In the present article, we use Robbas method to give an estimation of the Newton polygon for the L function on torus.
In this paper, we propose a novel video super-resolution method that aims at generating high-fidelity high-resolution (HR) videos from low-resolution (LR) ones. Previous methods predominantly leverage temporal neighbor frames to assist the super-reso
lution of the current frame. Those methods achieve limited performance as they suffer from the challenge in spatial frame alignment and the lack of useful information from similar LR neighbor frames. In contrast, we devise a cross-frame non-local attention mechanism that allows video super-resolution without frame alignment, leading to be more robust to large motions in the video. In addition, to acquire the information beyond neighbor frames, we design a novel memory-augmented attention module to memorize general video details during the super-resolution training. Experimental results indicate that our method can achieve superior performance on large motion videos comparing to the state-of-the-art methods without aligning frames. Our source code will be released.
Kepler Missions single-band photometry suffers from astrophysical false positives, the most common of background eclipsing binaries (BEBs) and companion transiting planets (CTPs). Multi-color photometry can reveal the color-dependent depth feature of
false positives and thus exclude them. In this work, we aim to estimate the fraction of false positives that are unable to be classified by Kepler alone but can be identified with their color-dependent depth feature if a reference band (z, Ks and TESS) were adopted in follow-up observation. We build up physics-based blend models to simulate multi-band signals of false positives. Nearly 65-95% of the BEBs and more than 80% of the CTPs that host a Jupiter-size planet will show detectable depth variations if the reference band can achieve a Kepler-like precision. Ks band is most effective in eliminating BEBs exhibiting any depth sizes, while z and TESS band prefer to identify giant candidates and their identification rates are more sensitive to photometric precision. Provided the radius distribution of planets transiting the secondary star in binary systems, we derive formalism to calculate the overall identification rate for CTPs. By comparing the likelihood distribution of the double-band depth ratio for BEB and planet models, we calculate the false positive probability (FPP) for typical Kepler candidates. Additionally, we show that the FPP calculation helps distinguish the planet candidates host star in an unresolved binary system. The analysis framework of this paper can be easily adapted to predict the multi-color photometry yield for other transit surveys, especially for TESS.
We analyze a game of technology development where players allocate resources between exploration, which continuously expands the public domain of available technologies, and exploitation, which yields a flow payoff by adopting the explored technologi
es. The qualities of the technologies are correlated and initially unknown, and this uncertainty is fully resolved once the technologies are explored. We consider Markov perfect equilibria with the quality difference between the best available technology and the latest technology under development as the state variable. In all such equilibria, while the players do not fully internalize the benefit of failure owing to free-riding incentives, they are more tolerant of failure than in the single-agent optimum thanks to an encouragement effect. In the unique symmetric equilibrium, the cost of exploration determines whether free-riding prevails as team size grows. Pareto improvements over the symmetric equilibrium can be achieved by asymmetric equilibria where players take turns performing exploration.
This paper aims to investigate the characteristics of durations of discretionary lane changes (LCs) on freeways based on an enriched dataset containing LC vehicle trajectories of 2905 passenger cars and 433 heavy vehicles. A comprehensive analysis of
LC duration is conducted and four stochastic LC duration models are built according to vehicle types and LC directions. It is found that the LC duration varies across different vehicle types and LC directions. The modelling results show that different variables have different effects on LC duration for different vehicle types and LC directions. Fixed-parameter, latent class, and random parameter accelerated hazard time (AFT) models were built considering driver heterogeneity. Results show that heavy vehicle drivers show more heterogeneity. Different variables were found for different vehicle types and LC directions. The results of this study can be beneficial to understand the mechanism of LC process and the influence of LC on traffic flow.
Magnetism of fullerene C60 was studied by three methods of the density functional theory (DFT) calculation, laboratory experiment and astronomical observation. DFT revealed that the most stable spin state was non-magnetic one of Sz=0/2. This is contr
ary to our recent study on void induced graphene molecules of C23 and C53 to be magnetic one of Sz=2/2. Two graphene molecules combined model suggested that two up-spin at every carbon pentagon ring may cancel each other to bring Sz=0/2. Similar cancelation may occur on C60. Molecular vibrational infrared spectrum of C60 show four major bands, which coincide with gas-phase laboratory experiment, also with astronomically observed one of carbon rich planetary nebula Tc1 and Lin49. However, there remain many unidentified bands on astronomical one. We supposed multiple voids on graphene sheet, which may create both C60 and complex graphene molecules. It was revealed that spectrum of two voids induced graphene molecule coincident well with major astronomical bands. Simple sum of C60 and graphene molecules could successfully reproduce astronomical bands in detail.
Observationally, the interstellar gas-phase abundance of deuterium (D) is considerably depleted and the missing D atoms are often postulated to have been locked up into carbonaceous solids and polycyclic aromatic hydrocarbon (PAH) molecules. An accur
ate knowledge of the fractional amount of D (relative to H) tied up in carbon dust and PAHs has important cosmological implications since D originated exclusively from the Big Bang and the present-day D abundance, after accounting for the astration it has experienced during the Galactic evolution, provides essential clues to the primordial nucleosynthesis and the cosmological parameters. To quantitatively explore the extent to which PAHs could possibly accommodate the observed D depletion, we have previously quantum-chemically computed the infrared vibrational spectra of mono-deuterated PAHs and derived the mean intrinsic band strengths of the 3.3 $mu$m C--H stretch (A$_{3.3}$) and the 4.4 $mu$m C--D stretch (A$_{4.4}$). Here we extend our previous work to multi-deuterated PAH species of different deuterations, sizes and structures. We find that both the intrinsic band strengths A$_{3.3}$ and A$_{4.4}$ and their ratios A$_{4.4}$/A$_{3.3}$ not only show little variations among PAHs of different deuterations, sizes and structures, they are also closely similar to that of mono-deuterated PAHs. Therefore, a PAH deuteration level (i.e., the fraction of peripheral atoms attached to C atoms in the form of D) of ~2.4% previously estimated from the observed 4.4 $mu$m to 3.3 $mu$m band ratio based on the A$_{4.4}$/A$_{3.3}$ ratio of mono-deuterated PAHs is robust.
Low-complexity models such as linear function representation play a pivotal role in enabling sample-efficient reinforcement learning (RL). The current paper pertains to a scenario with value-based linear representation, which postulates the linear re
alizability of the optimal Q-function (also called the linear $Q^{star}$ problem). While linear realizability alone does not allow for sample-efficient solutions in general, the presence of a large sub-optimality gap is a potential game changer, depending on the sampling mechanism in use. Informally, sample efficiency is achievable with a large sub-optimality gap when a generative model is available but is unfortunately infeasible when we turn to standard online RL settings. In this paper, we make progress towards understanding this linear $Q^{star}$ problem by investigating a new sampling protocol, which draws samples in an online/exploratory fashion but allows one to backtrack and revisit previous states in a controlled and infrequent manner. This protocol is more flexible than the standard online RL setting, while being practically relevant and far more restrictive than the generative model. We develop an algorithm tailored to this setting, achieving a sample complexity that scales polynomially with the feature dimension, the horizon, and the inverse sub-optimality gap, but not the size of the state/action space. Our findings underscore the fundamental interplay between sampling protocols and low-complexity structural representation in RL.
The interstellar traveler, 2I/Borisov, is the first clearly active extrasolar comet, ever detected in our Solar system. We obtained high-resolution interferometric observations of 2I/Borisov with the Atacama Large Millimeter/submillimeter Array (ALMA
), and multi-color optical observations with the Very Large Telescope (VLT) to gain a comprehensive understanding of the dust properties of this comet. We found that the dust coma of 2I/Borisov consists of compact pebbles of radii exceeding ~1 mm, suggesting that the dust particles have experienced compaction through mutual impacts during the bouncing collision phase in the protoplanetary disk. We derived a dust mass loss rate of >= 200 kg/s and a dust-to-gas ratio >=3. Our long term monitoring of 2I/Borisov with VLT indicates a steady dust mass loss with no significant dust fragmentation and/or sublimation occurring in the coma. We also detected emissions from carbon monoxide gas (CO) with ALMA and derived the gas production rate of Q(CO) (3.3+/-0.8)x10^{26} mole/s. We found that the CO/H$_2$O mixing ratio of 2I/Borisov changed drastically before and after perihelion, indicating the heterogeneity of the cometary nucleus, with components formed at different locations beyond the volatile snow-line with different chemical abundances. Our observations suggest that 2I/Borisovs home system, much like our own system, experienced efficient radial mixing from the innermost parts of its protoplanetary disk to beyond the frost line of CO.
Void-defect induced magnetism of graphene molecule was recently reported in our previous paper of this series study. This paper investigated the case of hydrogenated graphene molecule, in chemical term, polycyclic aromatic hydrocarbon (PAH). Molecula
r infrared spectrum obtained by density functional theory was compared with astronomical observation. Void-defect on PAH caused serious structure change. Typical example of C23H12 had two carbon pentagon rings among hexagon networks. Stable spin state was non-magnetic singlet state. This is contrary to pure carbon case of C23, which show magnetic triplet state. It was discussed that Hydrogen played an important role to diminish magnetism by creating an SP3-bond among SP2-networks. Such a structure change affected molecular vibration and finally to photoemission spectrum in infrared region. The dication-C23H12 showed featured bands at 3.2, 6.3, 7.7, 8.6, 11.2, and 12.7 micrometer. It was surprising that those calculated bands coincided well with astronomically observed bands in many planetary nebulae. To confirm our study, large size molecule of C53H18 was studied. Calculation reproduced again similar astronomical bands. Also, small size molecule of C12H8 showed good coincidence with the spectrum observed for young stars. This paper would be the first report to indicate the specific PAH in space.
