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Valvular heart diseases (such as stenosis and regurgitation) are recognized as a rapidly growing cause of global deaths and major contributors to disability. The most effective treatment for these pathologies is the replacement of the natural valve with a prosthetic one. Our work considers an innovative design for prosthetic aortic valves that combines the reliability and durability of artificial valves with the flexibility of tissue valves. It consists of a rigid support and three polymer leaflets which can be cut from an extruded flat sheet, and is referred to hereafter as the Wheatley aortic valve (WAV). As a first step towards the understanding of the mechanical behavior of the WAV, we report here on the implementation of a numerical model built with the ICFD multi-physics solver of the LS-DYNA software. The model is calibrated and validated using data from a basic pulsatile-flow experiment in a water-filled straight tube. Sensitivity to model parameters (contact parameters, mesh size, etc.) and to design parameters (height, material constants) is studied. The numerical data allow us to describe the leaflet motion and the liquid flow in great detail, and to investigate the possible failure modes in cases of unfavorable operational conditions (in particular, if the leaflet height is inadequate). In future work the numerical model developed here will be used to assess the thrombogenic properties of the valve under physiological conditions.

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P-Delta is a nonlinear phenomenon that results from the consideration of axial loads acting on the deformed configuration of a member of the structure, usually a beam-column. This effect is especially significant in slender members, which can undergo large transversal displacements which tend to increase the bending moment caused by an axial load P acting upon them. The P-delta effect can be computed through a geometrically nonlinear analysis, usually employing the Finite Element Method, which subdivides each bar of the frame in finite segments known as elements. Since discretization (subdivision) and the use of iterative schemes (like Newton-Raphson) are sometimes undesirable, especially for students, avoiding it can be didactically interesting. This work proposes the use of a new approach to perform a simplified nonlinear analysis using the two-cycle method and a tangent stiffness matrix obtained directly from the homogeneous solution of the problem's (beam-column) differential equation. The proposed approach is compared to the results obtained by the traditional two-cycle method which uses geometric and elastic stiffness matrices based on cubic (Hermitian) polynomials and a P-Delta approximation using the pseudo (fictitious) lateral load method.

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The nonlinear optical (NLO) response of photonic materials plays an important role in the understanding of light-matter interaction as well as pointing out a diversity of photonic and optoelectronic applications. Among the recently studied materials, 2D-LTMDs (bi-dimensional layered transition metal dichalcogenides) have appeared as a beyond-graphene nanomaterial with semiconducting and metallic optical properties. In this article, we review most of our work in studies of the NLO response of a series of 2D-LTMDs nanomaterials in suspension, using six different NLO techniques, namely hyper Rayleigh scattering, Z-scan, photoacoustic Z-scan, optical Kerr gate, and spatial self-phase modulation, besides the Fourier transform nonlinear optics technique, to infer the nonlinear optical response of semiconducting MoS2, MoSe2, MoTe2, WS2, semimetallic WTe2, ZrTe2, and metallic NbS2 and NbSe2. The nonlinear optical response from a thermal to non-thermal origin was studied, and the nonlinear refraction index and nonlinear absorption coefficient, where present, were measured. Theoretical support was given to explain the origin of the nonlinear responses, which is very dependent on the spectro-temporal regime of the optical source employed in the studies.

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Several heart rate variability (HRV) characteristics of patients with myocardial ischemia are associated with a higher mortality risk. However, the immediate effect of acute ischemia on the HRV nonlinear dynamical behavior is unknown. The objective of this work is to explore the presence of nonlinearity through surrogate data testing and describe the dynamical behavior of HRV in acutely induced ischemia by percutaneous transluminal coronary angioplasty (PTCA) with linear and recurrence quantification analysis (RQA). Short-term electrocardiographic recordings from 68 patients before and after being treated with elective PTCA were selected from a publicly available database. The presence of nonlinear behavior was confirmed by determinism and laminarity in a relevant proportion of HRV time series, in up to 29.4% during baseline conditions and 30.9% after PTCA without statistical difference between these scenarios. After PTCA, the mean value and standard deviation of HRV time series decreased, while determinism and laminarity values increased. Here, the diminishment in overall variability caused by PTCA is not accompanied by a change in nonlinearity detection. Therefore, the presence of nonlinear behavior in HRV time series is not necessarily in agreement with the change of traditional and RQA measures.

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The ecological footprint has currently become a highly popular environmental performance indicator. It provides the basis for setting goals, identifying options for action, and tracking progress toward stated goals. Because the examination of the existence of convergence is important for the climate change protection of the earth, the convergence of ecological footprint and its subcomponents are a major concern for scholars and policymakers. To this end, this study aims to investigate the stochastic convergence of ecological footprint and its subcomponents. We employ the recently developed Hepsag (2021) unit root test that allows nonlinearity and smooth structural change simultaneously to study stochastic convergence in per-capita ecological footprint over the period 1961-2018 for the most polluting countries. The results provide mixed evidence of the presence of stochastic convergence in conventional unit root tests such as ADF, KPSS and Fourier KPSS. According to the Hepsag (2021) unit root test results for all countries, built-up land footprint converges except Australia, Malaysia, Poland, and Turkey. Carbon footprint converges for Indonesia, Malaysia, Mexico, South Africa, Thailand, Turkey, the UK, and the USA. Cropland footprint converges for Australia, Canada, China, France, Indonesia, Italy, Japan, Korea, Malaysia, Mexico, Poland, South Africa, the UK, and Vietnam. Fishing grounds footprint converges in Brazil, France, Germany, Indonesia, Italy, Mexico, South Africa, and Vietnam. Forest product footprint converges in Australia, Canada, France, Germany, India, Korea, Mexico, Poland, Turkey, and Vietnam. Grazing land footprint converges in Canada, France, India, Indonesia, Japan, Korea, Poland, South Africa, Thailand, and Vietnam. And lastly, the total ecological footprint converges in Canada, France, Korea, Malaysia, Mexico, South Africa, the UK, and the USA.

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The retina hosts all processes needed to convert external visual stimuli into a neural code. Light phototransduction and its conversion into an electrical signal involve biochemical cascades, ionic regulations, and different kinds of coupling, among other relevant processes. These create a nonlinear processing scheme and light-dependent adaptive responses. The dynamical adaptation model formulated in recent years is an excellent phenomenological candidate to resume all these phenomena into a single feedforward processing scheme. In this work, we analyze this description in highly nonlinear conditions and find that responses do not match those resulting from a very detailed microscopic model, developed to reproduce electrophysiological recordings on horizontal cells. When a delayed light-dependent gain factor incorporates into the description, responses are in excellent agreement, even when spanning several orders of magnitude in light intensity, contrast, and duration, for simple and complex stimuli. This extended model may be instrumental for studies of the retinal function, enabling the linking of the microscopic domain to the understanding of signal processing properties, and further incorporated in spatially extended retinal networks.

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Abstract: Processes producing sigmoid curves are common in many areas such as biology, agrarian sciences, demography and engineering. Several mathematical functions have been proposed for modeling sigmoid curves. Some models such as the logistic, Gompertz, Richards and Weibull are widely used. This work introduces the Gudermannian function as an option for modeling sigmoid growth curves. The original function was transformed and the resulting equation was called the "Gudermannian growth model." This model was applied to four sets of experimental growth data to illustrate its practical application. The results were compared with those obtained by the logistic and Gompertz models. Since all these models are nonlinear in the parameters, the statistical properties of the least squares estimators were evaluated using measures of nonlinearity. For each experimental data set, the Akaike's corrected information criterion was utilized to discriminate among the models. In general, the Gudermannian model fitted better to the experimental data than the logistic and Gompertz models. The results showed that the Gudermannian model can be a good alternative to the classical sigmoid models.

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Resumen El presente artículo problematiza la relación entre psicoanálisis freudiano y la perspectiva del desarrollo lineal, determinista y teleológica. A pesar de las impregnaciones evolucionistas del contexto histórico en que Freud gesta sus ideas, se encuentran conceptos que muestran una fuerte ruptura con la idea de un despliegue guiado por el ritmo de etapas prefijadas por edades. Así se postula la a-temporalidad de los procesos inconscientes y la Nachträglichkeit a la luz de las perspectivas no lineales emergentes desde las ciencias de la complejidad. Finalmente, se reflexiona sobre una psique que, en su carácter abierto y complejo, contempla lo aleatorio, lo impredecible y el azar en su devenir, y se transforma mediante trabajo elaborativo simbólico del yo. Así, sólo la historización, nunca lineal, contempla lo nuevo como posibilidad de (re)constituir la historia pasada.

Abstract This article problematizes the relationship between Freudian psychoanalysis and the linear, deterministic, and teleological perspective on development. Despite the evolutionist impregnations of the historical context in which Freud conceives his ideas, there are concepts that show a sharp break with the idea of an unfolding guided by a rhythm of stages prefixed by ages. Thus, the a-temporality of the unconscious processes and the Nachträglichkeit is postulated considering the non-linear perspectives that emerge from the sciences of complexity. Finally, we reflect on a psyche that, in its open and complex character, contemplates the fortuitous, the unpredictable and chance in its becoming, and is transformed through the elaborative symbolic work on the self. Like this, only the historicization, which is never linear, contemplates what is new as a possibility to (re)construct the past history.

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Generating Boolean Functions (BFs) with high nonlinearity is a complex task that is usually addresses through algebraic constructions. Metaheuristics have also been applied extensively to this task. However, metaheuristics have not been able to attain so good results as the algebraic techniques. This paper proposes a novel diversity-aware metaheuristic that is able to excel. This proposal includes the design of a novel cost function that combines several information from the Walsh Hadamard Transform (WHT) and a replacement strategy that promotes a gradual change from exploration to exploitation as well as the formation of clusters of solutions with the aim of allowing intensification steps at each iteration. The combination of a high entropy in the population and a lower entropy inside clusters allows a proper balance between exploration and exploitation. This is the first memetic algorithm that is able to generate 10-variable BFs of similar quality than algebraic methods. Experimental results and comparisons provide evidence of the high performance of the proposed optimization mechanism for the generation of high quality BFs.

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The evolution of the optical absorptive effects exhibited by plasmonic nanoparticles was systematically analyzed by electronic signals modulated by a Rössler attractor system. A sol-gel approach was employed for the preparation of the studied Au nanoparticles embedded in a TiO2 thin solid film. The inclusion of the nanoparticles in an inhomogeneous biological sample integrated by human cells deposited in an ITO glass substrate was evaluated with a high level of sensitivity using an opto-electronic chaotic circuit. The optical response of the nanoparticles was determined using nanosecond laser pulses in order to guarantee the sensing performance of the system. It was shown that high-intensity irradiances at a wavelength of 532 nm could promote a change in the absorption band of the localized surface plasmon resonance associated with an increase in the nanoparticle density of the film. Moreover, it was revealed that interferometrically-controlled energy transfer mechanisms can be useful for thermo-plasmonic functions and sharp selective optical damage induced by the vectorial nature of light. Immediate applications of two-wave mixing techniques, together with chaotic effects, can be contemplated in the development of nanostructured sensors and laser-induced controlled explosions, with potential applications for biomedical photo-thermal processes.

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This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz's portfolio allocation model, evaluating the technique's performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance.

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The growth of plants and animals can be described through a growth curve. This curve is given by the equation of a nonlinear model, such as the Logistic model and the Gompertz model. The objective of this study was to adjust the Chanter model, as well as Logistic and Gompertz, using a set of cocoa (clone Sial-105) fruit whose length and diameter measurements were evaluated from 30 to 180 days after pollination, every 15 days. The Chanter model is a hybrid between the Logistic model and Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaikes information criterion (AIC), the Akaikes weights criterion, Bayesian information criterion (BIC), residual standard deviation (RSD),the adjusted coefficient of determination (R²aj) and the measures of non-linearity Boxs bias and curvature of Bates and Watts. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.(AU)

O crescimento de plantas e animais pode ser descrito por meio de uma curva. Essa curva é dada pela equação de um modelo não linear, como o modelo Logístico e o modelo Gompertz. O objetivo deste trabalho foi ajustar o modelo Chanter, assim como o Logístico e Gompertz, utilizando um conjunto de dados do fruto do cacaueiro do clone SIAL - 105, cujas medidas de comprimento e diâmetro foram avaliadas de 30 até 180 dias após a polinização, a cada 15 dias. O modelo Chanter é um híbrido entre o modelo Logístico e o modelo Gompertz cujos parâmetros podem ser interpretados similarmente. A avaliação da qualidade do ajuste entre os modelos foi feita utilizando as seguintes medidas estatísticas: o critério de informação de Akaike (AIC), o critério Peso de Akaike, o critério de informação de Bayes (BIC), o desvio padrão residual (DPR), o coeficiente de determinação ajustado (R²aj) e as medidas de não linearidade, vício de Box e curvatura de Bates e Watts. Verificou-se que o modelo Chanter dentre os modelos estudados neste trabalho é o mais adequado para o ajuste aos dados do fruto do cacaueiro.(AU)

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ABSTRACT: The growth of plants and animals can be described through a growth curve. This curve is given by the equation of a nonlinear model, such as the Logistic model and the Gompertz model. The objective of this study was to adjust the Chanter model, as well as Logistic and Gompertz, using a set of cocoa (clone Sial-105) fruit whose length and diameter measurements were evaluated from 30 to 180 days after pollination, every 15 days. The Chanter model is a hybrid between the Logistic model and Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaike's information criterion (AIC), the Akaike's weights criterion, Bayesian information criterion (BIC), residual standard deviation (RSD),the adjusted coefficient of determination (R²aj) and the measures of non-linearity Box's bias and curvature of Bates and Watts. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.

RESUMO: O crescimento de plantas e animais pode ser descrito por meio de uma curva. Essa curva é dada pela equação de um modelo não linear, como o modelo Logístico e o modelo Gompertz. O objetivo deste trabalho foi ajustar o modelo Chanter, assim como o Logístico e Gompertz, utilizando um conjunto de dados do fruto do cacaueiro do clone SIAL - 105, cujas medidas de comprimento e diâmetro foram avaliadas de 30 até 180 dias após a polinização, a cada 15 dias. O modelo Chanter é um híbrido entre o modelo Logístico e o modelo Gompertz cujos parâmetros podem ser interpretados similarmente. A avaliação da qualidade do ajuste entre os modelos foi feita utilizando as seguintes medidas estatísticas: o critério de informação de Akaike (AIC), o critério Peso de Akaike, o critério de informação de Bayes (BIC), o desvio padrão residual (DPR), o coeficiente de determinação ajustado (R²aj) e as medidas de não linearidade, vício de Box e curvatura de Bates e Watts. Verificou-se que o modelo Chanter dentre os modelos estudados neste trabalho é o mais adequado para o ajuste aos dados do fruto do cacaueiro.

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Purpose: To assess the nature and extent of non-linear processes in pupil responses using rod- and cone-isolating visual beat stimuli. Methods: A four-primary photostimulating method based on the principle of silent substitution was implemented to generate rod or cone isolating and combined sinusoidal stimuli at a single component frequency (1, 4, 5, 8, or 9 Hz) or a 1 Hz beat frequency (frequency pairs: 4 + 5, 8 + 9 Hz). The component frequencies were chosen to minimize the melanopsin photoresponse of intrinsically photosensitive retinal ganglion cells (ipRGCs) such that the pupil response was primarily driven by outer retinal photoreceptor inputs. Full-field (Ganzfeld) pupil responses and electroretinograms (ERGs) were recorded to the same stimuli at two mesopic light levels (-0.9 and 0 log cd/m2). Fourier analysis was used to derive the amplitudes and phases of the pupil and ERG responses. Results: For the beat frequency condition, when modulation was restricted to the same photoreceptor type at the higher mesopic level (0 log cd/m2), there was a pronounced pupil response to the 1 Hz beat frequency with the 4 + 5 Hz frequency pair and rare beat responses for the 8 + 9 Hz frequency pair. At the lower mesopic level there were few and inconsistent beat responses. When one component modulated the rod excitation and the other component modulated the cone excitation, responses to the beat frequency were rare and lower than the 1 Hz component frequency condition responses. These results were confirmed by ERG recordings. Conclusions: There is non-linearity in both the pupil response and electroretinogram to rod and cone inputs at mesopic light levels. The presence of a beat response for modulation components restricted to a single photoreceptor type, but not for components with cross-photoreceptor types, indicates that the location of a non-linear process in the pupil pathway occurs at a retinal site earlier than where the rod and cone signals are combined, that is, at the photoreceptor level.

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We determined multiple closed-shell Hartree-Fock-Roothaan solutions for the systems: BH, FH, LiH, and OH-, considering double and triple zeta bases. To calculate them, we used the self-consistent field method and the algebraic method. The Hartree-Fock solutions obtained were classified with respect to the kind of extreme. All these extremes generate the same configuration interaction space. Our key objective in this work is to illustrate that it is possible to obtain a wide variety of Hartree-Fock solutions for any molecular system.

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Managing production environments in ways that promote weed community diversity may enhance both crop production and the development of a more sustainable agriculture. This study analyzed data of productivity of maize (corn) and soybean in plots in the Main Cropping System Experiment (MCSE) at the W. K. Kellogg Biological Station Long-Term Ecological Research (KBS-LTER) in Michigan, USA, from 1996 to 2011. We used models derived from population ecology to explore how weed diversity, temperature, and precipitation interact with crop yields. Using three types of models that considered internal and external (climate and weeds) factors, with additive or non-linear variants, we found that changes in weed diversity were associated with changes in rates of crop yield increase over time for both maize and soybeans. The intrinsic capacity for soybean yield increase in response to the environment was greater under more diverse weed communities. Soybean production risks were greatest in the least weed diverse systems, in which each weed species lost was associated with progressively greater crop yield losses. Managing for weed community diversity, while suppressing dominant, highly competitive weeds, may be a helpful strategy for supporting long term increases in soybean productivity. In maize, there was a negative and non-additive response of yields to the interaction between weed diversity and minimum air temperatures. When cold temperatures constrained potential maize productivity through limited resources, negative interactions with weed diversity became more pronounced. We suggest that: (1) maize was less competitive in cold years allowing higher weed diversity and the dominance of some weed species; or (2) that cold years resulted in increased weed richness and prevalence of competitive weeds, thus reducing crop yields. Therefore, we propose to control dominant weed species especially in the years of low yield and extreme minimum temperatures to improve maize yields. Results of our study indicate that through the proactive management of weed diversity, it may be possible to promote both high productivity of crops and environmental sustainability.

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How can experts, sometimes in exacting detail, almost immediately and very precisely recall memory items from a vast repertoire? The problem in which we will be interested concerns models of theoretical neuroscience that could explain the speed and robustness of an expert's recollection. The approach is based on Sparse Distributed Memory, which has been shown to be plausible, both in a neuroscientific and in a psychological manner, in a number of ways. A crucial characteristic concerns the limits of human recollection, the "tip-of-tongue" memory event-which is found at a non-linearity in the model. We expand the theoretical framework, deriving an optimization formula to solve this non-linearity. Numerical results demonstrate how the higher frequency of rehearsal, through work or study, immediately increases the robustness and speed associated with expert memory.

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The nonlinear properties of biological suspensions have been previously presented as a bulk phenomenon without the influences of the electrodes. However, some authors have showed that the behaviour of a biological suspension is due to the nonlinear characteristics of the electrode-electrolyte interface (EEI), which is modulated by the presence of yeast cells. We have developed a method, complementary to the nonlinear dielectric spectroscopy (NLDS) which is used for the study of the behaviour of EEI with resting cell suspensions of Saccharomyces cerevisiae. The method allows researchers to detect simply and quickly the voltage and frequency ranges where the metabolic activity of yeasts is detectable. This method does not replace NLDS, and aims to reduce the time during which the electrodes are exposed to corrosion by high voltages. In this paper we applied AC overpotentials (10-630 mV) with frequencies in the range from 1 to 1000 Hz. Also, we measured current harmonic distortion produced by the nonlinearity of the interface. Changes in the transfer function were observed when yeast suspension was used. Apart from the nonlinear response typical of the EEI, we also observed the biological nonlinear behaviour. The changes in the transfer functions were assessed using the overlapping index which was defined in terms of the conditional probability. The methodology was contrasted favourably with Fourier analysis. This novel strategy has the advantages of simplicity, sensitivity, reproducibility and involves basic tools such as the usual measurement of current.

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In the present work, we performed a discrimination analysis of the nonlinear equations used to describe sorption isotherms of the lettuce seeds. The equilibrium data were obtained by the static method using saturated salt solutions. The best model to describe the equilibrium moisture of lettuce seeds was selected using measures of curvature and bias. The obtained results showed that the Copace equation was the best model in terms of nonsignificance for bias and nonlinearity measures.

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Este trabalho tem como objetivo verificar as diferenças funcionais entre sinapses proximais e distais e investigar as interações não line­ares de ativações sinápticas em modelos de motoneurônios em con­dições passivas. Os modelos utilizados, implementados em C++, são uma versão expandida dos desenvolvidos por Vieira e Kohn (2005), com uma arborização dendrítica mais detalhada: 5 ramos dendríti­cos equivalentes com 17 ou 19 compartimentos dendríticos cada um. Testes verificaram as diferenças funcionais de sinapses que ocorrem próximas ao soma e ao longo do dendrito além de avaliarem o grau de não linearidade de resposta da arborização dendrítica para dife­rentes ativações sinápticas em diferentes sítios. As diferenças funcio­nais entre as sinapses proximais e distais foram avaliadas pela injeção de senoides puras em diferentes compartimentos dendríticos. Os re­sultados mostraram atenuações mais intensas nas altas frequências e frequência de corte mais baixas em compartimentos dendríticos mais distantes do soma. As interações não lineares foram avaliadas apli­cando entradas sinápticas senoidais com frequências primas entre si, em dois ou mais ramos dendríticos equivalentes simultaneamente e em compartimentos dendríticos diferentes. O espectro de frequên­cia da corrente efetiva foi analisado, comparando a amplitude do pico das distorções harmônicas e por intermodulação com o pico da frequência fundamental de menor amplitude: quanto menores estas diferenças maior o grau de não linearidade entre as ativações sinápti­cas em compartimentos dendríticos distintos. Os resultados sugerem expressivo grau de não linearidade entre as entradas sinápticas nos dendritos. Notou­-se que, em todas as situações, quando se variou a condutância sináptica, maior foi o grau de não linearidade em relação aos casos em que se variou a corrente sináptica, bem como entradas sinápticas mais próximas eletrotonicamente apresentaram maior grau de não linearidade em...

The aim of this work was to verify the functional differences between proximal and distal synapses and to investigate the nonlinear interactions of synaptic activation in models of motoneurons in passive conditions. The models, implemented in C++, are an expanded version of that developed by Vieira and Kohn (2005), with a more detailed dendritic arborization: five equivalent dendrites with 17 or 19 dendritic compartments each one. Tests verified the functional differences of synapses that occur close to the soma and along the dendrite in addition to evaluating the degree of nonlinearity response from dendritic arborization for different synaptic activation at different sites. The functional differences between the proximal and distal synapses were evaluated by injection of pure sinusoids in different dendritic compartments. The results showed severe attenuation at high frequencies and a lower cut-off frequency in more distant dendritic compartments of the soma. The nonlinear interactions were evaluated by applying sinusoidal synaptic input at prime frequencies with each other in two or more dendritic branches simultaneously and at different dendritic compartments. The frequency spectrum of the effective current was analyzed by comparing the peak amplitude of harmonics and spurious rays with the peak amplitude of the fundamental frequency of smaller amplitude: the smaller these differences are, the greater the degree of nonlinearity between the synaptic activation of distinct dendritic compartments. The results suggest a high degree of nonlinearity between the dendrites. In all situations was noted that when the synaptic conductance was varied, the nonlinearities was greater in relation to the cases in which the synaptic current was varied, and nonlinear summation is expected for synapses located electrotonically close together in relation for electrotonically separated inputs, suggesting a dependence on membrane potential.

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