Probing Dark Energy with the Kunlun Dark Universe Survey Telescope

Dark energy is an important science driver of many upcoming large-scale surveys. With small, stable seeing and low thermal infrared background, Dome A, Antarctica, offers a unique opportunity for shedding light on fundamental questions about the universe. We show that a deep, high-resolution imaging survey of 10,000 square degrees in \emph{ugrizyJH} bands can provide competitive constraints on dark energy equation of state parameters using type Ia supernovae, baryon acoustic oscillations, and weak lensing techniques. Such a survey may be partially achieved with a coordinated effort of the Kunlun Dark Universe Survey Telescope (KDUST) in \emph{yJH} bands over 5000--10,000 deg$^2$ and the Large Synoptic Survey Telescope in \emph{ugrizy} bands over the same area. Moreover, the joint survey can take advantage of the high-resolution imaging at Dome A to further tighten the constraints on dark energy and to measure dark matter properties with strong lensing as well as galaxy--galaxy weak lensing.Comment: 9 pages, 6 figure

Designing shipping policies with top-up options to qualify for free delivery

Motivated by the booming online grocery market and the extensive use of contingent free-shipping (CFS) policies in the e-grocery industry, we investigate the optimal CFS and pricing decisions for online grocers. Under a CFS policy, consumers enjoy free shipping for orders exceeding a certain threshold value; otherwise, they are charged a flat fee for orders below this threshold. We adopt a utility-based model to capture consumers' behavior of purchasing additional items to qualify for free shipping under a CFS policy and analyze its impact on policy structure and consumer surplus. We characterize the e-grocer's optimal pricing and CFS policy and find that consumer heterogeneity and demand distribution lead to different forms of the optimal shipping policy. When consumer heterogeneity is large enough, the optimal policy induces some consumers to top up and may allow some others to ship for free. In this case, the e-grocer can charge a high-profit margin. Otherwise, a top-up option is unnecessary, and a flat-rate shipping fee policy is optimal. Moreover, while the optimal policy never induces all consumers to top up when they are rational, it is possible to do so when consumers associate some psychological disutility with the shipping fee. Surprisingly, the total consumer surplus under the optimal policy may increase in the latter case. We further model a Stackelberg game between an e-grocer and an offline channel and find that the difference between the e-grocer's internal shipping cost and consumers' inconvenience cost of shopping offline is a main driver for market segmentation. Lastly, we show that a subscription-based free-shipping program, in addition to the jointly optimized CFS and pricing policy, cannot improve profits when consumers' order size and frequency are independent. Our findings help online grocers make operational and marketing decisions under the impact of consumers' top-up behavior

Computing the Loewner driving process of random curves in the half plane

We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion. We find that just testing the normality of the process at a fixed time is not effective at determining if the process is Brownian motion. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N^1.35) rather than the usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph to conclusion section; improved figures cosmeticall

Computed tomography data colouring based on photogrammetric images

Nowadays various methods and sensors are available for 3D reconstruction tasks; however, it is still necessary to integrate advantages of different technologies for optimizing the quality 3D models. Computed tomography (CT) is an imaging technique which takes a large number of radiographic measurements from different angles, in order to generate slices of the object, however, without colour information. The aim of this study is to put forward a framework to extract colour information from photogrammetric images for corresponding Computed Tomography (CT) surface data with high precision. The 3D models of the same object from CT and photogrammetry methods are generated respectively, and a transformation matrix is determined to align the extracted CT surface to the photogrammetric point cloud through a coarse-to-fine registration process. The estimated pose information of images to the photogrammetric point clouds, which can be obtained from the standard image alignment procedure, also applies to the aligned CT surface data. For each camera pose, a depth image of CT data is calculated by projecting all the CT points to the image plane. The depth image is in principle should agree with the corresponding photogrammetric image. The points, which cannot be seen from the pose, but are also projected on the depth image, are excluded from the colouring process. This is realized by comparing the range values of neighbouring pixels and finding the corresponding 3D points with larger range values. The same procedure is implemented for all the image poses to obtain the coloured CT surface. Thus, by using photogrammetric images, we achieve a coloured CT dataset with high precision, which combines the advantages from both methods. Rather than simply stitching different data, we deep-dive into the photogrammetric 3D reconstruction process and optimize the CT data with colour information. This process can also provide an initial route and more options for other data fusion processes

Interaction induced decay of a heteronuclear two-atom system

Two-atom systems in small traps are of fundamental interest, first of all for understanding the role of interactions in degenerate cold gases and for the creation of quantum gates in quantum information processing with single-atom traps. One of the key quantities is the inelastic relaxation (decay) time when one of the atoms or both are in a higher hyperfine state. Here we measure this quantity in a heteronuclear system of $^{87}$Rb and $^{85}$Rb in a micro optical trap and demonstrate experimentally and theoretically the presence of both fast and slow relaxation processes, depending on the choice of the initial hyperfine states. The developed experimental method allows us to single out a particular relaxation process and, in this sense, our experiment is a "superclean platform" for collisional physics studies. Our results have also implications for engineering of quantum states via controlled collisions and creation of two-qubit quantum gates.Comment: 8 pages, 3 figure

Synthesizing SystemC Code from Delay Hybrid CSP

Delay is omnipresent in modern control systems, which can prompt oscillations and may cause deterioration of control performance, invalidate both stability and safety properties. This implies that safety or stability certificates obtained on idealized, delay-free models of systems prone to delayed coupling may be erratic, and further the incorrectness of the executable code generated from these models. However, automated methods for system verification and code generation that ought to address models of system dynamics reflecting delays have not been paid enough attention yet in the computer science community. In our previous work, on one hand, we investigated the verification of delay dynamical and hybrid systems; on the other hand, we also addressed how to synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP (HCSP) without delay. In this paper, we give a first attempt to synthesize SystemC code from a verified delay hybrid system modelled by Delay HCSP (dHCSP), which is an extension of HCSP by replacing ordinary differential equations (ODEs) with delay differential equations (DDEs). We implement a tool to support the automatic translation from dHCSP to SystemC

Stationarity of SLE

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.Comment: 14 pages with 1 figur