Quantifying Spin-Mixed States in Ferromagnets.

We quantify the presence of spin-mixed states in ferromagnetic 3D transition metals by precise measurement of the orbital moment. While central to phenomena such as Elliot-Yafet scattering, quantification of the spin-mixing parameter has hitherto been confined to theoretical calculations. We demonstrate that this information is also available by experimental means. Comparison of ferromagnetic resonance spectroscopy with x-ray magnetic circular dichroism results show that Kittel's original derivation of the spectroscopic g factor requires modification, to include spin mixing of valence band states. Our results are supported by ab initio relativistic electronic structure theory.

Breaking of Galilean Invariance in the Hydrodynamic Formulation of Ferromagnetic Thin Films.

Microwave magnetodynamics in ferromagnets are often studied in the small-amplitude or weakly nonlinear regime corresponding to modulations of a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned approximations are not applicable, have become experimentally accessible. By reinterpreting the governing Landau-Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are shown to, in general, break Galilean invariance. A magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHSs), which exhibit fluidlike behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpretation opens up novel possibilities in magnetic research.

Mode- and size-dependent Landau-Lifshitz damping in magnetic nanostructures: evidence for nonlocal damping.

We demonstrate a strong dependence of the effective damping on the nanomagnet size and the particular spin-wave mode that can be explained by the theory of intralayer transverse-spin pumping. The effective Landau-Lifshitz damping is measured optically in individual, isolated nanomagnets as small as 100 nm. The measurements are accomplished by use of a novel heterodyne magneto-optical microwave microscope with unprecedented sensitivity. Experimental data reveal multiple standing spin-wave modes that we identify by use of micromagnetic modeling as having either localized or delocalized character, described generically as end and center modes. The damping parameter of the two modes depends on both the size of the nanomagnet as well as the particular spin-wave mode that is excited, with values that are enhanced by as much as 40% relative to that measured for an extended film. Contrary to expectations based on the ad hoc consideration of lithography-induced edge damage, the damping for the end mode decreases as the size of the nanomagnet decreases. The data agree with the theory for damping caused by the flow of intralayer transverse spin currents driven by the magnetization curvature. These results have serious implications for the performance of nanoscale spintronic devices such as spin-torque-transfer magnetic random access memory.

Calculating Route: Functional Trajectories and Long-Term Outcomes in Survivors of Severe COVID-19.

OBJECTIVES: We investigated functional trajectories after severe COVID-19 and estimated their associations with adverse outcomes (falls, rehospitalizations, institutionalization, or death), cognition and post COVID-19 condition within 1-year of hospital discharge. DESIGN: Prospective cohort study. SETTING: A large academic medical center in Sao Paulo, Brazil. PARTICIPANTS: Survivors of COVID-19 admissions to an intensive care unit. INTERVENTIONS: None. MEASUREMENTS: We evaluated participants' disability status before hospital admission and three, six, nine, and twelve months after discharge using 15 activities of daily living. During follow-up, cognition and post COVID-19 condition (defined as persistent symptoms with duration ≥2 months) were assessed. A latent class growth analysis was performed to investigate functional trajectories after discharge. RESULTS: We included 422 participants (median age 63 years, 13.5% were frail before COVID-19). Four distinct functional trajectories could be identified: "minimal disability trajectory" (37.4% of participants), "mild disability trajectory" (37.9%), "moderate disability trajectory" (16.8%), and "severe disability trajectory" (7.8%). Compared with minimal disability trajectory, the odds ratios (95% confidence interval) for 1-year adverse outcomes were 2.28 (1.38-3.76) for minor disability trajectory; 4.21 (2.10-8.42) for moderate disability trajectory; and 4.16 (1.51-11.46) for severe disability trajectory, even after adjustments. The occurrence of post COVID-19 condition was 67.5% and associated with functional trajectories (p=0.004). Cognition was also associated with functional trajectories. CONCLUSION: Severe COVID-19 survivors can experience diverse functional trajectories, with those presenting higher levels of disability at increased risk for long-term adverse outcomes. Further investigations are essential to confirm our findings and assess the effectiveness of rehabilitation interventions, aiming to improve health outcomes in those who survived severe COVID-19 and other causes of sepsis.

Digital Forensics Experimentation: Analysis and Recommendations.

Digital forensics (DF) is becoming one of the most prestigious research areas in computer science due to its inherent nature of providing a means to acquire, examine, analyze, and report evidence to be used in legal processes. To successfully perform it, novel techniques, approaches, and tools have been proposed, experimented on, and evaluated by researchers. However, the experimentation process is not a trivial task in this area as substantial evidence is not accepted in court. Therefore, the experimentation process has to be improved in DF, especially its documentation and data sharing to enable its reproducibility. The objective of this paper is to characterize the state-of-the-art research on DF experiments. We conducted a Systematic Mapping Study (SMS), analyzing 107 primary studies reporting DF experiments. We demonstrate that DF experimentation somehow fails at documenting the most essential elements of an experiment, such as hypothesis, variables, design, instrumentation, validity evaluation, setup, training, datasets and benchmarks, statistical techniques (descriptive, hypothesis, and effect-size test), limitations, and data sharing. In this work, we also propose a set of recommendations to improve experimentation in DF, especially regarding its replication and reproducibility. DF experimentation should evolve if the community intends to provide reliable and reproducible studies. By embracing this, both academicians and practitioners might benefit from such experiments and evidence.

Population genetics analysis of Podocnemis sextuberculata (Testudines, Podocnemidae): lack of population structure in the central Amazon Basin.

The chelonians are, in general, important for the economy of the traditional populations of the Amazon region, especially as a source of animal protein. Furthermore, sub-products, such as eggs and fat, are utilized in the manufacture of cosmetics, and the plastron and carapace are used in the manufacture of adornments. The freshwater turtle species Podocnemis sextuberculata, locally known as "iaçá" or "pitiú", is widely distributed in the Amazon Basin in Brazil and also in Colombia and Peru. This species is on the International Union for Conservation of Nature Red List in the category of vulnerable species. We examined the genetic variability and population structure of three populations represented by 64 individuals sampled from Reserva Federal de Abufari, Tapauá, Amazonas State; Reserva de Desenvolvimento Sustentável Mamirauá, Tefé, Amazonas State, and Terra Santa, Pará State. All of these are over 1000 km from each other. A partial 415-bp sequence of the mitochondrial gene ND1 was utilized as a molecular marker. Seven haplotypes were observed; the most common haplotype was shared by all the areas sampled, while the rarest haplotypes were represented by a single individual and were thus restricted to a single locality. The sharing of the most common haplotype, the high number of migrants (Nm) and the AMOVA results indicate a lack of genetic structure among the sampling localities. The levels of genetic variability observed were homogeneous among the sampling localities. These results (Ó¨(ST) and Nm) are compatible with what is known about the ecology of this species, which has a great migratory capacity.

The Impact of Frailty on the Relationship between Life-Space Mobility and Quality of Life in Older Adults during the COVID-19 Pandemic.

BACKGROUND: The COVID-19 pandemic has led to abrupt restrictions of life-space mobility. The impact of shelter-in-place orders on older adults' health and well-being is still unclear. OBJECTIVE: To investigate the relationship between life-space mobility and quality of life (QoL) in older adults with and without frailty during the COVID-19 pandemic. DESIGN: Multicenter prospective cohort study based on structured telephone interviews. SETTING: Four geriatric outpatient clinics in the metropolitan area of Sao Paulo, Brazil. PARTICIPANTS: 557 community-dwelling adults aged 60 years and older. MEASUREMENTS: The Life-Space Assessment was used to measure community mobility before and during the COVID-19 pandemic, and a previously validated decrease of ≥ 5 points defined restricted life-space mobility. Frailty was assessed through the FRAIL (fatigue, resistance, ambulation, illnesses, and loss of weight) scale. The impact of shelter-in-place orders on QoL was evaluated with the question «How is the COVID-19 pandemic affecting your QoL?¼, to which participants could respond «not at all¼, «to some extent¼, or «to a great extent¼. We used ordinal logistic regressions to investigate the relationship between restricted life-space mobility and impact on QoL, adjusting our analyses for demographics, frailty, comorbidities, cognition, functionality, loneliness, depression, and anxiety. We explored whether frailty modified the association between life-space mobility and impact on QoL. RESULTS: Participants were on average 80±8 years old, 65% were women, and 33% were frail. The COVID-19 quarantine led to a restriction of community mobility in 79% of participants and affected the QoL for 77% of participants. We found that restricted life-space mobility was associated with impact on QoL in older adults during the pandemic, although frailty modified the magnitude of the association (P-value for interaction=0.03). Frail participants who experienced restricted life-space mobility had twice the odds of reporting an impact on QoL when compared with non-frail individuals, with respective adjusted odds ratios of 4.20 (95% CI=2.36-7.50) and 2.18 (95% CI=1.33-3.58). CONCLUSION: Older adults experienced substantial decreases in life-space mobility during the COVID-19 pandemic, and this unexpected change impacted their QoL. Providers should be particularly watchful for the consequences of abrupt life-space restrictions on frail individuals.

Ultrafast optically induced spin transfer in ferromagnetic alloys.

The vision of using light to manipulate electronic and spin excitations in materials on their fundamental time and length scales requires new approaches in experiment and theory to observe and understand these excitations. The ultimate speed limit for all-optical manipulation requires control schemes for which the electronic or magnetic subsystems of the materials are coherently manipulated on the time scale of the laser excitation pulse. In our work, we provide experimental evidence of such a direct, ultrafast, and coherent spin transfer between two magnetic subsystems of an alloy of Fe and Ni. Our experimental findings are fully supported by time-dependent density functional theory simulations and, hence, suggest the possibility of coherently controlling spin dynamics on subfemtosecond time scales, i.e., the birth of the research area of attomagnetism.

Ultrafast demagnetization dynamics at the M edges of magnetic elements observed using a tabletop high-harmonic soft x-ray source.

We use few-femtosecond soft x-ray pulses from high-harmonic generation to extract element-specific demagnetization dynamics and hysteresis loops of a compound material for the first time. Using a geometry where high-harmonic beams are reflected from a magnetized Permalloy grating, large changes in the reflected intensity of up to 6% at the M absorption edges of Fe and Ni are observed when the magnetization is reversed. A short pump pulse is used to destroy the magnetic alignment, which allows us to measure the fastest, elementally specific demagnetization dynamics, with 55 fs time resolution. The use of high harmonics for probing magnetic materials promises to combine nanometer spatial resolution, elemental specificity, and femtosecond-to-attosecond time resolution, making it possible to address important fundamental questions in magnetism.

Effect of Calcium and Fluoride Addition to Hydrogen Peroxide Bleaching Gel On Tooth Diffusion, Color, and Microhardness.

OBJECTIVES: The aim of this study was to evaluate the effect of calcium and fluoride addition to a 35% hydrogen peroxide (HP) bleaching gel with regard to its diffusion through the tooth structure, enamel microhardness, and bleaching efficacy. METHODS AND MATERIALS: Eighty specimens (6 mm in diameter and 2 mm in height; 1 mm/enamel and 1 mm/dentin) were obtained from bovine incisors that were polished and divided into four groups (n=20) according to the remineralizing agent added to the gel: Ca = 0.5% calcium gluconate; F = 0.2% sodium fluoride; Ca+F = 0.5% calcium gluconate and 0.2% sodium fluoride; and control = no agent. Initial microhardness and color were assessed. The samples were positioned over simulated pulpal chambers filled with acetate buffer solution to capture the HP. Gels were applied over enamel for 30 minutes, and HP diffusion was assessed by spectrophotometry two hours after bleaching. Microhardness was measured immediately after bleaching and then the specimens were immersed into artificial saliva for seven days for final color assessment. Data were analyzed by one-way analysis of variance followed by Tukey test. RESULTS: Bleaching reduced microhardness for all groups (p=0.0001), but the Ca+F and F groups showed lower reductions after bleaching. The addition of Ca, F, and Ca+F decreased the peroxide penetration through the tooth structure (p=0.0001), but there were no differences in color change for ΔL (p=0.357), Δa (p=0.061), Δb (p=0.823), and ΔE (p=0.581). CONCLUSION: The addition of calcium and fluoride in the gel did not affect bleaching efficacy, but it was able to reduce both the peroxide diffusion and the bleached enamel microhardness loss.

Near-unity spin Hall ratio in Ni x Cu1-x alloys.

We report a large spin Hall effect in the 3d transition metal alloy Ni x Cu1-x for x ∈ {0.3, 0.75}, detected via the ferromagnetic resonance of a permalloy (Py = Ni80Fe20) film deposited in a bilayer with the alloy. A thickness series at x = 0.6, for which the alloy is paramagnetic at room temperature, allows us to determine the spin Hall ratio θ SH ≈ 1, spin diffusion length λs, spin mixing conductance G ⇅, and damping due to spin memory loss αSML. We compare our results with similar experiments on Py/Pt bilayers measured using the same method. Ab initio band structure calculations with disorder and spin-orbit coupling suggest an intrinsic spin Hall effect in Ni x Cu1-x alloys, although the experiments here cannot distinguish between extrinsic and intrinsic mechanisms.

Analogue of dynamic Hall effect in cavity magnon polariton system and coherently controlled logic device.

Cavity magnon polaritons are mixed quasiparticles that arise from the strong coupling between cavity photons and quantized magnons. Combining high-speed photons with long-coherence-time magnons, such polaritons promise to be a potential candidate for quantum information processing. For harnessing coherent information contained in spatially distributed polariton states, it is highly desirable to manipulate cavity magnon polaritons in a two-dimensional system. Here, we demonstrate that tunable cavity magnon polariton transport can be achieved by strongly coupling magnons to microwave photons in a cross-cavity. An analog to the dynamic Hall effect has been demonstrated in a planar cavity spintronic device, where the propagation of cavity-magnon-polaritons is deflected transversally due to hybrid magnon-photon dynamics. Implementing this device as a Michelson-type interferometer using the coherent nature of the dynamic Hall and longitudinal signals, we have developed a proof-of-principle logic device to control the amplitude of cavity-magnon-polaritons by encoding the input microwave phase.

Anomalous spin-orbit torques in magnetic single-layer films.

The spin Hall effect couples charge and spin transport1-3, enabling electrical control of magnetization4,5. A quintessential example of spin-Hall-related transport is the anomalous Hall effect (AHE)6, first observed in 1880, in which an electric current perpendicular to the magnetization in a magnetic film generates charge accumulation on the surfaces. Here, we report the observation of a counterpart of the AHE that we term the anomalous spin-orbit torque (ASOT), wherein an electric current parallel to the magnetization generates opposite spin-orbit torques on the surfaces of the magnetic film. We interpret the ASOT as being due to a spin-Hall-like current generated with an efficiency of 0.053 ± 0.003 in Ni80Fe20, comparable to the spin Hall angle of Pt7. Similar effects are also observed in other common ferromagnetic metals, including Co, Ni and Fe. First-principles calculations corroborate the order of magnitude of the measured values. This work suggests that a strong spin current with spin polarization transverse to the magnetization can be generated within a ferromagnet, despite spin dephasing8. The large magnitude of the ASOT should be taken into consideration when investigating spin-orbit torques in ferromagnetic/non-magnetic bilayers.

Spin-current-mediated rapid magnon localisation and coalescence after ultrafast optical pumping of ferrimagnetic alloys.

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of a universal rapid magnetic order recovery in ferrimagnets with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify magnon localisation and coalescence processes, whereby localised magnetic textures nucleate and subsequently interact and grow in accordance with a power law formalism. A hydrodynamic representation of the numerical simulations indicates that the appearance of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of 107 A cm-2. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. The magnon processes discussed here provide new insights for the stabilization of desired meta-stable states.

Observation of spin-orbit effects with spin rotation symmetry.

The spin-orbit interaction enables interconversion between a charge current and a spin current. It is usually believed that in a nonmagnetic metal (NM) or at a NM/ferromagnetic metal (FM) bilayer interface, the symmetry of spin-orbit effects requires that the spin current, charge current, and spin orientation are all orthogonal to each other. Here we demonstrate the presence of spin-orbit effects near the NM/FM interface that exhibit a very different symmetry, hereafter referred to as spin-rotation symmetry, from the conventional spin Hall effect while the spin polarization is rotating about the magnetization. These results imply that a perpendicularly polarized spin current can be generated with an in-plane charge current simply by use of a FM/NM bilayer with magnetization collinear to the charge current. The ability to generate a spin current with arbitrary polarization using typical magnetic materials will benefit the development of magnetic memories.Converting charge to spin currents using spin-orbit interactions has useful applications in spintronics but symmetry constraints can limit the control over spin polarization. Here the authors demonstrate spin-orbit effects with a different symmetry, which could help generate arbitrary spin polarizations.

Inhibitory effect of the Pseudobrickellia brasiliensis (Spreng) R.M. King & H. Rob. aqueous extract on human lymphocyte proliferation and IFN-γ and TNF-α production in vitro.

Pseudobrickellia brasiliensis (Asteraceae) is a plant commonly known as arnica-do-campo and belongs to the native flora of the Brazilian Cerrado. The alcoholic extract of the plant has been used as an anti-inflammatory agent in folk medicine, but the biological mechanism of action has not been elucidated. The present study evaluated the composition of P. brasiliensis aqueous extract and its effects on pro-inflammatory cytokine production and lymphocyte proliferation. The extracts were prepared by sequential maceration of P. brasiliensis leaves in ethanol, ethyl acetate, and water. Extract cytotoxicity was evaluated by trypan blue exclusion assay, and apoptosis and necrosis were measured by staining with annexin V-FITC and propidium iodide. The ethanolic (ETA) and acetate (ACE) extracts showed cytotoxic effects. The aqueous extract (AQU) was not cytotoxic. Peripheral blood mononuclear cells stimulated with phorbol myristate acetate and ionomycin and treated with AQU (100 µg/mL) showed reduced interferon (IFN)-γ and tumor necrosis factor (TNF)-α expression. AQU also inhibited lymphocyte proliferative response after nonspecific stimulation with phytohemagglutinin. The aqueous extract was analyzed by liquid chromatography coupled with photodiode array detection and mass spectrometry. Quinic acid and its derivatives 5-caffeoylquinic acid and 3,5-dicaffeoylquinic acid, as well as the flavonoids luteolin and luteolin dihexoside, were detected. All these compounds are known to exhibit anti-inflammatory activity. Taken together, these findings demonstrate that P. brasiliensis aqueous extract can inhibit the pro-inflammatory cytokine production and proliferative response of lymphocytes. These effects may be related to the presence of chemical substances with anti-inflammatory actions previously reported in scientific literature.

Effects of transport time and rest period on the quality of electrically stimulated male cattle carcasses.

Forty-five castrated Nelore-breed male cattle, with average age of 37 months, were randomly chosen. The cattle were submitted to the combination of two transport times (up to 2h and approximately 5h) and five rest periods (0h, 6h, 12h, 18h and 24h). The carcasses were electrically stimulated. After 24h postmortem, the average of the ultimate pH in the M. Longissimus dorsi (LD) was considered normal (5.57-5.72) for eight out of nine cattle groups. The shear force (SF) was higher for cattle that were not allowed a rest period (0h) on both transport times, however it was not significant (p>0.05). This result was compatible with the sarcomere length (SL), which were shorter for those carcasses. The rest period and transport time had no influence on the L(∗) (lightness) values, but a(∗) (redness) values increased until the 12th hour of rest. The b(∗) (yellowness) value was negative for the cattle without a rest period (0h) and transported for 5h. The cattle transported for up to 2h could be allowed a 6-h rest period only, and the cattle transported for 5h could be allowed a 12-h rest period without the meat quality being affected significantly.

Folha de amendoeira como aditivo em dietas para Betta splendens / Use of almond leaf as additive in diets for Betta splendens

O objetivo do presente estudo foi avaliar o desempenho zootécnico, os parâmetrosmorfométricos, o comportamento social, a viabilidade econômica e a análise microbiológica da água de cultivo e de tecidos corpóreos de Betta splendens alimentados com folha da amendoeira Terminalia catappa (FFDA) como aditivo. Foram utilizados 28 machos de Bettas, acondicionados individualmente em aquários de 1,5L, por 50 dias. O experimento foi realizado em delineamento experimental inteiramente ao acaso, com quatro tratamentos: 0,00%; 0,25%; 0,50% e 0,75% de inclusão da FFAD e sete repetições. Ao término do experimento, foram avaliados os parâmetros: desempenho zootécnico (ganho de peso diário, consumo de ração, conversão alimentar aparente, taxa de eficiência proteica, taxa de crescimento específico e fator de condição), morfométrico (comprimento total, padrão e da cabeça, altura, índice de perfil e índice de cabeça), comportamento social, viabilidade econômica da ração, análise microbiana do conteúdo intestinal, filé e escama e análise microbiológica da água. Pela ANOVA, pelo teste de Tukey e pela regressão (P>0,05), os parâmetros: peso final, ganho de peso, comprimento padrão, comprimento total e taxa de crescimento específico foram influenciados pelos tratamentos (P<0,05), apresentando um efeito quadrático. Assim, recomenda-se o nível de 0,50% de Terminalia catappa como aditivo em dietas de Betta splendens.(AU)

The objective of this study was to evaluate the performance, morphometric parameters, social behavior, economic viability, the presence of enterobacteria in the intestinal contents and a microbiological analysis of the water culture of Betta splendens fed with almond-tree-leaf flour (ATLF) as an additive. Twenty-eight male B. splendens were individually put in 1.5 L aquariums. The experiment was done in a completely randomized experimental design with four treatments: 0.00%; 0.25%; 0.50% and 0.75%, of the ATLF, dehydrated Terminalia catappa with seven repetitions each. At the end of the experimental period, the parameters were evaluated: performance (daily weight gain, feed intake, apparent feed conversion, protein efficiency rate, specific growth rate and condition factor), morphometric (total length, standard head, height, profile index and head index), social behavior, economic viability of the feed, microbial analysis of intestinal contents, fillet and scales, and microbiological analysis of the water. Though ANAVA, Tukey test and regression analysis (P> 0.05), the parameters: final weight, weight gain, standard length, total length and specific growth rate were influenced by the treatments (P< 0.05), presenting a quadratic effect. Therefore, the 0.50% level of Terminalia catappa is recommended as additive in Betta splendens diets.(AU)

Predictive value of the human immunodeficiency virus 1 antigen test in children born to infected mothers.

Our objective was to examine the utility of the human immunodeficiency virus (HIV-1) antigen test as an early predictor of HIV-1 infection among children born to infected mothers and to collect information about its performance as a diagnostic test. The Abbott HIVAG-1 Enzyme Immunoassay was used to analyze serial serum samples from patients enrolled in a longitudinal cohort study of children born to mothers infected with HIV-1. There were 85 subjects who were followed from birth whose HIV-1 infection status could be definitely determined as of March, 1990. Of these 22 (26%) were infected with HIV-1 and 63 (74%) were uninfected. Overall the sensitivity of the test was 77% (95% confidence interval (CI), 55 to 92%) and the specificity was 97% (95% CI, 89 to 99%). The positive predictive value of a single positive test was 89% (95% CI, 67 to 99%) and of two or more positive tests was 100% (95% CI, 50 to 100%). The sensitivity of the test varied greatly with age. For 36 children from whom sera were collected during the first month of life the specificity of the antigen test was 100% but the sensitivity was only 20%. Overall in the first 6 months of life the sensitivity was less than 50%. The Abbott HIV-1 antigen test is useful as an early predictor of HIV-1 infection in children whose mothers are infected.

Kinetic roughening model with opposite Kardar-Parisi-Zhang nonlinearities.

We introduce a model that simulates a kinetic roughening process with two kinds of particle: one follows ballistic deposition (BD) kinetics and the other restricted solid-on-solid Kim-Kosterlitz (KK) kinetics. Both of these kinetics are in the universality class of the nonlinear Kardar-Parisi-Zhang equation, but the BD kinetics has a positive nonlinear constant while the KK kinetics has a negative one. In our model, called the BD-KK model, we assign the probabilities p and (1-p) to the KK and BD kinetics, respectively. For a specific value of p, the system behaves as a quasilinear model and the up-down symmetry is restored. We show that nonlinearities of odd order are relevant in this low nonlinear limit.