Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

The effect of carbohydrate mouth rinsing on fencing performance and cognitive function following fatigue-inducing fencing

This study investigated the impact that mouth rinsing carbohydrate solution has on skill-specific performance and reaction time following a fatigue inducing bout of fencing in epee fencers. Nine healthy, national level epee fencers visited a laboratory on 2 occasions, separated by a minimum of 5 days, to complete a 1-minute lunge test and Stroop test pre and post fatigue. Heart rate and ratings of perceived exertion (RPE) were recorded during completion of the fatiguing protocol. Between fights the participants mouth rinsed for 10 seconds, either 25ml of 6.7% maltodextrin solution (MALT) or water (PLAC). Blood lactate and glucose were recorded at baseline, pre- and post-testing. Results showed an increase in heart rate and overall RPE over time in both conditions. There were no differences in blood glucose (F(1,8)=.63, P=.4, ηp=.07) or blood lactate levels (F(1,8)=.12, P=.70, ηp=.01) between conditions as a function of time. There was a significant improvement in lunge test accuracy during the MALT trial (F(1,8)=5.21, P=.05, ηp=.40) with an increase from pre (81.2 ±8.3%) to post (87.6 ±9.4%), whereas there was no significant change during the placebo (pre 82.1 ±8.8%, post 78.8 ±6.4%). There were no recorded differences between conditions in response time to congruent (F(1,8)=.33, P=.58, ηp=.04) or incongruent stimuli (F(1,8)=.19, P=.68, ηp=.02). The study indicates that when fatigued mouth rinsing MALT significantly improves accuracy of skill-specific fencing performance but no corresponding influence on reaction time was observed.

Quantitative evaluation of visual function 12 months after bilateral implantation of a diffractive trifocal IOL

PURPOSE: To quantitatively evaluate visual function 12 months after bilateral implantation of the Physiol FineVision® trifocal intraocular lens (IOL) and to compare these results with those obtained in the first postoperative month. METHODS: In this prospective case series, 20 eyes of 10 consecutive patients were included. Monocular and binocular, uncorrected and corrected visual acuities (distance, near, and intermediate) were measured. Metrovision® was used to test contrast sensitivity under static and dynamic conditions, both in photopic and low-mesopic settings. The same software was used for pupillometry and glare evaluation. Motion, achromatic, and chromatic contrast discrimination were tested using 2 innovative psychophysical tests. A complete ophthalmologic examination was performed preoperatively and at 1, 3, 6, and 12 months postoperatively. Psychophysical tests were performed 1 month after surgery and repeated 12 months postoperatively. RESULTS: Final distance uncorrected visual acuity (VA) was 0.00 ± 0.08 and distance corrected VA was 0.00 ± 0.05 logMAR. Distance corrected near VA was 0.00 ± 0.09 and distance corrected intermediate VA was 0.00 ± 0.06 logMAR. Glare testing, pupillometry, contrast sensitivity, motion, and chromatic and achromatic contrast discrimination did not differ significantly between the first and last visit (p>0.05) or when compared to an age-matched control group (p>0.05). CONCLUSIONS: The Physiol FineVision® trifocal IOL provided satisfactory full range of vision and quality of vision parameters 12 months after surgery. Visual acuity and psychophysical tests did not vary significantly between the first and last visit.

Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

SMS length and function: A comparative study of 13- to 18-year-old girls and boys

International audience

Assessment of iodine intake and related cognitive function impairments in elementary schoolchildren from Terceira Island, Azores (Portugal)

Dissertação de Mestrado, Ciências Biomédicas, 28 de Junho de 2016, Universidade dos Açores.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Compressão fractal de imagens

Neste trabalho será apresentado um método recente de compressão de imagens baseado na teoria dos Sistemas de Funções Iteradas (SFI), designado por Compressão Fractal. Descrever-se-á um modelo contínuo para a compressão fractal sobre o espaço métrico completo Lp, onde será definido um operador de transformação fractal contractivo associado a um SFI local com aplicações. Antes disso, será introduzida a teoria dos SFIs no espaço de Hausdorff ou espaço fractal, a teoria dos SFIs Locais - uma generalização dos SFIs - e dos SFIs no espaço Lp. Fornecida a fundamentação teórica para o método será apresentado detalhadamente o algoritmo de compressão fractal. Serão também descritas algumas estratégias de particionamento necessárias para encontrar o SFI com aplicações, assim como, algumas estratégias para tentar colmatar o maior entrave da compressão fractal: a complexidade de codificação. Esta dissertação assumirá essencialmente um carácter mais teórico e descritivo do método de compressão fractal, e de algumas técnicas, já implementadas, para melhorar a sua eficácia.

STRUCTURE AND FUNCTION OF THE GROUP III CHAPERONINS, A UNIQUE CLADE OF PROTEIN FOLDING NANOMACHINES

The survival and descent of cells is universally dependent on maintaining their proteins in a properly folded condition. It is widely accepted that the information for the folding of the nascent polypeptide chain into a native protein is encrypted in the amino acid sequence, and the Nobel Laureate Christian Anfinsen was the first to demonstrate that a protein could spontaneously refold after complete unfolding. However, it became clear that the observed folding rates for many proteins were much slower than rates estimated in vivo. This led to the recognition of required protein-protein interactions that promote proper folding. A unique group of proteins, the molecular chaperones, are responsible for maintaining protein homeostasis during normal growth as well as stress conditions. Chaperonins (CPNs) are ubiquitous and essential chaperones. They form ATP-dependent, hollow complexes that encapsulate polypeptides in two back-to-back stacked multisubunit rings, facilitating protein folding through highly cooperative allosteric articulation. CPNs are usually classified into Group I and Group II. Here, I report the characterization of a novel CPN belonging to a third Group, recently discovered in bacteria. Group III CPNs have close phylogenetic association to the Group II CPNs found in Archaea and Eukarya, and may be a relic of the Last Common Ancestor of the CPN family. The gene encoding the Group III CPN from Carboxydothermus hydrogenoformans and Candidatus Desulforudis audaxviator was cloned in E. coli and overexpressed in order to both characterize the protein and to demonstrate its ability to function as an ATPase chaperone. The opening and closing cycle of the Chy chaperonin was examined via site-directed mutations affecting the ATP binding site at R155. To relate the mutational analysis to the structure of the CPN, the crystal structure of both the AMP-PNP (an ATP analogue) and ADP bound forms were obtained in collaboration with Sun-Shin Cha in Seoul, South Korea. The ADP and ATP binding site substitutions resulted in frozen forms of the structures in open and closed conformations. From this, mutants were designed to validate hypotheses regarding key ATP interacting sites as well as important stabilizing interactions, and to observe the physical properties of the resulting complexes by calorimetry.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

The aim of this paper is to present new results on H-infinity control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H-infinity analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from H-infinity theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.

Development of a Predictive Control Function for a Plug-in Hybrid Electric Vehicle with Electrically-heated Catalyst

This master thesis work is focused on the development of a predictive EHC control function for a diesel plug-in hybrid electric vehicle equipped with a EURO 7 compliant exhaust aftertreatment system (EATS), with the purpose of showing the advantages provided by the implementation of a predictive control strategy with respect to a rule-based one. A preliminary step will be the definition of an accurate powertrain and EATS physical model, starting from already existing and validated applications. Then, a rule-based control strategy managing the torque split between the electric motor (EM) and the internal combustion engine (ICE) will be developed and calibrated, with the main target of limiting tailpipe NOx emission by taking into account EM and ICE operating conditions together with EATS conversion efficiency. The information available from vehicle connectivity will be used to reconstruct the future driving scenario, also referred to as electronic horizon (eHorizon), and in particular to predict ICE first start. Based on this knowledge, an EATS pre-heating phase can be planned to avoid low pollutant conversion efficiencies, thus preventing high NOx emission due to engine cold start. Consequently, the final NOx emission over the complete driving cycle will be strongly reduced, allowing to comply with the limits potentially set by the incoming EURO 7 regulation. Moreover, given the same NOx emission target, the gain achieved thanks to the implementation of an EHC predictive control function will allow to consider a simplified EATS layout, thus reducing the related manufacturing cost. The promising results achieved in terms of NOx emission reduction show the effectiveness of the application of a predictive control strategy focused on EATS thermal management and highlight the potential of a complete integration and parallel development of involved vehicle physical systems, control software and connectivity data management.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.