A connection between the Kontsevich-Witten and Brezin-Gross-Witten tau-functions

The Brezin-Gross-Witten model is one of the basic examples in the class of non-eigenvalue unitary matrix models. In the Kontsevich phase, it is a tau-function for the KdV hierarchy. In this paper we present an explicit formula that connects the Kontsevich-Witten and Brezin-Gross-Witten tau-functions using the $\widehat{\mathfrak{sl}_2}$ operators, which preserves the KdV integrability. The differential operators used in the formula are simply the Virasoro and Heisenberg operators. While the geometric interpretation of the Brezin-Gross-Witten model remains unknown, the formula provides a possible way to identify this model with enumerative geometry invariants.Comment: The description about the differential operators \hat{L}_{2m} being sl_2 operators is incorrect in Section 2.

Connecting the Kontsevich-Witten and Hodge tau-functions by the GL(∞)^\hat{GL(\infty)} operators

In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be connected using Virasoro operators. This proves a conjecture posted by Alexandrov in [1].Comment: 48 page

The ordered exponential representation of GKM using the W1+∞W_{1+\infty} operator

The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an $r$-reduced tau-function that governs the $r$-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the $W_{1+\infty}$ operators that preserves the KP integrability. In fact, this representation is naturally the solution of a $W_{1+\infty}$ constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their $W_{1+\infty}$ representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints.Comment: 21 page

Generating sets of Affine groups of low genus

We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy group is a primitive affine permutation group

REPOFUSE: Repository-Level Code Completion with Fused Dual Context

The success of language models in code assistance has spurred the proposal of repository-level code completion as a means to enhance prediction accuracy, utilizing the context from the entire codebase. However, this amplified context can inadvertently increase inference latency, potentially undermining the developer experience and deterring tool adoption - a challenge we termed the Context-Latency Conundrum. This paper introduces REPOFUSE, a pioneering solution designed to enhance repository-level code completion without the latency trade-off. REPOFUSE uniquely fuses two types of context: the analogy context, rooted in code analogies, and the rationale context, which encompasses in-depth semantic relationships. We propose a novel rank truncated generation (RTG) technique that efficiently condenses these contexts into prompts with restricted size. This enables REPOFUSE to deliver precise code completions while maintaining inference efficiency. Through testing with the CrossCodeEval suite, REPOFUSE has demonstrated a significant leap over existing models, achieving a 40.90% to 59.75% increase in exact match (EM) accuracy for code completions and a 26.8% enhancement in inference speed. Beyond experimental validation, REPOFUSE has been integrated into the workflow of a large enterprise, where it actively supports various coding tasks

CodeFuse-13B: A Pretrained Multi-lingual Code Large Language Model

Code Large Language Models (Code LLMs) have gained significant attention in the industry due to their wide applications in the full lifecycle of software engineering. However, the effectiveness of existing models in understanding non-English inputs for multi-lingual code-related tasks is still far from well studied. This paper introduces CodeFuse-13B, an open-sourced pre-trained code LLM. It is specifically designed for code-related tasks with both English and Chinese prompts and supports over 40 programming languages. CodeFuse achieves its effectiveness by utilizing a high quality pre-training dataset that is carefully filtered by program analyzers and optimized during the training process. Extensive experiments are conducted using real-world usage scenarios, the industry-standard benchmark HumanEval-x, and the specially designed CodeFuseEval for Chinese prompts. To assess the effectiveness of CodeFuse, we actively collected valuable human feedback from the AntGroup's software development process where CodeFuse has been successfully deployed. The results demonstrate that CodeFuse-13B achieves a HumanEval pass@1 score of 37.10%, positioning it as one of the top multi-lingual code LLMs with similar parameter sizes. In practical scenarios, such as code generation, code translation, code comments, and testcase generation, CodeFuse performs better than other models when confronted with Chinese prompts.Comment: 10 pages with 2 pages for reference

Genus zero systems for primitive groups of affine type

Let M$_g$ be the moduli space of genus g curves. A Hurwitz locus in M$_g$ is a locus of points representing G-covers of fixed genus g with a given ramification type. The classification of Hurwitz loci of complex curves admitting G is by the computation of orbits of a suitable surface braid group acting on the generating tuples of G. When the genus of the curve is low, the braid orbits can be enumerated explicitly using GAP (Groups, Algorithm, Programming) computer algebra system and the BRAID package by Magaard, Shpectorov and Volklein. However, the length of the orbits dramatically increases with the size of G and genus of the curve. In order to handle larger orbits, we propose to break up the tuples into two or more shorter pieces which can be computed within reasonable time, and then recombine them together as direct products to form the braid orbits

Enhancing Consensus Security and Privacy with Multichain Ring Signatures Based on HotStuff

The paper introduces a novel consensus algorithm named MRPBFT, which is derived from the HotStuff consensus protocol and improved upon to address security deficiencies in traditional consensus algorithms within the domain of digital asset transactions. MRPBFT aims to enhance security and privacy protection while pursuing higher consensus efficiency. It employs a multi-primary-node approach and a ring signature mechanism to reinforce security and privacy preservation features in the consensus system. This algorithm primarily focuses on two main improvements: Firstly, it proposes the ed25519LRS signature algorithm and discusses its anonymity for transaction participants and the non-forgeability of signature information in the identity verification and message verification processes within the consensus algorithm. Secondly, the paper introduces MPBFT asynchronous view changes and a multi-primary-node mechanism to enhance consensus efficiency, allowing for view switching in the absence of global consensus. With the introduction of the multi-primary-node mechanism, nodes can be flexibly added or removed, supporting parallel processing of multiple proposals and transactions. Finally, through comparative experiments, the paper demonstrates that the improved algorithm performs significantly better in terms of throughput and network latency

Amplitude Distribution of Partial Discharge Signals on Tunnel-Installed High-Voltage Cables

For 110 kV and above tunnel-installed high-voltage (HV) cross-linked poly-ethylene (XLPE) cable systems, it is a normal procedure to adopt a cross-bonding scheme. The high-frequency current method is frequently used in the cross-bonded cable systems for on-site or online partial discharge (PD) detection by monitoring the signals on the cross-bonding wires. To further study the amplitude distribution characteristics of the PD signals, a parametric characteristic admittance model of a three-phase cable system in a tunnel is established based on Tylavsky’s formulas. The model is used to calculate the amplitude distribution formula of the PD pulse current on the cross-bonding wires. In addition, the influence of cable laying and tunnel environment on the amplitude distribution is also studied. Finally, the correctness of the model and the conclusion are verified by simulation experiments and on-site tests. The results show that the signal amplitude distribution is determined by the ratio of the characteristic admittances. As the distance between the cables and the distance from the inner wall of the tunnel increase, the amplitude difference gradually decreases