Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

CO2-response function of radiation use efficiency in rice for climate change scenarios

The objective of this work was to evaluate a generalized response function to the atmospheric CO2 concentration [f(CO2)] by the radiation use efficiency (RUE) in rice. Experimental data on RUE at different CO2 concentrations were collected from rice trials performed in several locations around the world. RUE data were then normalized, so that all RUE at current CO2 concentration were equal to 1. The response function was obtained by fitting normalized RUE versus CO2 concentration to a Morgan-Mercer-Flodin (MMF) function, and by using Marquardt's method to estimate the model coefficients. Goodness of fit was measured by the standard deviation of the estimated coefficients, the coefficient of determination (R²), and the root mean square error (RMSE). The f(CO2) describes a nonlinear sigmoidal response of RUE in rice, in function of the atmospheric CO2 concentration, which has an ecophysiological background, and, therefore, renders a robust function that can be easily coupled to rice simulation models, besides covering the range of CO2 emissions for the next generation of climate scenarios for the 21st century.

Multicontrast connectometry: A new tool to assess cerebellum alterations in early relapsing-remitting multiple sclerosis.

BACKGROUND: Cerebellar pathology occurs in late multiple sclerosis (MS) but little is known about cerebellar changes during early disease stages. In this study, we propose a new multicontrast "connectometry" approach to assess the structural and functional integrity of cerebellar networks and connectivity in early MS. METHODS: We used diffusion spectrum and resting-state functional MRI (rs-fMRI) to establish the structural and functional cerebellar connectomes in 28 early relapsing-remitting MS patients and 16 healthy controls (HC). We performed multicontrast "connectometry" by quantifying multiple MRI parameters along the structural tracts (generalized fractional anisotropy-GFA, T1/T2 relaxation times and magnetization transfer ratio) and functional connectivity measures. Subsequently, we assessed multivariate differences in local connections and network properties between MS and HC subjects; finally, we correlated detected alterations with lesion load, disease duration, and clinical scores. RESULTS: In MS patients, a subset of structural connections showed quantitative MRI changes suggesting loss of axonal microstructure and integrity (increased T1 and decreased GFA, P < 0.05). These alterations highly correlated with motor, memory and attention in patients, but were independent of cerebellar lesion load and disease duration. Neither network organization nor rs-fMRI abnormalities were observed at this early stage. CONCLUSION: Multicontrast cerebellar connectometry revealed subtle cerebellar alterations in MS patients, which were independent of conventional disease markers and highly correlated with patient function. Future work should assess the prognostic value of the observed damage. Hum Brain Mapp 36:1609-1619, 2015. © 2014 Wiley Periodicals, Inc.

Entropy Analysis of Industrial Accident Data Series

Complex industrial plants exhibit multiple interactions among smaller parts and with human operators. Failure in one part can propagate across subsystem boundaries causing a serious disaster. This paper analyzes the industrial accident data series in the perspective of dynamical systems. First, we process real world data and show that the statistics of the number of fatalities reveal features that are well described by power law (PL) distributions. For early years, the data reveal double PL behavior, while, for more recent time periods, a single PL fits better into the experimental data. Second, we analyze the entropy of the data series statistics over time. Third, we use the Kullback–Leibler divergence to compare the empirical data and multidimensional scaling (MDS) techniques for data analysis and visualization. Entropy-based analysis is adopted to assess complexity, having the advantage of yielding a single parameter to express relationships between the data. The classical and the generalized (fractional) entropy and Kullback–Leibler divergence are used. The generalized measures allow a clear identification of patterns embedded in the data.

Enhanced diastolic reflections on arterial pressure pulse during exercise recovery.

During recovery from a maximal or submaximal aerobic exercise, augmentation of central (aortic) systolic pressure by reflected pressure waves is blunted in healthy humans. However, the extent to which reflected pressure waves modify the central pulse in diastole in these conditions remains unknown. We evaluated systolic and diastolic central reflected waves in 11 endurance-trained athletes on recovery from a maximal running test on a treadmill (treadmill-max) and a 4000 m run in field conditions. On both occasions in each subject, the radial pulse was recorded with applanation tonometry in the resting preexercise state and then 5, 15, 25, 35, and 45 min after exercise termination. From the central waveform, as reconstructed by application of a generalized transfer function, we computed a systolic (AIx) and a diastolic index (AId) of pressure augmentation by reflections. At 5 min, both indices were below preexercise. At further time-points, AIx remained low, while AId progressively increased, to overshoot above preexercise at 45 min. The same behavior was observed with both exercise types. Beyond the first few minutes of recovery following either maximal or submaximal aerobic exercise, reflected waves selectively augment the central pressure pulse in diastole, at least in endurance-trained athletes.

Enhanced diastolic reflections on arterial pressure pulse during exercise recovery

RESUMEDurant la phase de récupération d'un exercice de course à pied d'intensité maximale ou submaximale, une augmentation de la pression artérielle systolique centrale (aortique) résultant de la réflexion des ondes de pouls sur l'arbre vasculaire est constatée chez l'individu en bonne santé. En diastole cependant, l'impact de la réflexion de ces ondes de pouls sur la pression centrale demeure inconnu durant la récupération d'un exercice.Nous avons évalué les ondes de pouls centrales systolique et diastolique chez onze athlètes d'endurance durant la phase de récupération d'un exercice de course à pied dans des conditions d'effort maximal (sur tapis de course) et lors d'un effort submaximal lors d'une course à pied de 4000 mètres en plein air sur terrain mixte.Pour chaque sujet et lors des deux exercices, l'onde de pouls a été mesurée au niveau radial par tonométrie d'aplanation durant une phase de repos précédant l'exercice, puis à 5, 15, 25, 35 et 45 minutes après la fin de l'exercice. En utilisant une fonction mathématique de transfert, l'onde de pouls centrale a été extrapolée à partir de l'onde de pouls radiale. En compilant la forme de l'onde de pouls centrale avec une mesure simultanée de la pression artérielle brachiale, un index d'augmentation de l'onde de pouls en systole (Alx) et en diastole (Als) peut être calculé, reflétant l'augmentation des pressions résultant de la réflexion des ondes sur l'arbre vasculaire périphérique.A 5 minutes de la fin de l'exercice, les deux index ont été mesurés moindres que ceux mesurés lors de la phase précédant celui-ci. Lors des mesures suivantes, Alx est resté bas, alors que Aid a progressivement augmenté pour finalement dépasser la valeur de repos après 45 minutes de récupération. Le même phénomène a été constaté pour les deux modalités d'exercice (maximal ou submaximal). Ainsi, au-delà de quelques minutes de récupération après un exercice de course d'intensité maximale ou submaximale, nous avons montré par ces investigations que les ondes de pouls réfléchies en périphérie augmentent de façon sélective la pression centrale en diastole chez l'athlète d'endurance.ABSTRACTDuring recovery from a maximal or submaximal aerobic exercise, augmentation of central (aortic) systolic pressure by reflected pressure waves is blunted in healthy humans. However, the extent to which reflected pressure waves modify the central pulse in diastole in these conditions remains unknown. We evaluated systolic and diastolic central reflected waves in 11 endurance-trained athletes on recovery from a maximal running test on a treadmill (treadmill-max) and a 4000m run in field conditions. On both occasions in each subject, the radial pulse was recorded with applanation tonometry in the resting preexercise state and then 5, 15, 25, 35, and 45 minutes after exercise termination. From the central waveform, as reconstructed by application of a generalized transfer function, we computed a systolic (Alx) and a diastolic index (Aid) of pressure augmentation by reflections. At 5 minutes, both indices were below preexercise. At further time-points, Alx remained low, while Aid progressively increased, to overshoot above preexercise at 45 minutes. The same behavior was observed with both exercise types. Beyond the first few minutes of recovery following either maximal or submaximal aerobic exercise, reflected waves selectively augment the central pressure pulse in diastole, at least in endurance- trained athletes.

Diffusion Spectrum Imaging after stroke shows structural changes in the contra-lateral motor network correlating with functional recovery

There is growing interest in understanding the role of the non-injured contra-lateral hemisphere in stroke recovery. In the experimental field, histological evidence has been reported that structural changes occur in the contra-lateral connectivity and circuits during stroke recovery. In humans, some recent imaging studies indicated that contra-lateral sub-cortical pathways and functional and structural cortical networks are remodeling, after stroke. Structural changes in the contra-lateral networks, however, have never been correlated to clinical recovery in patients. To determine the importance of the contra-lateral structural changes in post-stroke recovery, we selected a population of patients with motor deficits after stroke affecting the motor cortex and/or sub-cortical motor white matter. We explored i) the presence of Generalized Fractional Anisotropy (GFA) changes indicating structural alterations in the motor network of patientsâeuro? contra-lateral hemisphere as well as their longitudinal evolution ii) the correlation of GFA changes with patientsâeuro? clinical scores, stroke size and demographics data iii) and a predictive model.

Characterizing the connectome in schizophrenia with diffusion spectrum imaging.

Schizophrenia is a complex psychiatric disorder characterized by disabling symptoms and cognitive deficit. Recent neuroimaging findings suggest that large parts of the brain are affected by the disease, and that the capacity of functional integration between brain areas is decreased. In this study we questioned (i) which brain areas underlie the loss of network integration properties observed in the pathology, (ii) what is the topological role of the affected regions within the overall brain network and how this topological status might be altered in patients, and (iii) how white matter properties of tracts connecting affected regions may be disrupted. We acquired diffusion spectrum imaging (a technique sensitive to fiber crossing and slow diffusion compartment) data from 16 schizophrenia patients and 15 healthy controls, and investigated their weighted brain networks. The global connectivity analysis confirmed that patients present disrupted integration and segregation properties. The nodal analysis allowed identifying a distributed set of brain nodes affected in the pathology, including hubs and peripheral areas. To characterize the topological role of this affected core, we investigated the brain network shortest paths layout, and quantified the network damage after targeted attack toward the affected core. The centrality of the affected core was compromised in patients. Moreover the connectivity strength within the affected core, quantified with generalized fractional anisotropy and apparent diffusion coefficient, was altered in patients. Taken together, these findings suggest that the structural alterations and topological decentralization of the affected core might be major mechanisms underlying the schizophrenia dysconnectivity disorder. Hum Brain Mapp, 36:354-366, 2015. © 2014 Wiley Periodicals, Inc.

Structural abnormalities in the thalamus of migraineurs with aura: a multiparametric study at 3 T.

BACKGROUND AND OBJECTIVES: The thalamus exerts a pivotal role in pain processing and cortical excitability control, and migraine is characterized by repeated pain attacks and abnormal cortical habituation to excitatory stimuli. This work aimed at studying the microstructure of the thalamus in migraine patients using an innovative multiparametric approach at high-field magnetic resonance imaging (MRI). DESIGN: We examined 37 migraineurs (22 without aura, MWoA, and 15 with aura, MWA) as well as 20 healthy controls (HC) in a 3-T MRI equipped with a 32-channel coil. We acquired whole-brain T1 relaxation maps and computed magnetization transfer ratio (MTR), generalized fractional anisotropy, and T2* maps to probe microstructural and connectivity integrity and to assess iron deposition. We also correlated the obtained parametric values with the average monthly frequency of migraine attacks and disease duration. RESULTS: T1 relaxation time was significantly shorter in the thalamus of MWA patients compared with MWoA (P < 0.001) and HC (P ≤ 0.01); in addition, MTR was higher and T2* relaxation time was shorter in MWA than in MWoA patients (P < 0.05, respectively). These data reveal broad microstructural alterations in the thalamus of MWA patients compared with MWoA and HC, suggesting increased iron deposition and myelin content/cellularity. However, MWA and MWoA patients did not show any differences in the thalamic nucleus involved in pain processing in migraine. CONCLUSIONS: There are broad microstructural alterations in the thalamus of MWA patients that may underlie abnormal cortical excitability control leading to cortical spreading depression and visual aura.

A new early and automated MRI-based predictor of motor improvement after stroke.

OBJECTIVES: In this study, we investigated the structural plasticity of the contralesional motor network in ischemic stroke patients using diffusion magnetic resonance imaging (MRI) and explored a model that combines a MRI-based metric of contralesional network integrity and clinical data to predict functional outcome at 6 months after stroke. METHODS: MRI and clinical examinations were performed in 12 patients in the acute phase, at 1 and 6 months after stroke. Twelve age- and gender-matched controls underwent 2 MRIs 1 month apart. Structural remodeling after stroke was assessed using diffusion MRI with an automated measurement of generalized fractional anisotropy (GFA), which was calculated along connections between contralesional cortical motor areas. The predictive model of poststroke functional outcome was computed using a linear regression of acute GFA measures and the clinical assessment. RESULTS: GFA changes in the contralesional motor tracts were found in all patients and differed significantly from controls (0.001 ≤ p < 0.05). GFA changes in intrahemispheric and interhemispheric motor tracts correlated with age (p ≤ 0.01); those in intrahemispheric motor tracts correlated strongly with clinical scores and stroke sizes (p ≤ 0.001). GFA measured in the acute phase together with a routine motor score and age were a strong predictor of motor outcome at 6 months (r(2) = 0.96, p = 0.0002). CONCLUSION: These findings represent a proof of principle that contralesional diffusion MRI measures may provide reliable information for personalized rehabilitation planning after ischemic motor stroke. Neurology® 2012;79:39-46.