Two main weaknesses have been identified for permutation entropy (PE): the neglect of subsequence pattern differences in terms of amplitude and the possible ambiguities introduced by equal values in the subsequences. A number of variations or customizations to the original PE method to address these issues have been proposed in the scientific literature recently. Specifically for ties, methods have tried to remove the ambiguity by assigning different weighted or computed orders to equal values. Although these methods are able to circumvent such ambiguity, they can substantially increase the algorithm costs, and a general characterization of their practical effectiveness is still lacking. This paper analyses the performance of PE using several biomedical datasets (electroencephalogram, heartbeat interval, body temperature, and glucose records) in order to quantify the influence of ties on its signal class segmentation capability. This capability is assessed in terms of statistical significance of the PE differences between classes and classification sensitivity and specificity. Being obvious that ties modify the PE results, we hypothesize that equal values are intrinsic to the acquisition process, and therefore, they impact all the classes more or less equally. The experimental results confirm ties are often not the limiting factor for PE, even they can be beneficial as a sort of stochastic resonance, and it can be far more effective to focus on the embedding dimension instead.

Many entropy-related methods for signal classification have been proposed and exploited successfully in the last several decades. However, it is sometimes difficult to find the optimal measure and the optimal parameter configuration for a specific purpose or context. Suboptimal settings may therefore produce subpar results and not even reach the desired level of significance. In order to increase the signal classification accuracy in these suboptimal situations, this paper proposes statistical models created with uncorrelated measures that exploit the possible synergies between them. The methods employed are permutation entropy (PE), approximate entropy (ApEn), and sample entropy (SampEn). Since PE is based on subpattern ordinal differences, whereas ApEn and SampEn are based on subpattern amplitude differences, we hypothesized that a combination of PE with another method would enhance the individual performance of any of them. The dataset was composed of body temperature records, for which we did not obtain a classification accuracy above 80% with a single measure, in this study or even in previous studies. The results confirmed that the classification accuracy rose up to 90% when combining PE and ApEn with a logistic model.

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ÔØ Å ÒÙ× Ö ÔØThis is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Keywords Thermometry · Fever · Temperature monitoring · Infectious diseases · Entropy · ApEn A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTAbstract Body temperature monitoring provides healthcarers with key clinical information about the physiological status of patients. Temperature readings are taken periodically to detect febrile episodes and consequently implement the appropriate medical countermeasures. However, fever is often difficult to assess at early stages, or remains undetected until the next reading, probably a few hours later. The objective of this paper is to develop a statistical model to forecast fever before a temperature threshold is exceeded to improve the therapeutic approach to the subjects involved. To this end, temperature series of nine patients admitted to a general Internal Medicine ward were obtained with a continuous monitoring holter device, collecting measurements of peripheral and core temperature once per minute. These series were used to develop different statistical models that could quantify the probability of having a fever spike in the following 60 minutes. A validation series was collected to assess the accuracy of the models. Finally, the results were compared with the analysis of some series by experienced clinicians. Two different models were developed: a logistic regression model and a linear discrimination analysis model. Both of them exhibited a fever peak forecasting accuracy above 84%. When compared with experts assessment, both models identified 35 out of 36 fever spikes (97.2%). The models proposed are highly accurate in forecasting the appearance of fever spikes within a short period of time in patients with suspected or confirmed febrile related illnesses.

Approximate Entropy (ApEn) and Sample Entropy (SampEn) have proven to be a valuable analyzing tool for a number of physiological signals. However, the characterization of these metrics is still lacking. We applied ApEn and SampEn to body temperature time series recorded from patients in critical state. This study was aimed at finding the optimal analytical configuration to best distinguish between survivor and non-survivor records, and at gaining additional insight into the characterization of such tools. A statistical analysis of the results was conducted to support the parameter and metric selection criteria for this type of physiological signal.

Body temperature is a health or disease marker that has been in clinical use for centuries. The threshold currently applied to define fever, with small variations, is 38 • C. However, current approaches do not provide a full picture of the thermoregulation process and its correlation with disease.This paper describes a new non-invasive body temperature device that improves the understanding of the pathophysiology of diseases by integrating a variety of temperature data from different body locations. This device enables to gain a deeper insight into fever, endogenous rhythms, subject activity and ambient temperature to provide anticipatory and more efficient treatments. Its clinical use would be a big step in the overcoming of the anachronistic febrile/afebrile dichotomy and walking towards a system medicine approach to certain diseases.This device has already been used in some clinical applications successfully. Other possible applications based on the device features and clinical requirements are also described in this paper.

There is a growing interest in the analysis of hyperglycemia and its relationship with other pathologies. The level of glucose in blood is regulated by the flux/reflux and controlled by hyperglycemia hormones and hypoglycemic insulin. Glycemic profiles are characterized by a nonlinear and nonstationary behavior but also influenced by circadian rhythms and patient daily routine which introduce quasi-periodic trends into them. This type of signals are commonly analyzed by Detrended Fluctuation Analysis (DFA) which states that the control system in charge of regulating the glucose level usually holds a long-range negative correlation. But there is an inconsistency about the windowing lengths, as no standard or rules are set. This work studies the influence of the windowing length sequence, and shows that there is a need for selecting the optimal values in order to obtain a good differentiation between different groups, and these values are somehow determined by signal characteristics.

This paper describes a new application of the recently developed Coefficient of Sample Entropy (CosEn) measure. This entropy estimator is specially suited for cases where the length of the time series is extremely short. CosEn has already been used successfully to characterize and detect atrial fibrillation, using as few as 12 heartbeats. We have customized the methodology employed for heartbeat interval series to blood pressure hypertensive (BPHT) human records. Little can be found about BPHT records and its nonlinear regularity analysis. The method described in this paper provides a good segmentation between control and pathologic groups, based on the corresponding labeled BPHT records. The experimental dataset was drawn from the available records at the Hypertension Unit of the University Hospital of Mostoles, in Spain. The hypertension related variables studied were systolic blood pressure (SBP), diastolic blood pressure (DBP) and mean blood pressure (MBP). The hypothesis test yielded the following results in each case: acceptance probability of 0 for SBP, 0.005 for DBP and 0 for MBP. The confidence intervals for the three variables were nonoverlapping.