Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence

We analyze the empirical series of malaria incidence, using the concepts of autocorrelation, Hurst exponent and Shannon entropy with the aim of uncovering hidden variables in those series. From the simulations of an agent model for malaria spreading, we first derive models of the malaria incidence, the Hurst exponent and the entropy as functions of gametocytemia, measuring the infectious power of a mosquito to a human host. Second, upon estimating the values of three observables—incidence, Hurst exponent and entropy—from the data set of different malaria empirical series we predict a value of the gametocytemia for each observable. Finally, we show that the independent predictions show considerable consistency with only a few exceptions which are discussed in further detail.

The Integrated Optokinetic Nystagmus Inter-saccadic Interval Scales Statistical Different In a Group of Vertigo Patients Depended On The Stimulation Velocity, But Not For Healthy Subjects

Optokinetic nystagmus is rhythmic eye movements, back and forth, with a slow and fast phase, when the eyes are presented for full-field visual stimulus. OKN was recorded in 20 healthy subjects and 20 patients suffering from vertigo, for four conditions: stripes moving 30 o/s left and right and 60 o/s left and right. Calculating the scaling, the spread over time, for the integrated optokinetic nystagmus inter-saccadic interval, the time intervals between the onsets of consecutive fast components, shows lower Hurst exponent for velocity stimulation of 30o/s compared to 60o/s for both patients and health subjects, but only reach statistical differences for the group of patients.

A Novel Clock Skew Estimator and Its Performance for the IEEE 1588v2 (PTP) Case in Fractional Gaussian Noise/Generalized Fractional Gaussian Noise Environment

Papers in the literature dealing with the Ethernet network characterize packet delay variation (PDV) as a long-range dependence (LRD) process. Fractional Gaussian noise (fGn) or generalized fraction Gaussian noise (gfGn) belong to the LRD process. This paper proposes a novel clock skew estimator for the IEEE1588v2 applicable for the white-Gaussian, fGn, or gfGn environment. The clock skew estimator does not depend on the unknown asymmetry between the fixed delays in the forward and reverse paths nor on the clock offset between the Master and Slave. In addition, we supply a closed-form-approximated expression for the mean square error (MSE) related to our new proposed clock skew estimator. This expression is a function of the Hurst exponent H, as a function of the parameter a for the gfGn case, as a function of the total sent Sync messages, as a function of the Sync period, and as a function of the PDV variances of the forward and reverse paths. Simulation results confirm that our closed-form-approximated expression for the MSE indeed supplies the performance of our new proposed clock skew estimator efficiently for various values of the Hurst exponent, for the parameter a in gfGn case, for different Sync periods, for various values for the number of Sync periods and for various values for the PDV variances of the forward and reverse paths. Simulation results also show the advantage in the performance of our new proposed clock skew estimator compared to the literature known ML-like estimator (MLLE) that maximizes the likelihood function obtained based on a reduced subset of observations (the first and last timing stamps). This paper also presents designing graphs for the system designer that show the number of the Sync periods needed to get the required clock skew performance (MSE = 10–12). Thus, the system designer can approximately know in advance the total delay or the time the system has to wait until getting the required system’s performance from the MSE point of view.

Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness.

Spatial Multi-Criterion Decision Making (SMDM) Drought Assessment and Sustainability over East Africa from 1982 to 2015

Droughts are ranked among the most devastating agricultural disasters that occur naturally in the world. East Africa is the most vulnerable and drought-prone region worldwide. In this study, four drought indices were used as input variables for drought assessment from 1982 to 2015. This work applied the SMDM algorithm to the integrated approach of OLR and Hurst exponent. The Detrended Fluctuation Analysis (DFA) and Ordinary Least Square (OLR) were merged to compute the trend and persistence (Hurst exponent) of the drought indices. Result indicates that the OLR at time scale 1, 6, and 12 shows a similar distribution with positive (negative) trends scattered in the Northwest (Northeast and Southern) parts of the study area which differs with the OLR aggregated at a 3-month time scale. The percentage pixel distribution for OLR-1, OLR-3, OLR-6, and OLR-12 is 18.2 (81.8), 72.5 (27.5), 32.9 (67.1), and 36.9 (63.1) for increasing (decreasing) trends respectively. Additionally, results indicate that DFA-1 is highly persistent with few random pixels scattered around Ethiopia, South Sudan and Tanzania, with percentage pixels as 88.7, 11.3 and 0.1 representing h > 0.5, h = 0.5, and h < 0.5, respectively. DFA-6 shows high (low) pixels representing h > 0.5 (h > 1), respectively. Meanwhile, for DFA-3 and DFA-12, the distribution shows persistence and a random walk, respectively. Drought conditions may eventually persist, reverse or vary drastically in an unpredictable manner depending on the driving forces. Overall, the drought risk map at 1-, 3-, and 6-month aggregates has shown severe degradation in Southern Kenya and Tanzania while noticeable improvements are seen in western Ethiopia and South Sudan.

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.