Exact results of one-dimensional repulsive Hubbard model

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.Comment: slight changes, 50 pages +18 figures, new analytical result

Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model

A rigorous understanding of the spin incoherent Tomonaga-Luttinger liquid (TLL), which displays solely a propagating charge mode but not a spin mode, and the interaction-driven quantum phase transitions in one-dimensional (1D) systems still remain elusive. In this Letter, we report the universal properties of spin incoherent TLL and interaction-driven criticality of the 1D repulsive Hubbard model by means of fractional charge and spin excitations, asymptotic of correlation functions as well as the lattice Contact. We build up an essential connection of Contact susceptibilities to the variations of density, magnetization and entropy with respect to the interaction strength, providing a rigorous understanding of interaction-driven phase transitions, Mott insulator and quantum cooling in the model. These relations hold true for higher dimensional systems.Comment: 4 figures 6 page

Not All Instances Contribute Equally: Instance-adaptive Class Representation Learning for Few-Shot Visual Recognition

Few-shot visual recognition refers to recognize novel visual concepts from a few labeled instances. Many few-shot visual recognition methods adopt the metric-based meta-learning paradigm by comparing the query representation with class representations to predict the category of query instance. However, current metric-based methods generally treat all instances equally and consequently often obtain biased class representation, considering not all instances are equally significant when summarizing the instance-level representations for the class-level representation. For example, some instances may contain unrepresentative information, such as too much background and information of unrelated concepts, which skew the results. To address the above issues, we propose a novel metric-based meta-learning framework termed instance-adaptive class representation learning network (ICRL-Net) for few-shot visual recognition. Specifically, we develop an adaptive instance revaluing network with the capability to address the biased representation issue when generating the class representation, by learning and assigning adaptive weights for different instances according to their relative significance in the support set of corresponding class. Additionally, we design an improved bilinear instance representation and incorporate two novel structural losses, i.e., intra-class instance clustering loss and inter-class representation distinguishing loss, to further regulate the instance revaluation process and refine the class representation. We conduct extensive experiments on four commonly adopted few-shot benchmarks: miniImageNet, tieredImageNet, CIFAR-FS, and FC100 datasets. The experimental results compared with the state-of-the-art approaches demonstrate the superiority of our ICRL-Net

PartSeg: Few-shot Part Segmentation via Part-aware Prompt Learning

In this work, we address the task of few-shot part segmentation, which aims to segment the different parts of an unseen object using very few labeled examples. It is found that leveraging the textual space of a powerful pre-trained image-language model (such as CLIP) can be beneficial in learning visual features. Therefore, we develop a novel method termed PartSeg for few-shot part segmentation based on multimodal learning. Specifically, we design a part-aware prompt learning method to generate part-specific prompts that enable the CLIP model to better understand the concept of ``part'' and fully utilize its textual space. Furthermore, since the concept of the same part under different object categories is general, we establish relationships between these parts during the prompt learning process. We conduct extensive experiments on the PartImageNet and Pascal$\_$Part datasets, and the experimental results demonstrated that our proposed method achieves state-of-the-art performance

Is exponential gravity a viable description for the whole cosmological history?

Here we analysed a particular type of $F(R)$ gravity, the so-called exponential gravity which includes an exponential function of the Ricci scalar in the action. Such term represents a correction to the usual Hilbert-Einstein action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic Microwave Background and $H(z)$ data, the free parameters of the model are well constrained. The results show that such corrections to General Relativity become important at cosmological scales and at late-times, providing an alternative to the dark energy problem. In addition, the fits do not determine any significant difference statistically with respect to the $\Lambda$CDM model. Finally, such model is extended to include the inflationary epoch in the same gravitational Lagrangian. As shown in the paper, the additional terms can reproduce the inflationary epoch and satisfy the constraints from Planck data.Comment: 20 pages, 6 figures, analysis extended, version published in EPJ

Double Scattering Effect in Transverse Momentum Distribution of Inclusive J/ψJ/\psi Production in Photo-Nucleus Collision

In terms of multiple scattering picture, we calculate the double scattering effect in the transverse momentum distribution of $J/\psi$ photoproduction. Applying the generalized factorization theorem, we find that the contributions from double scattering can be expressed in terms of twist-4 nuclear parton correlation functions, which is the same as that used to explain the nuclear dependence in di-jet momentum imbalance and in direct photon production. Using the known information on the twist-4 parton correlation functions, we estimate that the double scattering contributes a small suppression in $J/\psi$ photoproduction. In the analysis we only take into account the leading order in the small velocity expansion for the nonperturbative parts related to the quarkonium.Comment: 23 pages LaTex (9 figures included), to appear in Nucl. Phys.

FedABC: Targeting Fair Competition in Personalized Federated Learning

Federated learning aims to collaboratively train models without accessing their client's local private data. The data may be Non-IID for different clients and thus resulting in poor performance. Recently, personalized federated learning (PFL) has achieved great success in handling Non-IID data by enforcing regularization in local optimization or improving the model aggregation scheme on the server. However, most of the PFL approaches do not take into account the unfair competition issue caused by the imbalanced data distribution and lack of positive samples for some classes in each client. To address this issue, we propose a novel and generic PFL framework termed Federated Averaging via Binary Classification, dubbed FedABC. In particular, we adopt the ``one-vs-all'' training strategy in each client to alleviate the unfair competition between classes by constructing a personalized binary classification problem for each class. This may aggravate the class imbalance challenge and thus a novel personalized binary classification loss that incorporates both the under-sampling and hard sample mining strategies is designed. Extensive experiments are conducted on two popular datasets under different settings, and the results demonstrate that our FedABC can significantly outperform the existing counterparts.Comment: 9 pages,5 figure