Exact Finite-Dimensional Filter for Exponential Functionals of the State of Beneš Systems

The purpose of this article is to derive finite-dimensional filters for exponential functionals of the state of nonlinear Bene? type filtering systems with correlated noises. These new filters can be applied in the state reconstruction of doubly–stochastic auto–regressive processes.     

Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.     

Pattern Recognition of Sweeteners in Biological Fluids,Beverages, and Ketchup using Stochastic Sensors

Three stochastic sensors based on nanodiamond (nDP) paste modified with α, β, and γ‐cyclodextrin were designed and characterized for pattern recognition of aspartame, acesulfame K and sodium cyclamate in beverages, ketchup, and biological fluids. The linear concentration ranges obtained for acesulfame K (between 1.00×10^?10 mol L^?1and 1.00×10^?3 mol L^?1), for aspartame (between 1.00×10^?12 mol L^?1 and 1.00×10^?3 mol L^?1) and for sodium cyclamate (between 4.97×10^?12 mol L^?1 and 4.97×10^?3 mol L^?1) allow their assay in biological fluids, beverages and ketchup. The lowest limits of quantification were obtained using the stochastic sensor based on γ‐CD/nDP: for acesulfame K 1.00×10^?10 mol L^?1, for aspartame 1.00×10^?12 mol L^?1 and for sodium cyclamate 4.97×10^?12 mol L^?1. All three stochastic sensors revealed very high values of sensitivities. The proposed method was reliable for qualitative and quantitative assay of aspartame, acesulfame K and sodium cyclamate in beverages, ketchup, and in biological fluids such as urine.     

Chemical profiling and marker characterization of Huangqin decoction prepared with three types of peony root by liquid chromatography with electrospray ionization mass spectrometry

Clarification of the quality and biological effect equivalence of traditional Chinese medicines containing multi‐origin species is essential to improve their current quality standards, and also is the core problem to clarify the origins of single herbs with multi‐species in Chinese formulas that will guarantee their clinical application. Huangqin decoction is the typical one of multi‐origin formulas frequently used in traditional Chinese medicine and Kampo medicine. An ultra high performance liquid chromatography with electrospray ionization–tandem mass spectrometry was developed for chemical profiling and marker quantification of Huangqin decoction prepared with two different original types of peony root, white and red peony root. Forty‐seven main peaks in chemical profiling of Huangqin decoction prepared with white and red peony root were identified: nine were from peony root, 20 from baical skullcap root, 17 from licorice root, and one from jujubae fruit. The markers characteristics of the respective types of peony root in Huangqin decoction differ from that in single herbs, especially in terms of monoterpenoids and hydrolysable tannins. Subsequently, 17 representative markers in Huangqin decoction prepared with three types of peony root and their chemical characteristics and content distribution were carried out.     

关于无套利市场的二叉树期权定价模型性质的讨论

本文讨论了二叉树期权市场的无套利条件,引入有随机因素存在的二叉树欧式期权定价模型,并推出单阶段、多阶段情况下欧式期权的计算公式,证明了多阶段市场未定权益的重要性质.     

股本稀释效应下的认股权证定价模型与数值方法

本文研究了在股本稀释效应下认股权证的定价问题.假设随机利率服从Vasicek模型,利用Δ-对冲方法建立了权证价格所满足的偏微分方程.然后,通过计价单位变换,将偏微分方程降维,求得了权证价格的显式解,并给出了一种较好的数值计算方法,可运用市场的可观测变量来计算权证价值.     

The Existence and Global $p$-Exponential Stability of Periodic Solution for Stochastic BAM Neural Networks with Delays

In this paper, we consider a class of stochastic BAM neural networks with delays. By establishing new integral inequalities and using the properties of spectral radius of nonnegative matrix, some sufficient conditions for the existence and global $p$-exponential stability of periodic solution for stochastic BAM neural networks with delays are given. An example is provided to show the effectiveness of the theoretical results.     

Structural Entropy of the Stochastic Block Models

With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction is to compress the data while keeping the “structural information” only and ignoring the concrete labelings. Under this direction, Choi and Szpankowski introduced the structures (unlabeled graphs) which allowed them to compute the structural entropy of the Erdős–Rényi random graph model. Moreover, they also provided an asymptotically optimal compression algorithm that (asymptotically) achieves this entropy limit and runs in expectation in linear time. In this paper, we consider the stochastic block models with an arbitrary number of parts. Indeed, we define a partitioned structural entropy for stochastic block models, which generalizes the structural entropy for unlabeled graphs and encodes the partition information as well. We then compute the partitioned structural entropy of the stochastic block models, and provide a compression scheme that asymptotically achieves this entropy limit.