur: 1) The solution leaves a tube near soliton in finite time; 2) the solution blows up in finite time; 3) the solution is global and locally converges to a soliton. In addition, we show that for initial data near a soliton with non-positive energy and above the threshold mass, the corresponding solution will blow up as described in Case 2. Our proof is inspired by the techniques developed for mass-critical generalized Korteweg-de Vries equation (gKdV) equation in a similar context by Martel-Merle-Rapha\"el. More precisely, our proof relies on refined modulation estimates and a modified energy-virial Lyapunov functional. The primary challenge in our problem is the lack of coercivity of the Schr\"odinger operator which appears in the virial-type estimate. To overcome the difficulty, we apply a transform, which was first introduced in Kenig-Martel [13], to perform the virial computations after converting the original problem to the adjoint one. Th coercivity of the Schr\"odinger operator in the adjoint problem has been numerically verified by Farah-Holmer-Roudenko-Yang [9]., Comment: 65 pages

Precise crop yield predictions are of national importance for ensuring food security and sustainable agricultural practices. While AI-for-science approaches have exhibited promising achievements in solving many scientific problems such as drug discovery, precipitation nowcasting, etc., the development of deep learning models for predicting crop yields is constantly hindered by the lack of an open and large-scale deep learning-ready dataset with multiple modalities to accommodate sufficient information. To remedy this, we introduce the CropNet dataset, the first terabyte-sized, publicly available, and multi-modal dataset specifically targeting climate change-aware crop yield predictions for the contiguous United States (U.S.) continent at the county level. Our CropNet dataset is composed of three modalities of data, i.e., Sentinel-2 Imagery, WRF-HRRR Computed Dataset, and USDA Crop Dataset, for over 2200 U.S. counties spanning 6 years (2017-2022), expected to facilitate researchers in developing versatile deep learning models for timely and precisely predicting crop yields at the county-level, by accounting for the effects of both short-term growing season weather variations and long-term climate change on crop yields. Besides, we develop the CropNet package, offering three types of APIs, for facilitating researchers in downloading the CropNet data on the fly over the time and region of interest, and flexibly building their deep learning models for accurate crop yield predictions. Extensive experiments have been conducted on our CropNet dataset via employing various types of deep learning solutions, with the results validating the general applicability and the efficacy of the CropNet dataset in climate change-aware crop yield predictions., Comment: 13 pages

Anomaly detection (such as telecom fraud detection and medical image detection) has attracted the increasing attention of people. The complex interaction between multiple entities widely exists in the network, which can reflect specific human behavior patterns. Such patterns can be modeled by higher-order network structures, thus benefiting anomaly detection on attributed networks. However, due to the lack of an effective mechanism in most existing graph learning methods, these complex interaction patterns fail to be applied in detecting anomalies, hindering the progress of anomaly detection to some extent. In order to address the aforementioned issue, we present a higher-order structure based anomaly detection (GUIDE) method. We exploit attribute autoencoder and structure autoencoder to reconstruct node attributes and higher-order structures, respectively. Moreover, we design a graph attention layer to evaluate the significance of neighbors to nodes through their higher-order structure differences. Finally, we leverage node attribute and higher-order structure reconstruction errors to find anomalies. Extensive experiments on five real-world datasets (i.e., ACM, Citation, Cora, DBLP, and Pubmed) are implemented to verify the effectiveness of GUIDE. Experimental results in terms of ROC-AUC, PR-AUC, and Recall@K show that GUIDE significantly outperforms the state-of-art methods.

Federated learning (FL) is an emerging distributed machine learning paradigm enabling collaborative model training on decentralized devices without exposing their local data. A key challenge in FL is the uneven data distribution across client devices, violating the well-known assumption of independent-and-identically-distributed (IID) training samples in conventional machine learning. Clustered federated learning (CFL) addresses this challenge by grouping clients based on the similarity of their data distributions. However, existing CFL approaches require a large number of communication rounds for stable cluster formation and rely on a predefined number of clusters, thus limiting their flexibility and adaptability. This paper proposes FedClust, a novel CFL approach leveraging correlations between local model weights and client data distributions. FedClust groups clients into clusters in a one-shot manner using strategically selected partial model weights and dynamically accommodates newcomers in real-time. Experimental results demonstrate FedClust outperforms baseline approaches in terms of accuracy and communication costs.

Deep hashing has been intensively studied and successfully applied in large-scale image retrieval systems due to its efficiency and effectiveness. Recent studies have recognized that the existence of adversarial examples poses a security threat to deep hashing models, that is, adversarial vulnerability. Notably, it is challenging to efficiently distill reliable semantic representatives for deep hashing to guide adversarial learning, and thereby it hinders the enhancement of adversarial robustness of deep hashing-based retrieval models. Moreover, current researches on adversarial training for deep hashing are hard to be formalized into a unified minimax structure. In this paper, we explore Semantic-Aware Adversarial Training (SAAT) for improving the adversarial robustness of deep hashing models. Specifically, we conceive a discriminative mainstay features learning (DMFL) scheme to construct semantic representatives for guiding adversarial learning in deep hashing. Particularly, our DMFL with the strict theoretical guarantee is adaptively optimized in a discriminative learning manner, where both discriminative and semantic properties are jointly considered. Moreover, adversarial examples are fabricated by maximizing the Hamming distance between the hash codes of adversarial samples and mainstay features, the efficacy of which is validated in the adversarial attack trials. Further, we, for the first time, formulate the formalized adversarial training of deep hashing into a unified minimax optimization under the guidance of the generated mainstay codes. Extensive experiments on benchmark datasets show superb attack performance against the state-of-the-art algorithms, meanwhile, the proposed adversarial training can effectively eliminate adversarial perturbations for trustworthy deep hashing-based retrieval. Our code is available at https://github.com/xandery-geek/SAAT.

Precise crop yield prediction provides valuable information for agricultural planning and decision-making processes. However, timely predicting crop yields remains challenging as crop growth is sensitive to growing season weather variation and climate change. In this work, we develop a deep learning-based solution, namely Multi-Modal Spatial-Temporal Vision Transformer (MMST-ViT), for predicting crop yields at the county level across the United States, by considering the effects of short-term meteorological variations during the growing season and the long-term climate change on crops. Specifically, our MMST-ViT consists of a Multi-Modal Transformer, a Spatial Transformer, and a Temporal Transformer. The Multi-Modal Transformer leverages both visual remote sensing data and short-term meteorological data for modeling the effect of growing season weather variations on crop growth. The Spatial Transformer learns the high-resolution spatial dependency among counties for accurate agricultural tracking. The Temporal Transformer captures the long-range temporal dependency for learning the impact of long-term climate change on crops. Meanwhile, we also devise a novel multi-modal contrastive learning technique to pre-train our model without extensive human supervision. Hence, our MMST-ViT captures the impacts of both short-term weather variations and long-term climate change on crops by leveraging both satellite images and meteorological data. We have conducted extensive experiments on over 200 counties in the United States, with the experimental results exhibiting that our MMST-ViT outperforms its counterparts under three performance metrics of interest.

In this note, we prove the quantitative observability with an explicit control cost for the 1D Schr\"odinger equation over $\mathbb{R}$ with real-valued, bounded continuous potential on thick sets. Our proof relies on different techniques for low-frequency and high-frequency estimates. In particular, we extend the large time observability result for the 1D free Schrodinger equation in Theorem 1.1 of Huang-Wang-Wang [20] to any short time. As another byproduct, we extend the spectral inequality of Lebeau-Moyano [27] for real-analytic potentials to bounded continuous potentials in the one-dimensional case., Comment: 26 pages, comments are welcome

Federated learning (FL) has been widely deployed to enable machine learning training on sensitive data across distributed devices. However, the decentralized learning paradigm and heterogeneity of FL further extend the attack surface for backdoor attacks. Existing FL attack and defense methodologies typically focus on the whole model. None of them recognizes the existence of backdoor-critical (BC) layers-a small subset of layers that dominate the model vulnerabilities. Attacking the BC layers achieves equivalent effects as attacking the whole model but at a far smaller chance of being detected by state-of-the-art (SOTA) defenses. This paper proposes a general in-situ approach that identifies and verifies BC layers from the perspective of attackers. Based on the identified BC layers, we carefully craft a new backdoor attack methodology that adaptively seeks a fundamental balance between attacking effects and stealthiness under various defense strategies. Extensive experiments show that our BC layer-aware backdoor attacks can successfully backdoor FL under seven SOTA defenses with only 10% malicious clients and outperform the latest backdoor attack methods., Comment: Accepted to ICLR'24

We are interested in the three-dimensional quasilinear wave equations with null condition. Global existence and pointwise decay for this model have been proved in the celebrated works of Klainerman \cite{Klainerman86} and Christodoulou \cite{Christodoulou86} for small smooth initial data. In this work, we illustrate the precise pointwise asymptotic behavior of the solutions for initial data posed on a hyperboloid and show that the decay rate $v^{-1}u^{-1}$ is optimal for a generic set of initial data., Comment: 40 pages, all comments are welcome

In this era of information explosion, a personalized recommendation system is convenient for users to get information they are interested in. To deal with billions of users and items, large-scale online recommendation services usually consist of three stages: candidate generation, coarse-grained ranking, and fine-grained ranking. The success of each stage depends on whether the model accurately captures the interests of users, which are usually hidden in users' behavior data. Previous research shows that users' interests are diverse, and one vector is not sufficient to capture users' different preferences. Therefore, many methods use multiple vectors to encode users' interests. However, there are two unsolved problems: (1) The similarity of different vectors in existing methods is too high, with too much redundant information. Consequently, the interests of users are not fully represented. (2) Existing methods model the long-term and short-term behaviors together, ignoring the differences between them. This paper proposes a Hierarchical Multi-Interest Co-Network (HCN) to capture users' diverse interests in the coarse-grained ranking stage. Specifically, we design a hierarchical multi-interest extraction layer to update users' diverse interest centers iteratively. The multiple embedded vectors obtained in this way contain more information and represent the interests of users better in various aspects. Furthermore, we develop a Co-Interest Network to integrate users' long-term and short-term interests. Experiments on several real-world datasets and one large-scale industrial dataset show that HCN effectively outperforms the state-of-the-art methods. We deploy HCN into a large-scale real world E-commerce system and achieve extra 2.5\% improvements on GMV (Gross Merchandise Value).

On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, we aim to establish the uniform boundedness of the total energy of the solution for this system. The proof relies on Klainerman's vector field and Alinhac's ghost weight methods. The main difficulty originates from the slow decay nature of the Dirac and wave components in three space dimensions. To overcome the difficulty, a sharp understanding of the structure for this system, and a new weighted conformal energy estimate are required. In addition, we also provide a few scattering results for the system., Comment: 36 pages, four sections. All suggestions and comments are welcome

While quantum computers provide exciting opportunities for information processing, they currently suffer from noise during computation that is not fully understood. Incomplete noise models have led to discrepancies between quantum program success rate (SR) estimates and actual machine outcomes. For example, the estimated probability of success (ESP) is the state-of-the-art metric used to gauge quantum program performance. The ESP suffers poor prediction since it fails to account for the unique combination of circuit structure, quantum state, and quantum computer properties specific to each program execution. Thus, an urgent need exists for a systematic approach that can elucidate various noise impacts and accurately and robustly predict quantum computer success rates, emphasizing application and device scaling. In this article, we propose quantum vulnerability analysis (QVA) to systematically quantify the error impact on quantum applications and address the gap between current success rate (SR) estimators and real quantum computer results. The QVA determines the cumulative quantum vulnerability (CQV) of the target quantum computation, which quantifies the quantum error impact based on the entire algorithm applied to the target quantum machine. By evaluating the CQV with well-known benchmarks on three 27-qubit quantum computers, the CQV success estimation outperforms the estimated probability of success state-of-the-art prediction technique by achieving on average six times less relative prediction error, with best cases at 30 times, for benchmarks with a real SR rate above 0.1%. Direct application of QVA has been provided that helps researchers choose a promising compiling strategy at compile time., Comment: 11pages, 11 figures

In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: 1) we show sharp time decay for the pointwise estimates of the solutions which imply the asymptotic stability of this system; 2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, high-regular initial data, in particular, there is no restriction on the support of the initial data., Comment: 42 Pages, 3 sections. All comments and suggestions are warmly welcome

We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{\alpha\beta}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small in some weighted Sobolev space, which do not necessarily have compact support, and we also show the optimal time decay of the solution. The major difficulties lie in the slow decay nature of the wave and the Klein-Gordon components in two space dimensions, in addition, extra difficulties arise due to the presence of the null form $Q_0$ which is not of divergence form and is not compatible with the Klein-Gordon equations. To overcome the difficulties, a new observation for the structure of the null form $Q_0$ is required., Comment: 28 pages, three sections. All suggestions and comments are welcome

Locating the critical endpoint of QCD and the region of a first-order phase transition at finite baryon chemical potential is an active research area for QCD matter. We provide a gravitational dual description of QCD matter at finite baryon chemical potential and finite temperature using the non-perturbative approach from gauge/gravity duality. After fixing all model parameters using state-of-the-art lattice QCD data at zero chemical potential, the predicted equations of state and QCD trace anomaly relation are in quantitative agreement with the latest lattice results. We then give the exact location of the critical endpoint as well as the first-order transition line, which is within the coverage of many upcoming experimental measurements. Moreover, using the data from our model at finite baryon chemical potential, we calculate the spectrum of the stochastic gravitational wave background associated with the first-order QCD transition in the early universe, which could be observable via pulsar timing in the future., Comment: 5 + 10 pages, 13 figures

Serverless computing automates fine-grained resource scaling and simplifies the development and deployment of online services with stateless functions. However, it is still non-trivial for users to allocate appropriate resources due to various function types, dependencies, and input sizes. Misconfiguration of resource allocations leaves functions either under-provisioned or over-provisioned and leads to continuous low resource utilization. This paper presents Freyr, a new resource manager (RM) for serverless platforms that maximizes resource efficiency by dynamically harvesting idle resources from over-provisioned functions to under-provisioned functions. Freyr monitors each function's resource utilization in real-time, detects over-provisioning and under-provisioning, and learns to harvest idle resources safely and accelerates functions efficiently by applying deep reinforcement learning algorithms along with a safeguard mechanism. We have implemented and deployed a Freyr prototype in a 13-node Apache OpenWhisk cluster. Experimental results show that 38.8% of function invocations have idle resources harvested by Freyr, and 39.2% of invocations are accelerated by the harvested resources. Freyr reduces the 99th-percentile function response latency by 32.1% compared to the baseline RMs., Comment: Accepted by the ACM WebConf 2022

Most sequential recommendation models capture the features of consecutive items in a user-item interaction history. Though effective, their representation expressiveness is still hindered by the sparse learning signals. As a result, the sequential recommender is prone to make inconsistent predictions. In this paper, we propose a model, SSI, to improve sequential recommendation consistency with Self-Supervised Imitation. Precisely, we extract the consistency knowledge by utilizing three self-supervised pre-training tasks, where temporal consistency and persona consistency capture user-interaction dynamics in terms of the chronological order and persona sensitivities, respectively. Furthermore, to provide the model with a global perspective, global session consistency is introduced by maximizing the mutual information among global and local interaction sequences. Finally, to comprehensively take advantage of all three independent aspects of consistency-enhanced knowledge, we establish an integrated imitation learning framework. The consistency knowledge is effectively internalized and transferred to the student model by imitating the conventional prediction logit as well as the consistency-enhanced item representations. In addition, the flexible self-supervised imitation framework can also benefit other student recommenders. Experiments on four real-world datasets show that SSI effectively outperforms the state-of-the-art sequential recommendation methods., Comment: accepted by IJCAI 2021

Consider the focusing 4D cubic wave equation \[ \partial_{tt}u-\Delta u-u^{3}=0,\quad \mbox{on}\ (t,x)\in [0,\infty)\times \mathbb{R}^{4}.\] The main result states the existence in energy space $\dot{H}^{1}\times L^{2}$ of multi-solitary waves where each traveling wave is generated by Lorentz transform from a specific excited state, with different but collinear Lorentz speeds. The specific excited state is deduced from the non-degenerate sign-changing state constructed in Musso-Wei [34]. The proof is inspired by the techniques developed for the 5D energy-critical wave equation and the nonlinear Klein-Gordon equation in a similar context by Martel-Merle [30] and C\^ote-Martel [6]. The main difficulty originates from the strong interactions between solutions in the 4D case compared to other dispersive and wave-type models. To overcome the difficulty, a sharp understanding of the asymptotic behavior of the excited states involved and of the kernel of their linearized operator is needed.

We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with $\alpha>0$, $2 \le N\le 5$ and energy subcritical exponents $p>2$. We study the behavior of solutions for which it is supposed that only one nonlinear object appears asymptotically for large times, at least for a sequence of times. We first prove that the nonlinear object is necessarily a bound state. Next, we show that when the nonlinear object is a non-degenerate state or a degenerate excited state satisfying a simplicity condition, the convergence holds for all positive times, with an exponential or algebraic rate respectively. Last, we provide an example where the solution converges exactly at the rate $t^{-1}$ to the excited state.

For the 5D energy-critical wave equation, we construct excited $N$-solitons with collinear speeds, i.e. solutions $u$ of the equation such that \begin{equation*} \lim_{t\to+\infty}\bigg\|\nabla_{t,x}u(t)-\nabla_{t,x}\bigg(\sum_{n=1}^{N}Q_{n}(t)\bigg)\bigg\|_{L^{2}}=0, \end{equation*} where for $n=1,\ldots,N$, $Q_n(t,x)$ is the Lorentz transform of a non-degenerate and sufficiently decaying excited state, each with different but collinear speeds. The existence proof follows the ideas of Martel-Merle and C\^ote-Martel developed for the energy-critical wave and nonlinear Klein-Gordon equations. In particular, we rely on an energy method and on a general coercivity property for the linearized operator.

We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-1}u+|u|^{q-1}u=0,\quad \mbox{on}\ [0,\infty)\times \mathbb{R}, \end{equation*} with $1

For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove that any global finite energy solution either converges to $0$ or behaves asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate signs and their distances are of order $\log t$.

We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on $\bf R^N$, for $1\leq N\leq 5$ and energy subcritical exponents $p>2$. The description is twofold. First, we prove that 2-solitary waves with same sign do not exist. Second, we construct and classify the full family of 2-solitary waves in the case of opposite signs. Close to the sum of two remote solitary waves, it turns out that only the components of the initial data in the unstable direction of each ground state are relevant in the large time asymptotic behavior of the solution. In particular, we show that $2$-solitary waves have a universal behavior: the distance between the solitary waves is asymptotic to $\log t$ as $t\to \infty$. This behavior is due to damping of the initial data combined with strong interactions between the solitary waves.

In this paper, we construct $K$-solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions $u$ of the equation such that \begin{equation*} \|\nabla_{t,x}u(t)-\nabla_{t,x}\big(\sum_{k=1}^{K}W_{k}(t)\big)\|_{L^{2}}\to 0\quad \mathrm{as}\ t\to \infty, \end{equation*} where for any $k\in \{1,\dots,K\}$, $W_{k}$ is Lorentz transform of the explicit standing soliton $W(x)=(1+|x|^{2}/15)^{-3/2}$, with any speed $\boldsymbol{\ell}_{k}\in \mathbb{R}^{5}$ ,$|\boldsymbol{\ell}_{k}|<1$ ($\boldsymbol{\ell}_{k'}\ne \boldsymbol{\ell}_{k}$ for $k'\ne k$) satisfying an explicit smallness condition., Comment: 30 pages. minor revisions. arXiv admin note: substantial text overlap with arXiv:1708.09712, arXiv:1504.01595 by other authors

We calculate the forward backward asymmetry of the top-pair production at TEVATRON up to next to leading order (NLO) in the little Higgs model (LHM). We find that the contribution of $Z_H$ can be large enough to make up the gap between standard model (SM) prediction and data. With the database of $7.65\pm0.20\pm0.36$ pb, therefore, the parameter space for flavor-changing coupling of $Z_H$ is constrained. Thus this model can result in the required asymmetry while the total cross section of top-pair production remaining consistent with data., Comment: 8 figures

Because at the tree level $B_s\rightarrow K^+K^-$ is Cabibbo-triple suppressed, so its branching ratio should be smaller than that of $B_s\to \pi^+ K^-$. The measurements present a reversed ratio as $R=\mathcal B(B_s\rightarrow \pi^+K^-)/\mathcal B(B_s\rightarrow K^+ K^-)\sim{4.9/33}$. Therefore, It has been suggested that the transition $B_s\to K^+K^-$ is dominated by the penguin mechanism, which is proportional to $V_{cb}V^*_{cs}$. In this work, we show that an extra contribution from the final state interaction (FSI) to $B_s\to K^+K^-$ via sequential processes $B_s\to D^{(*)}_{(s)} \bar D_s^{(*)}\to K^+K^-$ is also substantial and should be superposed on the penguin contribution. Indeed, taking into account of the FSI effects, the theoretical prediction on $R$ is well consistent with the data., Comment: 9 pages, 1 figures, 3 tables. Accepted by PRD

The successful operation of LHC provides a great opportunity to study the processes where heavy baryons are involved. {In this work we mainly study} the weak transitions of $\Sigma_b\to \Sigma_c$. Assuming the reasonable quark-diquark structure where the two light quarks constitute an axial vector, we calculate the widths of semi-leptonic decay $\Sigma_{b}\to\Sigma_c e\nu_e$ and non-leptonic decay modes $\Sigma_{b}\to\Sigma_c +M$ (light mesons) in terms of the light front quark model. We first construct the vertex function for the concerned baryons and then deduce the form factors which are related to two Isgur-Wise functions for the $\Sigma_{b}\to\Sigma_c$ transition under the heavy quark limit. Our numerical results indicate that $\Gamma(\Sigma_{b}\to\Sigma_c e\nu_e)$ is about $1.38\times10^{10}{\rm s}^{-1}$ and $\Gamma(\Sigma_{b}\to\Sigma_c +M)$ is slightly below $1\times10^{10}{\rm s}^{-1}$ which may be accessed at the LHCb detector. By the flavor SU(3) symmetry we estimate the rates of $\Omega_b\to\Omega_c$. We suggest to measure weak decays of $\Omega_b\to\Omega_c$, because $\Omega_b$ does not decay via strong interaction, the advantage is obvious., Comment: 17 pages 3 figures. To avoid overlap with our previous work, we have deleted most repeated and unnecessary parts. The whole version is re-written

Whether molecular states indeed exist in nature has been disputed for a long time. Several new resonances have been observed in the recent experiments and they seem to be of exotic structures and some of them have been proposed to be molecular states. The very recent observation of $Z_b(10610)[(10608.4\pm 2.0)$ MeV] and $Z_b(10650)[(10653.2\pm 1.5)$ MeV] encourages the interpretation of multi-quark states. In the Beter-Salpeter (BS) approach, we study the possibility if two heavy mesons can form a molecular state by exchanging light mesons. Our results indicate that two heavy mesons can form an isospin singlet (I=0) bound state but cannot form an isospin triplet (I=1) when the contribution of $\sigma-$ exchange is reasonably small, i.e. as the coupling of $\sigma$ with mesons $g_{\sigma}$ takes the value given in previous literatures. Thus we conclude that the newly observed $Z_b(10610)$ should not be a molecular state, but a tetraquark state instead, at most, the fraction of the molecular state in the physical resonance $Z_b(10610)$ is tiny., Comment: 15 pages, 2 figures, an important reference added; Accepted by JHEP

In this work, we calculate the mass spectrum of doubly heavy baryons with the diquark model in terms of the QCD sum rules. The interpolating currents are composed of a heavy diquark field and a light quark field. Contributions of the operators up to dimension six are taken into account in the operator product expansion. Within a reasonable error tolerance, our numerical results are compatible with other theoretical predictions. This indicates that the diquark picture reflects the reality and is applicable to the study of doubly heavy baryons., Comment: 23 pages, 9 figures, minor corrections in expressions

We calculate the correlation functions of $0^{++}$ $q\bar q$, $s\bar s$ and glueball in the QCD sum rules and obtain the mass matrix where non-diagonal terms are determined by the cross correlations among the three states. Diagonalizing the mass matrix and identifying the eigenstates as the physical $0^{++}$ scalar mesons, we can determine the mixing. Concretely, our calculations determine the fractions of $q\bar q$, $s\bar s$ and glueball in the physical states $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, the results are consistent with that gained by the phenomenological research., Comment: 15 pages, 6 figures, discussion slightly modified and more references added

It is interesting to determine the fraction of the gluonium component in $\eta$ and $\eta'$ which has been under serious discussion for many years. Measurements on different decay and/or production modes were employed in literatures, thus larger uncertainties were unavoidable. In this paper we suggest to determine the mixing angles of $\eta-\eta'-G$ using the data of semileptonic decays of $D$ and $D_s$. We extract the mixing angles $\phi'$, $\phi_G$ and the model parameters simultaneously. Thanks to the new measurements carried out by CLEO Collaboration and there are sufficient decay modes to determine both the model parameters and mixing angles. The mixing angles from data are $\phi'=(41.5\pm2.0)^\circ$ and $\sin\phi_G=0.00\pm0.36$. Even though the central value of $\sin\phi_G$ is still zero, an upper bound is set. Moreover, as suggested in literature, $\eta(1405)$ is a glueball candidate whereas in our picture, $\eta(1405)$ may be identified as $G$ with glueonium being its main content. Using all the model-parameters obtained above, we estimate the branching ratios of $D_s^+(D^+)\rightarrow Ge^+\nu_e$ where G is identified as $\eta(1405)$., Comment: 7 pages, 1 figure, Acceptted by Int. J. Mod. Phys. A

We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation is different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $b\bar c(\bar b c)$ family. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $b\bar c$ family. We also consider the Lamb shift of the spectra.

We indicated in our previous work that for QED the contributions of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation may be different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce the scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia. Taking into account both vector and scalar potentials, by fitting the well measured charmonia spectra, we re-fix the relevant parameters and test them by calculating other states of the charmonia family. We also consider the role of the Lamb shift and present the numerical results with and without involving the Lamb shift.

Contributions of fermions to the mass of the scalar glueball $0^{++}$ are calculated at two-loop level in the framework of QCD sum rules. It obviously changes the coefficients in the operator product expansion (OPE) and shifts the mass of glueball., Comment: 5 pages, 2 figures

The full potential linearized augmented plane wave (FLAPW) method was used to study the crystal structure and electronic structure properties of PbFe0.5Nb0.5O3 (PFN). The optimized crystal structure, density of states, band structure and electron density distribution have been obtained to understand the ferroelectric behavior of PFN. From the density of states analysis, it is shown that there is a hybridization of Fe d - O p and Nb d - O p in ferroelectric PFN. This is consistent with the calculation of electronic band structure. This hybridization is responsible for the tendency to its ferroelectricity., Comment: 10 pages