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Gehao Wang

Publications and source records attributed to Gehao Wang.

9 recordsLinked to original sources
arXiv2026

Optimization of the directed spanning trees using the weighted matroid intersection algorithm

In this paper, we consider the problem of updating the directed minimum spanning tree (DMST), when the given sample tree is subject to the weight changes, edge deletions and edge insertions. We present an implementation for updating the tree to a DMST using the weighted matroid intersection algorithm. Our algorithm focuses on maintaining a dynamic auxiliary graph, which plays a central role in the matroid intersection algorithm, and governs the iterations from the given tree to a DMST. Each iteration is guaranteed to yield an improved solution. We also provide an implementation of this algorithm and some experimental analysis.

cs.DS↗
arXiv2025

The identification of the extended refined open partition function and the Kontsevich-Penner matrix model

The open intersection theory has been initiated by R. Pandharipande, J. P. Solomon and R. J. Tessler. In the scope of matrix model theory, A. Buryak and R. J. Tessler have constructed a matrix model $\mathcal{Z}^o$ for the open partition function based on a Kontsevich type combinatorial formula for the open intersection numbers found by R. J. Tessler. In this paper, using the Harish-Chandra-Itzykson-Zuber formula and operational calculus, we transform $\mathcal{Z}^o$ into another simple form, and define the matrix model $\mathcal{Z}_N^{o,ext,s}$ for the extended refined open partition function from it. The expression of $\mathcal{Z}_N^{o,ext,s}$ will immediately lead us to the Kontsevich-Penner matrix model $Z_N$ under the Miwa parametrization $s_i=2^ii!\operatorname{tr} \Lambda^{-2i-2}$. Hence it confirms the identification between the two models for general $N\geq 1$.

math-ph↗
arXiv2025

Stability analysis of Runge-Kutta methods for nonlinear delay-integro-differential-algebraic equations

This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and compound quadrature rules are analyzed for nonlinear DIDAEs. Criteria for ensuring the global and asymptotic stability of the proposed schemes are established. Several numerical examples are provided to validate the theoretical findings.

math.NA↗
arXiv2022

The ordered exponential representation of GKM using the $W_{1+\infty}$ 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.

math-ph↗
arXiv2018

From Kontsevich-Witten to linear Hodge integrals via Virasoro operators

We give a proof of Alexandrov's conjecture on a formula connecting the Kontsevich-Witten and Hodge tau-functions using only the Virasoro operators. This formula has been confirmed up to an unknown constant factor. In this paper, we show that this factor is indeed equal to one by investigating series expansions for the Lambert W function on different points.

math-ph↗
arXiv2017

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

The Brezin-Gross-Witten (BGW) model is one of the basic examples in the class of non-eigenvalue unitary matrix models. The generalized BGW tau-function $\tau_N$ was constructed from a one parametric deformation of the original BGW model using the generalized Kontsevich model representation. It is a tau-function of the KdV hierarchy for any value of $N\in{\mathbb C}$, where the case $N=0$ reduces to the original BGW tau-function. In this paper, we present a representation of $\tau_N$ in terms of the $W_{1+\infty}$ operators that preserves the KP integrability. This naturally establishes a connection between the (generalized) BGW and Kontsevich-Witten tau-functions using $GL(\infty)$ operators, both considered as the basic building blocks in the theory of matrix models and partition functions.

math-ph↗
arXiv2016

Virasoro constraints and polynomial recursion for the linear Hodge integrals

The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.

math-ph↗
arXiv2011

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.

math.GR↗