arXiv subjects

Jingtao Zhu

Publications and source records attributed to Jingtao Zhu.

5 recordsLinked to original sources

arXiv2025

Strong error analysis and first-order convergence of Milstein-type schemes for McKean-Vlasov SDEs with superlinear coefficients

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong convergence of order one under globally Lipschitz coefficients. Nevertheless, many MV-SDEs arising from applications possess super-linearly growing drift and diffusion terms, where classical methods may diverge and particle corruption can occur. In the present work, we aim to fill this gap by developing a unified class of Milstein-type discretizations handling both super-linear drift and diffusion coefficients. The proposed framework includes the tamed-, tanh-, and sine-Milstein methods as special cases and establishes order-one strong convergence for the associated interacting particle system under mild regularity assumptions, requiring only once differentiable coefficients. In particular, our results complement Chen et al. (Electron. J. Probab., 2025), where a taming-based Euler scheme was only tested numerically without theoretical guarantees, by providing a rigorous convergence theory within a broader Milstein-type framework. The analysis relies on discrete-time arguments and binomial-type expansions, avoiding the continuous-time Itô approach that is standard in the literature. Numerical experiments are presented to illustrate the convergence behavior and support the theoretical findings.

math.NA↗

arXiv2025

Euler-type methods for Levy-driven McKean-Vlasov SDEs with super-linear coefficients: mean-square error analysis

We develop and analyze a general class of Euler-type numerical schemes for Levy-driven McKean-Vlasov stochastic differential equations (SDEs), where the drift, diffusion and jump coefficients grow super-linearly in the state variable. These numerical schemes are derived by incorporating projections or nonlinear transformations into the classical Euler method, with the primary objective of establishing moment bounds for the numerical solutions. This class of schemes includes the tanh-Euler, tamed-Euler and sine-Euler schemes as special cases. In contrast to existing approaches that rely on a coercivity condition (e.g., Assumption B-1 in Kumar et al., arXiv:2010.08585), the proposed schemes remove such a restrictive assumption. We provide a rigorous mean-square convergence analysis and establish that the proposed schemes achieve convergence rates arbitrarily close to 1/2 for the interacting particle systems associated with Levy-driven McKean-Vlasov SDEs. Several numerical examples are presented to illustrate the convergence behavior and validate the theoretical results.

math.NA↗

arXiv2024

Detecting collagen by machine learning improved photoacoustic spectral analysis for breast cancer diagnostics: feasibility studies with murine models

Collagen, a key structural component of the extracellular matrix, undergoes significant remodeling during carcinogenesis. However, the important role of collagen levels in breast cancer diagnostics still lacks effective in vivo detection techniques to provide a deeper understanding. This study presents photoacoustic spectral analysis improved by machine learning as a promising non-invasive diagnostic method, focusing on exploring collagen as a salient biomarker. Murine model experiments revealed more profound associations of collagen with other cancer components than in normal tissues. Moreover, an optimal set of feature wavelengths was identified by a genetic algorithm for enhanced diagnostic performance, among which 75% were from collagen-dominated absorption wavebands. Using optimal spectra, the diagnostic algorithm achieved 72% accuracy, 66% sensitivity, and 78% specificity, surpassing full-range spectra by 6%, 4%, and 8%, respectively. The proposed photoacoustic methods examine the feasibility of offering valuable biochemical insights into existing techniques, showing great potential for early-stage cancer detection.

physics.optics↗

arXiv2015

X-ray fluorescence induced by standing waves in the grazing-incidence and grazing-exit modes: study of the Mg--Co--Zr system

We present the characterization of Mg-Co-Zr tri-layer stacks by using x-ray fluorescence induced by x-ray standing waves, both in the grazing incidence (GI) and grazing exit (GE) modes. The introduction of a slit in the direction of the detector improves the angular resolution by a factor 2 and significantly the sensitivity of the technique for the chemical characterization of the buried interfaces. By observing the intensity variations of the Mg Kalpha and Co Lalpha characteristic emissions as a function of the incident (GI mode) or detection (GE mode) angle, we show that the interfaces of the Si/[Mg/Co/Zr] x30 multilayer are abrupt, whereas in the Si/[Mg/Zr/Co] x30 multilayer a strong intermixing occurs at the Co-on-Zr interfaces. The explanation of this opposite behaviour of the Co-on-Zr and Zr-on-Co interfacesis given by the calculation of the mixing enthalpies of the Co-Mg, Co-Zr and Mg-Zr systems, which shows that the Co-Zr system presents anegative value and the two others positive values. Together with the difference of the surface free energies of Zr and Co, this leads us to consider the Mg/Zr/Co system as aMg/Co x Zr y bi-layer stack, with x/y estimated around 3.5.

cond-mat.mtrl-sci↗

arXiv2015

Interface observation of heat-treated Co/Mo2C multilayers

We study the interface evolution of a series of periodic Co/Mo2C multilayers as a function of the annealing temperature up to 600{\textdegree}C. Different complementary techniques are implemented to get information on the phenomenon taking place at the interfaces of the stack. The periodical structure of Co/Mo2C multilayer is proven by Time-of-flight secondary ion mass spectrometry (ToF-SIMS) depth profiles which demonstrate the formation of an oxide layer at both air/stack and stack/substrate interfaces. From Nuclear magnetic resonance (NMR) spectra, we observed the intermixing phenomenon of Co and C atoms for the as-deposited sample, and then at annealing temperature above 300{\textdegree}C Co and C atoms separate from their mixed regions. Comparison of NMR results between Co/Mo 2 C and Co/C references confirms this phenomenon. This is in agreement with x-ray emission spectroscopy (XES) measurements. Furthermore the calculation of the Co-C, Co-Mo and Mo-C mixing enthalpy using Miedema's model gives a proof of the demixing of Co and C atoms present within the stacks above 300{\textdegree}C. From the transmission electron microscopy (TEM) analysis, we found the presence of some crystallites within the as-deposited sample as well as the mainly amorphous nature of all layers. This is confirmed using x-ray diffraction (XRD) patterns which also demonstrate the growth of crystallites induced upon annealing.

cond-mat.mtrl-sci↗