The correspondence between the canonical and semicanonical bases

Given any symmetric Cartan datum, Lusztig has provided a pair of key lemmas to construct the perverse sheaves over the corresponding quiver and the functions of irreducible components over the corresponding preprojective algebra respectively. In the present article, we prove that these two inductive algorithms of Lusztig coincide. Consequently we can define two colored graphs and prove that they are isomorhic. This result finishes the statement that Lusztig's functions of irreducible components are basis of the enveloping algebra and deduces the crystal structure (in the sense of Kashiwara-Saito) from the semicanonical basis directly inside Lusztig's convolution algebra of the preprojective algebra. As an application, we prove that the transition matrix between the canonical basis and the semicanonical basis is upper triangular with all diagonal entries equal to 1

Sheaf realization of Bridgeland's Hall algebra of Dynkin type

As one of results in [6], Bridgeland realized the quantum group $\mathrm{U}_v(\mathfrak{g})$ via the localization of Ringel-Hall algebra for two-periodic projective complexes of quiver representations over a finite field. In the present paper, we generalize Lusztig's categorical construction and (dual) canonical basis for the nilpotent part $\mathrm{U}_v(\mathfrak{n}^+)$ to Bridgeland's Hall algebra of Dynkin type, and obtain a perverse sheaf realization of global basis for Bridgeland's localizing algebra. In particular, we prove that the dual of canonical basis elements are part of our basis up to powers of $v$.Comment: In the new version, we add some content including: in section 6, we refine our construction and complete the perverse sheaves realization of Bridgeland's Hall algebra which is essentially isomorphic to the integral form of the whole quantum group; in section 7, we obtain new results about the global basis; in section 8, we compare our basis with Lusztig's (dual) canonical basi

Examining Inter-Consistency of Large Language Models Collaboration: An In-depth Analysis via Debate

Large Language Models (LLMs) have shown impressive capabilities in various applications, but they still face various inconsistency issues. Existing works primarily focus on the inconsistency issues within a single LLM, while we complementarily explore the inter-consistency among multiple LLMs for collaboration. To examine whether LLMs can collaborate effectively to achieve a consensus for a shared goal, we focus on commonsense reasoning, and introduce a formal debate framework (FORD) to conduct a three-stage debate among LLMs with real-world scenarios alignment: fair debate, mismatched debate, and roundtable debate. Through extensive experiments on various datasets, LLMs can effectively collaborate to reach a consensus despite noticeable inter-inconsistencies, but imbalances in their abilities can lead to domination by superior LLMs. Leveraging a more advanced LLM like GPT-4 as an authoritative judge can boost collaboration performance. Our work contributes to understanding the inter-consistency among LLMs and lays the foundation for developing future collaboration methods. Codes and data are available at https://github.com/Waste-Wood/FORDComment: EMNLP 2023 Findings Camera Ready Versio

Thermal conductivity, structure and mechanical properties of konjac glucomannan/starch based aerogel strengthened by wheat straw

This study presents the preparation and property characterization of a konjac glucomannan (KGM)/starch based aerogel as a thermal insulation material. Wheat straw powders (a kind of agricultural waste) and starch are used to enhance aerogel physical properties such as mechanical strength and pore size distribution. Aerogel samples were made using environmentally friendly sol–gel and freeze drying methods. Results show that starch addition could strengthen the mechanical strength of aerogel significantly, and wheat straw addition could decrease aerogel pore size due to its special micron-cavity structure, with appropriate gelatin addition as the stabilizer. The aerogel formula was optimized to achieve lowest thermal conductivity and good thermal stability. Within the experimental range, aerogel with the optimized formula had a thermal conductivity 0.04641 Wm−1 K−1, a compression modulus 67.5 kPa and an elasticity 0.27. The results demonstrate the high potential of KGM/starch based aerogels enhanced with wheat straw for application in thermal insulation

Embedding Security into Ferroelectric FET Array via In-Situ Memory Operation

Non-volatile memories (NVMs) have the potential to reshape next-generation memory systems because of their promising properties of near-zero leakage power consumption, high density and non-volatility. However, NVMs also face critical security threats that exploit the non-volatile property. Compared to volatile memory, the capability of retaining data even after power down makes NVM more vulnerable. Existing solutions to address the security issues of NVMs are mainly based on Advanced Encryption Standard (AES), which incurs significant performance and power overhead. In this paper, we propose a lightweight memory encryption/decryption scheme by exploiting in-situ memory operations with negligible overhead. To validate the feasibility of the encryption/decryption scheme, device-level and array-level experiments are performed using ferroelectric field effect transistor (FeFET) as an example NVM without loss of generality. Besides, a comprehensive evaluation is performed on a 128x128 FeFET AND-type memory array in terms of area, latency, power and throughput. Compared with the AES-based scheme, our scheme shows around 22.6x/14.1x increase in encryption/decryption throughput with negligible power penalty. Furthermore, we evaluate the performance of our scheme over the AES-based scheme when deploying different neural network workloads. Our scheme yields significant latency reduction by 90% on average for encryption and decryption processes

KMT2A promotes melanoma cell growth by targeting hTERT signaling pathway.

Melanoma is an aggressive cutaneous malignancy, illuminating the exact mechanisms and finding novel therapeutic targets are urgently needed. In this study, we identified KMT2A as a potential target, which promoted the growth of human melanoma cells. KMT2A knockdown significantly inhibited cell viability and cell migration and induced apoptosis, whereas KMT2A overexpression effectively promoted cell proliferation in various melanoma cell lines. Further study showed that KMT2A regulated melanoma cell growth by targeting the hTERT-dependent signal pathway. Knockdown of KMT2A markedly inhibited the promoter activity and expression of hTERT, and hTERT overexpression rescued the viability inhibition caused by KMT2A knockdown. Moreover, KMT2A knockdown suppressed tumorsphere formation and the expression of cancer stem cell markers, which was also reversed by hTERT overexpression. In addition, the results from a xenograft mouse model confirmed that KMT2A promoted melanoma growth via hTERT signaling. Finally, analyses of clinical samples demonstrated that the expression of KMT2A and hTERT were positively correlated in melanoma tumor tissues, and KMT2A high expression predicted poor prognosis in melanoma patients. Collectively, our results indicate that KMT2A promotes melanoma growth by activating the hTERT signaling, suggesting that the KMT2A/hTERT signaling pathway may be a potential therapeutic target for melanoma