Uncorrelated Stochastic Process Research Articles

Chaos Identification Based on Component Reordering and Visibility Graph**Supported by the National Natural Science Foundation of China under Grant No U1530126.

The identification between chaotic systems and stochastic processes is not easy since they have numerous similarities. In this study, we propose a novel approach to distinguish between chaotic systems and stochastic processes based on the component reordering procedure and the visibility graph algorithm. It is found that time series and their reordered components will show diverse characteristics in the ‘visibility domain’. For chaotic series, there are huge differences between the degree distribution obtained from the original series and that obtained from the corresponding reordered component. For correlated stochastic series, there are only small differences between the two degree distributions. For uncorrelated stochastic series, there are slight differences between them. Based on this discovery, the well-known Kullback–Leible divergence is used to quantify the difference between the two degree distributions and to distinguish between chaotic systems, correlated and uncorrelated stochastic processes. Moreover, one chaotic map, three chaotic systems and three different stochastic processes are utilized to illustrate the feasibility and effectiveness of the proposed method. Numerical results show that the proposed method is not only effective to distinguish between chaotic systems, correlated and uncorrelated stochastic processes, but also easy to operate.

Temporal code versus rate code for binary Information Sources

Neuroscientists formulate very different hypotheses about the nature of neural coding. At one extreme, it has been argued that neurons encode information through relatively slow changes in the arrival rates of individual spikes (rate codes) and that the irregularity in the spike trains reflects the noise in the system. At the other extreme, this irregularity is the code itself (temporal codes) so that the precise timing of every spike carries additional information about the input. It is well known that in the estimation of Shannon Information Transmission Rate, the patterns and temporal structures are taken into account, while the “rate code” is already determined by the firing rate, i.e. by the spike frequency. In this paper we compare these two types of codes for binary Information Sources, which model encoded spike trains. Assuming that the information transmitted by a neuron is governed by an uncorrelated stochastic process or by a process with a memory, we compare the Information Transmission Rates carried by such spike trains with their firing rates. Here we show that a crucial role in the relation between information transmission and firing rates is played by a factor that we call the “jumping” parameter. This parameter corresponds to the probability of transitions from the no-spike-state to the spike-state and vice versa. For low jumping parameter values, the quotient of information and firing rates is a monotonically decreasing function of the firing rate, and there therefore a straightforward, one-to-one, relation between temporal and rate codes. However, it turns out that for large enough values of the jumping parameter this quotient is a non-monotonic function of the firing rate and it exhibits a global maximum, so that in this case there is an optimal firing rate. Moreover, there is no one-to-one relation between information and firing rates, so the temporal and rate codes differ qualitatively. This leads to the observation that the behavior of the quotient of information and firing rates for a large jumping parameter value is especially important in the context of bursting phenomena.

Bird's-eye view on noise-based logic.

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss various questions such as (i) What does practical determinism mean? (ii) Is noise-based logic a Turing machine? (iii) Is there hope to beat (the dreams of) quantum computation by a classical physical noise-based processor, and what are the minimum hardware requirements for that? Finally, (iv) we address the problem of random number generators and show that the common belief that quantum number generators are superior to classical (thermal) noise-based generators is nothing but a myth.

Statistical properties of short term price trends in high frequency stock market data

We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths were measured. We found that such a distribution does not fit to the results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives a qualitative agreement with the real data.

Analytical Treatment of Nonexponential Electron Transfer Coupled to Intramolecular and Medium Modes

A many-mode model for electron transfer is developed. The electron transfer is coupled to the classical solvent dynamics and to a molecular subsystem, consisting of many internal modes which form a dense manifold of states for electron transfer in the inverted region. The fluctuations of the solvent coordinate are treated as an uncorrelated stochastic process. For the limit of slow fluctuations it is shown that a transition from a solvent-controlled transfer to a solvent-independent one occurs as a function of the free energy of reaction. The model predicts a nonexponential electron-transfer kinetics of the intermediate region

Maximum likelihood TM classification — Taking the effect of pixel to pixel correlation into account

Abstract To investigate the effect of a pixel to pixel correlation on classification performance for TM data, some experiments have been conducted. One of the results shows that the pixel to pixel correlation in homogeneous fields of TM data is larger than that of the simultaneously acquired MSS data. This implies that it is more important to take into account the pixel correlation for TM classification rather than MSS classification. To overcome the effect of the correlation, the following methods have been investigated. Divided the correlated image into several uncorrelated sub‐images and Based on the auto‐regressive model, modify the Gaussian statistical parameters for the correlated image to those for uncorrelated stochastic process. An example using agricultural TM data shows a slight improvement weighted mean percentage of correct classification. Through the investigation of the correlation structures, a more realistic model for TM data has been developed.

Classification by Re-Estimating Statistical Parameters Based on the Autoregressive Model

To investigate the effect of pixel-to-pixel correlation on classification performance for TM data, some experiments were conducted. One result was that the pixel-to-pixel correlation in homogeneous fields of TM data is larger than that of the simultaneously acquired MSS data, a finding that implies it is more important to consider the pixel correlation for TM classification rather than MSS classification.To overcome the effect of the correlation, the following methods were investigated. Based on the autoregressive model, the Gaussian statistical parameters for the correlated image were modified to those for uncorrelated stochastic process. An example using agricultural TM data shows a slight improvement in terms of the weighted mean percentage of correct classification. By investigating the correlation structures, a more realistic model for TM data was realized.

A comparison of SIC and MRP, two methods for material procurement in industry

In industry it is essential to have the materials needed for production, available at the right times and in the right quantities. Two methods to control material procurement can be found in the literature and in practice: Statistical Inventory Control (SIC), which is part-oriented, ignores the dependency between the demands for the various items, and mainly deals with quantities; and Material Requirements Planning (MRP), which is product-oriented, uses the dependency between the various items given by the product structure, and considers quantity as well as timing of the material procurement. SIC and MRP have both their advantages and drawbacks, as a qualitative comparison easily reveals. A quantitative comparison, however, has not been reported. In this paper (logistic) costs and service levels of SIC and MRP are compared for a simple production-inventory model, in which one finished product is manufactured from two components, and with uncertainty only in the demand for the finished product. This demand, represented by a stationary, uncorrelated stochastic process, remains constant during a given number of periods once its random value is known. The results of this model analysis justify the intuitive preference for MRP: 1. (1) when safety stocks are equal, MRP leads to a higher service level than SIC; 2. (2) the difference is especially evident when safety stocks are small; 3. (3) SIC incurs higher logistics costs than MRP to achieve the same service level. . Two probability density functions have been assigned to the demand process: the normal and the logistic density function. They produced numerical results with negligible differences.