Universal Estimation of Directed Information

Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verd\'u (2005) and Cai, Kulkarni, and Verd\'u (2006) for estimation of other information measures. We show the almost sure and $L_1$ convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting relative merits such as smoothness, nonnegativity, and boundedness. We establish the consistency of these estimators in almost sure and $L_1$ senses, and derive near-optimal rates of convergence in the minimax sense under mild conditions. These estimators carry over directly to estimating other information measures of stationary ergodic finite-alphabet processes, such as entropy rate and mutual information rate, with near-optimal performance and provide alternatives to classical approaches in the existing literature. Guided by these theoretical results, the proposed estimators are implemented using the context-tree weighting algorithm as the universal probability assignment. Experiments on synthetic and real data are presented, demonstrating the potential of the proposed schemes in practice and the utility of directed information estimation in detecting and measuring causal influence and delay.Comment: 23 pages, 10 figures, to appear in IEEE Transactions on Information Theor

The Valuation of Service of Recreation Function of Dalinor National Natural Reserve

Dalinor National Natural Reserve is located in the west of Keshketeng Banner of Chifeng City, Inner Mongolia Autonomous Region (IMAR). It covers a total area of 119,413.35 ha, and is in drought or semi-drought continental climatic zone. DNNR is a comprehensive natural reserve made up of different ecosystems including lakes, prairies, wetlands, and forests. Dalinor Lake in DNNR is regarded as the paradise of birds, covering an area of 238 km2 between sandy lands and grasslands. DNNR was established in 1987 as a provincial natural reserve and was upgraded to a National Natural Reserve by the State Council of China in 1997. DNNR not only serves as an ideal resort for eco-tourism but also serves as an important scientific research base. The value of service of recreation function of DNNR depends heavily on the environmental quality that offers tourists various ecosystem amenities and opportunities for viewing wild plants and animals. So it is meaningful to value the recreation function of DNN

Decoy State Quantum Key Distribution With Modified Coherent State

To beat PNS attack, decoy state quantum key distribution (QKD) based on coherent state has been studied widely. We present a decoy state QKD protocol with modified coherent state (MCS). By destruction quantum interference, MCS with fewer multi-photon events can be get, which may improve key bit rate and security distance of QKD. Through numerical simulation, we show about 2-dB increment on security distance for BB84 protocol.Comment: 4 pages, 4 figure

Spatial-Temporal Imaging of Anisotropic Photocarrier Dynamics in Black Phosphorus

As an emerging single elemental layered material with a low symmetry in-plane crystal lattice, black phosphorus (BP) has attracted significant research interest owing to its unique electronic and optoelectronic properties, including its widely tunable bandgap, polarization dependent photoresponse and highly anisotropic in-plane charge transport. Despite extensive study of the steady-state charge transport in BP, there has not been direct characterization and visualization of the hot carriers dynamics in BP immediately after photoexcitation, which is crucial to understanding the performance of BP-based optoelectronic devices. Here we use the newly developed scanning ultrafast electron microscopy (SUEM) to directly visualize the motion of photo-excited hot carriers on the surface of BP in both space and time. We observe highly anisotropic in-plane diffusion of hot holes, with a 15-times higher diffusivity along the armchair (x-) direction than that along the zigzag (y-) direction. Our results provide direct evidence of anisotropic hot carrier transport in BP and demonstrate the capability of SUEM to resolve ultrafast hot carrier dynamics in layered two-dimensional materials.Comment: 21 pages, 6 figure

Heteroepitaxy of N-type β-Ga2O3 Thin Films on Sapphire Substrate by Low Pressure Chemical Vapor Deposition

This paper presents the heteroepitaxial growth of ultrawide bandgap β-Ga2O3 thin films on c-plane sapphire substrates by low pressure chemical vapor deposition. N-type conductivity in silicon (Si)-doped β-Ga2O3 films grown on sapphire substrate is demonstrated. The thin films were synthesized using high purity metallic gallium (Ga) and oxygen (O2) as precursors. The morphology, crystal quality, and properties of the as-grown thin films were characterized and analyzed by field emission scanning electron microscopy, X-ray diffraction, electron backscatter diffraction, photoluminescence and optical, photoluminescence excitation spectroscopy, and temperature dependent van der Pauw/Hall measurement. The optical bandgap is ∼4.76 eV, and room temperature electron mobility of 42.35 cm2/V s was measured for a Si-doped heteroepitaxial β-Ga2O3 film with a doping concentration of 1.32 × 1018 cm−3

Effect of Binary Source Companions on the Microlensing Optical Depth Determination toward the Galactic Bulge Field

Currently, gravitational microlensing survey experiments toward the Galactic bulge field utilize two different methods of minimizing blending effect for the accurate determination of the optical depth \tau. One is measuring \tau based on clump giant (CG) source stars and the other is using `Difference Image Analysis (DIA)' photometry to measure the unblended source flux variation. Despite the expectation that the two estimates should be the same assuming that blending is properly considered, the estimates based on CG stars systematically fall below the DIA results based on all events with source stars down to the detection limit. Prompted by the gap, we investigate the previously unconsidered effect of companion-associated events on $\tau$ determination. Although the image of a companion is blended with that of its primary star and thus not resolved, the event associated with the companion can be detected if the companion flux is highly magnified. Therefore, companions work effectively as source stars to microlensing and thus neglect of them in the source star count could result in wrong \tau estimation. By carrying out simulations based on the assumption that companions follow the same luminosity function of primary stars, we estimate that the contribution of the companion-associated events to the total event rate is ~5f_{bi}% for current surveys and can reach up to ~6f_{bi}% for future surveys monitoring fainter stars, where f_{bi} is the binary frequency. Therefore, we conclude that the companion-associated events comprise a non-negligible fraction of all events. However, their contribution to the optical depth is not large enough to explain the systematic difference between the optical depth estimates based on the two different methods.Comment: 4 pages, 1 figure, 1 table, ApJ, submitte

Improved Detection Rates for Close Binaries Via Astrometric Observations of Gravitational Microlensing Events

In addition to constructing a Galactic matter mass function free from the bias induced by the hydrogen-burning limit, gravitational microlensing allows one to construct a mass function which is less affected by the problem of unresolved binaries (Gaudi & Gould). However, even with the method of microlensing, the photometric detection of binaries is limited to binary systems with relatively large separations of $b\gtrsim 0.4$ of their combined Einstein ring radius, and thus the mass function is still not totally free from the problem of unresolved binaries. In this paper, we show that by detecting distortions of the astrometric ellipse of a microlensing event with high precision instruments such as the {\it Space Interferometry Mission}, one can detect close binaries at a much higher rate than by the photometric method. We find that by astrometrically observing microlensing events, $\sim 50$ of binaries with separations of $0.1r_{\rm E}$ can be detected with the detection threshold of 3%. The proposed astrometric method is especially efficient at detecting very close binaries. With a detection threshold of 3% and a rate of 10%, one can astrometrically detect binaries with separations down to $\sim 0.01r_{\rm E}$.Comment: total 14 pages, including 5 Figures and no Table (For figure 1, please send a request mail to [email protected]), accepted to ApJ (Vol 525, 000), updated versio

Fundamental Cycles and Graph Embeddings

In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum genus of a graph

Surface plasmon polaritons assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling

Metal films grown on Si wafer perforated with a periodic array of subwavelength holes have been fabricated and anomalous enhanced transmission in the mid-infrared regime has been observed. High order transmission peaks up to Si(2,2) are clearly revealed due to the large dielectric constant contrast of the dielectrics at the opposite interfaces. Si(1,1) peak splits at oblique incidence both in TE and TM polarization, which confirms that anomalous enhanced transmission is a surface plasmon polaritons (SPPs) assisted diffraction phenomenon. Theoretical transmission spectra agree excellently with the experimental results and confirm the role of SPPs diffraction by the lattice.Comment: 4 pages, 5 figures, 26 reference