Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities

We theoretically study complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities. We investigate quantum dynamics of micro-micro and micro-macro entanglement in the micro-macro system. It is found that strong micro-macro entanglement between Rydberg impurities and the BEC can be generated by the use of initial micro-micro entanglement between two Rydberg impurities, which acts as the seed entanglement to create micro-macro entanglement. We demonstrate a curious complementarity relation between micro-micro and micro-macro entanglement, and find that the complementarity property can be sustained to some extent even though in the presence of the BEC decoherence.     

Analysis,design and simulation of MIM plasmonic filters with different geometries for technical parameters improvement

In this paper, four optical filter topologies based on metal–insulator–metal waveguides are proposed and the designed structures are investigated numerically using finite-difference timedomain method. Triangular-shaped adjunctions have been added to the filter structures to improve their transmission spectrum. These improved structures consist of air as the insulator and silver as the metal. The relative permittivity of metal has been described via the Drude,Drude–Lorentz, and Palik models. The first filter's transmission spectrum shows an acceptable transmittance. In the second optimized filter, the transmission spectrum has been improved. The transmittance spectrum can be tuned through adjusting the edge of the triangle in these four optimized filters. As a result, the bandwidths of resonance spectra can be adjusted. The theory of such tapered structures will be investigated by the tapered transmission line and will be solved with the transfer matrix method. This method shows a better performance and higher transmission efficiency in comparison with the basic structures. On the other hand, the final filter has been chosen as the best one because of its hexagonal resonator. The main reason for having a better result is due to a longer interaction length in comparison with the circular resonator. This in turn creates much better energy coupling and results in higher transmission.     

第三族金属氧化物离子对二氧化碳转化的红外光谱研究

本文利用红外光解离光谱研究了第三族金属氧化物离子对二氧化碳分子的转化机制. 研究表明，对于[ScO(CO₂)_n]⁺体系，在n≤4时，形成了溶剂化结构；在n=5时，形成了碳酸盐结构，实现了二氧化碳的转化. 对于[YO(CO₂)_n]⁺体系，需要4个二氧化碳分子就可以实现二氧化碳的转化. 而在[YO(CO₂)_n]⁺体系中，只发现了溶剂化结构，没有观察到碳酸盐结构. 理论计算表明，[YO(CO₂)_n]⁺体系拥有最小的溶剂化结构向碳酸盐结构转化能垒，[LaO(CO₂)_n]⁺体系拥有最大的溶剂化结构向碳酸盐结构转化能垒. 本文从分子水平揭示了不同金属氧化物离子对二氧化碳分子转化的影响规律.     

Assessing the nucleophilic character of 2-amino-4-arylthiazoles through coupling with 4,6-dinitrobenzofuroxan: Experimental and theoretical approaches based on structure-reactivity relationships

A kinetic study of the reactions of potentially bioactive 2-amino-4-arylthiazoles with highly reactive 4,6-dinitrobenzofuroxan (DNBF) is reported herein in acetonitrile solution. The complexation reaction was followed by recording the UV–vis spectra with time at λ_max = 482 nm. Electronic effects of substituents influencing the rate of reaction have been studied using structure-reactivity relationships. It is shown that the Hammett plot relative to the reaction of DNBF with 2-amino-4-(4-chlorophenyl)thiazole exhibit positive deviation from the log k₁ versus σ correlation, while it showed excellent linear correlation in terms of Yukawa–Tsuno equation. It has be noticed that the nonlinear Hammett plot observed for 2-amino-4-(4-chlorophenyl) thiazole is not attributed to a change in rate-determining step but is due to nature of electronic effect of substituent caused by the resonance of stabilization of substrates. The second-order rate constant (k₁) relating to the bond C–C and C-N forming step of the complexation processes of DNBF with 4-substituted-aminothiazoles and 2-amino-5-methyl-4-phenylthiazole, respectively, is fit into the linear relationship log k = s_N (N + E), thereby permitting the assessment of the nucleophilicity parameter (N) of the 2-amino-4-arylthiazoles of the range (4.90 < N < 6.85). 2-amino-4-arylthiazoles is subsequently ranked by positioning its reactivity on the general nucleophilicity scale developed recently by Mayr and coworkers (2003) leading an interesting and a direct comparison over a large domain of π-, σ -, and n-nucleophiles. The global electrophilicity/nucleophilicity reactivity indexes of the 2-amino-4-arylthiazoles have been investigated by means of a density functional theory (DFT) method. .     

A differential-equation-based model of the glass ceiling in career progression

ABSTRACT

We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities; however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e., based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization’s composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.     

On-chip multiphoton Greenberger–Horne–Zeilinger state based on integrated frequency combs

One of the most important multipartite entangled states, Greenberger–Horne–Zeilinger state (GHZ), serves as a fundamental resource for quantum foundation test, quantum communication and quantum computation. To increase the number of entangled particles, significant experimental efforts should been invested due to the complexity of optical setup and the difficulty in maintaining the coherence condition for high-fidelity GHZ state. Here, we propose an ultra-integrated scalable on-chip GHZ state generation scheme based on frequency combs. By designing several microrings pumped by different lasers, multiple partially overlapped quantum frequency combs are generated to supply as the basis for on-chip polarization-encoded GHZ state with each qubit occupying a certain spectral mode. Both even and odd numbers of GHZ states can be engineered with constant small number of integrated components and easily scaled up on the same chip by only adjusting one of the pump wavelengths. In addition, we give the on-chip design of projection measurement for characterizing GHZ states and show the reconfigurability of the state. Our proposal is rather simple and feasible within the existing fabrication technologies and we believe it will boost the development of multiphoton technologies.     

澄清对相对论性原理和协变性的误解

近来有些文章断言,在一个惯性参考系里能量守恒的物理系统,在别的参考系看来能量也一定守恒.实际上这些作者混淆了物理方程式的协变性和相对性原理.本文将澄清这一误解.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.