On the Fibonacci sequence and the Linear Time Invariant systems

The Fibonacci sequence (FS) possesses exceptional mathematical properties that have captivated mathematicians, scientists, and artists across centuries. Its intriguing nature lies in its profound connection to the golden ratio, as well as its prevalence in the natural world, exhibited through phenomena such as spiral galaxies, plant seeds, the arrangement of petals, and branching structures. This report delves into the fundamental characteristics of the FS, explores its relationship with the golden ratio using Linear Time Invariant (LTI) systems, and investigates its diverse applications in various fields. Approaching the topic from the standpoint of a digital signal processing instructor in a grade course, we depict the FS as the consequential outcome of an LTI system when subjected to the unit impulse function. This LTI system can be regarded as the original source from which one of the most renowned formulas in mathematics emerges, and its parametric definition, along with the associated systems, is intricately tied to the golden ratio, symbolized by the irrational number Phi. This perspective naturally elucidates the well-established intricate relationship between the FS and Phi. Furthermore, building upon this perspective, we showcase other LTI systems that exhibit the same magnitude in the frequency domain. These systems are characterized by either an impulse response or a difference equation, resulting in a comparable or equivalent FS in terms of absolute value. By exploring these connections, we shed light on the remarkable similarities and variations that arise within the FS under different LTI systems.Comment: 11 pages, 9 figure

Real Time QRS Detection Based on M-ary Likelihood Ratio Test on the DFT Coefficients

This paper shows an adaptive statistical test for QRS detection of electrocardiography (ECG) signals. The method is based on a M-ary generalized likelihood ratio test (LRT) defined over a multiple observation window in the Fourier domain. The motivations for proposing another detection algorithm based on maximum a posteriori (MAP) estimation are found in the high complexity of the signal model proposed in previous approaches which i) makes them computationally unfeasible or not intended for real time applications such as intensive care monitoring and (ii) in which the parameter selection conditions the overall performance. In this sense, we propose an alternative model based on the independent Gaussian properties of the Discrete Fourier Transform (DFT) coefficients, which allows to define a simplified MAP probability function. In addition, the proposed approach defines an adaptive MAP statistical test in which a global hypothesis is defined on particular hypotheses of the multiple observation window. In this sense, the observation interval is modeled as a discontinuous transmission discrete-time stochastic process avoiding the inclusion of parameters that constraint the morphology of the QRS complexes.This work has received research funding from the Spanish government (www.micinn.es) under project TEC2012 34306 (DiagnoSIS, Diagnosis by means of Statistical Intelligent Systems, 70K€) and projects P09-TIC-4530 (300K€) and P11-TIC-7103 (156K€) from the Andalusian government (http://www.juntadeandalucia.es/organismo​s/economiainnovacioncienciayempleo.html)

Case-Based Statistical Learning: A Non-Parametric Implementation with a Conditional-Error Rate SVM

© 2013 IEEE. Machine learning has been successfully applied to many areas of science and engineering. Some examples include time series prediction, optical character recognition, signal and image classification in biomedical applications for diagnosis and prognosis and so on. In the theory of semi-supervised learning, we have a training set and an unlabeled data, that are employed to fit a prediction model or learner, with the help of an iterative algorithm, such as the expectation-maximization algorithm. In this paper, a novel non-parametric approach of the so-called case-based statistical learning is proposed in a low-dimensional classification problem. This supervised feature selection scheme analyzes the discrete set of outcomes in the classification problem by hypothesis-testing and makes assumptions on these outcome values to obtain the most likely prediction model at the training stage. A novel prediction model is described in terms of the output scores of a confidence-based support vector machine classifier under class-hypothesis testing. To have a more accurate prediction by considering the unlabeled points, the distribution of unlabeled examples must be relevant for the classification problem. The estimation of the error rates from a well-trained support vector machines allows us to propose a non-parametric approach avoiding the use of Gaussian density function-based models in the likelihood ratio test

Automatic autism spectrum disorder detection using artificial intelligence methods with MRI neuroimaging: A review

Autism spectrum disorder (ASD) is a brain condition characterized by diverse signs and symptoms that appear in early childhood. ASD is also associated with communication deficits and repetitive behavior in affected individuals. Various ASD detection methods have been developed, including neuroimaging modalities and psychological tests. Among these methods, magnetic resonance imaging (MRI) imaging modalities are of paramount importance to physicians. Clinicians rely on MRI modalities to diagnose ASD accurately. The MRI modalities are non-invasive methods that include functional (fMRI) and structural (sMRI) neuroimaging methods. However, diagnosing ASD with fMRI and sMRI for specialists is often laborious and time-consuming; therefore, several computer-aided design systems (CADS) based on artificial intelligence (AI) have been developed to assist specialist physicians. Conventional machine learning (ML) and deep learning (DL) are the most popular schemes of AI used for diagnosing ASD. This study aims to review the automated detection of ASD using AI. We review several CADS that have been developed using ML techniques for the automated diagnosis of ASD using MRI modalities. There has been very limited work on the use of DL techniques to develop automated diagnostic models for ASD. A summary of the studies developed using DL is provided in the Supplementary Appendix. Then, the challenges encountered during the automated diagnosis of ASD using MRI and AI techniques are described in detail. Additionally, a graphical comparison of studies using ML and DL to diagnose ASD automatically is discussed. We suggest future approaches to detecting ASDs using AI techniques and MRI neuroimaging

Identifying associations between diabetes and acute respiratory distress syndrome in patients with acute hypoxemic respiratory failure: an analysis of the LUNG SAFE database

Background: Diabetes mellitus is a common co-existing disease in the critically ill. Diabetes mellitus may reduce the risk of acute respiratory distress syndrome (ARDS), but data from previous studies are conflicting. The objective of this study was to evaluate associations between pre-existing diabetes mellitus and ARDS in critically ill patients with acute hypoxemic respiratory failure (AHRF). Methods: An ancillary analysis of a global, multi-centre prospective observational study (LUNG SAFE) was undertaken. LUNG SAFE evaluated all patients admitted to an intensive care unit (ICU) over a 4-week period, that required mechanical ventilation and met AHRF criteria. Patients who had their AHRF fully explained by cardiac failure were excluded. Important clinical characteristics were included in a stepwise selection approach (forward and backward selection combined with a significance level of 0.05) to identify a set of independent variables associated with having ARDS at any time, developing ARDS (defined as ARDS occurring after day 2 from meeting AHRF criteria) and with hospital mortality. Furthermore, propensity score analysis was undertaken to account for the differences in baseline characteristics between patients with and without diabetes mellitus, and the association between diabetes mellitus and outcomes of interest was assessed on matched samples. Results: Of the 4107 patients with AHRF included in this study, 3022 (73.6%) patients fulfilled ARDS criteria at admission or developed ARDS during their ICU stay. Diabetes mellitus was a pre-existing co-morbidity in 913 patients (22.2% of patients with AHRF). In multivariable analysis, there was no association between diabetes mellitus and having ARDS (OR 0.93 (0.78-1.11); p = 0.39), developing ARDS late (OR 0.79 (0.54-1.15); p = 0.22), or hospital mortality in patients with ARDS (1.15 (0.93-1.42); p = 0.19). In a matched sample of patients, there was no association between diabetes mellitus and outcomes of interest. Conclusions: In a large, global observational study of patients with AHRF, no association was found between diabetes mellitus and having ARDS, developing ARDS, or outcomes from ARDS. Trial registration: NCT02010073. Registered on 12 December 2013

Spontaneous Breathing in Early Acute Respiratory Distress Syndrome: Insights From the Large Observational Study to UNderstand the Global Impact of Severe Acute Respiratory FailurE Study

OBJECTIVES: To describe the characteristics and outcomes of patients with acute respiratory distress syndrome with or without spontaneous breathing and to investigate whether the effects of spontaneous breathing on outcome depend on acute respiratory distress syndrome severity. DESIGN: Planned secondary analysis of a prospective, observational, multicentre cohort study. SETTING: International sample of 459 ICUs from 50 countries. PATIENTS: Patients with acute respiratory distress syndrome and at least 2 days of invasive mechanical ventilation and available data for the mode of mechanical ventilation and respiratory rate for the 2 first days. INTERVENTIONS: Analysis of patients with and without spontaneous breathing, defined by the mode of mechanical ventilation and by actual respiratory rate compared with set respiratory rate during the first 48 hours of mechanical ventilation. MEASUREMENTS AND MAIN RESULTS: Spontaneous breathing was present in 67% of patients with mild acute respiratory distress syndrome, 58% of patients with moderate acute respiratory distress syndrome, and 46% of patients with severe acute respiratory distress syndrome. Patients with spontaneous breathing were older and had lower acute respiratory distress syndrome severity, Sequential Organ Failure Assessment scores, ICU and hospital mortality, and were less likely to be diagnosed with acute respiratory distress syndrome by clinicians. In adjusted analysis, spontaneous breathing during the first 2 days was not associated with an effect on ICU or hospital mortality (33% vs 37%; odds ratio, 1.18 [0.92-1.51]; p = 0.19 and 37% vs 41%; odds ratio, 1.18 [0.93-1.50]; p = 0.196, respectively ). Spontaneous breathing was associated with increased ventilator-free days (13 [0-22] vs 8 [0-20]; p = 0.014) and shorter duration of ICU stay (11 [6-20] vs 12 [7-22]; p = 0.04). CONCLUSIONS: Spontaneous breathing is common in patients with acute respiratory distress syndrome during the first 48 hours of mechanical ventilation. Spontaneous breathing is not associated with worse outcomes and may hasten liberation from the ventilator and from ICU. Although these results support the use of spontaneous breathing in patients with acute respiratory distress syndrome independent of acute respiratory distress syndrome severity, the use of controlled ventilation indicates a bias toward use in patients with higher disease severity. In addition, because the lack of reliable data on inspiratory effort in our study, prospective studies incorporating the magnitude of inspiratory effort and adjusting for all potential severity confounders are required

Epidemiology and patterns of tracheostomy practice in patients with acute respiratory distress syndrome in ICUs across 50 countries

Background: To better understand the epidemiology and patterns of tracheostomy practice for patients with acute respiratory distress syndrome (ARDS), we investigated the current usage of tracheostomy in patients with ARDS recruited into the Large Observational Study to Understand the Global Impact of Severe Acute Respiratory Failure (LUNG-SAFE) study. Methods: This is a secondary analysis of LUNG-SAFE, an international, multicenter, prospective cohort study of patients receiving invasive or noninvasive ventilation in 50 countries spanning 5 continents. The study was carried out over 4 weeks consecutively in the winter of 2014, and 459 ICUs participated. We evaluated the clinical characteristics, management and outcomes of patients that received tracheostomy, in the cohort of patients that developed ARDS on day 1-2 of acute hypoxemic respiratory failure, and in a subsequent propensity-matched cohort. Results: Of the 2377 patients with ARDS that fulfilled the inclusion criteria, 309 (13.0%) underwent tracheostomy during their ICU stay. Patients from high-income European countries (n = 198/1263) more frequently underwent tracheostomy compared to patients from non-European high-income countries (n = 63/649) or patients from middle-income countries (n = 48/465). Only 86/309 (27.8%) underwent tracheostomy on or before day 7, while the median timing of tracheostomy was 14 (Q1-Q3, 7-21) days after onset of ARDS. In the subsample matched by propensity score, ICU and hospital stay were longer in patients with tracheostomy. While patients with tracheostomy had the highest survival probability, there was no difference in 60-day or 90-day mortality in either the patient subgroup that survived for at least 5 days in ICU, or in the propensity-matched subsample. Conclusions: Most patients that receive tracheostomy do so after the first week of critical illness. Tracheostomy may prolong patient survival but does not reduce 60-day or 90-day mortality. Trial registration: ClinicalTrials.gov, NCT02010073. Registered on 12 December 2013

More than just child’s play?: An experimental investigation of the impact of an appearance-focused internet game on body image and career aspirations of young girls

© 2017, The Author(s). In recent years, elements of the modern environment (such as television, Internet, toys and clothes) have been criticized for having an increasingly sexualized or appearance focus, which has been suggested to be detrimental to girls’ development. The current study examined the impact of an appearance-focused Internet game on young girls’ body image and career cognitions and aspirations. Eighty British girls aged 8–9 years were randomly assigned to play an appearance-focused or a non-appearance focused game for 10 minutes. Girls in the appearance-focused game condition displayed greater body dissatisfaction compared to the control condition. Type of game did not impact girls’ perceived capacity to do various jobs. However, girls who played the appearance-focused game reported a greater preference for feminine careers compared to the control group. This provides preliminary evidence that appearance-focused Internet games may be detrimental to young girls’ body image and aspirations. Internet games should be included in our consideration of influential messages for young girls