Simplifying Deep-Learning-Based Model for Code Search

To accelerate software development, developers frequently search and reuse existing code snippets from a large-scale codebase, e.g., GitHub. Over the years, researchers proposed many information retrieval (IR) based models for code search, which match keywords in query with code text. But they fail to connect the semantic gap between query and code. To conquer this challenge, Gu et al. proposed a deep-learning-based model named DeepCS. It jointly embeds method code and natural language description into a shared vector space, where methods related to a natural language query are retrieved according to their vector similarities. However, DeepCS' working process is complicated and time-consuming. To overcome this issue, we proposed a simplified model CodeMatcher that leverages the IR technique but maintains many features in DeepCS. Generally, CodeMatcher combines query keywords with the original order, performs a fuzzy search on name and body strings of methods, and returned the best-matched methods with the longer sequence of used keywords. We verified its effectiveness on a large-scale codebase with about 41k repositories. Experimental results showed the simplified model CodeMatcher outperforms DeepCS by 97% in terms of MRR (a widely used accuracy measure for code search), and it is over 66 times faster than DeepCS. Besides, comparing with the state-of-the-art IR-based model CodeHow, CodeMatcher also improves the MRR by 73%. We also observed that: fusing the advantages of IR-based and deep-learning-based models is promising because they compensate with each other by nature; improving the quality of method naming helps code search, since method name plays an important role in connecting query and code

Validity of single-channel model for a spin-orbit coupled atomic Fermi gas near Feshbach resonances

We theoretically investigate a Rashba spin-orbit coupled Fermi gas near Feshbach resonances, by using mean-field theory and a two-channel model that takes into account explicitly Feshbach molecules in the close channel. In the absence of spin-orbit coupling, when the channel coupling $g$ between the closed and open channels is strong, it is widely accepted that the two-channel model is equivalent to a single-channel model that excludes Feshbach molecules. This is the so-called broad resonance limit, which is well-satisfied by ultracold atomic Fermi gases of $^{6}$Li atoms and $^{40}$K atoms in current experiments. Here, with Rashba spin-orbit coupling we find that the condition for equivalence becomes much more stringent. As a result, the single-channel model may already be insufficient to describe properly an atomic Fermi gas of $^{40}$K atoms at a moderate spin-orbit coupling. We determine a characteristic channel coupling strength $g_{c}$ as a function of the spin-orbit coupling strength, above which the single-channel and two-channel models are approximately equivalent. We also find that for narrow resonance with small channel coupling, the pairing gap and molecular fraction is strongly suppressed by SO coupling. Our results can be readily tested in $^{40}$K atoms by using optical molecular spectroscopy.Comment: 6 pages, 6 figure

Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure