Fractional Newton-Raphson Method Accelerated with Aitken's Method

The Newton-Raphson (N-R) method is characterized by the fact that generating a divergent sequence can lead to the creation of a fractal, on the other hand the order of the fractional derivatives seems to be closely related to the fractal dimension, based on the above, a method was developed that makes use of the N-R method and the fractional derivative of Riemann-Liouville (R-L) that has been named as the Fractional Newton-Raphson (F N-R) method. In the following work we present a way to obtain the convergence of the F N-R method, which seems to be at least linearly convergent for the case where the order $\alpha$ of the derivative is different from one, a simplified way to construct the fractional derivative and fractional integral operators of R-L is presented, an introduction to the Aitken's method is made and it is explained why it has the capacity to accelerate the convergence of iterative methods to finally present the results that were obtained when implementing the Aitken's method in F N-R method.Comment: Newton-Raphson Method, Fractional Calculus, Fractional Derivative of Riemann-Liouville, Method of Aitken. arXiv admin note: substantial text overlap with arXiv:1710.0763

Cannabidiol Attenuates Sensorimotor Gating Disruption and Molecular Changes Induced by Chronic Antagonism of NMDA receptors in Mice

Background: Preclinical and clinical data suggest that cannabidiol (CBD), a major non-psychotomimetic compound from Cannabis sativa, induces antipsychotic-like effects. However, the antipsychotic properties of repeated CBD treatment have been poorly investigated. Behavioral changes induced by repeated treatment with glutamate N-methyl-D-aspartate receptor (NMDAR) antagonists have been proposed as an animal model of schizophrenia-like signs. In the present study, we evaluated if repeated treatment with CBD would attenuate the behavioral and molecular modifications induced by chronic administration of one of these antagonists, MK-801. Methods: Male C57BL/6J mice received daily i.p. injections of MK-801 (0.1, 0.5, or 1mg/kg) for 14, 21, or 28 days. Twenty-four hours after the last injection, animals were submitted to the prepulse inhibition (PPI) test. After that, we investigated if repeated treatment with CBD (15, 30, and 60mg/kg) would attenuate the PPI impairment induced by chronic treatment with MK-801 (1mg/kg; 28 days). CBD treatment began on the 6th day after the start of MK-801 administration and continued until the end of the treatment. Immediately after the PPI, the mice brains were removed and processed to evaluate the molecular changes. We measured changes in FosB/ΔFosB and parvalbumin (PV) expression, a marker of neuronal activity and a calciumbinding protein expressed in a subclass of GABAergic interneurons, respectively. Changes in mRNA expression of the NMDAR GluN1 subunit gene (GRN1) were also evaluated. CBD effects were compared to those induced by the atypical antipsychotic clozapine. Results: MK-801 administration at the dose of 1mg/kg for 28 days impaired PPI responses. Chronic treatment with CBD (30 and 60mg/kg) attenuated PPI impairment. MK-801 treatment increased FosB/ΔFosB expression and decreased PV expression in the medial prefrontal cortex. A decreased mRNA level of GRN1 in the hippocampus was also observed. All the molecular changes were attenuated by CBD. CBD by itself did not induce any effect. Moreover, CBD effects were similar to those induced by repeated clozapine treatment

The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

Prolonged maternal separation induces undernutrition and systemic inflammation with disrupted hippocampal development in mice

Objective: Prolonged maternal separation (PMS) in the first 2 wk of life has been associated with poor growth with lasting effects in brain structure and function. This study aimed to investigate whether PMS-induced undernutrition could cause systemic inflammation and changes in nutrition-related hormonal levels, affecting hippocampal structure and neurotransmission in C57BL/6J suckling mice. Methods: This study assessed mouse growth parameters coupled with insulin-like growth factor-1 (IGF-1) serum levels. In addition, leptin, adiponectin, and corticosterone serum levels were measured following PMS. Hippocampal stereology and the amino acid levels were also assessed. Furthermore, we measured myelin basic protein and synapthophysin (SYN) expression in the overall brain tissue and hippocampal SYN immunolabeling. For behavioral tests, we analyzed the ontogeny of selected neonatal reflexes. PMS was induced by separating half the pups in each litter from their lactating dams for defined periods each day (4 h on day 1, 8 h on day 2, and 12 h thereafter). A total of 67 suckling pups were used in this study. Results: PMS induced significant slowdown in weight gain and growth impairment. Significant reductions in serum leptin and IGF-1 levels were found following PMS. Total CA3 area and volume were reduced, specifically affecting the pyramidal layer in PMS mice. CA1 pyramidal layer area was also reduced. Overall hippocampal SYN immunolabeling was lower, especially in CA3 field and dentate gyrus. Furthermore, PMS reduced hippocampal aspartate, glutamate, and gammaaminobutyric acid levels, as compared with unseparated controls. Conclusion: These findings suggest that PMS causes significant growth deficits and alterations in hippocampal morphology and neurotransmission.This work was supported in part by National Institutes of Health (NIH) research grant 5R01HD053131, funded by the Eunice Kennedy Shriver National Institute of Child Health and Human Development and the NIH Office of Dietary Supplements, and Brazilian grants from CNPq and CAPES (Grant # RO1 HD053131). The authors would like to thank Dr. Patricia Foley for veterinarian technical support and Dr. Jose Paulo Andrade for the excellent comments and suggestions to improve this manuscript. N.S. contributed with the stereological studies. I.L.F. and R.B.O. contributed with the behavioral studies. I.L.F., R.B.O., and R.L.G. contributed with the study design, study analysis, and manuscript preparation. G.A.M. and P.B.F. contributed with neurochemical brain analyses. J.I.A.L. and G.M.A. contributed with hormonal and CRP serum analyses. D.G.C., K.M.C., and R.S.R. contributed with animal experimentation and data collection

Effects of ultrasound treatments on wine microorganisms

Ultrasound is one of the most promising non-thermal an emerging technique in food technology. The objective of the present work was to evaluate the effect of different ultrasonic treatments on the most important wine microbiota (Saccharomyces and non-Saccharomyces yeasts and lactic acid bacteria). Two stages were carried out: the assessment step, where six different ultrasonic treatments (with varying power, time, and pulses) were used on Saccharomyces cerevisiae, Brettanomyces spp., and Lactiplantibacillus plantarum; and the validation step, where two chosen ultrasonic treatments were used on Zigosaccharomyces bailli, Brettanomyces spp., Saccharomyces cerevisiae, Saccharomyces bayanus, Pichia membranifaciens, Schizosaccharomyces pombe, and Hanseniaspora osmophila. The most sensitive microorganism was Brettanomyces spp., and the most resistant was Lactiplantibacillus plantarum. Ultrasonic treatments had varying effects on vitality (delay of growth or maximum OD reduction) and on viability (reduction of microbial growth)

Inflammation, genetic background and longevity

Ageing is an inexorable intrinsic process that affects all cells, tissues, organs and individuals. Due to a diminished homeostasis and increased organism frailty, ageing causes a reduction of the response to environmental stimuli and, in general, is associated to an increased predisposition to illness and death. Actually, it is characterized by a state of reduced ability to maintain health and general homeodynamics of the organism.Alarge part of the ageing phenotype is explained by an imbalance between inflammatory and anti-inflammatory networks, which results in the low grade chronic pro-inflammatory status of ageing, ‘‘inflamm-ageing’’. It is strictly linked to immunosenescence, and on the whole they are the major contributory factors to the increased frequency of morbidity and mortality among elderly. Inflammageing is compatible with longevity; even if centenarians have an increased level of inflammatory mediators in comparison to old subjects and they are very frail, they also have high level of anti-inflammatory cytokines together with protective genotypes. Actually, data on case control studies performed in Italian centenarians suggest that a pro-inflammatory genotype is unfavourable to reach extreme longevity in good health and likely favours the onset of age-related diseases such as cardiovascular diseases and Alzheimer’s disease, the leading causes of mortality and disability in the elderly. However, many associations between gene variants and longevity have been found only in Italian population. This should not be unexpected, since ageing and longevity are complex traits resulting not only and not exclusively from genetics, but rather from the interactions between genetics, environment and chance

Variación altitudinal en caracteres morfológicos de Pinus patula en el estado de Oaxaca (México) y su uso en la zonificación

Populations of forest species with a distribution across altitudinal gradients tend to differ in morphology, allowing zoning for conducting seed movement. The pattern of variation is not known to many Mexican pine species. The altitudinal pattern of morphological variation was explored in needles, cones and seeds of 13 Pinus patula populations sampled from the Native Indian Community forest of Ixtlán de Juárez, Oaxaca, Mexico, along an altitudinal gradient (from 2,450 to 3,050 m a.s.l); needles and cones being collected every 50 m of altitudinal step. Significant differences among populations and among trees within populations were detected for all the evaluated traits. The correlation was positive between the altitude of origin of populations and keel width, cone width and leaf-sheaths length; whereas it was negative between needle length and altitude of origin of populations. Using the phenotypic variation of the needle length we suggest a provisional delineation of two altitudinal seed zones (zone I: 2,150 to 2,600 m; zone II: 2,600 to 3,050 m), as a guideline to decide seed movements in reforestation programs. Altitudinal zones obtained in this work have wider altitudinal range per zone (meaning a more liberal seed movement) than the one obtained from twenty four-months-old seedling height growing in a provenance test, and show that it is possible to make provisional altitudinal zoning based on patterns of phenotypic variation across environmental gradients.Las poblaciones de especies forestales con distribución a través de gradientes altitudinales tienden a diferenciarse en sus caracteres morfológicos, lo que determina zonificaciones para el movimiento de semillas. El patrón de variación es desconocido para muchas especies de pinos mexicanos. Se exploró el patrón de variación morfológica en acículas, conos y semillas de 13 poblaciones de Pinus patula, muestreadas en bosques de la comunidad indígena de Ixtlán de Juárez, Oaxaca, México, a lo largo de un gradiente altitudinal (2.450 a 3.050 m s.n.m.), cada 50 m de diferencia altitudinal. Se encontró variación significativa entre poblaciones y entre árboles dentro de poblaciones para todas las características evaluadas. La correlación entre la altitud de las poblaciones y el ancho de quilla, el grueso del cono y la longitud de la vaina de la acícula fue positiva, mientras que entre la longitud de acícula y la elevación fue negativa. Según la variación fenotípica de la longitud de acícula, se sugiere la delimitación provisional de dos zonas semilleras altitudinales (zona I: 2.150 a 2.600 m; zona II: 2.600 a 3.050 m), como criterio para decidir el movimiento de semillas en programas de reforestación. La zonificación altitudinal obtenida en el presente trabajo tiene mayor amplitud altitudinal por cada zona (lo que significa movimiento más libre de las semillas), que el obtenido a partir del crecimiento en altura de las plantas a los 24 meses de edad en ensayo de procedencias y muestra cómo realizar zonificaciones preliminares según el patrón de variación fenotípica en gradientes ambientales

Waveforms of molecular oscillations reveal circadian timekeeping mechanisms

Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian clocks. We derive a mathematical framework where waveforms do reveal hidden biochemical mechanisms of circadian timekeeping. We find that the cost of synthesizing proteins with particular waveforms can be substantially reduced by rhythmic protein half-lives over time, as supported by previous plant and mammalian data, as well as our own seedling experiment. We also find that previously-enigmatic, cyclic expression of positive arm components within the mammalian and insect clocks allows both a broad range of peak time differences between protein waveforms and the symmetries of the waveforms about the peak times. Such various peak-time differences may facilitate tissue-specific or developmental stage-specific multicellular processes. Our waveform-guided approach can be extended to various biological oscillators, including cell-cycle and synthetic genetic oscillators.Comment: Supplementary material is available at the journal websit