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Jiaming Chen

Publications and source records attributed to Jiaming Chen.

At least 37 records · Page 2Linked to original sources
arXiv2025

Small Ball Probabilities for the Fractional Stochastic Heat Equation Driven by a Colored Noise

We consider the fractional stochastic heat equation on the $d$-dimensional torus $\mathbb{T}^d:=\left[-\frac{1}{2},\frac{1}{2}\right]^d$, $d\geq 1$, with periodic boundary conditions: \[ \partial_t u(t,\textbf{x})= -(-Δ)^{α/2}u(t,\textbf{x})+σ(t,\textbf{x},u)\dot{F}(t,\textbf{x})\quad \textbf{x}\in \mathbb{T}^d,t\in\mathbb{R}_+ ,\] where $α\in(1,2]$ and $\dot{F}(t,\textbf{x})$ is a generalized Gaussian noise which is white in time and colored in space. Assuming that $σ$ is Lipschitz in $u$ and uniformly bounded, we estimate small ball probabilities for the solution $u$ when $u(0,\textbf{x})\equiv 0$.

math.PR↗
arXiv2024

Splitting algorithm and normed convergence for drawing the random fractal Loewner curves

In the first part of the paper we propose and study the approximation of the $SLE_κ$ trace via the Ninomiya-Victoir splitting algorithm. We prove the uniform convergence in probability with respect to the sup-norm to the distance between the $SLE_κ$ trace and the output of the Ninomiya-Victoir splitting algorithm when applied in the context of the Loewner differential equation. Further investigations on the $L^p$-norm convergence is also exhibited, shedding light on the more delicate convergence structure. In the second part we show the uniform convergence of the approximation of the $SLE_κ$ trace obtained using a different scheme that is based on the linear interpolation of the Brownian driving force.

math.PR↗
arXiv2024

Small ball probabilities for the stochastic heat equation with colored noise

We consider the stochastic heat equation on the 1-dimensional torus $\mathbb{T}:=\left[-1,1\right]$ with periodic boundary conditions: $$ \partial_t u(t,x)=\partial^2_x u(t,x)+σ(t,x,u)\dot{F}(t,x),\quad x\in \mathbb{T},t\in\mathbb{R}_+, $$ where $\dot{F}(t,x)$ is a generalized Gaussian noise, which is white in time and colored in space. Assuming that $σ$ is Lipschitz in $u$ and uniformly bounded, we estimate small ball probabilities for the solution $u$ when $u(0,x)\equiv 0$.

math.PR↗
arXiv2024

VLMPC: Vision-Language Model Predictive Control for Robotic Manipulation

Although Model Predictive Control (MPC) can effectively predict the future states of a system and thus is widely used in robotic manipulation tasks, it does not have the capability of environmental perception, leading to the failure in some complex scenarios. To address this issue, we introduce Vision-Language Model Predictive Control (VLMPC), a robotic manipulation framework which takes advantage of the powerful perception capability of vision language model (VLM) and integrates it with MPC. Specifically, we propose a conditional action sampling module which takes as input a goal image or a language instruction and leverages VLM to sample a set of candidate action sequences. Then, a lightweight action-conditioned video prediction model is designed to generate a set of future frames conditioned on the candidate action sequences. VLMPC produces the optimal action sequence with the assistance of VLM through a hierarchical cost function that formulates both pixel-level and knowledge-level consistence between the current observation and the goal image. We demonstrate that VLMPC outperforms the state-of-the-art methods on public benchmarks. More importantly, our method showcases excellent performance in various real-world tasks of robotic manipulation. Code is available at~\url{https://github.com/PPjmchen/VLMPC}.

cs.RO↗
arXiv2024

Convex Fujita numbers are not determined by the fundamental group

We study effective global generation of adjoint line bundles on smooth projective varieties. To measure the effectivity we introduce the concept of the convex Fujita number of a smooth projective variety and compute its value for a class of varieties with prescribed dimension $d \geq 2$ and an arbitrary projective group as fundamental group.

math.AG↗
arXiv2023

Chung's Law of the Iterated Logarithm for a Class of Stochastic Heat Equations

We establish a Chung-type law of the iterated logarithm for the solutions of a class of stochastic heat equations driven by a multiplicative noise whose coefficient depends on the solution, and this dependence takes us away from Gaussian setting. Based on the literature on small ball probabilities and the technique of freezing coefficients, the limiting constant in Chung's law of the iterated logarithm can be evaluated almost surely.

math.PR↗
arXiv2023

Nowhere to Go: Benchmarking Multi-robot Collaboration in Target Trapping Environment

Collaboration is one of the most important factors in multi-robot systems. Considering certain real-world applications and to further promote its development, we propose a new benchmark to evaluate multi-robot collaboration in Target Trapping Environment (T2E). In T2E, two kinds of robots (called captor robot and target robot) share the same space. The captors aim to catch the target collaboratively, while the target will try to escape from the trap. Both the trapping and escaping process can use the environment layout to help achieve the corresponding objective, which requires high collaboration between robots and the utilization of the environment. For the benchmark, we present and evaluate multiple learning-based baselines in T2E, and provide insights into regimes of multi-robot collaboration. We also make our benchmark publicly available and encourage researchers from related robotics disciplines to propose, evaluate, and compare their solutions in this benchmark. Our project is released at https://github.com/Dr-Xiaogaren/T2E.

cs.RO↗
arXiv2023

Learning Point-Language Hierarchical Alignment for 3D Visual Grounding

This paper presents a novel hierarchical alignment model (HAM) that learns multi-granularity visual and linguistic representations in an end-to-end manner. We extract key points and proposal points to model 3D contexts and instances, and propose point-language alignment with context modulation (PLACM) mechanism, which learns to gradually align word-level and sentence-level linguistic embeddings with visual representations, while the modulation with the visual context captures latent informative relationships. To further capture both global and local relationships, we propose a spatially multi-granular modeling scheme that applies PLACM to both global and local fields. Experimental results demonstrate the superiority of HAM, with visualized results showing that it can dynamically model fine-grained visual and linguistic representations. HAM outperforms existing methods by a significant margin and achieves state-of-the-art performance on two publicly available datasets, and won the championship in ECCV 2022 ScanRefer challenge. Code is available at~\url{https://github.com/PPjmchen/HAM}.

cs.CV↗
arXiv2023

Analysis of the smoothly amnesia-reinforced multidimensional elephant random walk

In this work, we discuss the smoothly amnesia-reinforced multidimensional elephant random walk (MARW). The scaling limit of the MARW is shown to exist in the diffusive, critical and superdiffusive regimes. We also establish the almost sure convergence in all of the three regimes. The quadratic strong law is displayed in the diffusive regime as well as in the critical regime. The mean square convergence towards a non-Gaussian random variable is established in the superdiffusive regime. Similar results for the barycenter process are also derived. Finally, the last two Sections are devoted to a discussion of the convergence velocity of the mean square displacement and the Cram{é}r moderate deviations.

math.PR↗
arXiv2022

Perturbations of Multiple Schramm-Loewner Evolution with Two Non-colliding Dyson Brownian Motions

In this article, we study multiple $SLE_κ$, for $κ\in(0,4]$, driven by Dyson Brownian motion. This model was introduced in the unit disk by Cardy in connection with the Calogero-Sutherland model. We prove the Carathéodory convergence of perturbed Loewner chains under different initial conditions and under different diffusivity $κ\in (0,4]$ for the case of $N=2$ driving forces. Our proofs use the analysis of Bessel processes and estimates on Loewner differential equation with multiple driving forces. In the last section, we estimate the Hausdorff distance of the hulls under perturbations of the driving forces, with assumptions on the modulus of the derivative of the multiple Loewner maps.

math.PR↗
arXiv2022

Observation of Ultrafast Interfacial Exciton Formation and Recombination in Graphene/MoS2 Heterostructure

In this study,we combined time-resolved terahertz spectroscopy along with transient absorption spectroscopy to revisit the interlayer non-equilibrium carrier dynamics in largely lateral size Gr/MoS2 heterostructure fabricated with chemical vapor deposition method. Our experimental results reveal that, with photon-energy below the A-exciton of MoS2 monolayer, hot electrons transfer from graphene to MoS2 takes place in time scale of less than 0.5 ps, resulting in ultrafast formation of interfacial exciton in the heterostructure, subsequently, recombination relaxation of the interfacial exciton occurs in time scale of ~18 ps. A new model considering carrier heating and photogating effect in graphene is proposed to estimate the amount of carrier transfer in the heterostructure, which shows a good agreement with experimental result. Moreover, when the photon-energy is on-resonance with the A-exciton of MoS2, photogenerated holes in MoS2 are transferred to graphene layer within 0.5 ps, leading to the formation of interfacial exciton, the subsequent photoconductivity (PC) relaxation of graphene and bleaching recovery of A-exciton in MoS2 take place around ~10 ps time scale, ascribing to the interfacial exciton recombination. The faster recombination time of interfacial exciton with on-resonance excitation could come from the reduced interface barrier caused by bandgap renormalization effect. Our study provides deep insight into the understanding of interfacial charge transfer as well as the relaxation dynamics in graphene-based heterostructures, which are promising for the applications of graphene-based optoelectronic devices.

physics.optics↗
arXiv2022

Ultrafast Dynamics of Defect-Assisted Auger process in PdSe2 films: Synergistic Interaction Between Defect Trapping and Auger Effect

Strong Coulomb interactions in two-dimensional systems, together with quantum confinement, make many-body processes particularly effective for carrier dynamics, which plays a crucial role in determining carrier lifetime, photoconductivity, and emission yield of the materials. Hereby, by using optical pump and terahertz probe spectroscopy, we have investigated the photocarrier dynamics in the PdSe2 films with different thickness. The experimental results reveal that the photocarrier relaxation consists of two components: a fast component of 2.5 ps that shows the layer-thickness independence, and a slow component has typical lifetime of 7.3 ps decreasing with the layer thickness. Surprisingly, the relaxation times for both fast and slow components are exhibited both pump fluence and temperature independence, which suggests that synergistic interactions between defect trapping and Auger effect dominate the photocarrier dynamics in PdSe2 films. A model involving defect-assisted Auger process is proposed, which can reproduce the experimental results well. The fitting results reveal that the layer dependent lifetime is determined by the defect density rather than carrier occupancy rate after photoexcitation. Our results underscore the interplay between Auger process and defects in two-dimensional semiconductors.

cond-mat.mes-hall↗
arXiv2022

Temperature-driven Emergence of Negative Photoconductivity in Semimetal MoTe2 Film Probed with Terahertz Spectroscopy

Layered two-dimensional (2D) materials MoTe2 have been paid special attention due to the rich optoelectronic properties with various phases. The nonequilibrium carrier dynamics as well as its temperature dependence in MoTe2 are of prime importance, as it can shed light on understanding the anomalous optical response and potential applications in far infrared (IR) photodetection. Hereby, we employ time-resolved terahertz (THz) spectroscopy to study the temperature dependent nonequilibrium carrier dynamics in MoTe2 films. After photoexcitation of 1.59 eV, the 1T'-phase MoTe2 at high temperature behaves only THz positive photoconductivity (PPC) with relaxation time of less than 1 ps. In contrast, the Td-phase MoTe2 at low temperature shows ultrafast THz PPC initially followed by emerging THz negative photoconductivity (NPC), and the THz NPC signal relaxes to the equilibrium state in hundreds of ps time scale. Small polaron formation induced by hot carrier has been proposed to be ascribed to the THz NPC in the polar semimetal MoTe2 at low temperature. The polaron formation time after photoexcitation increases slightly with temperature, which is determined to be ~0.4 ps at 5 K and 0.5 ps at 100 K. Our experimental result demonstrates for the first time the dynamical formation of small poalron in MoTe2 Weyl semimetal, this is fundamental importance on the understanding the temperature dependent electron-phonon coupling and quantum phase transition, as well as the designing the MoTe2-based far IR photodetector.

cond-mat.str-el↗
arXiv2020

On the geometric André-Oort conjecture for variations of Hodge structures

Let $\mathbb{V}$ be a polarized variation of integral Hodge structure on a smooth complex quasi-projective variety $S$. In this paper, we show that the union of the non-factor special subvarieties for $(S, \mathbb{V})$, which are of Shimura type with dominant period maps, is a finite union of special subvarieties of $S$. This generalizes previous results of Clozel and Ullmo arXiv:math/0404131, Ullmo \cite{Ullmo07} on the distribution of the non-factor (in particular, strongly) special subvarieties in a Shimura variety to the non-classical setting and also answers positively the geometric part of a conjecture of Klingler on the André-Oort conjecture for variations of Hodge structures.

math.AG↗
arXiv2018

Predictive Modeling of Biomedical Signals Using Controlled Spatial Transformation

An important paradigm in smart health is developing diagnosis tools and monitoring a patient's heart activity through processing Electrocardiogram (ECG) signals is a key example, sue to high mortality rate of heart-related disease. However, current heart monitoring devices suffer from two important drawbacks: i) failure in capturing inter-patient variability, and ii) incapability of identifying heart abnormalities ahead of time to take effective preventive and therapeutic interventions. This paper proposed a novel predictive signal processing method to solve these issues. We propose a two-step classification framework for ECG signals, where a global classifier recognizes severe abnormalities by comparing the signal against a universal reference model. The seemingly normal signals are then passed through a personalized classifier, to recognize mild but informative signal morphology distortions. The key idea is to develop a novel deviation analysis based on a controlled nonlinear transformation to capture significant deviations of the signal towards any of predefined abnormality classes. Here, we embrace the proven but overlooked fact that certain features of ECG signals reflect underlying cardiac abnormalities before the occurrences of cardiac disease. The proposed method achieves a classification accuracy of 96.6% and provides a unique feature of predictive analysis by providing warnings before critical heart conditions. In particular, the chance of observing a severe problem (a red alarm) is raised by about 5% to 10% after observing a yellow alarm of the same type. Although we used this methodology to provide early precaution messages to elderly and high-risk heart-patients, the proposed method is general and applicable to similar bio-medical signal processing applications.

eess.SP↗