arXiv subjects

Wei Zhu

Publications and source records attributed to Wei Zhu.

At least 271 records · Page 15Linked to original sources

arXiv2019

Constructing curvelet-like bases and low-redundancy frames

We provide a detailed analysis of the obstruction (studied first by S. Durand and later by R. Yin and one of us) in the construction of multidirectional wavelet orthonormal bases corresponding to any admissible frequency partition in the framework of subband filtering with non-uniform subsampling. To contextualize our analysis, we build, in particular, multidirectional alias-free hexagonal wavelet bases and low-redundancy frames with optimal spatial decay. In addition, we show that a 2D cutting lemma can be used to subdivide the obtained wavelet systems in higher frequency rings so as to generate bases or frames that satisfy the ``parabolic scaling'' law enjoyed by curvelets and shearlets. Numerical experiments on high bit-rate image compression are conducted to illustrate the potential of the proposed systems.

math.NA↗

arXiv2019

A speculation about a puzzled result in energy spectrum of cosmic-ray electrons around TeV energies

Nuclear Coulomb potential at completely ionized and extremely thin atmosphere can leaks to a macroscopic spatial scale. This effect is used to explain the difference between the energy spectra of cosmic-ray electrons around $1 TeV$ measured by different experimental groups. The result inspires us to review the traditional electromagnetic shower theory at the extreme conditions. It is also reminds us that the energy spectrum of cosmic-ray electrons, which are measured by Fermi-LAT and DAMPE at a higher altitude is more closer to a true signature.

astro-ph.HE↗

arXiv2019

Improved Bethe-Heitler formula

The bremsstrahlung cross section of electron in the atomic electric field is re-derived using the time ordered perturbative theory. The results are compared with the Bethe-Heitler formula. We indicate that both the TOPT-description and a soft version for the bremsstrahlung process predict a strong screening parameter-dependent cross section, which is missed by previous bremsstrahlung theory.

hep-ph↗

arXiv2019

OGLE-2017-BLG-1186: first application of asteroseismology and Gaussian processes to microlensing

We present the analysis of the event OGLE-2017-BLG-1186 from the 2017 Spitzer microlensing campaign. This is a remarkable microlensing event because its source is photometrically bright and variable, which makes it possible to perform an asteroseismic analysis using ground-based data. We find that the source star is an oscillating red giant with average timescale of $\sim 9$ d. The asteroseismic analysis also provides us source properties including the source angular size ($\sim 27~μ{\rm as}$) and distance ($\sim 11.5$ kpc), which are essential for inferring the properties of the lens. When fitting the light curve, we test the feasibility of Gaussian Processes (GPs) in handling the correlated noise caused by the variable source. We find that the parameters from the GP model are generally more loosely constrained than those from the traditional $χ^2$ minimization method. We note that this event is the first microlensing system for which asteroseismology and GPs have been used to account for the variable source. With both finite-source effect and microlens parallax measured, we find that the lens is likely a $\sim 0.045~M_{\odot}$ brown dwarf at distance $\sim 9.0$ kpc, or a $\sim 0.073~M_{\odot}$ ultracool dwarf at distance $\sim 9.8$ kpc. Combining the estimated lens properties with a Bayesian analysis using a Galactic model, we find a $\sim 35$ per cent probability for the lens to be a bulge object and $\sim 65$ per cent to be a background disc object.

astro-ph.SR↗

arXiv2019

OGLE-2018-BLG-1011L\lowercase{b,c}: Microlensing Planetary System with Two Giant Planets Orbiting a Low-mass Star

We report a multiplanetary system found from the analysis of microlensing event OGLE-2018-BLG-1011, for which the light curve exhibits a double-bump anomaly around the peak. We find that the anomaly cannot be fully explained by the binary-lens or binary-source interpretations and its description requires the introduction of an additional lens component. The 3L1S (3 lens components and a single source) modeling yields three sets of solutions, in which one set of solutions indicates that the lens is a planetary system in a binary, while the other two sets imply that the lens is a multiplanetary system. By investigating the fits of the individual models to the detailed light curve structure, we find that the multiple-planet solution with planet-to-host mass ratios $\sim 9.5\times 10^{-3}$ and $\sim 15\times 10^{-3}$ are favored over the other solutions. From the Bayesian analysis, we find that the lens is composed of two planets with masses $1.8^{+3..4}_{-1.1}~M_{\rm J}$ and $2.8^{+5.1}_{-1.7}~M_{\rm J}$ around a host with a mass $0.18^{+0.33}_{-0.10}~M_\odot$ and located at a distance $7.1^{+1.1}_{-1.5}~{\rm kpc}$. The estimated distance indicates that the lens is the farthest system among the known multiplanetary systems. The projected planet-host separations are $a_{\perp,2}=1.8^{+2.1}_{-1.5}~{\rm au}$ ($0.8^{+0.9}_{-0.6}~{\rm au}$) and $a_{\perp,3}=0.8^{+0.9}_{-0.6}~{\rm au}$, where the values of $a_{\perp,2}$ in and out the parenthesis are the separations corresponding to the two degenerate solutions, indicating that both planets are located beyond the snow line of the host, as with the other four multiplanetary systems previously found by microlensing.

astro-ph.EP↗

arXiv2019

OGLE-2015-BLG-1670Lb: A Cold Neptune beyond the Snow Line in the Provisional WFIRST Microlensing Survey Field

We present the analysis of the microlensing event OGLE-2015-BLG-1670, detected in a high-extinction field, very close to the Galactic plane. Due to the dust extinction along the line of sight, this event was too faint to be detected before it reached the peak of magnification. The microlensing light-curve models indicate a high-magnification event with a maximum of $A_\mathrm{max}\gtrsim200$, very sensitive to planetary deviations. An anomaly in the light curve has been densely observed by the microlensing surveys MOA, KMTNet, and OGLE. From the light-curve modeling, we find a planetary anomaly characterized by a planet-to-host mass ratio, $q=\left(1.00^{+0.18}_{-0.16}\right)\times 10^{-4}$, at the peak recently identified in the mass-ratio function of microlensing planets. Thus, this event is interesting to include in future statistical studies about planet demography. We have explored the possible degeneracies and find two competing planetary models resulting from the $s\leftrightarrow1/s$ degeneracy. However, because the projected separation is very close to $s=1$, the physical implications for the planet for the two solutions are quite similar, except for the value of $s$. By combining the light-curve parameters with a Galactic model, we have estimated the planet mass $M_2=17.9^{+9.6}_{-8.8}\,\mathrm{M}_\oplus$ and the lens distance $D_\mathrm{L}=6.7^{+1.0}_{-1.3}\,\mathrm{kpc}$, corresponding to a Neptune-mass planet close to the Galactic bulge. Such events with a low absolute latitude ($|b|\approx 1.1\,\mathrm{deg}$) are subject to both high extinction and more uncertain source distances, two factors that may affect the mass measurements in the provisional Wide Field Infrared Survey Telescope fields. More events are needed to investigate the potential trade-off between the higher lensing rate and the difficulty in measuring masses in these low-latitude fields.

astro-ph.EP↗

arXiv2019

A Pair of Planets Likely in Mean-motion Resonance From Gravitational Microlensing

We combine statistical arguments and dynamical analysis to study the orbital configuration of the microlensing planetary system OGLE-2012-BLG-0026L. This system is known to host two massive planets, with both projected close to the Einstein ring at the time of the detection. Assuming an isotropic distribution for the orbital orientation, we find that the two planets should also be closely spaced in three-dimensional space and that the ratio of their orbital periods is almost certainly less than two. With N-body numerical integrations, we then identify two types of stable configurations: the two planets can be in first-order mean-motion resonances (MMRs) and have significant ($\gtrsim0.1$) eccentricities, or they stay out of MMRs and have nearly circular orbits. The latter is disfavored, given the absence of similar planet pairs in radial velocity (RV) observations as well as the theoretical difficulties in forming such a configuration. Therefore, the two massive planets in OGLE-2012-BLG-0026L are likely in a resonance configuration. Our work shows that the microlensing technique, which usually only measures the projected configurations, can also probe the detailed dynamical state of multi-planet systems. We also discuss theoretical implications of measuring the multiplicity and the orbital architecture of cold planets.

astro-ph.EP↗

arXiv2019

Diagnosis and Prediction of the 2015 Chinese Stock Market Bubble

In this study, we perform a novel analysis of the 2015 financial bubble in the Chinese stock market by calibrating the Log Periodic Power Law Singularity (LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early 2014 to June 2015. The back tests of the 2015 Chinese stock market bubbles indicates that the LPPLS model can readily detect the bubble behavior of the faster-than-exponential increase corrected by the accelerating logarithm-periodic oscillations in the 2015 Chinese Stock market. The existence of log-periodicity is detected by applying the Lomb spectral analysis on the detrended residuals. The Ornstein-Uhlenbeck property and the stationarity of the LPPLS fitting residuals are confirmed by the two Unit-root tests (Philips-Perron test and Dickery-Fuller test). According to our analysis, the actual critical day t_c can be well predicted by the LPPLS model as far back as two months before the actual bubble crash. Compared to the traditional optimization method used in the LPPLS model, we find the covariance matrix adaptation evolution strategy (CMA-ES) to have a significantly lower computation cost, and thus recommend this as a better alternative algorithm for LPPLS model fit. Furthermore, in the LPPLS fitting with expanding windows, the gap (tc -t2) shows a significant decrease when the end day t2 approaches the actual bubble crash time. The change rate of the gap (tc-t2) may be used as an additional indicator besides the key indicator tc to improve the prediction of bubble burst.

q-fin.ST↗

arXiv2019

Extension of Rough Set Based on Positive Transitive Relation

The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or the limitation of data comprehension, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relations typically discard one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the current rough set extension models, we define a new relation called the positive transitive relation and then propose a novel rough set extension model built upon which. The new model holds the merit of the existing rough set extension models while avoids their limitations of discarding transitivity or symmetry. In comparison to the existing extension models, the proposed model has a better performance in processing the incomplete information systems while substantially reducing the computational complexity, taking into account the relation of tolerance and similarity of positive transitivity, and supplementing the related theories in accordance to the intuitive classification of incomplete information. In summary, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the newly proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.

cs.AI↗

arXiv2019

Real-time Prediction of Bitcoin Bubble Crashes

In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity (LPPLS) confidence indicator as a diagnostic tool for identifying bubbles using the daily data on Bitcoin price in the past two years. We find that the LPPLS confidence indicator based on the daily Bitcoin price data fails to provide effective warnings for detecting the bubbles when the Bitcoin price suffers from a large fluctuation in a short time, especially for positive bubbles. In order to diagnose the existence of bubbles and accurately predict the bubble crashes in the cryptocurrency market, this study proposes an adaptive multilevel time series detection methodology based on the LPPLS model and finer (than daily) timescale for the Bitcoin price data. We adopt two levels of time series, 1 hour and 30 minutes, to demonstrate the adaptive multilevel time series detection methodology. The results show that the LPPLS confidence indicator based on this new method is an outstanding instrument to effectively detect the bubbles and accurately forecast the bubble crashes, even if a bubble exists in a short time. In addition, we discover that the short-term LPPLS confidence indicator highly sensitive to the extreme fluctuations of Bitcoin price can provide some useful insights into the bubble status on a shorter time scale - on a day to week scale, and the long-term LPPLS confidence indicator has a stable performance in terms of effectively monitoring the bubble status on a longer time scale - on a week to month scale. The adaptive multilevel time series detection methodology can provide real-time detection of bubbles and advanced forecast of crashes to warn of the imminent risk.

q-fin.ST↗

arXiv2019

Detection of Chinese Stock Market Bubbles with LPPLS Confidence Indicator

We present an advance bubble detection methodology based on the Log Periodic Power Law Singularity (LPPLS) confidence indicator for the early causal identification of positive and negative bubbles in the Chinese stock market using the daily data on the Shanghai Shenzhen CSI 300 stock market index from January 2002 through April 2018. We account for the damping condition of LPPLS model in the search space and implement the stricter filter conditions for the qualification of the valid LPPLS fits by taking account of the maximum relative error, performing the Lomb log-periodic test of the detrended residual, and unit-root tests of the logarithmic residual based on both the Phillips-Perron test and Dickey-Fuller test to improve the performance of LPPLS confidence indicator. Our analysis shows that the LPPLS detection strategy diagnoses the positive bubbles and negative bubbles corresponding to well-known historical events, implying the detection strategy based on the LPPLS confidence indicator has an outstanding performance to identify the bubbles in advance. We find that the probability density distribution of the estimated beginning time of bubbles appears to be skewed and the mass of the distribution is concentrated on the area where the price starts to have an obvious super-exponentially growth. This study is the first work in the literature that identifies the existence of bubbles in the Chinese stock market using the daily data of CSI 300 index with the advance bubble detection methodology of LPPLS confidence indicator. We have shown that it is possible to detect the potential positive and negative bubbles and crashes ahead of time, which in turn limits the bubble sizes and eventually minimizes the damages from the bubble crash.

q-fin.ST↗

arXiv2019

Revisiting the Long-Period Transiting Planets from Kepler

Currently, we have only limited means to probe the presence of planets at large orbital separations. Foreman-Mackey et al. searched for long-period transiting planets in the Kepler light curves using an automated pipeline. Here, we apply their pipeline, with minor modifications, to a larger sample and use updated stellar parameters from Gaia DR2. The latter boosts the stellar radii for most of the planet candidates found by FM16, invalidating a number of them as false positives. We identify 15 candidates, including two new ones. All have sizes from 0.3 to 1 $R_{\rm J}$, and all but two have periods from 2 to 10 yr. We report two main findings based on this sample. First, the planet occurrence rate for the above size and period ranges is $0.70^{+0.40}_{-0.20}$ planets per Sun-like star, with the frequency of cold Jupiters agreeing with that from radial velocity surveys. Planet occurrence rises with decreasing planet size, roughly describable as $dN/d\log R \propto R^α$ with $α= -1.6^{+1.0}_{-0.9}$, i.e., Neptune-sized planets are some four times more common than Jupiter-sized ones. Second, five out of our 15 candidates orbit stars with known transiting planets at shorter periods, including one with five inner planets. We interpret this high incidence rate to mean: (1) almost all our candidates should be genuine; (2) across a large orbital range (from $\sim 0.05$ to a few astronomical units), mutual inclinations in these systems are at most a few degrees; and (3) large outer planets exist almost exclusively in systems with small inner planets.

astro-ph.EP↗

arXiv2019

OGLE-2018-BLG-0532Lb: Cold Neptune With Possible Jovian Sibling

We report the discovery of the planet OGLE-2018-BLG-0532Lb, with very obvious signatures in the light curve that lead to an estimate of the planet-host mass ratio $q=M_{\rm planet}/M_{\rm host}\simeq 1\times10^{-4}$. Although there are no obvious systematic residuals to this double-lens/single-source (2L1S) fit, we find that $χ^2$ can be significantly improved by adding either a third lens (3L1S, $Δχ^2=81$) or second source (2L2S, $Δχ^2=65$) to the lens-source geometry. After thorough investigation, we conclude that we cannot decisively distinguish between these two scenarios and therefore focus on the robustly-detected planet. However, given the possible presence of a second planet, we investigate to what degree and with what probability such additional planets may affect seemingly single-planet light curves. Our best estimates for the properties of the lens star and the secure planet are: a host mass $M\sim 0.25\,M_\odot$, system distance $D_L\sim 1\,$kpc and planet mass $m_{p,1}= 8\,M_\oplus$ with projected separation $a_{1,\perp}=1.4\,$au. However, there is a relatively bright $I=18.6$ (and also relatively blue) star projected within $<50\,$mas of the lens, and if future high-resolution images show that this is coincident with the lens, then it is possible that it is the lens, in which case, the lens would be both more massive and more distant than the best-estimated values above.

astro-ph.EP↗

arXiv2019

$Spitzer$ Parallax of OGLE-2018-BLG-0596: A Low-mass-ratio Planet around an M-dwarf

We report the discovery of a $Spitzer$ microlensing planet OGLE-2018-BLG-0596Lb, with preferred planet-host mass ratio $q \sim 2\times10^{-4}$. The planetary signal, which is characterized by a short $(\sim 1~{\rm day})$ "bump" on the rising side of the lensing light curve, was densely covered by ground-based surveys. We find that the signal can be explained by a bright source that fully envelops the planetary caustic, i.e., a "Hollywood" geometry. Combined with the source proper motion measured from $Gaia$, the $Spitzer$ satellite parallax measurement makes it possible to precisely constrain the lens physical parameters. The preferred solution, in which the planet perturbs the minor image due to lensing by the host, yields a Uranus-mass planet with a mass of $M_{\rm p} = 13.9\pm1.6~M_{\oplus}$ orbiting a mid M-dwarf with a mass of $M_{\rm h} = 0.23\pm0.03~M_{\odot}$. There is also a second possible solution that is substantially disfavored but cannot be ruled out, for which the planet perturbs the major image. The latter solution yields $M_{\rm p} = 1.2\pm0.2~M_{\oplus}$ and $M_{\rm h} = 0.15\pm0.02~M_{\odot}$. By combining the microlensing and $Gaia$ data together with a Galactic model, we find in either case that the lens lies on the near side of the Galactic bulge at a distance $D_{\rm L} \sim 6\pm1~{\rm kpc}$. Future adaptive optics observations may decisively resolve the major image/minor image degeneracy.

astro-ph.EP↗

arXiv2019

Thermal-demagnetization-enhanced hybrid fiber-based thermometer coupled with nitrogen-vacancy centers

Nitrogen-vacancy centers in diamond are attractive as quantum sensors owing to their remarkable optical and spin properties under ambient conditions. Here we experimentally demonstrated a hybrid fiber-based thermometer coupled with nitrogen-vacancy center ensemble and a permanent magnet, where the temperature sensitivity was improved by converting the temperature variation to the magnetic field change based on the thermal-demagnetization of the permanent magnet. We have achieved both large temperature working range (room temperature to 373 K) and millikelvin sensitivity (1.6 mK/sqrt(Hz)), nearly 6-fold improvement compared with conventional technique. This stable and compact hybrid thermometer will enable a wide range of applications for large-area detection and imaging with high temperature sensitivity.

physics.ins-det↗

arXiv2019

UV Background Fluctuations and Three-Point Correlations in the Large Scale Clustering of the Lyman-alpha Forest

Using the Ly$α$ mass assignment scheme (LyMAS), we make theoretical predictions for the 3-dimensional 3-point correlation function (3PCF) of the Ly$α$ forest at redshift $z=2.3$. We bootstrap results from the (100 $h^{-1} \mbox{ Mpc}$)$^3$ Horizon hydrodynamic simulation to a (1 $h^{-1}$ Gpc)$^3$ $N$-body simulation, considering both a uniform UV background (UVB) and a fluctuating UVB sourced by quasars with a comoving $n_q \approx 10^{-5}$ $h^3$ Mpc$^{-3}$ placed either in massive halos or randomly. On scales of $10-30$ $h^{-1} \mbox{ Mpc}$, the flux 3PCF displays hierarchical scaling with the square of the 2PCF, but with an unusual value of $Q \equiv ζ_{123}/(ξ_{12} ξ_{13} + ξ_{12} ξ_{23} + ξ_{13} ξ_{23}) \approx -4.5$ that reflects the low bias of the Ly$α$ forest and the anti-correlation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of $λ= 300$ $h^{-1} \mbox{ Mpc}$ comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on $Q$. For $λ= 100$ $h^{-1} \mbox{ Mpc}$ or 50 $h^{-1} \mbox{ Mpc}$, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to $Q \approx -3$. We scale our simulation results to derive rough estimate of the 3PCF detectability in observational data sets for the redshift range $z=2.1 - 2.6$. At $r = 10$ $h^{-1} \mbox{ Mpc}$ and 20 $h^{-1} \mbox{ Mpc}$, we predict a signal-to-noise (SNR) of $\sim$ 9 and $\sim$ 7, respectively, for both BOSS and eBOSS, and $\sim$ 37 and $\sim$ 25 for DESI. At $r = 40$ $h^{-1} \mbox{ Mpc}$ the predicted SNR is lower by $\sim$ 3$-$5 times. Measuring the flux 3PCF would be a novel test of the conventional paradigm of the Ly$α$ forest and help separate the contributions of UVB fluctuations and density fluctuations to Ly$α$ forest clustering.

astro-ph.CO↗

arXiv2019

A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

The rapid growth of wireless and mobile Internet has led to wide applications of exchanging resources over network, in which how to fairly allocate resources has become a critical challenge. To motivate sharing, a BD Mechanism is proposed for resource allocation, which is based on a combinatorial structure called bottleneck decomposition. The mechanism has been shown with properties of fairness, economic efficiency [17], and truthfulness against two kinds of strategic behaviors [2,3]. Unfortunately, the crux on how to compute a bottleneck decomposition of any graph is remain untouched. In this paper, we focus on the computation of bottleneck decomposition to fill the blanks and prove that the bottleneck decomposition of a network $G = (V, E; w_v)$ can be computed in $O(n^6 log(nU))$, where $n = |V|$ and $U = max_{v\in V} w_v$. Based on the bottleneck decomposition, a fair allocation in resource exchange system can be obtained in polynomial time. In addition, our work completes the computation of a market equilibrium and its relationship to two concepts of fairness in resource exchange.

cs.GT↗

arXiv2019

Spitzer Microlensing parallax reveals two isolated stars in the Galactic bulge

We report the mass and distance measurements of two single-lens events from the 2017 Spitzer microlensing campaign. The ground-based observations yield the detection of finite-source effects, and the microlens parallaxes are derived from the joint analysis of ground-based observations and Spitzer observations. We find that the lens of OGLE-2017-BLG-1254 is a $0.60 \pm 0.03 M_{\odot}$ star with $D_{\rm LS} = 0.53 \pm 0.11~\text{kpc}$, where $D_{\rm LS}$ is the distance between the lens and the source. The second event, OGLE-2017-BLG-1161, is subject to the known satellite parallax degeneracy, and thus is either a $0.51^{+0.12}_{-0.10} M_{\odot}$ star with $D_{\rm LS} = 0.40 \pm 0.12~\text{kpc}$ or a $0.38^{+0.13}_{-0.12} M_{\odot}$ star with $D_{\rm LS} = 0.53 \pm 0.19~\text{kpc}$. Both of the lenses are therefore isolated stars in the Galactic bulge. By comparing the mass and distance distributions of the eight published Spitzer finite-source events with the expectations from a Galactic model, we find that the Spitzer sample is in agreement with the probability of finite-source effects occurrence in single lens events.

astro-ph.SR↗