Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model

In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.     

Analysis of risk bounds in partially specified additive factor models

The study of worst case scenarios for risk measures (e.g. the Value at Risk) when the underlying risk vector (or portfolio of risks) is not completely specified is a central topic in the literature on robust risk measurement. In this paper we discuss partially specified factor models as introduced in Bernard et al. (2017) in more detail for the class of additive factor models which admit more explicit results. These results allow to describe in more detail the reduction of risk bounds obtainable by this method in dependence on the degree of positive resp. negative dependence induced by the systematic risk factors. The insight may help in applications of this reduction method to get a better qualitative impression on the range of influence of the partially specified factor structure.     

Non parametric estimation of the diffusion coefficients of a diffusion with jumps

In this article, we consider a jump diffusion process ${\left(X_t\right)}_{t\ge 0}$, with drift function $b$, diffusion coefficient $\sigma$ and jump coefficient ${\xi }^2$. This process is observed at discrete times $t=0,\Delta ,\dots ,n\Delta$. The sampling interval $\Delta$ tends to 0 and the time interval $n\Delta$ tends to infinity. We assume that ${\left(X_t\right)}_{t\ge 0}$ is ergodic, strictly stationary and exponentially $\beta$-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions ${\sigma }^2+{\xi }^2$ and ${\sigma }^2$. We provide bounds for the risks of the two estimators.     

直觉模糊模型检测在工程决策上的应用

将直觉模糊Kripke结构扩展到加权直觉模糊Kripke结构,将直觉模糊计算树逻辑诱导到加权直觉模糊计算树逻辑;研究在此之上的直觉模糊期望测度和多属性工程决策问题。用加权直觉模糊Kripke结构的权值自然地刻画了工程问题中的成本和收益,直觉模糊测度量化工程进展的不确定性,用加权直觉模糊计算树逻辑描述不确定性工程属性约束。给出了基于直觉模糊模型检测的多属性工程寻优算法,并讨论了算法的复杂度。     

Structural response of high solidity net cage models in uniform flow

Hydrodynamic loads acting on a fish farm may be affected by the growth of different biofouling organisms, mainly due to increased solidity of the nets. In this paper, the hydrodynamic loads acting on high solidity net cage models subjected to high uniform flow velocities and the corresponding deformation of the net cages are studied. Model tests of net cylinders with various solidities were performed in a flume tank with a simulated current. Standard Morison-type numerical analyses were performed based on the model tests, and their capability of simulating the occurring loads and the observed net cage deformations for different flow velocities was evaluated.Large deformations of the net cage models were observed, and at high velocities the deformations were close to what is physically possible. Net cage deformation appeared to be less dependent on solidity than on flow velocity and weights. Drag forces increased with increasing flow velocity and were dependent on both bottom weights and netting solidity. For the lowest solidity net, drag forces were close to proportional to flow velocity. For the three high solidity nets, the measured drag forces were of similar magnitude, and drag increased less with increasing flow velocity above approximately 0.5 m/s than at lower velocities.This study shows that a basic reduced velocity model is not sufficient to model the interaction between the fluid flow and net (hydroelasticity) for high solidity net cages subjected to high flow velocities.The standard numerical analysis was in general able to make good predictions of the net shape, and was capable of making an acceptable estimate of hydrodynamic loads acting on the lowest solidity net model (Sn=0.19). For high solidities and large deformations, numerical tools should account for changes in water flow and the global drag coefficient of the net.     

Muon g-2 discrepancy:new physics or a relatively light Higgs?

After a brief review of the muon g-2 status,we discuss hypothetical errors in the Standard Model prediction that might explain the present discrepancy with the experimental value.None of them seems likely.In particular,a hypothetical increase of the hadroproduction cross section in low-energy e+e-collisions could bridge the muon g-2 discrepancy,but it is shown to be unlikely in view of current experimental error estimates.If,nonetheless,this turns out to be the explanation of the discrepancy,then the 95% CL upper bound on the Higgs boson mass is reduced to about 135 GeV which,in conjunction with the experimental 114.4 GeV 95%CL lower bound,leaves a narrow window for the mass of this fundamental particle.     

A statistical model for global optimization by means of select and clone

A statistical model tor giobai optimization is constructed generalizing some properties ofthe Wiener process to the multidimensional case. A new approach, which is similar to the Branch and Bound approach, is proposed to the construction of algorithms based on statistical models. A two dimensional version of the algorithm is implemented, and test results are presented     

Reactivity profiles of ligands of mammalian retinoic acid receptors: A preliminary COREPA analysis

Retinoic acid and associated derivatives comprise a class of endogenous hormones that bind to and activate different families of retinoic acid receptors (RARs, RXRs), and control many aspects of vertebrate development. Identification of potential RAR and RXR ligands is of interest both from a pharmaceutical and toxicological perspective. The recently developed COREPA (COmmon REactivity PAttern) algorithm was used to establish reactivity profiles for a limited data set of retinoid receptor ligands in terms of activation of three RARs ( f , g , n ) and an RXR ( f ). Conformational analysis of a training set of retinoids and related analogues in terms of thermodynamic stability of conformers and rotational barriers showed that these chemicals tend to be quite flexible. This flexibility, and the observation that relatively small energy differences between conformers can result in significant variations in electronic structure, highlighted the necessity of considering all energetically reasonable conformers in defining common reactivity profiles. The derived reactivity patterns for three different subclasses of the RAR ( f , g , n ) were similar in terms of their global electrophilicity (nucleophilicity) and steric parameters. However, the profile of active chemicals with respect to interaction with the RXR- f differed qualitatively from that of the RARs. Variations in reactivity profiles for the RAR versus RXR families would be consistent with established differences in their affinity for endogenous retinoids, likely reflecting functional differences in the receptors.     

Quantitative prediction of biodegradability,metabolite distribution and toxicity of stable metabolites

An evaluation of the capability of organic chemicals to mineralize is an important factor to consider when assessing their fate in the environment. Microbial degradation can convert a toxic chemical into an innocuous one, and vice versa , or alter the toxicity of a chemical. Moreover, primary biodegradation can convert chemicals into stable products that can be difficult to mineralize. In this paper, we present some new results obtained on the basis of a recently developed probabilistic approach to modeling biodegradation based on microbial transformation pathways. The metabolic transformations and their hierarchy were calibrated by making use of the ready biodegradability data from the MITI-I test and expert knowledge for the most probable transformation pathways. A model was developed and integrated into an expert software system named CATABOL that is able to predict the probability of biodegradation of organic chemicals directly from their structure. CATABOL simulates the effects of microbial enzyme systems, generates the most plausible transformation pathways, and quantitatively predicts the persistence and toxicity of the biodegradation products. A subset of 300 organic chemicals were selected from Canada's Domestic Substances List and subjected to CATABOL to compare predicted properties of the parent chemicals with their respective first stable metabolite. The results show that most of the stable metabolites have a lower acute toxicity to fish and a lower bioaccumulation potential compared to the parent chemicals. In contrast, the metabolites appear to be generally more estrogenic than the parent chemicals.