arXiv subjects
Publications and source records attributed to Di Yang.
A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.
Enriched by natural language texts, Stack Overflow code snippets are an invaluable code-centric knowledge base of small units of source code. Besides being useful for software developers, these annotated snippets can potentially serve as the basis for automated tools that provide working code solutions to specific natural language queries. With the goal of developing automated tools with the Stack Overflow snippets and surrounding text, this paper investigates the following questions: (1) How usable are the Stack Overflow code snippets? and (2) When using text search engines for matching on the natural language questions and answers around the snippets, what percentage of the top results contain usable code snippets? A total of 3M code snippets are analyzed across four languages: C\#, Java, JavaScript, and Python. Python and JavaScript proved to be the languages for which the most code snippets are usable. Conversely, Java and C\# proved to be the languages with the lowest usability rate. Further qualitative analysis on usable Python snippets shows the characteristics of the answers that solve the original question. Finally, we use Google search to investigate the alignment of usability and the natural language annotations around code snippets, and explore how to make snippets in Stack Overflow an adequate base for future automatic program generation.
We extend to the Toda lattice hierarchy the approach of [3, 4] to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding differ- ence Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed.
The DArk Matter Particle Explorer (DAMPE) is a space experiment designed to search for dark matter indirectly by measuring the spectra of photons, electrons, and positrons up to 10 TeV. The BGO electromagnetic calorimeter (ECAL) is its main sub-detector for energy measurement. In this paper, the instrumentation and development of the BGO ECAL is briefly described. The calibration on the ground, including the pedestal, minimum ionizing particle (MIP) peak, dynode ratio, and attenuation length with the cosmic rays and beam particles is discussed in detail. Also, the energy reconstruction results of the electrons from the beam test are presented.
For a simple Lie algebra $\mathfrak g$ we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of $\mathfrak g$-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example $\mathfrak g=sl_2(\mathbb C)$ the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function was used in our previous work for computing logarithmic derivatives of the Witten - Kontsevich tau-function. For an arbitrary simple Lie algebra we construct a basis in the space of regular solutions to the topological equation called generalized Airy resolvents. We also outline applications of the generalized Airy resolvents to computing the Witten and Fan - Jarvis - Ruan invariants of the Deligne - Mumford moduli spaces of stable algebraic curves.
Based on the work of Itzykson and Zuber on Kontsevich's integrals, we give a geometric interpretation and a simple proof of Zhou's explicit formula for the Witten-Kontsevich tau function. More precisely, we show that the numbers $A_{m,n}^{Zhou}$ defined by Zhou coincide with the affine coordinates for the point of the Sato Grassmannian corresponding to the Witten-Kontsevich tau function. Generating functions and new recursion relations for $A_{m,n}^{Zhou}$ are derived. Our formulation on matrix-valued affine coordinates and on tau functions remains valid for generic Grassmannian solutions of the KdV hierarchy. A by-product of our study indicates an interesting relation between the matrix-valued affine coordinates for the Witten-Kontsevich tau function and the $V$-matrices associated to the $R$-matrix of Witten's $3$-spin structures.
We derive a particular solution of the extended $r$-reduced KP hierarchy, which is specified by a generalized string equation. The work is a generalization to arbitrary $r\geq 2$ of Buryak's recent results of a solution to the extended open KdV hierarchy which corresponds to $r=2$.
For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the intersection numbers of the Gromov--Witten classes and their descendents along with the characteristic classes of Hodge bundles on the moduli spaces of stable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy is a deformation of the Korteweg--de Vries hierarchy depending on an infinite number of parameters. Conjecturally this hierarchy is a universal object in the class of scalar Hamiltonian integrable hierarchies possessing tau-functions.
The DAMPE (DArk Matter Particle Explorer) is a scientific satellite being developed in China, aimed at cosmic ray study, gamma ray astronomy, and searching for the clue of dark matter particles, with a planned mission period of more than 3 years and an orbit altitude of about 500 km. The BGO Calorimeter, which consists of 308 BGO (Bismuth Germanate Oxid) crystal bars, 616 PMTs (photomultiplier tubes) and 1848 dynode signals, has approximately 32 radiation lengths. It is a crucial sub-detector of the DAMPE payload, with the functions of precisely measuring the energy of cosmic particles from 5 GeV to 10TeV, distinguishing positrons/electrons and gamma rays from hadron background, and providing trigger information for the whole DAMPE payload. The dynamic range for a single BGO crystal is about 2?105 and there are 1848 detector signals in total. To build such an instrument in space, the major design challenges for the readout electronics come from the large dynamic range, the high integrity inside the very compact structure, the strict power supply budget and the long term reliability to survive the hush environment during launch and in orbit. Currently the DAMPE mission is in the end of QM (Qualification Model) stage. This paper presents a detailed description of the readout electronics for the BGO calorimeter.
In a recent paper [3], Bakalov and Milanov proved that the total descendant potential of a simple singularity satisfies the W-constraints, which come from the W-algebra of the lattice vertex algebra associated to the root lattice of this singularity and a twisted module of this vertex algebra. In the present paper, we prove that the solution of these W-constraints is unique up to a constant factor, as conjectured by Bakalov and Milanov in their paper.
The problem of segmenting a given image into coherent regions is important in Computer Vision and many industrial applications require segmenting a known object into its components. Examples include identifying individual parts of a component for process control work in a manufacturing plant and identifying parts of a car from a photo for automatic damage detection. Unfortunately most of an object's parts of interest in such applications share the same pixel characteristics, having similar colour and texture. This makes segmenting the object into its components a non-trivial task for conventional image segmentation algorithms. In this paper, we propose a "Model Assisted Segmentation" method to tackle this problem. A 3D model of the object is registered over the given image by optimising a novel gradient based loss function. This registration obtains the full 3D pose from an image of the object. The image can have an arbitrary view of the object and is not limited to a particular set of views. The segmentation is subsequently performed using a level-set based method, using the projected contours of the registered 3D model as initialisation curves. The method is fully automatic and requires no user interaction. Also, the system does not require any prior training. We present our results on photographs of a real car.
Density-based cluster mining is known to serve a broad range of applications ranging from stock trade analysis to moving object monitoring. Although methods for efficient extraction of density-based clusters have been studied in the literature, the problem of summarizing and matching of such clusters with arbitrary shapes and complex cluster structures remains unsolved. Therefore, the goal of our work is to extend the state-of-art of density-based cluster mining in streams from cluster extraction only to now also support analysis and management of the extracted clusters. Our work solves three major technical challenges. First, we propose a novel multi-resolution cluster summarization method, called Skeletal Grid Summarization (SGS), which captures the key features of density-based clusters, covering both their external shape and internal cluster structures. Second, in order to summarize the extracted clusters in real-time, we present an integrated computation strategy C-SGS, which piggybacks the generation of cluster summarizations within the online clustering process. Lastly, we design a mechanism to efficiently execute cluster matching queries, which identify similar clusters for given cluster of analyst's interest from clusters extracted earlier in the stream history. Our experimental study using real streaming data shows the clear superiority of our proposed methods in both efficiency and effectiveness for cluster summarization and cluster matching queries to other potential alternatives.
The fluid dynamics video No.V058 is introduced, with brief descriptions of the numerical method used to generate the animation data, explanation of what is shown in the movies, and the main scientific findings obtained from this study.
Unidirectional start-up flow of a viscoelastic fluid in a pipe with fractional Maxwell's model is studied. The flow starting from rest is driven by a constant pressure gradient in an infinite long straight pipe. By employing the method of variable separations and Heaviside operational calculus, we obtain the exact solution, from which the flow characteristics are investigated. It is found that the start-up motion of fractional Maxwell's fluid with parameters $α$ and $β$, tends to be at rest as time goes to infinity, except the case of $β=1$. This observation, which also can be predicted from the mechanics analogue of fractional Maxwell's model, agrees with the classical work of Friedrich and it indicates fractional Maxwell's fluid presents solid-like behavior if $\be\neq 1$ and fluid-like behavior if $\be=1$. For an arbitrary viscoelastic model, a conjecture is proposed to give an intuitive way judging whether it presents fluid-like or solid-like behavior. Also oscillations may occur before the fluid tends to the asymptotic behavior stated above, which is a common phenomenon for viscoelastic fluids.