arXiv subjects
Publications and source records attributed to Di Yang.
The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application of this result, we prove a gap condition for certain special cubic Hodge integrals and give an algorithm for computing the coefficients that appear in the gap condition.
Taking advantage of human pose data for understanding human activities has attracted much attention these days. However, state-of-the-art pose estimators struggle in obtaining high-quality 2D or 3D pose data due to occlusion, truncation and low-resolution in real-world un-annotated videos. Hence, in this work, we propose 1) a Selective Spatio-Temporal Aggregation mechanism, named SST-A, that refines and smooths the keypoint locations extracted by multiple expert pose estimators, 2) an effective weakly-supervised self-training framework which leverages the aggregated poses as pseudo ground-truth instead of handcrafted annotations for real-world pose estimation. Extensive experiments are conducted for evaluating not only the upstream pose refinement but also the downstream action recognition performance on four datasets, Toyota Smarthome, NTU-RGB+D, Charades, and Kinetics-50. We demonstrate that the skeleton data refined by our Pose-Refinement system (SSTA-PRS) is effective at boosting various existing action recognition models, which achieves competitive or state-of-the-art performance.
Based on the Chen--Möller--Sauvaget formula, we apply the theory of integrable systems to derive three equations for the generating series of the Masur--Veech volumes ${\rm Vol} \, \mathcal{Q}_{g,n}$ associated with the principal strata of the moduli spaces of quadratic differentials, and propose refinements of the conjectural formulas given in [12,4] for the large genus asymptotics of ${\rm Vol} \, \mathcal{Q}_{g,n}$ and of the associated area Siegel--Veech constants.
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice hierarchy. Explicit formulae for generating series of logarithmic derivatives of the tau-functions are then obtained, and applications to enumeration of ribbon graphs with even valencies and to the special cubic Hodge integrals are considered.
Integrability condition of Hamiltonian perturbations of integrable Hamiltonian PDEs of hydrodynamic type up to the second order approximation is considered.
We extend a recent result of [13] for the KdV hierarchy to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we define a pair of wave functions, and use them to give explicit formulae for the generating series of $k$-point correlation functions of the solution. Applications to computing GUE correlators and Gromov--Witten invariants of the Riemann sphere are under consideration.
Programmers often write code that has similarity to existing code written somewhere. A tool that could help programmers to search such similar code would be immensely useful. Such a tool could help programmers to extend partially written code snippets to completely implement necessary functionality, help to discover extensions to the partial code which are commonly included by other programmers, help to cross-check against similar code written by other programmers, or help to add extra code which would fix common mistakes and errors. We propose Aroma, a tool and technique for code recommendation via structural code search. Aroma indexes a huge code corpus including thousands of open-source projects, takes a partial code snippet as input, searches the corpus for method bodies containing the partial code snippet, and clusters and intersects the results of the search to recommend a small set of succinct code snippets which both contain the query snippet and appear as part of several methods in the corpus. We evaluated Aroma on 2000 randomly selected queries created from the corpus, as well as 64 queries derived from code snippets obtained from Stack Overflow, a popular website for discussing code. We implemented Aroma for 4 different languages, and developed an IDE plugin for Aroma. Furthermore, we conducted a study where we asked 12 programmers to complete programming tasks using Aroma, and collected their feedback. Our results indicate that Aroma is capable of retrieving and recommending relevant code snippets efficiently.
In the context of many applications of turbulent multi-phase flows, knowledge of the dispersed phase size distribution and its evolution is critical to predicting important macroscopic features. We use a population dynamics model for polydisperse droplet distributions specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence. Following earlier methods used in the Reynolds averaged Navier--Stokes framework, the droplet breakup due to turbulent fluctuations is modelled by treating droplet-eddy collisions as in kinetic theory of gases. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. After initial comparisons of the one-dimensional model to measurements of oil droplets in an axisymmetric jet, it is then applied in a three-dimensional LES of a jet in crossflow with large oil droplets of a single size being released at the source of the jet. We model the concentration fields using $N_d =15$ bins of discrete droplet sizes and solve scalar transport equations for each bin. The resulting droplet size distributions are compared with published experimental data, and good agreement for the relative size distribution is obtained. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behavior.
Developers often resort to online Q&A forums such as Stack Overflow (SO) for filling their programming needs. Although code examples on those forums are good starting points, they are often incomplete and inadequate for developers' local program contexts; adaptation of those examples is necessary to integrate them to production code. As a consequence, the process of adapting online code examples is done over and over again, by multiple developers independently. Our work extensively studies these adaptations and variations, serving as the basis for a tool that helps integrate these online code examples in a target context in an interactive manner. We perform a large-scale empirical study about the nature and extent of adaptations and variations of SO snippets. We construct a comprehensive dataset linking SO posts to GitHub counterparts based on clone detection, time stamp analysis, and explicit URL references. We then qualitatively inspect 400 SO examples and their GitHub counterparts and develop a taxonomy of 24 adaptation types. Using this taxonomy, we build an automated adaptation analysis technique on top of GumTree to classify the entire dataset into these types. We build a Chrome extension called ExampleStack that automatically lifts an adaptation-aware template from each SO example and its GitHub counterparts to identify hot spots where most changes happen. A user study with sixteen programmers shows that seeing the commonalities and variations in similar GitHub counterparts increases their confidence about the given SO example, and helps them grasp a more comprehensive view about how to reuse the example differently and avoid common pitfalls.
Current research in clone detection suffers from poor ecosystems for evaluating precision of clone detection tools. Corpora of labeled clones are scarce and incomplete, making evaluation labor intensive and idiosyncratic, and limiting inter tool comparison. Precision-assessment tools are simply lacking. We present a semi-automated approach to facilitate precision studies of clone detection tools. The approach merges automatic mechanisms of clone classification with manual validation of clone pairs. We demonstrate that the proposed automatic approach has a very high precision and it significantly reduces the number of clone pairs that need human validation during precision experiments. Moreover, we aggregate the individual effort of multiple teams into a single evolving dataset of labeled clone pairs, creating an important asset for software clone research.
We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mariño--Vafa type [17, 28] and GUE correlators, and the conjecture proposed in [7] that the partition function of these Hodge integrals is a tau function of the discrete KdV hierarchy.
A conjectural formula for the $k$-point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \cite{DY2}. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the $k$-point function as a sum of $(k-1)!$ products of hypergeometric functions of one variable. We show that the $k$-point generating function coincides with the $ε\rightarrow 0$ asymptotics of the analytic $k$-point function, and also compute three more asymptotics of the analytic function for $ε\rightarrow \infty$, $q\rightarrow 0$, $q\rightarrow\infty$, thus defining new invariants for the Riemann sphere.
When programmers look for how to achieve certain programming tasks, Stack Overflow is a popular destination in search engine results. Over the years, Stack Overflow has accumulated an impressive knowledge base of snippets of code that are amply documented. We are interested in studying how programmers use these snippets of code in their projects. Can we find Stack Overflow snippets in real projects? When snippets are used, is this copy literal or does it suffer adaptations? And are these adaptations specializations required by the idiosyncrasies of the target artifact, or are they motivated by specific requirements of the programmer? The large-scale study presented on this paper analyzes 909k non-fork Python projects hosted on Github, which contain 290M function definitions, and 1.9M Python snippets captured in Stack Overflow. Results are presented as quantitative analysis of block-level code cloning intra and inter Stack Overflow and GitHub, and as an analysis of programming behaviors through the qualitative analysis of our findings.
In metal organic vapor phase epitaxy of GaN, the growth mode is sensitive to reactor temperature. In this study, V-pit-shaped GaN has been grown on normal c-plane cone-patterned sapphire substrate by decreasing the growth temperature of high-temperature-GaN to around 950 oC, which leads to the 3-dimensional growth of GaN. The so-called "WM" well describes the shape that the bottom of GaN V-pit is just right over the top of sapphire cone, and the regular arrangement of V-pits follows the patterns of sapphire substrate strictly. Two types of semipolar facets (1101) and (1122) expose on sidewalls of V-pits. Furthermore, by raising the growth temperature to 1000 oC, the growth mode of GaN can be transferred to 2-demonsional growth. Accordingly, the size of V-pits becomes smaller and the area of c-plane GaN becomes larger, while the total thickness of GaN keeps almost unchanged during this process. As long as the 2-demonsional growth lasts, the V-pits will disappear and only flat c-plane GaN remains. This means the area ratio of c-plane and semipolar plane GaN can be controlled by the duration time of 2-demonsional growth.
V-pit-defects in GaN-based light-emitting diodes induced by dislocations are considered beneficial to electroluminescence because they relax the strain in InGaN quantum wells and also enhance the hole lateral injection through sidewall of V-pits. In this paper, regularly arranged V-pits are formed on c-plane GaN grown by metal organic vapor phase epitaxy on conventional c-plane cone-patterned sapphire substrates. The size of V-pits and area of flat GaN can be adjusted by changing growth temperature. Five pairs of InGaN/GaN multi-quantumwell and also a light-emitting diode structure are grown on this V-pit-shaped GaN. Two peaks around 410 nm and 450 nm appearing in both photoluminescence and cathodeluminescence spectra are from the semipolar InGaN/GaN multi-quantum-well on sidewalls of V-pits and cplane InGaN/GaN multi-quantum-well, respectively. In addition, dense bright spots can be observed on the surface of light-emitting diode when it works under small injection current, which are believed owing to the enhanced hole injection around V-pits.
Software developers use Application Programming Interfaces (APIs) of libraries and frameworks extensively while writing programs. In this context, the recommendations provided in code completion pop-ups help developers choose the desired methods. The candidate lists recommended by these tools, however, tend to be large, ordered alphabetically and sometimes even incomplete. A fair amount of work has been done recently to improve the relevance of these code completion results, especially for statically typed languages like Java. However, these proposed techniques rely on the static type of the object and are therefore inapplicable for a dynamically typed language like Python. In this paper, we present PyReco, an intelligent code completion system for Python which uses the mined API usages from open source repositories to order the results based on relevance rather than the conventional alphabetic order. To recommend suggestions that are relevant for a working context, a nearest neighbor classifier is used to identify the best matching usage among all the extracted usage patterns. To evaluate the effectiveness of our system, the code completion queries are automatically extracted from projects and tested quantitatively using a ten-fold cross validation technique. The evaluation shows that our approach outperforms the alphabetically ordered API recommendation systems in recommending APIs for standard, as well as, third-party libraries.
Avalanche photodiode (APD) has been intensively investigated as a promising candidate to replace photomultiplier tubes (PMT) for weak light detection. However, in conventional APDs, a large portion of carrier energy drawn from the electric field is thermalized, and the multiplication efficiencies of electron and hole are low and close. In order to achieve high gain, the device should work under breakdown bias, where carrier multiplication proceeds bi-directionally to form a positive feedback multiplication circle. However, breakdown is hard to control, in practice, APDs should work under Geiger mode as a compromise between sustainable detection and high gain. The complexity of system seriously restricts the application. Here, we demonstrate an avalanche photodiode holding high gain without breakdown, which means no quenching circuit is needed for sustainable detection. The device is based on a GaN/AlN periodically-stacked-structure (PSS), wherein electron holds much higher efficiency than hole to draw energy from the electric field, and avalanche happens uni-directionally with high efficiency. and a recorded high gain (10^4) tested under constant bias is obtained in a prototype device, wherein the stable gain can be determined by the periodicity of the GaN/AlN PSS. This work not only brings a new light into avalanche multiplication mechanism, but also paves a technological path with high commercial value to realize highly sensitive avalanche devices working under constant bias like PMT.