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Nan Li

Publications and source records attributed to Nan Li.

At least 343 records · Page 19Linked to original sources

The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set

Let $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${\mathcal O}(P)$ is equal to that of the chain polytope ${\mathcal C}(P)$. Furthermore, it will be shown that the degree sequence of the finite simple graph which is the $1$-skeleton of ${\mathcal O}(P)$ is equal to that of ${\mathcal C}(P)$ if and only if ${\mathcal O}(P)$ and ${\mathcal C}(P)$ are unimodularly equivalent.

math.CO↗

PICS: Simulations of Strong Gravitational Lensing in Galaxy Clusters

Gravitational lensing has become one of the most powerful tools available for investigating the 'dark side' of the universe. Cosmological strong gravitational lensing, in particular, probes the properties of the dense cores of dark matter halos over decades in mass and offers the opportunity to study the distant universe at flux levels and spatial resolutions otherwise unavailable. Studies of strongly-lensed variable sources offer yet further scientific opportunities. One of the challenges in realizing the potential of strong lensing is to understand the statistical context of both the individual systems that receive extensive follow-up study, as well as that of the larger samples of strong lenses that are now emerging from survey efforts. Motivated by these challenges, we have developed an image-simulation pipeline, PICS (Pipeline for Images of Cosmological Strong lensing) to generate realistic strong gravitational lensing signals from group and cluster scale lenses. PICS uses a low-noise and unbiased density estimator based on (resampled) Delaunay Tessellations to calculate the density field; lensed images are produced by ray-tracing images of actual galaxies from deep Hubble Space Telescope observations. Other galaxies, similarly sampled, are added to fill in the light cone. The pipeline further adds cluster-member galaxies and foreground stars into the lensed images. The entire image ensemble is then observed using a realistic point spread function which includes appropriate detector artifacts for bright stars. Noise is further added, including such non-Gaussian elements as noise window-paning from mosaiced observations, residual bad pixels, and cosmic rays. The aim is to produced simulated images that appear identical - to the eye (expert or otherwise) - to real observations in various imaging surveys.

astro-ph.CO↗

Game-Theoretic Modeling of Driver and Vehicle Interactions for Verification and Validation of Autonomous Vehicle Control Systems

Autonomous driving has been the subject of increased interest in recent years both in industry and in academia. Serious efforts are being pursued to address legal, technical and logistical problems and make autonomous cars a viable option for everyday transportation. One significant challenge is the time and effort required for the verification and validation of the decision and control algorithms employed in these vehicles to ensure a safe and comfortable driving experience. Hundreds of thousands of miles of driving tests are required to achieve a well calibrated control system that is capable of operating an autonomous vehicle in an uncertain traffic environment where multiple interactions between vehicles and drivers simultaneously occur. Traffic simulators where these interactions can be modeled and represented with reasonable fidelity can help decrease the time and effort necessary for the development of the autonomous driving control algorithms by providing a venue where acceptable initial control calibrations can be achieved quickly and safely before actual road tests. In this paper, we present a game theoretic traffic model that can be used to 1) test and compare various autonomous vehicle decision and control systems and 2) calibrate the parameters of an existing control system. We demonstrate two example case studies, where, in the first case, we test and quantitatively compare two autonomous vehicle control systems in terms of their safety and performance, and, in the second case, we optimize the parameters of an autonomous vehicle control system, utilizing the proposed traffic model and simulation environment.

cs.AI↗

Order-Chain Polytopes

Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection $\mathcal{P}=\mathcal{P}_1\cap\mathcal{P}_2$, where $\mathcal{P}_1\in X$, $\mathcal{P}_2\in Y$. Two basic questions then arise: 1) when $\mathcal{P}$ is integral and 2) whether $\mathcal{P}$ inherits the "old type" from $\mathcal{P}_1, \mathcal{P}_2$ or has a "new type", that is, whether $\mathcal{P}$ is unimodularly equivalent to some polytope in $X\cup Y$ or not. In this paper, we focus on the families of order polytopes and chain polytopes and create a new class of polytopes following the above framework, which are named order-chain polytopes. In the study on their volumes, we discover a natural relation with Ehrenborg and Mahajan's results on maximizing descent statistics.

math.CO↗

Dark Energy and Normalization of the Cosmological Wave Function

Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor $q$, only when there is dark energy then can the cosmological wave function be normalized. This interesting observation may require further attention.

gr-qc↗

Galaxy-Galaxy Weak Lensing Measurements from SDSS: I. Image Processing and Lensing signals

As the first paper in a series on the study of the galaxy-galaxy lensing from Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our image processing pipeline that corrects the systematics primarily introduced by the Point Spread Function (PSF). Using this pipeline, we processed SDSS DR7 imaging data in $r$ band and generated a background galaxy catalog containing the shape information of each galaxy. Based on our own shape measurements of the galaxy images from SDSS DR7, we extract the galaxy-galaxy (GG) lensing signals around foreground spectroscopic galaxies binned in different luminosity and stellar mass. The overall signals are in good agreement with those obtained by \citet{Mandelbaum2005, Mandelbaum2006} from the SDSS DR4. The results in this paper with higher signal to noise ratio is due to the larger survey area than SDSS DR4, confirm that more luminous/massive galaxies bear stronger GG lensing signal. We also divide the foreground galaxies into red/blue and star forming/quenched subsamples and measured their GG lensing signals, respectively. We find that, at a specific stellar mass/luminosity, the red/quenched galaxies have relatively stronger GG lensing signals than their counterparts especially at large radii. These GG lensing signals can be used to probe the galaxy-halo mass relations and their environmental dependences in the halo occupation or conditional luminosity function framework.

astro-ph.CO↗

The Gini Coefficient as a Morphological Measurement of Strongly Lensed Galaxies in the Image Plane

Characterization of the morphology of strongly lensed galaxies is challenging because images of such galaxies are typically highly distorted. Lens modeling and source plane reconstruction is one approach that can provide reasonably undistorted images from which morphological measurements can be made, although at the expense of a highly spatially variable telescope PSF when mapped back to the source plane. Unfortunately, modeling the lensing mass is a time and resource intensive process, and in many cases there are too few constraints to precisely model the lensing mass. If, however, useful morphological measurements could be made in the image plane rather than the source plane, it would bypass this issue and obviate the need for a source reconstruction process for some applications. We examine the use of the Gini coefficient as one such measurement. Because it depends on the cumulative distribution of the light of a galaxy, but not the relative spatial positions, the fact that surface brightness is conserved by lensing means that the Gini coefficient may be well-preserved by strong gravitational lensing. Through simulations, we test the extent to which the Gini coefficient is conserved, including by effects due to PSF convolution and pixelization, to determine whether it is invariant enough under lensing to be used as a measurement of galaxy morphology that can be made in the image plane.

astro-ph.GA↗

Impacts of different SNLS3 light-curve fitters on cosmological consequences of interacting dark energy models

We explore the cosmological consequences of interacting dark energy (IDE) models using the SNLS3 supernova samples. In particular, we focus on the impacts of different SNLS3 light-curve fitters (LCF) (corresponding to "SALT2", "SiFTO", and "Combined" sample). Firstly, making use of the three SNLS3 data sets, as well as the Planck distance priors data and the galaxy clustering data, we constrain the parameter spaces of three IDE models. Then, we study the cosmic evolutions of Hubble parameter $H(z)$, deceleration diagram $q(z)$, statefinder hierarchy $S^{(1)}_3(z)$ and $S^{(1)}_4(z)$, and check whether or not these dark energy diagnosis can distinguish the differences among the results of different SNLS3 LCF. At last, we perform high redshift cosmic age test using three old high redshift objects (OHRO), and explore the fate of the Universe. We find that, the impacts of different SNLS3 LCF are rather small, and can not be distinguished by using $H(z)$, $q(z)$, $S^{(1)}_3(z)$, $S^{(1)}_4(z)$, and the age data of OHRO. In addition, we infer, from the current observations, how far we are from a cosmic doomsday in the worst case, and find that the "Combined" sample always gives the largest 2$σ$ lower limit of the time interval between "big rip" and today, while the results given by the "SALT2" and the "SiFTO" sample are close to each other. These conclusions are insensitive to a specific form of dark sector interaction. Our method can be used to distinguish the differences among various cosmological observations.

astro-ph.CO↗

The environment and star formation of HII region Sh2-163: a multi-wavelength study

To investigate the environment of HII region Sh2-163 and search for evidence of triggered star formation in this region, we performed a multi-wavelength study of this HII region. Most of our data were taken from large-scale surveys: 2MASS, CGPS, MSX and SCUBA. We also made CO molecular line observations, using the 13.7-m telescope. The ionized region of Sh2-163 is detected by both the optical and radio continuum observations. Sh2-163 is partially bordered by an arc-like photodissociation region (PDR), which is coincident with the strongest optical and radio emissions, indicating interactions between the HII region and the surrounding interstellar medium. Two molecular clouds were discovered on the border of the PDR. The morphology of these two clouds suggests they are compressed by the expansion of Sh2-163. In cloud A, we found two molecular clumps. And it seems star formation in clump A2 is much more active than in clump A1. In cloud B, we found new outflow activities and massive star(s) are forming inside. Using 2MASS photometry, we tried to search for embedded young stellar object (YSO) candidates in this region. The very good agreement between CO emission, infrared shell and YSOs suggest that it is probably a star formation region triggered by the expansion of Sh2-163.We also found the most likely massive protostar related to IRAS 23314+6033.

astro-ph.GA↗

Physical and chemical properties of Red MSX Sources in the southern sky: HII regions

We have studied the physical and chemical properties of 18 southern Red Midcourse Space Experiment Sources (RMSs), using archival data taken from the Atacama Pathfinder Experiment (APEX) Telescope Large Area Survey of the Galaxy, the Australia Telescope Compact Array, and the Millimeter Astronomy Legacy Team Survey at 90 GHz. Most of our sources have simple cometary/unresolved radio emissions at 4.8 and/or 8.6GHz. The large number of Lyman continuum fluxes (NL) indicates they are probably massive O- or early B-type star formation regions. Archival IRAS infrared data are used to estimate the dust temperature, which is about 30 K of our sources. Then, the H2 column densities and the volume-averaged H2 number densities are estimated using the 0.87 mm dust emissions. Large-scale infall and ionized accretions may be occurring in G345.4881+00.3148. We also attempt to characterize the chemical properties of these RMSs through molecular line (N2H+ (1-0) and HCO+ (1-0)) observations. Most of the detected N2H+ and HCO+ emissions match well with the dust emission, implying a close link to their chemical evolution in the RMSs. We found that the abundance of N2H+ is one order of magnitude lower than that in other surveys of infrared dark clouds, and a positive correlation between the abundances of N2H+ and HCO+. The fractional abundance of N2H+ with respect to H2 seems to decrease as a function of NL. These observed trends could be interpreted as an indication of enhanced destruction of N2H+, either by CO or through dissociative recombination with electrons produced by central UV photons.

astro-ph.GA↗

More Evidence for the Redshift Dependence of Color from the JLA Supernova Sample Using Redshift Tomography

In this work, by applying the redshift tomography method to Joint Light-curve Analysis (JLA) supernova sample, we explore the possible redshift-dependence of stretch-luminosity parameter $α$ and color-luminosity parameter $β$. The basic idea is to divide the JLA sample into different redshift bins, assuming that $α$ and $β$ are piecewise constants. Then, by constraining the $Λ$CDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the same technique to explore the possible evolution of $β$ in various subsamples of JLA. Using the full JLA data, we find that $α$ is always consistent with a constant. In contrast, at high redshift $β$ has a significant trend of decreasing, at $\sim 3.5σ$ confidence level (CL). Moreover, we find that low-$z$ subsample favors a constant $β$; in contrast, SDSS and SNLS subsamples favor a decreasing $β$ at 2$σ$ and $3.3σ$ CL, respectively. Besides, by using a binned parameterization of $β$, we study the impacts of $β$'s evolution on parameter estimation. We find that compared with a constant $β$, a varying $β$ yields a larger best-fit value of fractional matter density $Ω_{m0}$, which slightly deviates from the best-fit result given by other cosmological observations. However, for both the varying $β$ and the constant $β$ cases, the $1σ$ regions of $Ω_{m0}$ are still consistent with the result given by other observations.

astro-ph.CO↗

A comprehensive investigation on the slowing down of cosmic acceleration

Shafieloo ea al. firstly proposed the possibility that the current cosmic acceleration (CA) is slowing down. However, this is rather counterintuitive because a slowing down CA cannot be accommodated in most mainstream cosmological models. In this work, by exploring the evolutionary trajectories of dark energy equation of state $w(z)$ and deceleration parameter $q(z)$, we present a comprehensive investigation on the slowing down of CA from both the theoretical and the observational sides. For the theoretical side, we study the impact of different $w(z)$ by using six parametrization models, and then discuss the effects of spatial curvature. For the observational side, we investigate the effects of different type Ia supernovae (SNe Ia), different baryon acoustic oscillation (BAO), and different cosmic microwave background (CMB) data, respectively. We find that (1) The evolution of CA are insensitive to the specific form of $w(z)$; in contrast, a non-flat Universe more favors a slowing down CA than a flat Universe. (2) SNLS3 SNe Ia datasets favor a slowing down CA at 1$σ$ confidence level, while JLA SNe Ia samples prefer an eternal CA; in contrast, the effects of different BAO data are negligible. (3) Compared with CMB distance prior data, full CMB data more favor a slowing down CA. (4) Due to the low significance, the slowing down of CA is still a theoretical possibility that cannot be confirmed by the current observations.

astro-ph.CO↗

Difference analogue of Cartan's Second Main Theorem for slowly moving periodic targets

We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As applications, we obtain a new Picard type theorem and difference analogues of the deficiency relation for holomorphic curves.

math.CV↗

Explorations of two empirical formulae for fermion masses

Two empirical formulae for the lepton and quark masses (i.e. Kartavtsev's extended Koide formulae), $K_l=(\sum_l m_l)/(\sum_l\sqrt{m_l})^2=2/3$ and $K_q=(\sum_q m_q)/(\sum_q\sqrt{m_q})^2=2/3$, are explored in this paper. For the lepton sector, we show that $K_l=2/3$, only if the uncertainty of the tauon mass is relaxed to about $2σ$ confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and $K_q$ is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to $10^{12}$ GeV. However, $K_q$ is always slightly larger than $2/3$, but the discrepancy is merely about $5\%$.

hep-ph↗

Fisher-symmetric informationally complete measurements for pure states

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete---i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states---and it is maximal in the sense of a multi-parameter quantum Cramer-Rao bound. For a $d$-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below $4d-3$, for the usual notion of global pure-state informational completeness, to $2d-1$.

quant-ph↗

Cooperative Communication Using Network Coding

We consider a cognitive radio network scenario where a primary transmitter and a secondary transmitter, respectively, communicate a message to their respective primary receiver and secondary receiver over a packet-based wireless link, using a joint automatic-repeat-request (ARQ) error control scheme. The secondary transmitter assists in the retransmission of the primary message, which improves the primary performance, and is granted limited access to the transmission resources. Conventional ARQ, as well as two network-coding schemes are investigated for application in the retransmission phase; namely the static network-coding (SNC) scheme and the adaptive network-coding (ANC) scheme. For each scheme we analyze the transmission process by investigating the distribution of the number of transmission attempts and approximate it by normal distributions. Considering both the cases of an adaptive frame size and a truncated frame size, we derive analytical results on packet throughput and infer that the ANC scheme outperforms the SNC scheme.

cs.IT↗

The Gini Coefficient as a Tool for Image Family Idenitification in Strong Lensing Systems with Multiple Images

The sample of cosmological strong lensing systems has been steadily growing in recent years and with the advent of the next generation of space-based survey telescopes, the sample will reach into the thousands. The accuracy of strong lens models relies on robust identification of multiple image families of lensed galaxies. For the most massive lenses, often more than one background galaxy is magnified and multiply-imaged, and even in the cases of only a single lensed source, identification of counter images is not always robust. Recently, we have shown that the Gini coefficient in space-telescope-quality imaging is a measurement of galaxy morphology that is relatively well-preserved by strong gravitational lensing. Here, we investigate its usefulness as a diagnostic for the purposes of image family identification and show that it can remove some of the degeneracies encountered when using color as the sole diagnostic, and can do so without the need for additional observations since whenever a color is available, two Gini coefficients are as well.

astro-ph.GA↗

An Exploration of the Black Hole Entropy via the Weyl Tensor

The Weyl tensor is the trace-free part of the Riemann tensor. Therefore, it is independent of the energy-momentum tensor and is thus not linked to the dynamics of gravitational fields. In this paper, we explore its possible thermodynamical property (i.e. its relationship with the black hole entropy). For a Schwarzschild black hole, the Weyl scalar invariant, $C_{μνλρ}C^{μνλρ}$, is proportional to its Bekenstein--Hawking entropy. This observation inspires us to interpret $C_{μνλρ}C^{μνλρ}$ as the entropy density of the gravitational fields of black holes. A dimensional analysis indicates that this interpretation is only valid in 5-dimensional space-time. We calculate the volume integrals of $C_{μνλρ}C^{μνλρ}$ for the 5-dimensional Schwarzschild and Schwarzschild--anti-de Sitter black holes, and find that these integrals indeed lead to the correct entropy formulae, only up to some coefficients.

gr-qc↗