Optimal loss-carry-forward taxation for L\'{e}vy risk processes stopped at general draw-down time

Motivated by Kyprianou and Zhou (2009), Wang and Hu (2012), Avram et al. (2017), Li et al. (2017) and Wang and Zhou (2018), we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose reserve process (before taxes are deducted) evolves as a spectrally negative L\'{e}vy process with the usual exclusion of negative subordinator or deterministic drift. Tax payments are collected according to the very general loss-carry-forward tax system introduced in Kyprianou and Zhou (2009). To achieve a balance between taxation optimization and solvency, we consider an interesting modified objective function by considering the expected accumulated discounted tax payments of the company until the general draw-down time, instead of until the classical ruin time. The optimal tax return function together with the optimal tax strategy is derived, and some numerical examples are also provided

Exact Bivariate Polynomial Factorization in Q by Approximation of Roots

Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, we present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. Our method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable

Holistic Parameteric Reconstruction of Building Models from Point Clouds

Building models are conventionally reconstructed by building roof points planar segmentation and then using a topology graph to group the planes together. Roof edges and vertices are then mathematically represented by intersecting segmented planes. Technically, such solution is based on sequential local fitting, i.e., the entire data of one building are not simultaneously participating in determining the building model. As a consequence, the solution is lack of topological integrity and geometric rigor. Fundamentally different from this traditional approach, we propose a holistic parametric reconstruction method which means taking into consideration the entire point clouds of one building simultaneously. In our work, building models are reconstructed from predefined parametric (roof) primitives. We first use a well-designed deep neural network to segment and identify primitives in the given building point clouds. A holistic optimization strategy is then introduced to simultaneously determine the parameters of a segmented primitive. In the last step, the optimal parameters are used to generate a watertight building model in CityGML format. The airborne LiDAR dataset RoofN3D with predefined roof types is used for our test. It is shown that PointNet++ applied to the entire dataset can achieve an accuracy of 83% for primitive classification. For a subset of 910 buildings in RoofN3D, the holistic approach is then used to determine the parameters of primitives and reconstruct the buildings. The achieved overall quality of reconstruction is 0.08 meters for point-surface-distance or 0.7 times RMSE of the input LiDAR points. The study demonstrates the efficiency and capability of the proposed approach and its potential to handle large scale urban point clouds

Investigation of the Puzzling Abundance Pattern in the Stars of the Fornax Dwarf Spheroidal Galaxy

Many works have found unusual characteristics of elemental abundances in nearby dwarf galaxies. This implies that there is a key factor of galactic evolution that is different from that of the Milky Way (MW). The chemical abundances of the stars in the Fornax dwarf spheroidal galaxy (Fornax dSph) provide excellent information for setting constraints on the models of the galactic chemical evolution. In this work, adopting the five-component approach, we fit the abundances of the Fornax dSph stars, including $\alpha$ elements, iron group elements and neutron-capture elements. For most sample stars, the relative contributions from the various processes to the elemental abundances are not usually in the MW proportions. We find that the contributions from massive stars to the primary $\alpha$ elements and iron group elements increase monotonously with increasing [Fe/H]. This means that the effect of the galactic wind is not strong enough to halt star formation and the contributions from massive stars to $\alpha$ elements did not halted for [Fe/H]$\lesssim$-0.5. The average contributed ratios of various processes between the dSph stars and the MW stars monotonously decrease with increasing progenitor mass. This is important evidence of a bottom-heavy initial mass function (IMF) for the Fonax dSph, compared to the MW. Considering a bottom-heavy IMF for the dSph, the observed relations of [$\alpha$/Fe] versus [Fe/H], [iron group/Fe] versus [Fe/H] and [neutron-capture/Fe] versus [Fe/H] for the dSph stars can be explained.Comment: 38 pages, 11 figures, 2 tables. Accepted for publication in Ap

Astrophysical Origins for the Unusual Chemical Abundance of the Globular Cluster Palomar 1

We study the abundances of {\alpha} elements, Fe-peak elements, and neutron-capture elements in Pal 1. We found that the abundances of the SNe Ia and main s-process components of Pal 1 are larger than those of the disk stars and the abundances of the primary component of Pal 1 are smaller than those of the disk stars with similar metallicity. The Fe abundances of Pal 1 and the disk stars mainly originate from the SNe Ia and the primary component, respectively. Although the {\alpha} abundances dominantly produced by the primary process for the disk stars and Pal 1, the contributions of the primary component to Pal 1 are smaller than the corresponding contributions to the disk stars. The Fe-peak elements V and Co mainly originate from the primary and secondary components for the disk stars and Pal 1, but the contributions of the massive stars to Pal 1 are lower than those of the massive stars to the disk stars. The Yabundances mainly originate from the weak r-component for the disk stars. However, the contributions of the main s-components and main r-components to Y are close to those of the weak r-component for Pal 1. The Ba abundances of Pal 1 and the disk stars mainly originate from the main s-component and the main r-component, respectively. Our calculated results imply that the unusual abundances of Pal could be explained by the top-light IMF for Pal 1 progenitor-system

Estimating R-Process Yields from Abundances of the Metal-Poor Stars

The chemical abundances of metal-poor stars provide important clues to explore stellar formation history and set significant constraints on models of the r-process. In this work, we find that the abundance patterns of the light and iron group elements of the main r-process stars are very close to those of the weak r-process stars. Based on a detailed abundance comparison, we find that the weak r-process occurs in supernovae with a progenitor mass range of $\sim11-26M_{\odot}$. Using the SN yields given by Heger & Woosley and the abundances of the weak r-process stars, the weak r-process yields are derived. The SNe with a progenitor mass range of $15M_{\odot}<M<26M_{\odot}$ are the main sites of the weak r-process and their contributions are larger than 80%. Using the abundance ratios of the weak r-process and the main r-process in the solar system, the average yields of the main r-process are estimated. The observed correlations of the [neutron-capture/Eu] versus [Eu/Fe] can be explained by mixing of the two r-process abundances in various fractions.Comment: The article has been published by PASP, 2014, 126, 54

Is Germanium (Ge, Z=32) A Neutron-Capture Element?

Historically,Ge has been considered to be a neutron-capture element. In this case, the r-process abundance of Ge is derived by subtracting the s-process abundance from the total abundance in the Solar system. However, the Ge abundance of the metal-poor star HD 108317 is lower than that of the scaled residual r-process abundance in the Solar system, about 1.2 dex. In this paper, based on a comparison of the Ge abundances of metal-poor stars and stellar yields, we find that the Ge abundances are not the result of the primary-like yields in massive stars and come mainly from the r-process. Based on the observed abundances of metal-poor stars, we derived the Ge abundances of the weak r-process and main r-process. The contributed percentage of the neutron-capture process to Ge in the Solar system is about 59 per cent, which means that the contributed percentage of the Ge residual abundance in the Solar system is about 41 per cent. We find that the Ge residual abundance is produced as secondary-like yields in massive stars. This implies that the element Ge in the Solar system is not produced solely by the neutron-capture process.Comment: 12 pages, 8 figure

AutoSF: Searching Scoring Functions for Knowledge Graph Embedding

Scoring functions (SFs), which measure the plausibility of triplets in knowledge graph (KG), have become the crux of KG embedding. Lots of SFs, which target at capturing different kinds of relations in KGs, have been designed by humans in recent years. However, as relations can exhibit complex patterns that are hard to infer before training, none of them can consistently perform better than others on existing benchmark data sets. In this paper, inspired by the recent success of automated machine learning (AutoML), we propose to automatically design SFs (AutoSF) for distinct KGs by the AutoML techniques. However, it is non-trivial to explore domain-specific information here to make AutoSF efficient and effective. We firstly identify a unified representation over popularly used SFs, which helps to set up a search space for AutoSF. Then, we propose a greedy algorithm to search in such a space efficiently. The algorithm is further sped up by a filter and a predictor, which can avoid repeatedly training SFs with same expressive ability and help removing bad candidates during the search before model training. Finally, we perform extensive experiments on benchmark data sets. Results on link prediction and triplets classification show that the searched SFs by AutoSF, are KG dependent, new to the literature, and outperform the state-of-the-art SFs designed by humans.Comment: accepted by ICDE 202

Josephson Metamaterial with a widely tunable positive/negative Kerr constant

We report on the microwave characterization of a novel one-dimensional Josephson metamaterial composed of a chain of asymmetric superconducting quantum interference devices (SQUIDs) with nearest-neighbor coupling through common Josephson junctions. This metamaterial demonstrates a strong Kerr nonlinearity, with a Kerr constant tunable over a wide range, from positive to negative values, by a magnetic flux threading the SQUIDs. The experimental results are in good agreement with the theory of nonlinear effects in Josephson chains. The metamaterial is very promising as an active medium for Josephson traveling-wave parametric amplifiers; its use facilitates phase matching in a four-wave mixing process for efficient parametric gain.Comment: 5 pages, 4 figure

The odd-isotope fractions of Barium in the strongly r-process enhanced (r-II) stars

We determined the \fodd\ values, $0.46\pm0.08$, $0.51\pm0.09$, $0.50\pm0.13$, $0.48\pm0.12$, which correspond to the r-contribution 100\% for four r-II stars, \cs, \hen, \hes\, and \het, respectively. Our results suggest that almost all of the heavy elements (in the range from Ba to Pb) in r-II stars have a common origin, that is, from a single r-process (the main r-process). We found that the \fodd\ has a intrinsic nature, and should keep constant value of about 0.46 in the main r-process yields, which is responsible for the heavy element enhancement of r-II stars and of our Galaxy chemical enhancement. In addition, except the abundance ratio [Ba/Eu] the \fodd\ is also an important indicator, which can be used to study the relative contributions of the r- and s-process during the chemical evolution history of the Milky Way and the enhancement mechanism in stars with peculiar abundance of heavy elements.Comment: 13 pages, 2 figures, Accepted to Ap