Antiprotozoal and Antibacterial Activity of Ravenelin,a Xanthone Isolated from the Endophytic Fungus Exserohilum rostratum

The natural compound ravenelin was isolated from the biomass extracts of Exserohilum rostratum fungus, and its antimicrobial, antiplasmodial, and trypanocidal activities were evaluated. Ravenelin was isolated by column chromatography and HPLC and identified by NMR and MS. The susceptibility of Gram-positive and Gram-negative bacteria strains to ravenelin was determined by microbroth dilution assay. Cytotoxicity was evaluated in hepatocarcinoma cells (HepG2) and BALB/c peritoneal macrophages by using MTT. SYBR Green I-based assay was used in the asexual stages of Plasmodium falciparum. Trypanocidal activity was tested against the epimastigote and intracellular amastigote forms of Trypanosoma cruzi. Ravenelin was active against Gram-positive bacteria strains, with emphasis on Bacillus subtilis (MIC value of 7.5 µM). Ravenelin’s antiparasitic activities were assessed against both the epimastigote (IC₅₀ value of 5 ± 1 µM) and the intracellular amastigote forms of T. cruzi (IC₅₀ value of 9 ± 2 µM), as well as against P. falciparum (IC₅₀ value of 3.4 ± 0.4 µM). Ravenelin showed low cytotoxic effects on both HepG2 (CC₅₀ > 50 µM) and peritoneal macrophage (CC₅₀ = 185 ± 1 µM) cells with attractive selectivity for the parasites (SI values > 15). These findings indicate that ravenelin is a natural compound with both antibacterial and antiparasitic activities, and considerable selectivity indexes. Therefore, ravenelin is an attractive candidate for hit-to-lead development.     

Heterocyclic compounds as antiviral drugs: Synthesis,structure–activity relationship and traditional applications

A virus outbreak challenges the economic, medical, and public health infrastructure worldwide. More than one virus capable of triggering diseases have been identified per year since 1972, which requires the development of new ways of treatment and prevention, however, such processes are not rapid and easy. With the pandemic scenario experienced since early 2020, several drugs with well-known purposes have gained prominence, due to speculation of their use in the treatment against the new coronavirus. Among the main drugs studied, the vast majority contain a heterocyclic structure. In this review, we presented the traditional and efficient synthesis of 15 drugs that have been studied for the COVID-19 treatment, containing in their structure heterocycles like indole, quinoline, pyrimidone, tetrahydrofuran, pyrrolidine, triazole, pyridazine, pyrazole, pyrrolopyrimidine, azetidine, pyrrolotriazine, pyrazine, tetrahydropyran, benzofuran, spiroketal, and thiazole. Furthermore, we have shown the original applications, as well as their structure–activity relationship and what is their situation as a drug candidate against COVID-19. Thus, the objective was to consolidate the main synthetic and pharmacological aspects involving clinically developed heterocycles that at some point were presented as promising against SARS-CoV-2.     

Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime

We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett  29 .     

On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

Heart rate variability analysis by chaotic global techniques in children with attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is characterized by decreased attention span, impulsiveness, and hyperactivity. Autonomic nervous system imbalance was previously described in this population. We aim to compare the autonomic function of children with ADHD and controls by analyzing heart rate variability (HRV). Children with ADHD (22 boys, mean age 9.964 years) and 28 controls (15 boys, mean age 9.857 years) rested in supine position with spontaneous breathing for 20 min. Heart rate was recorded beat by beat. HRV analysis was performed by use of chaotic global techniques. ADHD promoted an increase in the chaotic forward parameter. The algorithm which applied all three chaotic global parameters was only the second optimum statistically measured by Kruskal–Wallis (P < 0.0001) and low standard deviations. It was also highly influential by principal component analysis with almost all variation covered by the first two components. The third algorithm which lacked the (high spectral Detrended Fluctuation Analysis) parameter performed best statistically. However, we chose the algorithm which applied all three chaotic globals due to previous studies mentioned in the text—forward and inverse problems. Comparison of the autonomic function by analyzing HRV with chaotic global techniques suggests an increase in chaotic activity in children with ADHD in relation to the control group. © 2015 Wiley Periodicals, Inc. Complexity 21: 412–419, 2016     

Highly symmetric hypertopes

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytope theory, we introduce the concept of chirality, a property of orderly asymmetry occurring frequently in nature as a natural phenomenon. The main result in this paper is that automorphism groups of regular and chiral thin residually connected geometries need to be C-groups in the regular case and \({C^+}\)-groups in the chiral case.     

Eigenfunctions and Very Singular Similarity Solutions of Odd‐Order Nonlinear Dispersion PDEs: Toward a “Nonlinear Airy Function” and Others

Asymptotic properties of nonlinear dispersion equations (1) with fixed exponents n > 0 and p > n+ 1 , and their (2k+ 1) th‐order analogies are studied. The global in time similarity solutions, which lead to “nonlinear eigenfunctions” of the rescaled ordinary differential equations (ODEs), are constructed. The basic mathematical tools include a “homotopy‐deformation” approach, where the limit in the first equation in ( 1 ) turns out to be fruitful. At n= 0 the problem is reduced to the linear dispersion one: whose oscillatory fundamental solution via Airy’s classic function has been known since the nineteenth century. The corresponding Hermitian linear non‐self‐adjoint spectral theory giving a complete countable family of eigenfunctions was developed earlier in [ 1 ]. Various other nonlinear operator and numerical methods for ( 1 ) are also applied. As a key alternative, the “super‐nonlinear” limit , with the limit partial differential equation (PDE) admitting three almost “algebraically explicit” nonlinear eigenfunctions, is performed. For the second equation in ( 1 ), very singular similarity solutions (VSSs) are constructed. In particular, a “nonlinear bifurcation” phenomenon at critical values {p=p_l(n)}_l≥0 of the absorption exponents is discussed.     

On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle

We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph.     

On-off scheduling schemes for power-constrained electric vehicle charging

In this paper, we study the problem of establishing a dynamic charging schedule of electric vehicles (EVs) at a charging station, assuming that limited power implies that only a limited number of EVs can charge simultaneously. The only control we assume to be available to the charging station is the ability to (at any given time) turn on or off the power supply to any EV, with this tool we want to develop a charging schedule that will satisfy the energy demands of the EVs in their intended deadlines. We propose two distinct approaches to this problem: a discretized time version, based on a greedy-like algorithm, and a continuous time version, based on linear programming. We compare these two approaches and numerically study the improvement they yield in the efficiency of the charging procedure, when applied to simulated data based on real parking data. Finally, we illustrate the flexibility of the models by sketching several possible extensions.     

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a ₀ + a ₁ x ₁ + . . . + a _n x _n subject to certain constraints to solve the problem of minimizing a rational function of the form (a ₀ + a ₁ x ₁ + . . . + a _n x _n )/(b ₀ + b ₁ x ₁ + . . . + b _n x _n ) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo’s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo’s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an α-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an α-approximation (1/α-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.