Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $\Delta k_F$ ($2\Delta k_F$). Here $\Delta k_F=\pi(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch $k=\Delta k_F$, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter $\beta$ representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.Comment: 26 pages, 4 figures, published version, a series of study on the 1D attractive Hubbard model, few typos were corrected, references were added, also see arXiv:1708.07784 and arXiv:1708.0777

NAIS: Neural Attentive Item Similarity Model for Recommendation

Item-to-item collaborative filtering (aka. item-based CF) has been long used for building recommender systems in industrial settings, owing to its interpretability and efficiency in real-time personalization. It builds a user's profile as her historically interacted items, recommending new items that are similar to the user's profile. As such, the key to an item-based CF method is in the estimation of item similarities. Early approaches use statistical measures such as cosine similarity and Pearson coefficient to estimate item similarities, which are less accurate since they lack tailored optimization for the recommendation task. In recent years, several works attempt to learn item similarities from data, by expressing the similarity as an underlying model and estimating model parameters by optimizing a recommendation-aware objective function. While extensive efforts have been made to use shallow linear models for learning item similarities, there has been relatively less work exploring nonlinear neural network models for item-based CF. In this work, we propose a neural network model named Neural Attentive Item Similarity model (NAIS) for item-based CF. The key to our design of NAIS is an attention network, which is capable of distinguishing which historical items in a user profile are more important for a prediction. Compared to the state-of-the-art item-based CF method Factored Item Similarity Model (FISM), our NAIS has stronger representation power with only a few additional parameters brought by the attention network. Extensive experiments on two public benchmarks demonstrate the effectiveness of NAIS. This work is the first attempt that designs neural network models for item-based CF, opening up new research possibilities for future developments of neural recommender systems

Custodial Symmetry Violation in Scalar Extensions of the Standard Model

The new measurement of the W boson mass from the CDF collaboration shows a significant tension with the Standard Model prediction, which evidences violation of custodial symmetry in the scalar sector. We study the scalar extensions of the Standard Model, which can be categorized into two classes, scalar sector with custodial symmetry (Georgi-Machacek model and its generalizations) and scalar sector without custodial symmetry, and explore how these extensions fit to the electroweak precision data and the CDF new $m_W$ . The favored oblique parameters are coming from either the large mass splitting in the multiplet via the loop contribution or the large vacuum expectation value which breaks custodial symmetry at the tree level. In particular, we find that $\mathcal{O}(100)$ GeV new particles are allowed in the scalar extension scenarios.Comment: 24 pages, 4 figure

Genome-wide comparative analysis of metacaspases in unicellular and filamentous cyanobacteria

<p>Abstract</p> <p>Background</p> <p>Cyanobacteria are an ancient group of photoautotrophic prokaryotes with wide variations in genome size and ecological habitat. Metacaspases (MCAs) are cysteine proteinases that have sequence homology to caspases and play essential roles in programmed cell death (PCD). MCAs have been identified in several prokaryotes, fungi and plants; however, knowledge about cyanobacterial metacaspases still remains obscure. With the availability of sequenced genomes of 33 cyanobacteria, we perform a comparative analysis of metacaspases and explore their distribution, domain structure and evolution.</p> <p>Results</p> <p>A total of 58 putative MCAs were identified, which are abundant in filamentous diazotrophic cyanobacteria and <it>Acaryochloris marina </it>MBIC 11017 and absent in all <it>Prochlorococcus </it>and marine <it>Synechococcus </it>strains, except <it>Synechococcus </it>sp. PCC 7002. The Cys-His dyad of caspase superfamily is conserved, while mutations (Tyr in place of His and Ser/Asn/Gln/Gly instead of Cys) are also detected in some cyanobacteria. MCAs can be classified into two major families (α and β) based on the additional domain structure. Ten types and a total of 276 additional domains were identified, most of which involves in signal transduction. Apoptotic related NACHT domain was also found in two cyanobacterial MCAs. Phylogenetic tree of MCA catalytic P20 domains coincides well with the domain structure and the phylogenies based on 16s rRNA.</p> <p>Conclusions</p> <p>The existence and quantity of MCA genes in unicellular and filamentous cyanobacteria are a function of the genome size and ecological habitat. MCAs of family α and β seem to evolve separately and the recruitment of WD40 additional domain occurs later than the divergence of the two families. In this study, a general framework of sequence-structure-function connections for the metacaspases has been revealed, which may provide new targets for function investigation.</p

Complete EFT Operator Bases for Dark Matter and Weakly-Interacting Light Particle

The standard model can be extended to include weakly-interacting light particle (WILP): real or complex singlet scalar, Majorana or Dirac neutral fermion, neutral or hidden-charged vector boson, etc. Imposing the $Z_2$ symmetry, these particles can be lifted as the weakly-interacting massive particle (WIMP), the candidate of dark matter. Instead, imposing the shift symmetry on the scalar components gives rise to the axion-like particle, dark photon, etc. Utilizing these light degree of freedom along with the standard model particles and imposing different symmetries, we construct the complete and independent sets of effective operators up to dimension eight with the Young tensor technique, consistent with counting from the Hilbert series.Comment: 109 pages. arXiv admin note: text overlap with arXiv:2305.1677