Psychic embedding — vision and delusion

The paper introduces the idea that the human brain may apply complex mathematical modules in order to process and understand the world. We speculate that the substrate of what appears outwardly as intuition, or prophetic power, may be a mathematical apparatus such as time-delay embedding. In this context, predictive accuracy may be the reflection of an appropriate choice of the embedding parameters. We further put this in the perspective of mental illness, and search for the possible differences between good intuition and delusive ideation. We speculate that the task at which delusional schizophrenic patients falter is not necessarily of perception, but rather of model selection. Failure of the psychotic patient to correctly choose the embedding parameters may readily lead to misinterpretation of an accurate perception through an altered reconstructed of the object perceived

Statistical Models of Reconstructed Phase Spaces for Signal Classification

This paper introduces a novel approach to the analysis and classification of time series signals using statistical models of reconstructed phase spaces. With sufficient dimension, such reconstructed phase spaces are, with probability one, guaranteed to be topologically equivalent to the state dynamics of the generating system, and, therefore, may contain information that is absent in analysis and classification methods rooted in linear assumptions. Parametric and nonparametric distributions are introduced as statistical representations over the multidimensional reconstructed phase space, with classification accomplished through methods such as Bayes maximum likelihood and artificial neural networks (ANNs). The technique is demonstrated on heart arrhythmia classification and speech recognition. This new approach is shown to be a viable and effective alternative to traditional signal classification approaches, particularly for signals with strong nonlinear characteristics

Modeling Stock Market Returns under Self-exciting Threshold Autoregressive Model: Evidence from West Africa

The study seeks to investigate whether non-linear patterns are present in the returns of two indices on the stock markets in Ghana and Nigeria between the period of 2011 and 2015.The results of applying four linearity tests on the returns concluded that the null of linearity is rejected on all four tests for the Ghanaian index but mixed for the Nigerian index. We modelled the indices under the non-linear self-exciting threshold autoregressive (SETAR) model. We compared the modelling performance of the non-linear SETAR model with that of the standard AR (1) and AR (2) by analyzing AIC values of the respective models. Our results show that the SETAR model ï¬ts the data well. Hence, modelling stock market returns from Ghana and Nigeria using linear models might lead to spurious conclusions. Keywords: Threshold models, Linearity tests, Self-Exciting Threshold Autoregressive (SETAR) model JEL Classifications: C12, C13, C2

CHARACTERIZATION OF UNIVARIATE LONG-TERM URBAN INTERNET TRAFFIC VOLUME

The proposed work deals with a real time hourly internet traffic data set in bits collected from ISPs located in 11 cities of European Country for the period 7th June 2005 to 31st July 2005. Then a thorough statistical inference has been drawn regarding the central tendency, dispersion and distribution of the data. Time-frequency analysis using Smoothed Pseudo Wigner Ville Distribution (SPWVD) is implied to infer knowledge about the non-stationarity of the system. A non-parametric test for normality, Anderson Darling Test (AD-Test) has been performed to detect the binary signature of nonlinearity in the signal. Delay Vector Variance Analysis (DVV) are being exploited to infer deeper knowledge about the determinism and nonlinearity in the system. The results confirm a nonstationary, relatively stochastic and nonlinear profile of the signal under observation

How to find a unicorn: a novel model-free, unsupervised anomaly detection method for time series

Recognition of anomalous events is a challenging but critical task in many scientific and industrial fields, especially when the properties of anomalies are unknown. In this paper, we present a new anomaly concept called "unicorn" or unique event and present a new, model-independent, unsupervised detection algorithm to detect unicorns. The Temporal Outlier Factor (TOF) is introduced to measure the uniqueness of events in continuous data sets from dynamic systems. The concept of unique events differs significantly from traditional outliers in many aspects: while repetitive outliers are no longer unique events, a unique event is not necessarily outlier in either pointwise or collective sense; it does not necessarily fall out from the distribution of normal activity. The performance of our algorithm was examined in recognizing unique events on different types of simulated data sets with anomalies and it was compared with the standard Local Outlier Factor (LOF). TOF had superior performance compared to LOF even in recognizing traditional outliers and it also recognized unique events that LOF did not. Benefits of the unicorn concept and the new detection method were illustrated by example data sets from very different scientific fields. Our algorithm successfully recognized unique events in those cases where they were already known such as the gravitational waves of a black hole merger on LIGO detector data and the signs of respiratory failure on ECG data series. Furthermore, unique events were found on the LIBOR data set of the last 30 years

Brain Network Changes in Fatigued Drivers: A Longitudinal Study in a Real-World Environment Based on the Effective Connectivity Analysis and Actigraphy Data

The analysis of neurophysiological changes during driving can clarify the mechanisms of fatigue, considered an important cause of vehicle accidents. The fluctuations in alertness can be investigated as changes in the brain network connections, reflected in the direction and magnitude of the information transferred. Those changes are induced not only by the time on task but also by the quality of sleep. In an unprecedented 5-month longitudinal study, daily sampling actigraphy and EEG data were collected during a sustained-attention driving task within a near-real-world environment. Using a performance index associated with the subjects' reaction times and a predictive score related to the sleep quality, we identify fatigue levels in drivers and investigate the shifts in their effective connectivity in different frequency bands, through the analysis of the dynamical coupling between brain areas. Study results support the hypothesis that combining EEG, behavioral and actigraphy data can reveal new features of the decline in alertness. In addition, the use of directed measures such as the Convergent Cross Mapping can contribute to the development of fatigue countermeasure devices

A differential entropy based method for determining the optimal embedding parameters of a signal

A novel method for determining the set of parameters for a phase space representation of a time series is proposed. Based upon the differential entropy, both the optimal embedding dimension m, and time lag tau, are simultaneously determined. The choice of these parameters is closely related to the length of the optimal tap input delay line of an adaptive filter or time-delay neural network. The method employs a single criterion – the “entropy ratio ” between the phase space representation of a signal and an ensemble of its surrogates – and is first systematically tested on synthetic time series for which the optimal embedding parameters are known, after which it is verified on a number of benchmark real-world time series. The proposed entropy ratio method is shown to consistently outperform some well-established methods