Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Disentangling the Information in Species Interaction Networks

Shannon’s entropy measure is a popular means for quantifying ecological diversity. We explore how one can use information-theoretic measures (that are often called indices in ecology) on joint ensembles to study the diversity of species interaction networks. We leverage the little-known balance equation to decompose the network information into three components describing the species abundance, specificity, and redundancy. This balance reveals that there exists a fundamental trade-off between these components. The decomposition can be straightforwardly extended to analyse networks through time as well as space, leading to the corresponding notions for alpha, beta, and gamma diversity. Our work aims to provide an accessible introduction for ecologists. To this end, we illustrate the interpretation of the components on numerous real networks. The corresponding code is made available to the community in the specialised Julia package EcologicalNetworks.jl.     

Viewing the noise propagation mechanism in a unidirectional transition cascade from the perspective of stability

Noise and noise propagation are inevitable and play a constructive role in various biological processes. The stability of cell homeostasis is also a critical issue. In the unidirectional transition cascade of colon cells, stem cells (SCs) are the source. They differentiate into transit-amplifying cells (TACs), and TACs differentiate into fully differentiated cells (FDCs). Two differentiation processes are irreversible. The stability factor is introduced so that the noise propagation mechanism from the perspective of stability is studied according to the noise propagation formulas. It is found that the value of the stability factor corresponding to the minimum noise in FDCs may be the best choice to enable colon cells to maintain high stability and low noise of the cascade. Moreover, for the source cell, the total noise only includes intrinsic noise; for the downstream cell with self-proliferation capability, the total noise mainly depends on its intrinsic noise and transmitted noise from upstream cells, and its intrinsic noise is dominant. For the downstream cell without self-proliferation capability, the total noise is mainly determined by transmitted noises from upstream cells, and there is a minimum value. This work provides a new approach for studying the mechanism of noise propagation while considering the stability of cell homeostasis in biological systems.     

Two-photon annihilation rate of the positronic HCN molecule

Positron binding by the HCN molecule was studied within a modified adiabatic approximation. This approach, in which the positron is treated as a light pseudonucleus with fractional charge, leads to the binding energy of 0.65?mHartree. Using effective positron mass which reproduces the Quantum Monte Carlo binding energy gives an estimation of the two-photon annihilation rate of e ⁺HCN, equal to 0.091?ns^?1.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

A simple formula for mean multiplexing delay for independent regenerative sources

Simple expressions are given for the mean delay, mean waiting time, and mean busy period length in a multiplexer. Data streams with active periods having a general distribution are permitted, and the data rate during the active periods can be random. Data can also arrive in batches. The key restrictions of the model are that the sources are independent, idle periods are exponentially distributed, and a source generates at least enough data during an active period to keep the server busy throughout the period. The exact formulas allow evaluation of the error in approximations such as a heavy traffic diffusion approximation.Both continuous and discrete time models are considered. The discrete-time model includes that studied by Viterbi and subsequently generalized by Neuts. The Pollaczek-Khinchine formula for the mean amount of work in anM/GI/1 queue is retrieved as a limiting case.Preliminary version presented at IEEE INFOCOM, San Francisco, April 1993.     

OnM-ideals and best approximation

In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China.