A 3d-3d appetizer

We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\cal N}=2$ "Lens space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition function of Chern-Simons theory arises from the index of a free theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed three-sphere $S^3_b$. This enables us to see clearly, at the level of partition function, to what extent $G_\mathbb{C}$ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group $G$.Comment: 27 pages. v2: misprints corrected, references added. v3: misprints corrected, a clarification adde

Sub-graph based joint sparse graph for sparse code multiple access systems

Sparse code multiple access (SCMA) is a promising air interface candidate technique for next generation mobile networks, especially for massive machine type communications (mMTC). In this paper, we design a LDPC coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, SCMA sparse graph (SSG) defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph based joint sparse graph of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC (B-LDPC) coded SGJSG- SCMA system. To combine the SCMA variable node (SVN) and LDPC variable node (LVN) into one joint variable node (JVN), a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NBLDPC coded SG-JSG-SCMA, a joint trellis representation (JTR) is introduced to represent the search space of NB-LDPC coded SG-JSG-SCMA. Based on JTR, a low complexity joint trellis based detection and decoding (JTDD) algorithm is proposed to reduce the computational complexity of NB-LDPC coded SGJSG- SCMA system. According to the simulation results, SG-JSGSCMA brings significant performance improvement compare to the conventional receiver using the disjoint approach, and it can also outperform a Turbo-structured receiver with comparable complexity. Moreover, the joint approach also has advantages in terms of processing latency compare to the Turbo approaches

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

The electron-phonon ($e$-ph) coupling system often has a large number of phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. To solve this problem, we propose a new and practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global $U(1)$ fermion symmetry, which maps $2^{N_p}$ bosonic degrees of freedom onto $N_p$ pseudosites, each with two states. This approach can handle arbitrary $e$-ph coupling Hamiltonians where pseudosite DMRG performs efficiently. We use this method to study the spectral functions of the doped extended Hubbard-Holstein model in a regime of strong Coulomb repulsion, which has not been studied extensively before. Key features of the excitation spectra are captured at a modest computational cost. Our results show that weak extended $e$-ph couplings can increase the spectral weight of the holon-folding branch at low phonon frequencies, in agreement with angle-resolved photoemission observations on one-dimensional (1D) cuprates.Comment: 12 pages, 8 figures, new results adde

Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters

We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the Hilbert spaces from quantization -- for four infinite families of M_H, giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising

Click: Controllable Text Generation with Sequence Likelihood Contrastive Learning

It has always been an important yet challenging problem to control language models to avoid generating texts with undesirable attributes, such as toxic language and unnatural repetition. We introduce Click for controllable text generation, which needs no modification to the model architecture and facilitates out-of-the-box use of trained models. It employs a contrastive loss on sequence likelihood, which fundamentally decreases the generation probability of negative samples (i.e., generations with undesirable attributes). It also adopts a novel likelihood ranking-based strategy to construct contrastive samples from model generations. On the tasks of language detoxification, sentiment steering, and repetition reduction, we show that Click outperforms strong baselines of controllable text generation and demonstrate the superiority of Click's sample construction strategy.Comment: Findings of ACL 202

Spectrum-effect relationship between HPLC fingerprints and inhibitory activity in MUC5AC mucin of Pinelliae Rhizoma Praeparatum Cum Alumine

Purpose: To investigate the spectrum-effect relationship between HPLC fingerprints and the inhibitory effect on MUC5AC mucin of Pinelliae Rhizoma Praeparatum Cum Alumine (PRPCA).Methods: The fingerprints of 20 PRPCA batches were established using HPLC and their similarities or differences were analyzed using hierarchical cluster analysis (HCA) and principal component analysis (PCA). The inhibitory effects of MUC5AC mucin were evaluated in LPS-treated NCI-H292 cells. The spectrum-effect relationship between common chromatographic peaks and MUC5AC inhibition was established using a partial least squares-discriminant analysis (PLS-DA).Results: Fifteen common chromatographic peaks were identified by analyzing HPLC fingerprints, with uridine, tyrosine, uracil, and inosine found as possible markers to distinguish the PRPCA from different sources. Spectrum-effect relationship analysis showed that the chromatographic peaks 5, 6, 10 (vernine), 12 (5-hydroxymethylfurfural), 14 (tryptophan) and 15 (adenosine) were closely associated with the inhibitory effect on MUC5AC mucin.Conclusion: The spectrum-effect relationship between HPLC fingerprints and the inhibitory effect on MUC5AC mucin of PRPCA was successfully established in the present study. Our findings further reveal the material basis of PRPCA and provide an effective method for its quality control

Defending Large Language Models Against Jailbreaking Attacks Through Goal Prioritization

Large Language Models (LLMs) continue to advance in their capabilities, yet this progress is accompanied by a growing array of safety risks. While significant attention has been dedicated to exploiting weaknesses in LLMs through jailbreaking attacks, there remains a paucity of exploration into defending against these attacks. We point out a pivotal factor contributing to the success of jailbreaks: the inherent conflict between the goals of being helpful and ensuring safety. To counter jailbreaking attacks, we propose to integrate goal prioritization at both training and inference stages. Implementing goal prioritization during inference substantially diminishes the Attack Success Rate (ASR) of jailbreaking attacks, reducing it from 66.4% to 2.0% for ChatGPT and from 68.2% to 19.4% for Vicuna-33B, without compromising general performance. Furthermore, integrating the concept of goal prioritization into the training phase reduces the ASR from 71.0% to 6.6% for LLama2-13B. Remarkably, even in scenarios where no jailbreaking samples are included during training, our approach slashes the ASR by half, decreasing it from 71.0% to 34.0%. Additionally, our findings reveal that while stronger LLMs face greater safety risks, they also possess a greater capacity to be steered towards defending against such attacks. We hope our work could contribute to the comprehension of jailbreaking attacks and defenses, and shed light on the relationship between LLMs' capability and safety. Our code will be available at \url{https://github.com/thu-coai/JailbreakDefense_GoalPriority}.Comment: 14 page