Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form $$x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon),$$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m$ are piecewise $C^{k+1}$ functions and $T$-periodic in the variable $t$. Assuming that the unperturbed system $x'=F_0(t,x)$ has a $d$-dimensional submanifold of periodic solutions with $d<m$, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated $T$-periodic solutions of the above differential system

Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant

Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. Working with these normal forms we complete the characterization of the phase portraits in QS3 having a Darboux invariant of the form f(x, y)est, with s ∈ R

On the periodic solutions of the Milchelson continuous and discontinuous piecewise linear differential system

Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michel- son differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. The tools here used can be applied to general nonsmooth differential systems

Applied immuno-epidemiological research: an approach for integrating existing knowledge into the statistical analysis of multiple immune markers.

BACKGROUND: Immunologists often measure several correlated immunological markers, such as concentrations of different cytokines produced by different immune cells and/or measured under different conditions, to draw insights from complex immunological mechanisms. Although there have been recent methodological efforts to improve the statistical analysis of immunological data, a framework is still needed for the simultaneous analysis of multiple, often correlated, immune markers. This framework would allow the immunologists' hypotheses about the underlying biological mechanisms to be integrated. RESULTS: We present an analytical approach for statistical analysis of correlated immune markers, such as those commonly collected in modern immuno-epidemiological studies. We demonstrate i) how to deal with interdependencies among multiple measurements of the same immune marker, ii) how to analyse association patterns among different markers, iii) how to aggregate different measures and/or markers to immunological summary scores, iv) how to model the inter-relationships among these scores, and v) how to use these scores in epidemiological association analyses. We illustrate the application of our approach to multiple cytokine measurements from 818 children enrolled in a large immuno-epidemiological study (SCAALA Salvador), which aimed to quantify the major immunological mechanisms underlying atopic diseases or asthma. We demonstrate how to aggregate systematically the information captured in multiple cytokine measurements to immunological summary scores aimed at reflecting the presumed underlying immunological mechanisms (Th1/Th2 balance and immune regulatory network). We show how these aggregated immune scores can be used as predictors in regression models with outcomes of immunological studies (e.g. specific IgE) and compare the results to those obtained by a traditional multivariate regression approach. CONCLUSION: The proposed analytical approach may be especially useful to quantify complex immune responses in immuno-epidemiological studies, where investigators examine the relationship among epidemiological patterns, immune response, and disease outcomes

Identification of Eschweilenol C in derivative of Terminalia fagifolia Mart. and green synthesis of bioactive and biocompatible silver nanoparticles

A green synthetic route was developed to prepare silver nanoparticles (AgNPs) in aqueous solution for biological applications. Eschweilenol C, a compound derivative ellagic acid was identified as the main constituent of the aqueous fraction of the ethanolic extract of Terminalia fagifolia Mart. by NMR analysis. In the green synthesis, the ethanolic extract of T. fagifolia and its aqueous fraction were used to promote silver reduction and nanoparticle stabilization. The synthesized AgNPs presented a spherical or polygonal morphology shape by TEM analysis and AgNPs showed high levels of antioxidant and considerable antibacterial and antifungal activities. Synthesized nanoparticles presented significant antioxidant activity by sequestration of DPPH and ABTS radicals, in addition to iron reduction (FRAP assay) and measurement of antioxidant capacity in ORAC units, in addition, AgNP synthesized with the aqueous fraction also demonstrated antioxidant potential in microglial cells. Gram-positive and Gram-negative bacteria were susceptible to growth inhibition by the nanoparticles, among which the AgNPs formed by the ethanolic extract was the most effective. The data obtained by AFM images suggested that AgNPs could lead to the lysis of bacteria and subsequent death. The antifungal assays showed high efficiency against yeasts and dermatophytes. This work represents the first description of antifungal activity by AgNPs against Fonsecaea pedrosoi, the etiologic agent of chromoblastomycosis. In relation to biocompatibility, the AgNPs induced lower haemolysis than AgNO3.We thank Herbert Kogler and Reinhard Wimmer for the identification of Eschweilenol C. The NMR laboratory at Aalborg University is supported by the Obel Family, SparNord and Carlsberg foundations.The authors are grateful to Carla Eiras (LIMAV/CT/UFPI) and to FCT and EU for financial support through project UID/QUI/50006/2013– POCI-01-0145-FEDER-007265 from COMPETE and projectNORTE-01-0145-FEDER-000011 from COMPETE. Thanks to Andreia Pinto for help with the TEM measurements at Instituto de Medicina Molecular (IMM). This work was supported by the Histology and Comparative Pathology Laboratory of the IMMinfo:eu-repo/semantics/publishedVersio

Identification of metabolic pathways influenced by the G-protein coupled receptors GprB and GprD in Aspergillus nidulans

Heterotrimeric G-protein-mediated signaling pathways play a pivotal role in transmembrane signaling in eukaryotes. Our main aim was to identify signaling pathways regulated by A. nidulans GprB and GprD G-protein coupled receptors (GPCRs). When these two null mutant strains were compared to the wild-type strain, the DeltagprB mutant showed an increased protein kinase A (PKA) activity while growing in glucose 1% and during starvation. In contrast, the DeltagprD has a much lower PKA activity upon starvation. Transcriptomics and (1)H NMR-based metabolomics were performed on two single null mutants grown on glucose. We noted modulation in the expression of 11 secondary metabolism gene clusters when the DeltagprB and DeltagprD mutant strains were grown in 1% glucose. Several members of the sterigmatocystin-aflatoxin gene cluster presented down-regulation in both mutant strains. The genes of the NR-PKS monodictyphenone biosynthesis cluster had overall increased mRNA accumulation in DeltagprB, while in the DeltagprD mutant strain the genes had decreased mRNA accumulation. Principal component analysis of the metabolomic data demonstrated that there was a significant metabolite shift in the DeltagprD strain. The (1)H NMR analysis revealed significant expression of essential amino acids with elevated levels in the DeltagprD strain, compared to the wild-type and DeltagprB strains. With the results, we demonstrated the differential expression of a variety of genes related mainly to secondary metabolism, sexual development, stress signaling, and amino acid metabolism. We propose that the absence of GPCRs triggered stress responses at the genetic level. The data suggested an intimate relationship among different G-protein coupled receptors, fine-tune regulation of secondary and amino acid metabolisms, and fungal development