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Large language models (LLMs) have brought significant advancements to code generation, benefiting both novice and experienced developers. However, their training using unsanitized data from open-source repositories, like GitHub, introduces the risk of inadvertently propagating security vulnerabilities. To effectively mitigate this concern, this paper presents a comprehensive study focused on evaluating and enhancing code LLMs from a software security perspective. We introduce SecuCoGen\footnote{SecuCoGen has been uploaded as supplemental material and will be made publicly available after publication.}, a meticulously curated dataset targeting 21 critical vulnerability types. SecuCoGen comprises 180 samples and serves as the foundation for conducting experiments on three crucial code-related tasks: code generation, code repair and vulnerability classification, with a strong emphasis on security. Our experimental results reveal that existing models often overlook security concerns during code generation, leading to the generation of vulnerable code. To address this, we propose effective approaches to mitigate the security vulnerabilities and enhance the overall robustness of code generated by LLMs. Moreover, our study identifies weaknesses in existing models' ability to repair vulnerable code, even when provided with vulnerability information. Additionally, certain vulnerability types pose challenges for the models, hindering their performance in vulnerability classification. Based on these findings, we believe our study will have a positive impact on the software engineering community, inspiring the development of improved methods for training and utilizing LLMs, thereby leading to safer and more trustworthy model deployment.

Let ${\mathbf U}^-_q$ be the negative half of the quantum group associated to a Kac-Moody algebra ${\mathfrak g}$, and $\underline{\mathbf U}^-_q$ the quantum group obtained by a folding of ${\mathfrak g}$. Let ${\mathbf A} = {\mathbf Z}[q,q^{-1}]$. McNamara showed that $\underline{\mathbf U}^-_q$ is categorified over a certain extenion ring $\widetilde{\mathbf A}$ of ${\mathbf A}$, by uing the folding theory of KLR algebras. He posed a question whether $\widetilde{\mathbf A}$ coincides with ${\mathbf A}$ or not. In this paper, we give an affirmative answer for this problem., Comment: 38 pages

Let ${\mathbf U}_q^-$ be the negative part of the quantum enveloping algebra, and $\sigma$ the algebra automorphism on ${\mathbf U}_q^-$ induced from a diagram automorphism. Let $\underline{\mathbf U}_q^-$ be the quantum algebra obtained from $\sigma$, and $\widetilde{\mathbf B}$ (resp. $\widetilde{\underline{\mathbf B}}$) the canonical signed basis of ${\mathbf U}_q^-$ (resp. $\underline{\mathbf U}_q^-$). Assume that ${\mathbf U}_q^-$ is simply-laced of finite or affine type. In our previous papers [SZ1, 2], we have proved by an elementary method, that there exists a natural bijection $\widetilde{\mathbf B}^{\sigma} \simeq \widetilde{\underline{\mathbf B}}$ in the case where $\sigma$ is admissible. In this paper, we show that such a bijection exists even if $\sigma$ is not admissible, possibly except some small rank cases., Comment: 48 PAGES

Adversarial waveform generation has been a popular approach as the backend of singing voice conversion (SVC) to generate high-quality singing audio. However, the instability of GAN also leads to other problems, such as pitch jitters and U/V errors. It affects the smoothness and continuity of harmonics, hence degrades the conversion quality seriously. This paper proposes to feed harmonic signals to the SVC model in advance to enhance audio generation. We extract the sine excitation from the pitch, and filter it with a linear time-varying (LTV) filter estimated by a neural network. Both these two harmonic signals are adopted as the inputs to generate the singing waveform. In our experiments, two mainstream models, MelGAN and ParallelWaveGAN, are investigated to validate the effectiveness of the proposed approach. We conduct a MOS test on clean and noisy test sets. The result shows that both signals significantly improve SVC in fidelity and timbre similarity. Besides, the case analysis further validates that this method enhances the smoothness and continuity of harmonics in the generated audio, and the filtered excitation better matches the target audio., Comment: Accepted by ICASSP 2022

Let ${\mathbf U}^-_q$ be the negative part of the quantized enveloping algebra associated to a Kac-Moody algebra ${\mathfrak g}$ of symmetric type, and $\underline{\mathbf U}^-_q$ the algebra corresponding to the orbit algebra ${\mathfrak g}^{\sigma}$ obtained from an admissible diagram automorphism $\sigma$ on ${\mathfrak g}$. Lusztig consructed the canonical basis ${\mathbf B}$ of ${\mathbf U}_q^-$ and the canonical signed basis $\underline{\widetilde{\mathbf B}}$ of $\underline{\mathbf U}_q^-$ by making use of the geometric theory of quivers. He proved that there is a natural bijection $\widetilde{\mathbf B}^{\sigma} \to \widetilde{\underline{\mathbf B}}$. In this paper, assuming the existence of the canonical basis ${\mathbf B}$ of ${\mathbf U}_q^-$, we construct the canonical signed basis $\widetilde{\underline{\mathbf B}}$ of $\underline{\mathbf U}_q^-$, and a natural bijection $\widetilde{\mathbf B}^{\sigma} \to \widetilde{\underline{\mathbf B}}$ by an elementary method., Comment: 41 pages, the final version, to appear in J. of Algebra

Let ${\mathbf U}^-_q$ be the negative part of the quantum enveloping algebra associated to a simply laced Kac-Moody Lie algebra ${\mathfrak g}$, and $\underline{\mathbf U}^-_q$ the algebra corresponding to the fixed point subalgebra of ${\mathfrak g}$ obtained from a diagram automorphism $\sigma$ on ${\mathfrak g}$. Let ${\mathbf B}^{\sigma}$ be the set of $\sigma$-fixed elements in the canonical basis of ${\mathbf U}_q^-$, and $\underline{\mathbf B}$ the canonical basis of $\underline{\mathbf U}_q^-$. Lusztig proved that there exists a canonical bijection ${\mathbf B}^{\sigma} \simeq \underline{\mathbf B}$ based on his geometric construction of canonical bases. In this paper, we prove (the signed bases version of) this fact, in the case where ${\mathfrak g}$ is finite or affine type, in an elementary way, in the sense that we don't appeal to the geometric theory of canonical bases nor Kashiwara's theory of crystal bases. We also discuss the correspondence between PBW-bases, by using a new type of PBW-bases of ${\mathbf U}_q^-$ obtained by Muthiah-Tingley, which is a generalization of PBW-bases constructed by Beck-Nakajima., Comment: 43 pages

The optical memristive switches are electrically activated optical switches that can memorize the current state. They can be used as optical latching switches in which the switching state is changed only by applying an electrical Write/Erase pulse and maintained without external power supply. We demonstrate an optical memristive switch based on a silicon MMI structure covered with nanoscale-size Ge2Sb2Te5 (GST) material on top. The phase change of GST is triggered by resistive heating of the silicon layer beneath GST with an electrical pulse. Experimental results reveal that the optical transmissivity can be tuned in a controllable and repeatable manner with the maximum transmission contrast exceeding 20 dB. Partial crystallization of GST is obtained by controlling the width and amplitude of the electric pulses. Crucially, we also demonstrate that both Erase and Write operations, to and from any intermediate level, are possible with accurate control of the electrical pulses. Our work marks a significant step forward towards realizing photonic memristive switches without static power consumption, which are highly demanded in high-density large-scale integrated photonics., Comment: 18 page, 5 figure

Let $U^-_q = U^-_q(\mathfrak g)$ be the negative part of the quantum group associated to a finite dimensional simple Lie algebra $\mathfrak g$, and $\sigma : \mathfrak g \to \mathfrak g$ be the automorphism obtained from the diagram automorphism. Let $\mathfrak g^{\sigma}$ be the fixed point subalgebra of $\mathfrak g$, and put $\underline U^-_q = U^-_q(\mathfrak g^{\sigma})$. Let $B$ be the canonical basis of $U_q^-$ and $\underline B$ the canonical basis of $\underline U_q^-$. $\sigma$ induces a natural action on $B$, and we denote by $B^{\sigma}$ the set of $\sigma$-fixed elements in $B$. Lusztig proved that there exists a canonical bijection $B^{\sigma} \simeq \underline B$ by using geometric considerations. In this paper, we construct such a bijection in an elementary way. We also consider such a bijection in the case of certain affine quantum groups, by making use of PBW-bases constructed by Beck and Nakajima., Comment: 35 pages, final version, to appear in J. of Math. Soc. of Japan

We demonstrated a novel on-chip polarization controlling structure, fabricated by standard 0.18-um foundry technology. It achieved polarization rotation with a size of 0.726 um * 5.27 um and can be easily extended into dynamic polarization controllers., Comment: 2 pages, 4 figures