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31 pages, 12545 KiB  
Article
Complexity Analysis of Environmental Time Series
by Holger Lange and Michael Hauhs
Entropy 2025, 27(4), 381; https://doi.org/10.3390/e27040381 - 3 Apr 2025
Cited by 1 | Viewed by 627
Abstract
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the [...] Read more.
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the intricate nature of processes acting on a large range of time scales. Nonlinear dynamics is an obvious framework to investigate catchment time series. We analyzed selected long-term data from three headwater catchments in the Bramke valley, Harz mountains, Lower Saxony in Germany at common biweekly resolution for the period 1991 to 2023. For every time series, we performed gap filling, detrending, and removal of the annual cycle using singular system analysis (SSA), and then calculated metrics based on ordinal pattern statistics: the permutation entropy, permutation complexity, and Fisher information, as well as their generalized versions (q-entropy and α-entropy). Further, the position of each variable in Tarnopolski diagrams is displayed and compared to reference stochastic processes, like fractional Brownian motion, fractional Gaussian noise, and β noise. Still another way of distinguishing deterministic chaos and structured noise, and quantifying the latter, is provided by the complexity from ordinal pattern positioned slopes (COPPS). We also constructed horizontal visibility graphs and estimated the exponent of the decay of the degree distribution. Taken together, the analyses create a characterization of the dynamics of these systems which can be scrutinized for universality, either across variables or between the three geographically very close catchments. Full article
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13 pages, 4152 KiB  
Article
The Pathogenomics of the Respiratory Mycoplasma bovis Strains Circulating in Cattle Around the Texas Panhandle, USA
by Ethan P. Dudley, Matthew A. Scott, Hatem Kittana, Alexis C. Thompson and Robert Valeris-Chacin
Pathogens 2025, 14(2), 167; https://doi.org/10.3390/pathogens14020167 - 8 Feb 2025
Viewed by 1190
Abstract
Bovine respiratory disease (BRD) is a major economic and animal welfare issue in the beef industry. Mycoplasma bovis is one of the main causal organisms, particularly in chronic cases. Due to the difficulty of isolating M. bovis from clinical isolates, there is a [...] Read more.
Bovine respiratory disease (BRD) is a major economic and animal welfare issue in the beef industry. Mycoplasma bovis is one of the main causal organisms, particularly in chronic cases. Due to the difficulty of isolating M. bovis from clinical isolates, there is a lack of information on the genetic diversity of this pathogen in the Texas panhandle region of the United States. Therefore, our objective was to provide genome-level characterization of M. bovis isolated from the lung lesions of beef and dairy cattle in the Texas panhandle. Fifty-four isolates displaying mycoplasma-like growth were recovered from bovine lung lesions by the Texas Veterinary Medical Diagnostic Laboratory in 2021 and 2022. Of these isolates, 32 were determined to be M. bovis via species-specific qPCR using the uvrC gene. Long-read whole-genome sequencing was used to identify key virulence factors, antimicrobial resistance genes, and to assess the genetic diversity of these isolates. Fisher’s exact tests were used to identify associations between isolate characteristics and host metadata, including the state of origin, type of operation, animal age, and animal sex. Our results indicate that there is considerable genetic diversity among the M. bovis isolates, despite their shared geography in the Texas panhandle, though significant clustering based on host metadata was observed. Analysis of the pangenome showed that the M. bovis isolates in this study also harbor a diverse array of virulence genes, but no antimicrobial resistance genes were identified in this study. Full article
(This article belongs to the Special Issue Mycoplasmas in Respiratory Tract Infections of Cattle)
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26 pages, 8634 KiB  
Article
New Insights on the Information Content of the Normalized Difference Vegetation Index Sentinel-2 Time Series for Assessing Vegetation Dynamics
by César Sáenz, Víctor Cicuéndez, Gabriel García, Diego Madruga, Laura Recuero, Alfonso Bermejo-Saiz, Javier Litago, Ignacio de la Calle and Alicia Palacios-Orueta
Remote Sens. 2024, 16(16), 2980; https://doi.org/10.3390/rs16162980 - 14 Aug 2024
Cited by 2 | Viewed by 3211
Abstract
The Sentinel-2 NDVI time series information content from 2017 to 2023 at a 10 m spatial resolution was evaluated based on the NDVI temporal dependency in five scenarios in central Spain. First, time series were interpolated and then filtered using the Savitzky–Golay, Fast [...] Read more.
The Sentinel-2 NDVI time series information content from 2017 to 2023 at a 10 m spatial resolution was evaluated based on the NDVI temporal dependency in five scenarios in central Spain. First, time series were interpolated and then filtered using the Savitzky–Golay, Fast Fourier Transform, Whittaker, and Maximum Value filters. Temporal dependency was assessed using the Q-Ljung-Box and Fisher’s Kappa tests, and similarity between raw and filtered time series was assessed using Correlation Coefficient and Root Mean Square Error. An Interpolating Efficiency Indicator (IEI) was proposed to summarize the number and temporal distribution of low-quality observations. Type of climate, atmospheric disturbances, land cover dynamics, and management were the main sources of variability in five scenarios: (1) rainfed wheat and barley presented high short-term variability due to clouds (lower IEI in winter and spring) during the growing cycle and high interannual variability due to precipitation; (2) maize showed stable summer cycles (high IEI) and low interannual variability due to irrigation; (3) irrigated alfalfa was cut five to six times during summer, resulting in specific intra-annual variability; (4) beech forest showed a strong and stable summer cycle, despite the short-term variability due to clouds (low IEI); and (5) evergreen pine forest had a highly variable growing cycle due to fast responses to temperature and precipitation through the year and medium IEI values. Interpolation after removing non-valid observations resulted in an increase in temporal dependency (Q-test), particularly a short term in areas with low IEI values. The information improvement made it possible to identify hidden periodicities and trends using the Fisher’s Kappa test. The SG filter showed high similarity values and weak influence on dynamics, while the MVF showed an overestimation of the NDVI values. Full article
(This article belongs to the Special Issue Crops and Vegetation Monitoring with Remote/Proximal Sensing II)
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13 pages, 2249 KiB  
Article
The Functional Characterization of DzCYP72A12-4 Related to Diosgenin Biosynthesis and Drought Adaptability in Dioscorea zingiberensis
by Weipeng Wang, Lixiu Hou, Song Li and Jiaru Li
Int. J. Mol. Sci. 2023, 24(9), 8430; https://doi.org/10.3390/ijms24098430 - 8 May 2023
Cited by 5 | Viewed by 2310
Abstract
Dioscorea zingiberensis is a perennial herb famous for the production of diosgenin, which is a valuable initial material for the industrial synthesis of steroid drugs. Sterol C26-hydroxylases, such as TfCYP72A616 and PpCYP72A613, play an important role in the diosgenin biosynthesis pathway. [...] Read more.
Dioscorea zingiberensis is a perennial herb famous for the production of diosgenin, which is a valuable initial material for the industrial synthesis of steroid drugs. Sterol C26-hydroxylases, such as TfCYP72A616 and PpCYP72A613, play an important role in the diosgenin biosynthesis pathway. In the present study, a novel gene, DzCYP72A12-4, was identified as C26-hydroxylase and was found to be involved in diosgenin biosynthesis, for the first time in D. zingiberensis, using comprehensive methods. Then, the diosgenin heterogenous biosynthesis pathway starting from cholesterol was created in stable transgenic tobacco (Nicotiana tabacum L.) harboring DzCYP90B71(QPZ88854), DzCYP90G6(QPZ88855) and DzCYP72A12-4. Meanwhile, diosgenin was detected in the transgenic tobacco using an ultra-performance liquid chromatography system (Vanquish UPLC 689, Thermo Fisher Scientific, Bremen, Germany) tandem MS (Q Exactive Hybrid Quadrupole-Orbitrap Mass Spectrometer, Thermo Fisher Scientific, Bremen, Germany). Further RT-qPCR analysis showed that DzCYP72A12-4 was highly expressed in both rhizomes and leaves and was upregulated under 15% polyethylene glycol (PEG) treatment, indicating that DzCYP72A12-4 may be related to drought resistance. In addition, the germination rate of the diosgenin-producing tobacco seeds was higher than that of the negative controls under 15% PEG pressure. In addition, the concentration of malonaldehyde (MDA) was lower in the diosgenin-producing tobacco seedlings than those of the control, indicating higher drought adaptability. The results of this study provide valuable information for further research on diosgenin biosynthesis in D. zingiberensis and its functions related to drought adaptability. Full article
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16 pages, 443 KiB  
Article
Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law
by Andrea A. Rey, Alejandro C. Frery, Magdalena Lucini, Juliana Gambini, Eduarda T. C. Chagas and Heitor S. Ramos
Entropy 2023, 25(5), 734; https://doi.org/10.3390/e25050734 - 28 Apr 2023
Cited by 6 | Viewed by 2128
Abstract
We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and [...] Read more.
We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and Fisher) are normal, describe well a variety of simulated data. In addition, we obtain test statistics for comparing (possibly different types of) entropies from two samples without requiring the same number of categories. Finally, we apply these tests to social survey data and verify that the results are consistent but more general than those obtained with a χ2 test. Full article
(This article belongs to the Special Issue Mathematics in Information Theory and Modern Applications)
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14 pages, 1301 KiB  
Article
The Use of Complementary and Alternative Medicine among Peritoneal Dialysis Patients at a Second-Level Hospital in Yucatán Mexico
by Carlos Gracida-Osorno, Sandra Luz Jiménez-Martínez, Andrés Humberto Uc-Cachón and Gloria María Molina-Salinas
Healthcare 2023, 11(5), 722; https://doi.org/10.3390/healthcare11050722 - 1 Mar 2023
Cited by 5 | Viewed by 2908
Abstract
Background: Complementary and alternative medicine (CAM) is widely used for multiple reasons such as treatment of diseases and their symptoms, empowerment, self-care, disease prevention, dissatisfaction, adverse effects or cost of conventional medicine, perception of compatibility with beliefs, and idiosyncrasy. This study investigated CAM [...] Read more.
Background: Complementary and alternative medicine (CAM) is widely used for multiple reasons such as treatment of diseases and their symptoms, empowerment, self-care, disease prevention, dissatisfaction, adverse effects or cost of conventional medicine, perception of compatibility with beliefs, and idiosyncrasy. This study investigated CAM use in patients with chronic kidney disease (CKD) undergoing peritoneal dialysis (PD). Methods: A cross-sectional survey study was conducted with 240 eligible patients with CKD in the PD program. By applying the I-CAM-Q-questionnaire, the frequency, level of satisfaction, and reasons for CAM use were explored, and the demographic and clinical data of users and non-users were analyzed. Data analysis included descriptive analysis, Student’s t-test, Mann-Whitney U, chi-square, and Fisher tests. Results: The main types of CAM used were herbal medicine, and chamomile was the most commonly used. To improve the state of well-being was the main reason for use, the attributable benefit of CAM was high, and only a low percentage of users reported side effects. Only 31.8% of the users informed their physicians. Conclusion: The use of CAM is popular among renal patients, and physicians are not adequately informed; in particular, the CAM type ingested represents a risk for drug interactions and toxicity. Full article
(This article belongs to the Topic Biosocial Studies)
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18 pages, 3041 KiB  
Article
Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures
by Omid Kharazmi, Narayanaswamy Balakrishnan and Hassan Jamali
Entropy 2022, 24(3), 341; https://doi.org/10.3390/e24030341 - 27 Feb 2022
Cited by 9 | Viewed by 2392
Abstract
In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a [...] Read more.
In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual χ2 divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual χ2 divergence measures. Further, we define Jensen-cumulative residual χ2 (JCR-χ2) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure. Full article
(This article belongs to the Special Issue Measures of Information II)
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12 pages, 2223 KiB  
Article
Mass Spectrometry Imaging Disclosed Spatial Distribution of Defense-Related Metabolites in Triticum spp.
by Laura Righetti, Sven Gottwald, Sara Tortorella, Bernhard Spengler and Dhaka Ram Bhandari
Metabolites 2022, 12(1), 48; https://doi.org/10.3390/metabo12010048 - 7 Jan 2022
Cited by 12 | Viewed by 2934
Abstract
Fusarium Head Blight is the most common fungal disease that strongly affects Triticum spp., reducing crop yield and leading to the accumulation of toxic metabolites. Several studies have investigated the plant metabolic response to counteract mycotoxins accumulation. However, information on the precise location [...] Read more.
Fusarium Head Blight is the most common fungal disease that strongly affects Triticum spp., reducing crop yield and leading to the accumulation of toxic metabolites. Several studies have investigated the plant metabolic response to counteract mycotoxins accumulation. However, information on the precise location where the defense mechanism is taking place is scarce. Therefore, this study aimed to investigate the specific tissue distribution of defense metabolites in two Triticum species and use this information to postulate on the metabolites’ functional role, unlocking the “location-to-function” paradigm. To address this challenge, transversal cross-sections were obtained from the middle of the grains. They were analyzed using an atmospheric-pressure (AP) SMALDI MSI source (AP-SMALDI5 AF, TransMIT GmbH, Giessen, Germany) coupled to a Q Exactive HF (Thermo Fisher Scientific GmbH, Bremen, Germany) orbital trapping mass spectrometer. Our result revealed the capability of (AP)-SMALDI MSI instrumentation to finely investigate the spatial distribution of wheat defense metabolites, such as hydroxycinnamic acid amides, oxylipins, linoleic and α-linoleic acids, galactolipids, and glycerolipids. Full article
(This article belongs to the Special Issue Spatial Metabolomics)
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28 pages, 474 KiB  
Review
Entropy-Like Properties and Lq-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics
by Jesús S. Dehesa
Symmetry 2021, 13(8), 1416; https://doi.org/10.3390/sym13081416 - 3 Aug 2021
Cited by 7 | Viewed by 2173
Abstract
In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means of the main entropy-like measures of their associated Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, [...] Read more.
In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means of the main entropy-like measures of their associated Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, the Rényi and Shannon entropies, and their corresponding spreading lengths are analytically expressed in terms of the degree and the parameter(s) of the orthogonality weight function. These entropic quantities are closely related to the gradient functional (Fisher) and the Lq-norms (Rényi, Shannon) of the polynomials. In addition, the degree asymptotics for these entropy-like functionals of the three canonical families of HPOs (i.e., Hermite, Laguerre, and Jacobi polynomials) are given and briefly discussed. Finally, a number of open related issues are identified whose solutions are both physico-mathematically and computationally relevant. Full article
(This article belongs to the Special Issue Special Functions and Polynomials)
16 pages, 6113 KiB  
Article
Investigations of Structural Requirements for BRD4 Inhibitors through Ligand- and Structure-Based 3D QSAR Approaches
by Adeena Tahir, Rima D. Alharthy, Saadia Naseem, Natasha Mahmood, Mahmood Ahmed, Khuram Shahzad, Malik Nadeem Akhtar, Abdul Hameed, Irfan Sadiq, Haq Nawaz and Muhammad Muddassar
Molecules 2018, 23(7), 1527; https://doi.org/10.3390/molecules23071527 - 25 Jun 2018
Cited by 15 | Viewed by 4786
Abstract
The bromodomain containing protein 4 (BRD4) recognizes acetylated histone proteins and plays numerous roles in the progression of a wide range of cancers, due to which it is under intense investigation as a novel anti-cancer drug target. In the present study, we performed [...] Read more.
The bromodomain containing protein 4 (BRD4) recognizes acetylated histone proteins and plays numerous roles in the progression of a wide range of cancers, due to which it is under intense investigation as a novel anti-cancer drug target. In the present study, we performed three-dimensional quantitative structure activity relationship (3D-QSAR) molecular modeling on a series of 60 inhibitors of BRD4 protein using ligand- and structure-based alignment and different partial charges assignment methods by employing comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) approaches. The developed models were validated using various statistical methods, including non-cross validated correlation coefficient (r2), leave-one-out (LOO) cross validated correlation coefficient (q2), bootstrapping, and Fisher’s randomization test. The highly reliable and predictive CoMFA (q2 = 0.569, r2 = 0.979) and CoMSIA (q2 = 0.500, r2 = 0.982) models were obtained from a structure-based 3D-QSAR approach using Merck molecular force field (MMFF94). The best models demonstrate that electrostatic and steric fields play an important role in the biological activities of these compounds. Hence, based on the contour maps information, new compounds were designed, and their binding modes were elucidated in BRD4 protein’s active site. Further, the activities and physicochemical properties of the designed molecules were also predicted using the best 3D-QSAR models. We believe that predicted models will help us to understand the structural requirements of BRD4 protein inhibitors that belong to quinolinone and quinazolinone classes for the designing of better active compounds. Full article
(This article belongs to the Special Issue Application of Computational Methods in Drug Design)
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22 pages, 569 KiB  
Article
Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors
by Gia-Thuy Pham, Rémy Boyer and Frank Nielsen
Entropy 2018, 20(3), 203; https://doi.org/10.3390/e20030203 - 17 Mar 2018
Cited by 3 | Viewed by 4453
Abstract
Evaluating the performance of Bayesian classification in a high-dimensional random tensor is a fundamental problem, usually difficult and under-studied. In this work, we consider two Signal to Noise Ratio (SNR)-based binary classification problems of interest. Under the alternative hypothesis, i.e., for a non-zero [...] Read more.
Evaluating the performance of Bayesian classification in a high-dimensional random tensor is a fundamental problem, usually difficult and under-studied. In this work, we consider two Signal to Noise Ratio (SNR)-based binary classification problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size N q × R , i.e., for 1 q Q , where R , N q with R 1 / q / N q converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear ( M 1 , , M Q ) -rank with large factors of size N q × M q , i.e., for 1 q Q , where N q , M q with M q / N q converge towards a finite constant. The classification of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the minimal Bayes’ error probability is mathematically intractable. To circumvent this difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s . In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s = 1 / 2 ) cannot solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s . However, thanks to powerful random matrix theory tools, a simple analytical expression of s is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. This work shows that the BUB is the tightest bound at low SNRs. However, for higher SNRs, the latest property is no longer true. Full article
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10 pages, 606 KiB  
Article
Higher Mortality in Trauma Patients Is Associated with Stress-Induced Hyperglycemia, but Not Diabetic Hyperglycemia: A Cross-Sectional Analysis Based on a Propensity-Score Matching Approach
by Cheng-Shyuan Rau, Shao-Chun Wu, Yi-Chun Chen, Peng-Chen Chien, Hsiao-Yun Hsieh, Pao-Jen Kuo and Ching-Hua Hsieh
Int. J. Environ. Res. Public Health 2017, 14(10), 1161; https://doi.org/10.3390/ijerph14101161 - 30 Sep 2017
Cited by 42 | Viewed by 4078
Abstract
Background: Stress-induced hyperglycemia (SIH) is a form of hyperglycemia secondary to stress and commonly occurs in patients with trauma. Trauma patients with SIH have been reported to have an increased risk of mortality. However, information regarding whether these trauma patients with SIH represent [...] Read more.
Background: Stress-induced hyperglycemia (SIH) is a form of hyperglycemia secondary to stress and commonly occurs in patients with trauma. Trauma patients with SIH have been reported to have an increased risk of mortality. However, information regarding whether these trauma patients with SIH represent a distinct group with differential outcomes when compared to those with diabetic hyperglycemia (DH) remains limited. Methods: Diabetes mellitus (DM) was determined by patient history and/or admission glycated hemoglobin (HbA1c) ≥6.5%. Non-diabetic normoglycemia (NDN) was determined by a serum glucose level <200 mg/dL in the patients without DM. Diabetic normoglycemia (DN) was determined by a serum glucose level <200 mg/dL in the patients with DM. DH and SIH was diagnosed by a serum glucose level ≥200 mg/dL in the patients with and without DM, respectively. Detailed data of these four groups of hospitalized patients, which included NDN (n = 7806), DN (n = 950), SIH (n = 493), and DH (n = 897), were retrieved from the Trauma Registry System at a level I trauma center between 1 January 2009 and 31 December 2015. Patients with incomplete registered data were excluded. Categorical data were compared with Pearson chi-square tests or two-sided Fisher exact tests. The unpaired Student’s t-test and the Mann–Whitney U-test were used to analyze normally distributed continuous data and non-normally distributed data, respectively. Propensity-score-matched cohorts in a 1:1 ratio were allocated using NCSS software with logistic regression to evaluate the effect of SIH and DH on the outcomes of patients. Results: The SIH (median [interquartile range: Q1–Q3], 13 [9–24]) demonstrated a significantly higher Injury Severity Score (ISS) than NDN (9 [4–10]), DN (9 [4–9]), and DH (9 [5–13]). SIH and DH had a 12.3-fold (95% confidence interval [CI] 9.31–16.14; p < 0.001) and 2.4-fold (95% CI 1.71–3.45; p < 0.001) higher odds of mortality, respectively, when compared to NDN. However, in the selected propensity-score-matched patient population, SIH had a 3.0-fold higher odd ratio of mortality (95% CI 1.96–4.49; p < 0.001) than NDN, but DH did not have a significantly higher mortality (odds ratio 1.2, 95% CI 0.99–1.38; p = 0.065). In addition, SIH had 2.4-fold higher odds of mortality (95% CI 1.46–4.04; p = 0.001) than DH. These results suggest that the characteristics and injury severity of the trauma patients contributed to the higher mortality of these patients with hyperglycemia upon admission, and that the pathophysiological effect of SIH was different from that of DH. Conclusions: Although there were worse mortality outcomes among trauma patients presenting with hyperglycemia, this effect was only seen in patients with SIH, but not DH when controlling for age, sex, pre-existed co-morbidities, and ISS. Full article
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15 pages, 196 KiB  
Review
Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation
by B. Roy Frieden
Entropy 2015, 17(11), 7453-7467; https://doi.org/10.3390/e17117453 - 28 Oct 2015
Viewed by 4393
Abstract
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering [...] Read more.
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
23 pages, 1274 KiB  
Article
Wavelet q-Fisher Information for Scaling Signal Analysis
by Julio Ramírez-Pacheco, Deni Torres-Román, Jesús Argaez-Xool, Luis Rizo-Dominguez, Joel Trejo-Sanchez and Francisco Manzano-Pinzón
Entropy 2012, 14(8), 1478-1500; https://doi.org/10.3390/e14081478 - 8 Aug 2012
Cited by 5 | Viewed by 6706
Abstract
Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides [...] Read more.
Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented. Full article
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