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We investigate the one-point restriction of the conformal blocks on $(\mathbb{P}^1,\infty, w,0)$ defined by modules over a vertex operator algebra. By restricting the module attached to the point $\infty$ to its bottom degree, we obtain a new formula to calculate fusion rules using a module over the degree-zero Borcherds' Lie algebra. This formula holds under more general assumptions than Frenkel-Zhu's fusion rules theorem. By restricting the module attached to the point $w$ to its bottom degree, we obtain a more general version of Li's nuclear democracy theorem for vertex operator algebras.

Preheating at the end of inflation is a violent nonlinear process that efficiently transfers the energy of the inflaton to a second field, the preheat field. When the preheat field is light during inflation and its background value modulates the preheating process, the superhorizon isocurvature perturbations of the preheat field may be converted to curvature perturbations that leave an imprint on the cosmic microwave background and the large-scale structure of the universe. We use high-precision lattice simulations to study kinetic preheating after $\alpha$-attractor inflation, a case where the effective mass of the preheat field is naturally suppressed during inflation. By comparing the expansion e-folds between different Hubble patches, we find that the conversion from isocurvature perturbations to curvature perturbations is very inefficient and can hardly be detected by cosmological observations., Comment: MEET-U project II

We propose a new cosmological model that considers dark matter as a barotropic fluid with a constant equation of state parameter and interprets dark energy as the phenomenological emergent dark energy rather than a cosmological constant. This proposal is based on extensive research on the extended properties of dark matter in the context of a cosmological constant and the intriguing findings that have emerged from our exploration of dark matter properties within the context of PEDE in our previous studies. We then place constraints on this model in light of the Planck 2018 Cosmic Microwave Background (CMB) anisotropies, baryon acoustic oscillation (BAO) measurements, the Pantheon compilation of Type Ia supernovae, a prior on $H_0$ that based on the latest local measurement by Riess et al., and the combination of KiDS and the VISTA Kilo-Degree Infrared Galaxy Survey (KiDS+VIKING-450). The results indicate a preference for a positive dark matter equation of state parameter at 68\% confidence level for CMB+BAO, CMB+BAO+Pantheon and CMB+BAO+Pantheon+$H_0$ datasets. Furthermore, the Hubble tension between all of the datasets we used with R22 is very close to those of the PEDE, and the $S_8$ tension between Planck 2018 and KiDS+VIKING-450 is reduced from 2.3$\sigma$ in the PEDE model to 0.4$\sigma$ in the new model. However, Bayesian evidence indicates that PEDE favors our new model with very strong evidence from all the datasets considered in this study. Consequently, we conclude that the PEDE+$w_{\rm dm}$ model is not a viable alternative to the PEDE model., Comment: 9 pages, 3 figures. arXiv admin note: text overlap with arXiv:2303.00961

The unified dark fluid model unifies dark matter and dark energy into a single component, providing an alternative and more concise framework for interpreting cosmological observations. We introduce a PAge-like Unified Dark Fluid (PUDF) model based on the PAge approximation (Huang 2020), which is parameterized by the age of the universe and an $\eta$ parameter indicating the deviation from Einstein-De Sitter Universe. The PUDF model shares many similar features of the standard Lambda cold dark matter ($\Lambda$CDM) model and can effectively describe the large-scale structure formation and late-time cosmic acceleration. We constrain the PUDF model with the Planck 2018 cosmic microwave background anisotropies, baryon acoustic oscillation measurements including those from the most recent DESI 2024, the Pantheon+ sample of Type Ia supernovae, and the Cosmic Chronometers compilation. Although the PUDF performs well in fitting all the cosmological datasets, the joint analysis of the data still favors the $\Lambda$CDM model over the PUDF model, according to the Bayesian evidence of model comparison., Comment: 6 pages, 4 figures, 1 table. Accepted for publication in the Journal of Cosmology and Astroparticle Physics

Joint analysis of the baryon acoustic oscillations (BAO) measurement by the Dark Energy Spectroscopic Instrument (DESI) first data release, Type Ia supernovae (SNe) of the Dark Energy Survey Year 5 (DES5YR) release and cosmic microwave background (CMB) data favors a quintom-like dynamic dark energy model over the standard Lambda cold dark matter ($\Lambda$CDM) model at $3.9\sigma$ level (Adame et al. 2024). We confirm the previous finding in the literature that the preference for dynamic dark energy does not rely on the detailed modeling of CMB physics and remains at a similar significance level ($3.2\sigma$) when the full CMB likelihood is replaced by a CMB acoustic-oscillation angle ($\theta_\star$) prior and a baryon abundance ($\Omega_bh^2$) prior. The computationally efficient $\theta_\star$ and $\Omega_bh^2$ priors allow us to take a frequentist approach by comparing DES5YR SNe and DESI BAO with a large number ($\gtrsim 10^4$) of Planck-constrained $\Lambda$CDM simulations. We find that $\geq 3.2\sigma$ preference for dynamic dark energy is very rare (occurrence rate = $0.28\%$) in simulations. When we combine DESI BAO with SN simulations or combine DES5YR SNe with BAO simulations, the occurrence rate of $\geq 3.2\sigma$ preference for dynamic dark energy increases to $1.2\%$ and $4.8\%$, respectively. These results indicate an internal inconsistency, i.e., a significant tension between DESI BAO + DES5YR SNe and Planck-constrained $\Lambda$CDM models in both Bayesian and frequentist points of view. Although both DESI BAO and DES5YR SNe contribute to the preference for dynamic dark energy, the contribution from DES5YR SNe is more significant. In the frequentist point of view, even DES5YR SNe alone is in tension with Planck-constrained $\Lambda$CDM models, though in Bayesian point of view this tension is prior dependent and inclusive., Comment: MEET-U project I; accepted for publication in PRD

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided., Comment: 54 pages. New applications are added

In this paper, we introduce and study new classes of subVOAs of the lattice vertex operator algebras, which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily strongly finitely generated, satisfy similar properties with the usual Borel and parabolic subalgebras of a Lie algebra. For the lowest-rank nontrivial example of Borel-type subVOA $V_{B}$ of $V_{\Z\al}$, we explicitly determine its Zhu's algebra $A(V_B)$ in terms of generators and relations.

In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\mathfrak{x}\colon\overline{C}\to\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of two $g$-twisted modules $M^2$ and $M^3$ over a vertex operator algebra $V$. We show that the space of twisted restricted conformal blocks is isomorphic to the space of $g$-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem., Comment: 52pages

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope (JWST) implies efficient structure formation or large star formation efficiency at high redshift $z\sim 10$. In the scenario of a low or moderate star formation efficiency, because massive neutrinos tend to suppress the growth of structure of the universe, the JWST observation tightens the upper bound of the neutrino masses. Assuming $\Lambda$ cold dark matter cosmology and a star formation efficiency $ \in [0.05, 0.3]$ (flat prior), we perform joint analyses of Planck+JWST and Planck+BAO+JWST, and obtain improved constraints $\sum m_\nu < 0.196\,\mathrm{eV}$ and $\sum m_\nu < 0.111\,\mathrm{eV}$ at 95% confidence level, respectively. Based on the above assumptions, the inverted mass ordering, which implies $\sum m_\nu\geq 0.1\mathrm{eV}$, is excluded by Planck+BAO+JWST at 92.7% confidence level., Comment: 9 pages, 8 figures

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone. The code is based on the extended Press-Schechter model and is computationally efficient, typically taking a few seconds on a personal laptop for a given set of cosmological parameters. The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope, as well as scanning the theory space with the Markov Chain Monte Carlo method. As an example application, we use the tool to study the cosmological implication of the candidate galaxies presented in Labb\'e et al. (2023). The standard $\Lambda$ cold dark matter ($\Lambda$CDM) model is well consistent with the data if the star formation efficiency can reach $\sim 0.3$ at high redshift. For a low star formation efficiency $\epsilon \sim 0.1$, $\Lambda$CDM model is disfavored at $\sim 2\sigma$-$3\sigma$ confidence level., Comment: 6 pages, 3 figures

Single object tracking (SOT) heavily relies on the representation of the target object as a bounding box. However, due to the potential deformation and rotation experienced by the tracked targets, the genuine bounding box fails to capture the appearance information explicitly and introduces cluttered background. This paper proposes RTrack, a novel object representation baseline tracker that utilizes a set of sample points to get a pseudo bounding box. RTrack automatically arranges these points to define the spatial extents and highlight local areas. Building upon the baseline, we conducted an in-depth exploration of the training potential and introduced a one-to-many leading assignment strategy. It is worth noting that our approach achieves competitive performance to the state-of-the-art trackers on the GOT-10k dataset while reducing training time to just 10% of the previous state-of-the-art (SOTA) trackers' training costs. The substantial reduction in training costs brings single-object tracking (SOT) closer to the object detection (OD) task. Extensive experiments demonstrate that our proposed RTrack achieves SOTA results with faster convergence.

The recent advancements in transformer-based visual trackers have led to significant progress, attributed to their strong modeling capabilities. However, as performance improves, running latency correspondingly increases, presenting a challenge for real-time robotics applications, especially on edge devices with computational constraints. In response to this, we introduce LiteTrack, an efficient transformer-based tracking model optimized for high-speed operations across various devices. It achieves a more favorable trade-off between accuracy and efficiency than the other lightweight trackers. The main innovations of LiteTrack encompass: 1) asynchronous feature extraction and interaction between the template and search region for better feature fushion and cutting redundant computation, and 2) pruning encoder layers from a heavy tracker to refine the balnace between performance and speed. As an example, our fastest variant, LiteTrack-B4, achieves 65.2% AO on the GOT-10k benchmark, surpassing all preceding efficient trackers, while running over 100 fps with ONNX on the Jetson Orin NX edge device. Moreover, our LiteTrack-B9 reaches competitive 72.2% AO on GOT-10k and 82.4% AUC on TrackingNet, and operates at 171 fps on an NVIDIA 2080Ti GPU. The code and demo materials will be available at https://github.com/TsingWei/LiteTrack.

Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the derivations, namely Rota-Baxter operators, in vertex (operator) algebras. The closely related notion of dendriform algebras is also defined for vertex operator algebras. It is shown that the classical relations among dendriform algebras, associative algebras, and Rota-Baxter algebras are preserved for their vertex algebra analogs.

In this paper we introduce an analog of the (classical) Yang-Baxter equation (CYBE) for vertex operator algebras (VOAs) in its tensor form, called the vertex operator Yang-Baxter equation (VOYBE). When specialized to level one of a vertex operator algebra, the VOYBE reduces to the CYBE for Lie algebras. To give an operator form of the VOYBE, we also introduce the notion of relative Rota-Baxter operators (RBOs) as the VOA analog of relative RBOs (classically called $\mathcal{O}$-operators) for Lie algebras. It is shown that skewsymmetric solutions $r$ to the VOYBE in a VOA $U$ are characterized by the condition that their corresponding linear maps $T_r:U'\to U$ from the graded dual $U'$ of $U$ are relative RBOs. On the other hand, strong relative RBOs on a VOA $V$ associated to an ordinary $V$-module $W$ are characterized by the condition that their antisymmetrizers are solutions to the $0$-VOYBE in the semidirect product VOA $V\rtimes W'$. Specializing to the first level of a VOA, these relations between the solutions of the VOYBE and the relative RBOs for VOAs recover the classical relations between the solutions of the CYBE and the relative RBOs for Lie algebras., Comment: 30 pages

In this paper, we study the endomorphism properties of vertex operator algebras over an arbitrary field $\mathbb{F}$, with $\text{Char}(\mathbb{F}) \neq 2$. Let $V$ be a strongly finitely generated vertex operator algebra over $\mathbb{F}$, and $M$ be an irreducible admissible $V$-module. We prove that every element in $\text{End}_V(M)$ is algebraic over $\mathbb{F}$ and that $\text{End}_V(M)$ is also finite-dimensional. As an application, we prove Schur's lemma for strongly finitely generated vertex operator algebras over arbitrary algebraically closed fields, and we give a test for absolute irreducibility of $V$-modules.

In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the representation theory of the VOA, and its fusion rules, and the Noetherian property gives the potential for (non-commutative) algebro-geometric methods to be employed in their study.