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The presence of extended Main Sequence Turn-Off (eMSTO) in the open clusters has been attributed to various factors, such as spread in rotation rates, binary stars, and dust-like extinction from stellar excretion discs. We present a comprehensive analysis of the eMSTO in the open cluster NGC 2355. Using spectra from the Gaia-ESO archives, we find that the stars in the red part of the eMSTO have a higher mean v sin i value of 135.3$\pm$4.6 km s$^{-1}$ compared to the stars in the blue part that have an average v sin i equal to 81.3$\pm$5.6 km s$^{-1}$. This suggests that the eMSTO in NGC 2355 is possibly caused by the spread in rotation rates of stars. We do not find any substantial evidence of the dust-like extinction from the eMSTO stars using ultraviolet data from the Swift survey. The estimated synchronization time for low mass ratio close binaries in the blue part of the eMSTO suggests that they would be mostly slow-rotating if present. However, the stars in the blue part of the eMSTO are preferentially located in the outer region of the cluster indicating that they may lack low mass ratio close binaries. The spread in rotation rates of eMSTO stars in NGC 2355 is most likely caused by the star-disc interaction mechanism. The stars in the lower main sequence beyond the eMSTO region of NGC 2355 are slow-rotating (mean v sin i = 26.5$\pm$1.3 km s$^{-1}$) possibly due to the magnetic braking of their rotations., Comment: 11 pages, 12 figures, accepted for publication in MNRAS

We present a detailed investigation of photometric, spectroscopic, and polarimetric observations of the Type II SN 2023ixf. Earlier studies have provided compelling evidence for a delayed shock breakout from a confined dense circumstellar matter (CSM) enveloping the progenitor star. The temporal evolution of polarization in SN~2023ixf revealed three distinct peaks in polarization evolution at 1.4 d, 6.4 d, and 79.2 d, indicating an asymmetric dense CSM, an aspherical shock front and clumpiness in the low-density extended CSM, and an aspherical inner ejecta/He-core. SN 2023ixf displayed two dominant axes, one along the CSM-outer ejecta and the other along the inner ejecta/He-core, showcasing the independent origin of asymmetry in the early and late evolution. The argument for an aspherical shock front is further strengthened by the presence of a high-velocity broad absorption feature in the blue wing of the Balmer features in addition to the P-Cygni absorption post 16 d. Hydrodynamical light curve modeling indicated a progenitor of 10 solar mass with a radius of 470 solar radii and explosion energy of 2e51 erg, along with 0.06 solar mass of 56-Ni, though these properties are not unique due to modeling degeneracies. The modeling also indicated a two-zone CSM: a confined dense CSM extending up to 5e14 cm, with a mass-loss rate of 1e-2 solar mass per year, and an extended CSM spanning from 5e14 cm to at least 1e16cm with a mass-loss rate of 1e-4 solar mass per year, both assuming a wind-velocity of 10 km/s. The early nebular phase observations display an axisymmetric line profile of [OI], red-ward attenuation of the emission of Halpha post 125 days, and flattening in the Ks-band, marking the onset of dust formation., Comment: 32 pages, 15 figures, 1 Table, Accepted in the Astrophysical Journal

Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the system or the environmental noise. In this paper, we analyze the stochastic within host compartment model for SARS-CoV-2 virus and explore its dynamics. We first examine the existence and positivity of the solution of the model using Ito's formula and the establish the stochastic boundedness and permanence of the model. Exponential stability of the infection free equilibrium state is established. Numerical simulations are conducted to complement the theoretical results. Environmental noise is found to play a crucial role in the dynamics of the disease and can even lead to the extinction of the disease. The model is also extended to a stochastic optimal control problem and the effectiveness of control measures, such as antiviral drugs and immunomodulators is investigated., Comment: 26 pages, 16 figures

We consider the community recovery problem on a one-dimensional random geometric graph where every node has two independent labels: an observed location label and a hidden community label. A geometric kernel maps the locations of pairs of nodes to probabilities. Edges are drawn between pairs of nodes based on their communities and the value of the kernel corresponding to the respective node locations. Given the graph so generated along with the location labels, the latent communities of the nodes are to be inferred. In this work, we will look into the fundamental statistical limits for recovering the communities in such models. Additionally, we propose a linear-time algorithm (in the number of edges) and show that it recovers the communities of nodes exactly up to the information theoretic threshold.

This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide whether to join the queue they arrived at, or shift to one of the nearest neighbours. Such shifting strategies affect the load on the servers, and may cause some of the servers to become overloaded. We derive a law of large numbers and a central limit theorem for the fraction of overloaded servers in the system as the total number of servers $N \to \infty$. Additionally, in the one-dimensional case ($d=1$), we evaluate the expected fraction of overloaded servers for any finite $N$. Numerical experiments are provided to support our theoretical results. Typical applications of the results include electric vehicles queueing at charging stations, and queues in airports or supermarkets., Comment: A part of this work was accepted to the conference International Teletraffic Congress (ITC 35) held between 3--5 October 2023 in Turin, Italy. Revised version generalizes to general stationary arrival processes to servers with service rate $\mu$. Several previous strategies are subsumed into a single main strategy

Although planning is a crucial component of the autonomous driving stack, researchers have yet to develop robust planning algorithms that are capable of safely handling the diverse range of possible driving scenarios. Learning-based planners suffer from overfitting and poor long-tail performance. On the other hand, rule-based planners generalize well, but might fail to handle scenarios that require complex driving maneuvers. To address these limitations, we investigate the possibility of leveraging the common-sense reasoning capabilities of Large Language Models (LLMs) such as GPT4 and Llama2 to generate plans for self-driving vehicles. In particular, we develop a novel hybrid planner that leverages a conventional rule-based planner in conjunction with an LLM-based planner. Guided by commonsense reasoning abilities of LLMs, our approach navigates complex scenarios which existing planners struggle with, produces well-reasoned outputs while also remaining grounded through working alongside the rule-based approach. Through extensive evaluation on the nuPlan benchmark, we achieve state-of-the-art performance, outperforming all existing pure learning- and rule-based methods across most metrics. Our code will be available at https://llmassist.github.io., Comment: 15 pages, 8 figures, 7 tables

The recent progress in language-based open-vocabulary object detection can be largely attributed to finding better ways of leveraging large-scale data with free-form text annotations. Training such models with a discriminative objective function has proven successful, but requires good positive and negative samples. However, the free-form nature and the open vocabulary of object descriptions make the space of negatives extremely large. Prior works randomly sample negatives or use rule-based techniques to build them. In contrast, we propose to leverage the vast knowledge built into modern generative models to automatically build negatives that are more relevant to the original data. Specifically, we use large-language-models to generate negative text descriptions, and text-to-image diffusion models to also generate corresponding negative images. Our experimental analysis confirms the relevance of the generated negative data, and its use in language-based detectors improves performance on two complex benchmarks. Code is available at \url{https://github.com/xiaofeng94/Gen-Enhanced-Negs}., Comment: Accepted to CVPR 2024. The supplementary document included