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Realizou-se um experimento em casa de vegetação do Departamento de Ciência do Solo da Universidade Federal de Lavras, para avaliar o efeito do silício na nutrição mineral e na produção de matéria seca de plantas de moringa submetidas ao estresse salino. Utilizaram-se o esquema fatorial e o delineamento de blocos casualizados, com três repetições, e uma planta por vaso de 3 L de capacidade, em que o primeiro fator referiu-se às doses de NaCl (0, 30, 60, 90 e 120 mol m-3) e o segundo às doses de SiO2 (0, 0,5, 1,0 e 1,5 mol m-3), em solução de Hoagland & Arnon (1950) a 50 % da concentração normal. As soluções foram renovadas em intervalos de 10 dias e, aos 35 dias, após a aplicação dos tratamentos, as plantas foram colhidas, separadas em folhas, caule e raízes, secas, para determinação da produção de matéria seca, e moídas, para determinação dos teores de N, P, K, Ca, Mg, S, Na, Cl e Si. A partir dos teores, determinaram-se as relações Na/K, Na/Ca e Na/Mg e a translocação dos nutrientes para a parte aérea. Observou-se que a adição do Si elevou os teores de K e de Ca nas folhas e reduziu os de Na e as relações Na/K, Na/Ca e Na/Mg. O Si não reduziu os efeitos depressivos do NaCl na produção de matéria seca das plantas de moringa.

Na Relatividade Geral, em sistemas com uma massa dominante, a curvatura do espaço-tempo é descrita pela métrica de Schwarzschild. Contudo, obter seus coeficientes métricos do campo gravitacional desta massa exige, em geral, o uso de ferramentas matemáticas avançadas, como geometria diferencial e cálculo tensorial. Neste artigo, para obter tais coeficientes métricos, usamos o Teorema Egrégio de Gauss sobre curvatura espacial e a hipótese desses coeficientes coincidirem, no limite de massa nula, com os da métrica de Minkowski válida para a Relatividade Restrita. Com essa formulação, o artigo contém, de forma didática, uma primeira apresentação quantitativa da Teoria da Relatividade Geral, a partir de conhecimentos da Relatividade Restrita, usando ferramentas básicas do cálculo diferencial e integral, sem o uso de tensores. Ademais, disponibilizamos videoaulas que têm como base o material deste artigo.

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In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the complete understanding of the complex dynamical evolution of chaotic trajectories is a challenge that, when overcome, may provide further knowledge into the behaviour of confined fusion plasma. This work presents two numerical investigations into characteristics of mixed phase spaces which model distinct magnetic configurations in tokamaks under different perturbation regimes. The first approach relies on a recurrence-based analysis of ensembles of chaotic trajectories to detect open field lines that widely differ from the average. The second focuses on the transient dynamical behaviour of field lines before they escape the systems. These two methods provide insights into the influence of stickiness and invariant manifolds on the evolution of chaotic trajectories, improving our understanding of how these features affect transport and diffusion properties in mixed phase spaces. These theoretical and numerical approaches may enhance our comprehension of confined plasma behaviour and plasma-wall interactions.

About 6.5 million people are infected with Chagas disease (CD) globally, and WHO estimates that $ > million people worldwide suffer from ChHD. Sudden cardiac death (SCD) represents one of the leading causes of death worldwide and affects approximately 65% of ChHD patients at a rate of 24 per 1000 patient-years, much greater than the SCD rate in the general population. Its occurrence in the specific context of ChHD needs to be better exploited. This paper provides the first evidence supporting the use of machine learning (ML) methods within non-invasive tests: patients' clinical data and cardiac restitution metrics (CRM) features extracted from ECG-Holter recordings as an adjunct in the SCD risk assessment in ChHD. The feature selection (FS) flows evaluated 5 different groups of attributes formed from patients' clinical and physiological data to identify relevant attributes among 57 features reported by 315 patients at HUCFF-UFRJ. The FS flow with FS techniques (variance, ANOVA, and recursive feature elimination) and Naive Bayes (NB) model achieved the best classification performance with 90.63% recall (sensitivity) and 80.55% AUC. The initial feature set is reduced to a subset of 13 features (4 Classification; 1 Treatment; 1 CRM; and 7 Heart Tests). The proposed method represents an intelligent diagnostic support system that predicts the high risk of SCD in ChHD patients and highlights the clinical and CRM data that most strongly impact the final outcome.

Como aplicação didática da Relatividade Geral, implementamos, a partir da métrica de Schwarzschild, uma simulação da órbita da estrela S2 em torno do buraco negro massivo Sagitário A*. Verificamos que a orbita simulada é quase uma elipse, com uma precessão lenta igual à observada recentemente. Nessa simulação utilizamos os aplicativos Geogebra e Excel.

Memristors (abbreviation of memory and resistor), introduced as the fourth fundamental electrical circuit element, remember the electric charge that flowed through it. These nonlinear elements are considered as a class of two terminal resistive devices and offers a lot of possible applications in various areas. In this article, we review the dynamical behaviour of some electrical circuits with memristors. Initially, we show that a simple circuit with a capacitor and an inductor connected to a memristor exhibits periodic and chaotic attractors. After that, we show that the known Chua circuit, with a nonlinear resistance, can generate bifurcations and chaos. Substituting the nonlinear resistance by a memristor, the modified Chua circuit exhibits coexistence of attractors. Another known circuit, the Colpitts, is made of a combination of capacitors and inductors containing a bipolar junction transistor. We show that the modified Colpitts circuit, created by substituting the transistor by a memristor, presents multistability and coexistence of many attractors.

We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by u(0,t)−2, our results show that the solution reaches a steady state governed by the parameters present in the logistic function in Fisher’s equation. The initial transient is an anomalous diffusion process, but a power law cannot describe the whole transient. In this sense, the main novelty of this work is to show that a q-exponential function gives a better description of the transient dynamics. In addition to this result, we extend the Fisher equation via non-integer operators. As a fractional definition, we employ the Caputo fractional derivative and use a discretized system for the numerical approach according to finite difference schemes. We consider the numerical solutions in three scenarios: fractional differential operators acting in time, space, and in both variables. Our results show that the time to reach the steady solution strongly depends on the fractional order of the differential operator, with more influence by the time operator. Our main finding shows that a generalized q-exponential, present in the Tsallis formalism, describes the transient dynamics. The adjustment parameters of the q-exponential depend on the fractional order, connecting the generalized thermostatistics with the anomalous relaxation promoted by the fractional operators in time and space.

Spiral waves are spatial-temporal patterns that can emerge in different systems as heart tissues, chemical oscillators, ecological networks and the brain. These waves have been identified in the neocortex of turtles, rats, and humans, particularly during sleep-like states. Although their functions in cognitive activities remain until now poorly understood, these patterns are related to cortical activity modulation and contribute to cortical processing. In this work, ,we construct a neuronal network layer based on the spatial distribution of pyramidal neurons. Our main goal is to investigate how local connectivity and coupling strength are associated with the emergence of spiral waves. Therefore, we propose a trustworthy method capable of detecting different wave patterns, based on local and global phase order parameters. As a result, we find that the range of connection radius ( R ) plays a crucial role in the appearance of spiral waves. For R

The fractional reaction–diffusion equation has been used in many real-world applications in fields such as physics, biology, and chemistry. Motivated by the huge application of fractional reaction–diffusion, we propose a numerical scheme to solve the fractional reaction–diffusion equation under different kernels. Our method can be particularly employed for singular and non-singular kernels, such as the Riemann–Liouville, Caputo, Fabrizio–Caputo, and Atangana–Baleanu operators. Moreover, we obtained general inequalities that guarantee that the stability condition depends explicitly on the kernel. As an implementation of the method, we numerically solved the diffusion equation under the power-law and exponential kernels. For the power-law kernel, we solved by considering fractional time, space, and both operators. In another example, we considered the exponential kernel acting on the time derivative and compared the numerical results with the analytical ones. Our results showed that the numerical procedure developed in this work can be employed to solve fractional differential equations considering different kernels.

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry, and so on. In this paper we introduce two examples of symplectic maps, the standard map and the standard non-twist map, exploring the phase space transformation as their control parameters are varied. Furthermore, for the non-twist map, we also present, that its chaotic motion is separated in phase space by the non-twist transport barrier.

Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking (RS) cells with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (I). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to the bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold (IL) and low-threshold (IT) ion channels play a role in increasing and decreasing the parameter conditions (gsyn and I) in which bistable dynamics occur, respectively. For high values of IL conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance IT increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

In the brain, the excitation-inhibition balance prevents abnormal synchronous behavior. However, known synaptic conductance intensity can be insufficient to account for the undesired synchronization. Due to this fact, we consider time delay in excitatory and inhibitory conductances and study its effect on the neuronal synchronization. In this work, we build a neuronal network composed of adaptive integrate-and-fire neurons coupled by means of delayed conductances. We observe that the time delay in the excitatory and inhibitory conductivities can alter both the state of the collective behavior (synchronous or desynchronous) and its type (spike or burst). For the weak coupling regime, we find that synchronization appears associated with neurons behaving with extremes highest and lowest mean firing frequency, in contrast to when desynchronization is present when neurons do not exhibit extreme values for the firing frequency. Synchronization can also be characterized by neurons presenting either the highest or the lowest levels in the mean synaptic current. For the strong coupling, synchronous burst activities can occur for delays in the inhibitory conductivity. For approximately equal-length delays in the excitatory and inhibitory conductances, desynchronous spikes activities are identified for both weak and strong coupling regimes. Therefore, our results show that not only the conductance intensity, but also short delays in the inhibitory conductance are relevant to avoid abnormal neuronal synchronization.

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.

La cucha real (Panaque nigrolineatus) es endémica de las cuencas del Orinoco y Amazonas. La información relacionada con el sistema visual de esta especie es muy escasa, a pesar de ser un sentido fundamental en la interacción del individuo con su ambiente. Los especímenes se clasificaron en dos grupos en base a su tamano corporal: pequenos (longitud estándar (media ± DE) de 5.92 ± 1.43 cm y peso promedio de 8.50 ± 6.8 g) y grandes (longitud estándar (media ± DE) de 15.9 ± 0.69 cm y peso promedio de 142.48 ± 18.71 g). En los ejemplares pequenos, el ojo presentó una morfología redondeada, y en los de mayor tamano presentó una morfología ligeramente alargada. Se obtuvieron cortes histológicos de 7 μηι que fueron coloreados con las técnicas H&E y Orceína. El tamano relativo del ojo fue mayor en los ejemplares pequenos (6.46 %) que en los de mayor tamano (4.55 %). El espesor de la córnea de los grupos evaluados, presentó variaciones morfométricas significativas, entre su espesor central y periférico. La esclera presentó tejido conectivo denso. Los individuos de mayor tamano corporal tienen una esclera significativamente más gruesa tanto en la región lateral como en la región posterior. Algo similar ocurre con el espesor del iris. La pupila presentó morfología omega. En el cristalino fueron evidenciadas interdigitaciones celulares ubicadas en las regiones laterales. La retina de P. nigrolineatus está compuesta por siete capas. No existen diferencias significativas entre el espesor de la retina de los dos grupos evaluados de P! nigrolineatus. Se observaron de 10 a 12 papilas del nervio óptico en la retina de P. nigrolineatus cuyo diámetro oscila entre 24.57 y 131.90 μηι. Teniendo en cuenta el análisis histológico y morfométrico del ojo de P. nigrolineatus, esta especie presenta adaptaciones orientadas a suplir los requerimientos visuales de organismos bentónicos que habitan ecosistemas con cuerpos de agua turbios, de baja luminosidad, corrientes rápidas y estructuralmente complejos.Royal pleco (Panaque nigrolineatus) is endemic from the Orinoco and Amazon basins. Information related to the visual system of this fish is scant, despite this sense is essential to the interactions with the environment. Specimens were classified into two groups based on their weight and standard length: small (standard length (mean ± SD) of 5.92 ± 1.43 cm and average weight (± SD) 8.50 ± 6.8 g) and large (standard length (mean ± SD) of 15.9 ± 0.69 cm and average weight (± SD) 142.48 ± 18.71 g). The eye of small individuals had a rounded morphology in contrast with the slightly elongated morphology of large individuals. Seven μΓη histological sections were obtained and stained with H&E and Orcein techniques. Relative size of the eye was higher in small individuals (6.46 %) than in larger (4.55 %). Corneal central and peripheral thickness presented significant morphometric differences, in both groups. The sclera is composed of dense connective tissue. Larger individuals had a significant thicker lateral and posterior sclera than small individuals. Iris thickness behaves in a similar way. Pupil has omega morphology. Evident cellular interdigitations were located in crystalline lateral regions. P! nigrolineatus retina is composed of seven layers. There are not significant differences between retinal thickness of two groups evaluated of P. nigrolineatus. There are 10 to 12 optic nerve papillae in P. nigrolineatus retina, with different diameters (24.57-131.90 μΓη). Histological and morphometric analysis of P. nigrolineatus eye fits with adaptations designed to supply visual requirements of benthic organisms that inhabit turbid, low light, with fast currents and structurally complex ecosystems.