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Hongfu Yang

Publications and source records attributed to Hongfu Yang.

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MindWatcher: Toward Smarter Multimodal Tool-Integrated Reasoning

Traditional workflow-based agents exhibit limited intelligence when addressing real-world problems requiring tool invocation. Tool-integrated reasoning (TIR) agents capable of autonomous reasoning and tool invocation are rapidly emerging as a powerful approach for complex decision-making tasks involving multi-step interactions with external environments. In this work, we introduce MindWatcher, a TIR agent integrating interleaved thinking and multimodal chain-of-thought (CoT) reasoning. MindWatcher can autonomously decide whether and how to invoke diverse tools and coordinate their use, without relying on human prompts or workflows. The interleaved thinking paradigm enables the model to switch between thinking and tool calling at any intermediate stage, while its multimodal CoT capability allows manipulation of images during reasoning to yield more precise search results. We implement automated data auditing and evaluation pipelines, complemented by manually curated high-quality datasets for training, and we construct a benchmark, called MindWatcher-Evaluate Bench (MWE-Bench), to evaluate its performance. MindWatcher is equipped with a comprehensive suite of auxiliary reasoning tools, enabling it to address broad-domain multimodal problems. A large-scale, high-quality local image retrieval database, covering eight categories including cars, animals, and plants, endows model with robust object recognition despite its small size. Finally, we design a more efficient training infrastructure for MindWatcher, enhancing training speed and hardware utilization. Experiments not only demonstrate that MindWatcher matches or exceeds the performance of larger or more recent models through superior tool invocation, but also uncover critical insights for agent training, such as the genetic inheritance phenomenon in agentic RL.

cs.AI

Wolbachia invasion to wild mosquito population in stochastic environment

Releasing sterile Wolbachia-infected mosquitoes to invade wild mosquito population is a method of mosquito control. In this paper, a stochastic mosquito population model with Wolbachia invasion perturbed by environmental fluctuation is studied. Firstly, well-posedness, positivity and Markov-Feller property of solution for this model are proved. Then a group of sharp threshold-type conditions is provided to characterize the long-term behavior of the model, which pinpoints the almost necessary and sufficient conditions for persistence and extinction of Wolbachia-infected and uninfected mosquito populations. Especially, our results indicates that even the initial Wolbachia infection frequency is low, the Wolbachia invasion into wild mosquito population can be promoted by stochastic environmental fluctuations. Finally, some numerical experiments are carried out to support our theoretical results.

math.DS

Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

Focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events, this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a Markov chain. Different kinds of easily implementable explicit schemes have been proposed to approximate the dynamical behaviors of switching diffusion systems with local Lipschitz continuous drift and diffusion coefficients in both finite and infinite intervals. Without additional restriction conditions except those which guarantee the exact solutions posses their dynamical properties, the numerical solutions converge strongly to the exact solutions in finite horizon, moreover, realize the approximation of long-time dynamical properties including the moment boundedness, stability and ergodicity. Some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach.

math.NA

First order strong convergence and extinction of positivity preserving logarithmic truncated Euler-Maruyama method for the stochastic SIS epidemic model

The well-known stochastic SIS model characterized by highly nonlinear in epidemiology has a unique positive solution taking values in a bounded domain with a series of dynamical behaviors. However, the approximation methods to maintain the positivity and long-time behaviors for the stochastic SIS model, while very important, are also lacking. In this paper, based on a logarithmic transformation, we propose a novel explicit numerical method for a stochastic SIS epidemic model whose coefficients violate the global monotonicity condition, which can preserve the positivity of the original stochastic SIS model. And we show the strong convergence of the numerical method and derive that the rate of convergence is of order one. Moreover, the extinction of the exact solution of stochastic SIS model is reproduced. Some numerical experiments are given to illustrate the theoretical results and testify the efficiency of our algorithm.

math.NA

Explicit numerical approximation for logistic models with regime switching in finite and infinite horizons

The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So, proposing appropriate numerical method for solving this model which preserves positivity and dynamical behaviors of the model's solution is very important. In this paper, we present a positivity preserving truncated Euler-Maruyama scheme for this model, which taking advantages of being explicit and easily implementable. Without additional restriction conditions, strong convergence of the numerical algorithm is studied, and 1/2 order convergence rate is obtained. In the particular case of this model without switching the first order strong convergence rate is obtained. Furthermore, the approximation of long-time dynamical properties is realized, including the stochastic permanence, extinctive and stability in distribution. Some simulations and examples are provided to confirm the theoretical results and demonstrate the validity of the approach.

math.NA

Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations

In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that without additional restriction conditions except those which guarantee the exact solutions possess their boundedness in expectation with respect to certain Lyapunov functions, the numerical solutions converge strongly to the exact solutions in finite-time. Moreover, based on the nonnegative semimartingale convergence theorem, positive results about the ability of explicit numerical approximation to reproduce the well-known LaSalle-type theorem of SDEs are proved here, from which we deduce the asymptotic stability of numerical solutions. Some examples and simulations are provided to support the theoretical results and to demonstrate the validity of the approach.

math.NA

The Numerical Invariant Measure of Stochastic Differential Equations With Markovian Switching

The existence and uniqueness of the numerical invariant measure of the backward Euler-Maruyama method for stochastic differential equations with Markovian switching is yielded, and it is revealed that the numerical invariant measure converges to the underlying invariant measure in the Wasserstein metric. Under the polynomial growth condition of drift term the convergence rate is estimated. The global Lipschitz condition on the drift coefficients required by Bao et al., 2016 and Yuan et al., 2005 is released. Several examples and numerical experiments are given to verify our theory.

math.PR