This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

In this paper, a dynamic linear approach was used over QT and RR series measured by an automatic delineator, to explore the interactions between QT interval variability (QTV) and heart rate variability (HRV). A low-order linear autoregressive model allowed to separate and quantify the QTV fractions correlated and not correlated with HRV, estimating their power spectral density measures. Simulated series and artificial ECG signals were used to assess the performance of the methods, considering a respiratory-like electrical axis rotation effect and noise contamination with a signal-to-noise ratio (SNR) from 30 to 10 dB. The errors found in the estimation of the QTV fraction related to HRV showed a nonrelevant performance decrease from automatic delineation. The joint performance of delineation plus variability analysis achieved less than 20% error in over 75% of cases for records presenting SNRs higher than 15 dB and QT standard deviation higher than 10 ms. The methods were also applied to real ECG records from healthy subjects where it was found a relevant QTV fraction not correlated with HRV (over 40% in 19 out of 23 segments analyzed), indicating that an important part of QTV is not linearly driven by HRV and may contain complementary information.

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

This study aimed to compare the performance of intra-oral autologous bone grafts versus porcine xenografts in a two-step lateral window sinus lift. This split-mouth randomised controlled trial sequentially enrolled 12 patients with a 6-month follow-up. For each patient, a simultaneous randomised bilateral maxillary sinus lift was performed and filled with autologous bone from the mandible (control) or a porcine xenograft (test). A bone biopsy sample was collected during the implant placement for histological and histomorphometric analysis. CT scans were performed at the beginning and at the end of the trial to assess radiological evolution. A comparison of initial and six-month CT scans indicated statistically significant increases in bone level for both materials (7.8 ± 2.4 mm for autologous and 8.7 ± 2.2 mm for xenograft, p < 0.05), and there were no significant differences between the performance of the two materials over time (p = 0.26). The histological analysis showed various stages of the remodelling process and no cells or other signs of inflammation or infection were visible in both groups. The porcine xenografts presented similar results for the studied variables when compared to autologous bone, being a reasonable alternative for a sinus lift.

Rao et al.'s mandibular canine index (MCI) is a simple odontometric method which uses the mandibular canine as the key to sex estimation. This index is defined as the ratio between the right canine mesiodistal dimension and the mandibular canine arch width. The aim of this study was to contribute to sex estimation using dental techniques by analysing the MCI efficiency, and to propose a new approach for its use. Measurements were taken from 120 plaster casts (70 females) in the 16–30 year age group. Although statistically significant sexual dimorphism was observed in both the mesiodistal dimension and the mandibular canine arch width, the MCI showed a low accuracy in sex classification (54.2% correct identifications). This accuracy was improved to 64.2% using receiver operating characteristics curve analysis. Yet, despite the better accuracy, these results reinforce the idea that the MCI may not be particularly useful in sex prediction, since it may not reflect the same degree of sexual dimorphism as its absolute measures.