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It is shown that in the "Comment on 'Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass,"' three crucial observations have gone unnoticed, thus restricting its conclusion on the legitimacy of the Langevin equation for a position-dependent mass, Eq. (46) of da Costa et al. [Phys. Rev. E 102, 062105 (2020)2470-004510.1103/PhysRevE.102.062105].

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The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n-s=∏pprime11-p-s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane z and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive entropy Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡-k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function lnqz≡z1-q-11-q(ln1z=lnz). It is already known that this function paves the way for the emergence of a q-generalized algebra, using q-numbers defined as ⟨x⟩q≡elnqx, which recover the number x for q=1. The q-prime numbers are then defined as the q-natural numbers ⟨n⟩q≡elnqn(n=1,2,3,⋯), where n is a prime number p=2,3,5,7,⋯ We show that, for any value of q, infinitely many q-prime numbers exist; for q≤1 they diverge for increasing prime number, whereas they converge for q>1; the standard prime numbers are recovered for q=1. For q≤1, we generalize the ζ(s) function as follows: ζq(s)≡⟨ζ(s)⟩q (s∈R). We show that this function appears to diverge at s=1+0, ∀q. Also, we alternatively define, for q≤1, ζq∑(s)≡∑n=1∞1⟨n⟩qs=1+1⟨2⟩qs+⋯ and ζq∏(s)≡∏pprime11-⟨p⟩q-s=11-⟨2⟩q-s11-⟨3⟩q-s11-⟨5⟩q-s⋯, which, for q<1, generically satisfy ζq∑(s)<ζq∏(s), in variance with the q=1 case, where of course ζ1∑(s)=ζ1∏(s).

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We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space where the linear (nonlinear) character of the FPE is associated with the employed deformed linear (nonlinear) derivative. The FPE for an inhomogeneous medium with a position-dependent diffusion coefficient is equivalent to a deformed FPE within a deformed space, described by generalized derivatives, and constant diffusion coefficient. The deformed FPE is consistent with the diffusion equation for inhomogeneous media when the temperature and the mobility have the same position-dependent functional form as well as with the nonlinear Langevin approach. The deformed version of the H-theorem permits to express the Boltzmann-Gibbs entropic functional as a sum of two contributions, one from the particles and the other from the inhomogeneous medium. The formalism is illustrated with the infinite square well and the confining potential with linear drift coefficient. Connections between superstatistics and position-dependent Langevin equations are also discussed.

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Chitin is a structural endogenous carbohydrate, which is a major component of fungal cell walls and arthropod exoskeletons. A renewable resource and the second most abundant polysaccharide in nature after cellulose, chitin is currently used for waste water clearing, cosmetics, medical, and veterinary applications. This work comprises data mining of protein sequences related to the chitin metabolic pathway of completely sequenced genomes of extant organisms pertaining to the three life domains, followed by meta-analysis using traditional sequence similarity comparison and complex network approaches. Complex networks involving proteins of the chitin metabolic pathway in extant organisms were constructed based on protein sequence similarity. Several usual network indices were estimated in order to obtain information on the topology of these networks, including those related to higher order neighborhood properties. Due to the assumed evolutionary character of the system, we also discuss issues related to modularity properties, with the concept of edge betweenness playing a particularly important role in our analysis. Complex network approach correctly identifies clusters of organisms that belong to phylogenetic groups without any a priori knowledge about the biological features of the investigated protein sequences. We envisage the prospect of using such a complex network approach as a high-throughput phylogenetic method.

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We consider nonequilibrium probabilistic dynamics in logisticlike maps x(t+1)=1-a|x(t)|(z), (z>1) at their chaos threshold: We first introduce many initial conditions within one among W>>1 intervals partitioning the phase space and focus on the unique value q(sen)<1 for which the entropic form S(q) identical with (1- summation operator Wp(q)(i))/(q-1) linearly increases with time. We then verify that S(q(sen))(t)-S(q(sen))( infinity ) vanishes like t(-1/[q(rel)(W)-1]) [q(rel)(W)>1]. We finally exhibit a new finite-size scaling, q(rel)( infinity )-q(rel)(W) proportional, variant W(-|q(sen)|). This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

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Se estudió el efecto protector de una decocción de las hojas de la planta Cymbopogon citratus (DC.) Stapf. (caña santa o caña de limón) frente al daño genético inducido por los agentes oxidantes H2O2 y etilnitrosourea (ENU). Se utilizó para ello un modelo esperimental in vitro y otro in vivo: cultivo de células de ovario de Hamster chino (CHO) y el insecto Drosophila melanogaster, respectivamente. La capacidad de formar colonias de la línea celular CHO, fue el indicador de toxicidad utilizado para evaluar 5 concentraciones (0,1; 1; 5; 10; 15 porciento) de la decocción de caña santa, en tanto que el porcentaje de sobrevivencia de adultos se usó para evaluar el efecto tóxico de 4 concentraciones de esta (5; 25; 50; 100 porciento) sobre las larvas mwh + / + flr3 de Drosophila melanogaster; en ambos casos los resultados evidenciaron efectos tóxicos dependientes de las concentraciones utilizadas. Los estudios citofluorimétricos con diclorofluoresceína-diacetato en células CHO permitieron demostrar la capacidad antioxidante de la decocción de caña santa. Dosis no tóxicas de 0,1; 1 y 5 porciento produjeron reducciones significativas del estrés oxidativo causado por el H2O2. La genotoxicidad y antigenotoxicidad de diferentes concentraciones de la decocción fueron evaluadas mediante los ensayos de aberraciones cromosómicas en células CHO y el SMART de alas de Drosophila melanogaster. Los resultados de actividad mutagénica obtenidos fueron negativos, en tanto que los correspondientes a la acción protectora de las concentraciones probadas reafirmaron la capacidad antioxidante mostrada por el extracto vegetal

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