arXiv subjects

Guangsheng Yu

Publications and source records attributed to Guangsheng Yu.

58 records · Page 4Linked to original sources

arXiv2021

Capacity Analysis of Public Blockchain

As distributed ledgers, blockchains run consensus protocols which trade capacity for consistency, especially in non-ideal networks with incomplete connectivity and erroneous links. Existing studies on the tradeoff between capacity and consistency are only qualitative or rely on specific assumptions. This paper presents discrete-time Markov chain models to quantify the capacity of Proof-of-Work based public blockchains in non-ideal networks. The comprehensive model is collapsed to be ergodic under the eventual consistency of blockchains, achieving tractability and efficient evaluations of blockchain capacity. A closed-form expression for the capacity is derived in the case of two miners. Another important aspect is that we extend the ergodic model to analyze the capacity under strong consistency, evaluating the robustness of blockchains against double-spending attacks. Validated by simulations, the proposed models are accurate and reveal the effect of link quality and the distribution of mining rates on blockchain capacity and the ratio of stale blocks.

cs.CR↗

arXiv2018

Cartan's Conjecture for Moving Hypersurfaces

Let $f$ be a holomorphic curve in $\mathbb{P}^n({\mathbb{C}})$ and let $\mathcal{D}=\{D_1,\ldots,D_q\}$ be a family of moving hypersurfaces defined by a set of homogeneous polynomials $\mathcal{Q}=\{Q_1,\ldots,Q_q\}$. For $j=1,\ldots,q$, denote by $Q_j=\sum\limits_{i_0+\cdots+i_n=d_j}a_{j,I}(z)x_0^{i_0}\cdots x_n^{i_n}$, where $I=(i_0,\ldots,i_n)\in\mathbb{Z}_{\ge 0}^{n+1}$ and $a_{j,I}(z)$ are entire functions on ${\mathbb{C}}$ without common zeros. Let $\mathcal{K}_{\mathcal{Q}}$ be the smallest subfield of meromorphic function field $\mathcal{M}$ which contains ${\mathbb{C}}$ and all $\frac{a_{j,I'}(z)}{a_{j,I''}(z)}$ with $a_{j,I''}(z)\not\equiv 0$, $1\le j\le q$. In previous known second main theorems for $f$ and $\mathcal{D}$, $f$ is usually assumed to be algebraically nondegenerate over $\mathcal{K}_{\mathcal{Q}}$. In this paper, we prove a second main theorem in which $f$ is only assumed to be nonconstant. This result can be regarded as a generalization of Cartan's conjecture for moving hypersurfaces.

math.CV↗

arXiv2018

Holomorphic Curves into Algebraic Varieties Intersecting Divisors in Subgeneral Position

Recently, there are many developments on the second main theorem for holomorphic curves into algebraic varieties intersecting divisors in general position or subgeneral position. In this paper, we refine the concept of subgeneral position by introducing the notion of the index of subgeneral position. With this new notion we give some surprising improvement of the previous known second main theorem type results. Moreover, via the analogue between Nevanlinna theory and Diophantine approximation, the corresponding Schmidt's subspace type theorems are also established in the final section.

math.CV↗

arXiv2016

L2-estimates on p-convex Riemannian manifolds

In this paper, we establish various L2-estimates for the exterior differential operator on p-convex Riemannian manifolds in the sense of Harvey and Lawson. As geometric applications, we prove vanishing and finiteness results for the de Rham cohomology groups.

math.DG↗