Approximate Solutions of Set-Valued Stochastic Differential Equations

Abstract In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state the Carathodory's approximate method and the Euler-Maruyama's approximate method for set-valued stochastic differential equations. We also investigate the errors between approximate solutions and accurate solutions

Mobile E-business Platform: Collaboration System of Wi-Fi and WAVE Based on Cognitive Radio

The new international standard IEEE802.11p (WAVE) defined enhancements to IEEE802.11 (Wi-Fi). A new mobile e-business platform of Wi-Fi and WAVE is described. Based on cognitive radio, the popular wireless network Wi-Fi can collaborate with WAVE in their common unlicensed spectrum band and licensed spectrum band. As a core technology in the cognitive radio field, OFDM is introduced, and a novel frequency estimation algorithm for them is presented

3D phase field modeling of multi-dendrites evolution in solidification and validation by synchrotron x-ray tomography

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. In this paper, the dynamics of multi-dendrite concurrent growth and coarsening of an Al-15 wt.% Cu alloy was studied using a highly computationally efficient 3D phase field model and real-time synchrotron X-ray micro-tomography. High fidelity multi-dendrite simulations were achieved and the results were compared directly with the time-evolved tomography datasets to quantify the relative importance of multi-dendritic growth and coarsening. Coarsening mechanisms under different solidification conditions were further elucidated. The dominant coarsening mechanisms change from small arm melting and interdendritic groove advancement to coalescence when the solid volume fraction approaches ~0.70. Both tomography experiments and phase field simulations indicated that multi-dendrite coarsening obeys the classical Lifshitz–Slyozov–Wagner theory Rn − Rn0=kc(t − t0), but with a higher constant of n = 4.3

EGFL6 regulates the asymmetric division, maintenance and metastasis of ALDH+ ovarian cancer cells

Little is known about the factors that regulate the asymmetric division of cancer stem-like cells. Here we demonstrate that EGFL6, a stem cell regulatory factor expressed in ovarian tumor cells and vasculature, regulates ALDH+ ovarian cancer stem-like cells (CSC). EGFL6 signaled at least in part via the oncoprotein SHP2 with concomitant activation of ERK. EGFL6 signaling promoted the migration and asymmetric division of ALDH+ ovarian CSC. As such, EGFL6 increased not only tumor growth but also metastasis. Silencing of EGFL6 or SHP2 limited numbers of ALDH+ cells and reduced tumor growth, supporting a critical role for EGFL6/SHP2 in ALDH+ cell maintenance. Notably, systemic administration of an EGFL6-neutralizing antibody we generated restricted tumor growth and metastasis, specifically blocking ovarian cancer cell recruitment to the ovary. Together, our results offer a preclinical proof of concept for EGFL6 as a novel therapeutic target for the treatment of ovarian cancer

Set-valued and interval-valued stationary time series

International audienceStationarity is a key tool in classical time series. In order to analyze the set-valued time series, it must be extended to the set-valued case. In this paper, stationary set-valued time series is defined via DpDp metric of set-valued random variables. Then, estimation methods of expectation and auto-covariance function of stationary set-valued time series are proposed. Unbiasedness and consistency of the expectation estimator and asymptotic unbiasedness of the auto-covariance function estimator are justified. After that, a special case of the set-valued time series, known as interval-valued time series, is considered. Two forecast methods of the stationary interval-valued time series are explicitly presented. Furthermore, the interval-valued time series is contextualized in the Box–Jenkins framework: an interval-valued autoregression model, along with its parameter estimation method, is introduced. Finally, experiments on both simulated and real data are presented to justify the efficiency of the parameters estimation method and the availability of the proposed model

On the solutions of set-valued stochastic differential equations in M-type 2 Banach spaces

In a certain Banach space called an M-type 2 Banach space (including Hilbert spaces), we consider a set-valued stochastic differential equation with a set-valued drift term and a single valued diffusion term, under the Lipschitz continuity conditions, and we prove the existence and uniqueness of strong solutions which are continuous in the Hausdorff distance