In the analysis of biological time series, the state space is comprised of a framework for the study of systems with presumably deterministic and stationary properties. However, a physiological experiment typically captures an observable that characterizes the temporal response of the physiological system under study; the dynamic variables that make up the state of the system at any time are not available. Only from the acquired observations should state vectors be reconstructed to emulate the different states of the underlying system. This is what is known as the reconstruction of the state space, called the phase space in real-world signals, in many cases satisfactorily resolved using the method of delays. Each state vector consists of m components, extracted from successive observations delayed a time $\tau$ . The morphology of the geometric structure described by the state vectors, as well as their properties depends on the chosen parameters $\tau$ and m. The real dynamics of the system under study is subject to the correct determination of the parameters $\tau$ and m. Only in this way can be deduced features have true physical meaning, revealing aspects that reliably identify the dynamic complexity of the physiological system. The biological signal presented in this work, as a case study, is the photoplethysmographic (PPG) signal. We find that m is five for all the subjects analyzed and that $\tau$ depends on the time interval in which it is evaluated. The Hénon map and the Lorenz flow are used to facilitate a more intuitive understanding of the applied techniques.

The 0–1 test distinguishes between regular and chaotic dynamics for a deterministic system using a time series as a starting point without appealing to any state space reconstruction method. A modification of the 0–1 test allows for the determination of a more comprehensive range of signal dynamic behaviors, particularly in the field of biological signals. We report the results of applying the test and study with more details the PhotoPlethysmoGraphic (PPG) signal behavior from different healthy young subjects, although its use is extensible to other biological signals. While mainly used for heart rate and blood oxygen saturation monitoring, the PPG signal contains extensive physiological dynamics information. We show that the PPG signal, on a healthy young individual, is predominantly quasi-periodic on small timescales (short span of time concerning the dominant frequency). However, on large timescales, PPG signals yield an aperiodic behavior that can be firmly chaotic or a prior transition via an SNA (Strange Nonchaotic Attractor). The results are based on the behavior of well-known time series that are random, chaotic, aperiodic, periodic, and quasi-periodic.

PhotoPlethysmoGraphic (PPG) signal is an easily accessible biological signal that gives valuable diagnostic information. The novelty is the study procedure of the dynamic of the PPG signals, in our case of young and healthy individuals, with Deep Neural Network, which allows finding the dynamic behavior at different timescales. On a small timescale, the dynamic behavior of the PPG signal is predominantly quasi-periodic. On a large timescale, a more complex dynamic diversity emerges, but never a chaotic behavior as earlier studies had reported. The procedure that determines the dynamics of the PPG signal consists of contrasting the dynamics of a PPG signal with well-known dynamics-named reference signals in this study-, mostly present in physical systems, such as periodic, quasi-periodic, aperiodic, chaotic or random dynamics. For this purpose, this paper provides two methods of analysis based on Deep Neural Network (DNN) architectures. The former uses a Convolutional Neural Network (CNN) architecture model. Upon training with reference signals, the CNN model identifies the dynamics present in the PPG signal at different timescales, assigning, according to a classification process, an occurrence probability to each of them. The latter uses a Recurrent Neural Network (RNN) based on a Long Short-Term Memory (LSTM) architecture. With each of the signals, whether reference signals or PPG signals, the RNN model infers an evolution function (nonlinear regression model) based on training data, and considers its predictive capability over a relatively short time horizon.

This paper presents the first photoplethysmographic (PPG) signal dynamic-based biometric authentication system with a Siamese convolutional neural network (CNN). Our method extracts the PPG signal’s biometric characteristics from its diffusive dynamics, characterized by geometric patterns in the $(p,q)$-planes specific to the 0–1 test. PPG signal diffusive dynamics are strongly dependent on the vascular bed’s biostructure, unique to each individual. The dynamic characteristics of the PPG signal are more stable over time than its morphological features, particularly in the presence of psychosomatic conditions. Besides its robustness, our biometric method is anti-spoofing, given the complex nature of the blood network. Our proposal trains using a national research study database with 40 real-world PPG signals measured with commercial equipment. Biometric system results for input data, raw and preprocessed, are studied and compared with eight primary biometric methods related to PPG, achieving the best equal error rate (ERR) and processing times with a single attempt, among all of them.

Infrared Thermography (IRT) is a widely used technique for the detection of temperature change patterns. In the present study, we are interested in its application to the non-invasive follow-up of temperature changes on emotionally stressed people. Nine subjects performed the arithmetic task of the Trier Social Stress Test (TSST) while IRT videos were acquired. A pipeline was implemented to follow the temperature changes on Regions-of-Interest (ROIs) of the facial IRT videos. The pipeline is divided in four main blocks: (1) Frame selection, (2) image preprocessing (i.e., noise reduction), (3) face segmentation, (4) detection of ROIs (i.e., forehead, nose) and temperature extraction. Block 2 relies in an implementation of Growing Hierarchical Self-Organizing Maps (GHSOM). Faces are segmented (Block 3) with Hybrid Geodesic Region-Based Active Contours (HGRBAC). The detection of the ROIs (Block 4) is performed using the Viola-Jones classification method and finally, the temperature is extracted on the ROIs as a function of the time to enable the identification of stress patterns. Each subject's performance on the TSST tasks was measured by an Efficiency Ratio, being its value related to the level of concentration of the subject while performing the exercise.

This paper shows how the dynamics of the PhotoPlethysmoGraphic (PPG) signal, an easily accessible biological signal from which valuable diagnostic information can be extracted, of young and healthy individuals performs at different timescales. On a small timescale, the dynamic behavior of the PPG signal is predominantly quasi-periodic. On a large timescale, a more complex dynamic diversity emerges, but never a chaotic behavior as earlier studies had reported. The procedure by which the dynamics of the PPG signal is determined consists of contrasting the dynamics of a PPG signal with well-known dynamics---named reference signals in this study---, mostly present in physical systems, such as periodic, quasi-periodic, aperiodic, chaotic or random dynamics. For this purpose, this paper provides two methods of analysis based on Deep Neural Network (DNN) architectures. The former uses a Convolutional Neural Network (CNN) architecture model. Upon training with reference signals, the CNN model identifies the dynamics present in the PPG signal at different timescales, assigning, according to a classification process, an occurrence probability to each of them. The latter uses a Recurrent Neural Network (RNN) based on a Long Short-Term Memory (LSTM) architecture. With each of the signals, whether reference signals or PPG signals, the RNN model infers an evolution function (nonlinear regression model) based on training data, and considers its predictive capability over a relatively short time horizon.