A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems

Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should the dynamics be given by a limiting value on one side or other of the discontinuity, or a member of some set containing those values? One way to remove the ambiguity is to regularize the discontinuity, the most common being either to smooth it out, or to introduce a hysteresis between switching in one direction or the other across it. Here we show that the two can in general lead to qualitatively different dynamical outcomes. We then define a higher dimensional model with both smoothing and hysteresis, and study the competing limits in which hysteretic or smoothing effects dominate the behaviour, only the former of which correspond to Filippov’s standard ‘sliding modes’.Peer ReviewedPostprint (author's final draft

Chaos in the hysteretic grazing-sliding codimension-one saddle-node bifurcation of piecewise dynamical systems

We present two ways of regularizing a parameter family of piecewise smooth dynamical systems undergoing a grazing- sliding bifurcation. We use the Sotomayor-Teixeira regularization and prove that the bifurcation is a saddle-node (see [ ? ]). Then we perform a hysteretic regularization. However, in spite that the two regularization will give the same dynamics in the sliding modes (see [ ? ]), when a tangency appears, so is in the case of grazing-sliding, the hysteretic process generate chaotic dynamics. Finally, we smooth the hysteresis by embedding the system in a higher dimension. Now the discontinuous control variable u is also a continuous time dependent variable although a fast-fast one. We then encounter loop feedback chaotic behaviourPostprint (author's final draft

The Leishmania infantum PUF proteins are targets of the humoral response during visceral leishmaniasis

<p>Abstract</p> <p>Background</p> <p>RNA-binding proteins of the PUF family share a conserved domain consisting of tandemly repeated 36-40 amino acid motifs (typically eight) known as Puf repeats. Proteins containing tandem repeats are often dominant targets of humoral responses during infectious diseases. Thus, we considered of interest to analyze whether <it>Leishmania </it>PUF proteins result antigenic during visceral leishmaniasis (VL).</p> <p>Findings</p> <p>Here, employing whole-genome databases, we report the composition, and structural features, of the PUF family in <it>Leishmania infantum</it>. Additionally, the 10 genes of the <it>L. infantum </it>PUF family were cloned and used to express the <it>Leishmania </it>PUFs in bacteria as recombinant proteins. Finally, the antigenicity of these PUF proteins was evaluated by determining levels of specific antibodies in sera from experimentally infected hamsters. The <it>Leishmania </it>PUFs were all recognized by the sera, even though with different degree of reactivity and/or frequency of recognition. The reactivity of hamster sera against recombinant LiPUF1 and LiPUF2 was particularly prominent, and these proteins were subsequently assayed against sera from human patients. High antibody responses against rLiPUF1 and rLiPUF2 were found in sera from VL patients, but these proteins resulted also recognized by sera from Chagas' disease patients.</p> <p>Conclusion</p> <p>Our results suggest that <it>Leishmania </it>PUFs are targets of the humoral response during <it>L. infantum </it>infection and may represent candidates for serodiagnosis and/or vaccine reagents; however, it should be kept in mind the cross-reactivity of LiPUFs with antibodies induced against other trypanosomatids such as <it>Trypanosoma cruzi</it>.</p

Regularization around a generic codimension one fold-fold singularity

This paper is devoted to study the generic fold-fold singularity of Filippov systems on the plane, its unfoldings and its Sotomayor–Teixeira regularization. We work with general Filippov systems and provide the bifurcation diagrams of the fold-fold singularity and their unfoldings, proving that, under some generic conditions, is a codimension one embedded submanifold of the set of all Filippov systems. The regularization of this singularity is studied and its bifurcation diagram is shown. In the visible–invisible case, the use of geometric singular perturbation theory has been useful to give the complete diagram of the unfolding, specially the appearance and disappearance of periodic orbits that are not present in the Filippov vector field. In the case of a linear regularization, we prove that the regularized system is equivalent to a general slow-fast system studied by Krupa and SzmolyanPeer ReviewedPostprint (published version

Cuban Coffee Production: An Analysis from 1950 to 2017

Coffee production in Cuba had its highest value in 1961, and since then it has steadily decreased. We evaluate Cuban coffee production from 1950 to 2017 through a chronological series of data production (production, yield) and cultivation areas, and determine the influence of the loss of productive areas on the productive values. In this period the evaluated variables decreased significantly. The maximum production reached 60,326 tonnes in 1961, and the minimum 4,973 tonnes in 2012. The maximum yield was 0.36 tonnes ha−1 in 1961 and the minimum was 0.08 tonnes ha−1 in 2005. The hectares of coffee plantations decreased from 185,947.52 in 1969 to 42,296 in 2017. This decrease explains 36.8% of the decline in production. We argue that this decline is mainly due to internal factors (armed conflicts, migration, inadequate management, and economic crisis). This multifactorial process and complex situation should be considered in future studies.La producción de café cubana tuvo su mayor récord en 1961, luego disminuyó constantemente. Nosotros la evaluamos desde 1950 hasta 2017 a través de una serie cronológica de datos de producción (producción, rendimiento) y las áreas de cultivo. Determinamos la influencia de la pérdida de áreas productivas en los valores productivos. En este período las variables evaluadas disminuyeron significativamente. La producción máxima fue de 60,326 t en 1961 y la mínima de 4,973 t en 2012. El rendimiento máximo fue de 0.36 t ha−1 en 1961 y el mínimo de 0.08 t ha−1 en 2005. Las hectáreas disminuyeron de 185,947 en 1969 a 42,296 en 2017. Esta disminución explica el 36.8% de la caída de la producción Este declive se debe principalmente a factores internos (conflictos armados, migraciones, gestión inadecuada, crisis económica). Este es un proceso complejo y multifactorial, lo que debe ser considerado en futuros estudios

Traveling waves in a model for cortical spreading depolarization with slow-fast dynamics

Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain activity. They are associated with various brain disorders such as migraine and ischemia. We consider a reduced version of a biophysical model of a neuron–astrocyte network for the initiation and propagation of CSD waves [Huguet et al., Biophys. J. 111(2), 452–462, 2016], consisting of reaction-diffusion equations. The reduced model considers only the dynamics of the neuronal and astrocytic membrane potentials and the extracellular potassium concentration, capturing the instigation process implicated in such waves. We present a computational and mathematical framework based on the parameterization method and singular perturbation theory to provide semi-analytical results on the existence of a wave solution and to compute it jointly with its velocity of propagation. The traveling wave solution can be seen as a heteroclinic connection of an associated system of ordinary differential equations with a slow–fast dynamics. The presence of distinct time scales within the system introduces numerical instabilities, which we successfully address through the identification of significant invariant manifolds and the implementation of the parameterization method. Our results provide a methodology that allows to identify efficiently and accurately the mechanisms responsible for the initiation of these waves and the wave propagation velocity.Work produced with support of the grant PID-2021-122954NB-100 funded by MCIN/AEI/ 10.13039/501100011033 and “ERDF: A way of making Europe.” T.M.S and G.H acknowledge the Maria de Maeztu Award for Centers and Units of Excellence in R&D (No. CEX2020-001084-M). T.M.S. is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. We also acknowledge the use of the UPC Dynamical Systems group’s cluster for research computing (https://dynamicalsystems.upc.edu/en/computing/)Peer ReviewedPostprint (published version

Surface waves in solar granulation observed with {\sc Sunrise}

Solar oscillations are expected to be excited by turbulent flows in the intergranular lanes near the solar surface. Time series recorded by the IMaX instrument aboard the {\sc Sunrise} observatory reveal solar oscillations at high resolution, which allow studying the properties of oscillations with short wavelengths. We analyze two times series with synchronous recordings of Doppler velocity and continuum intensity images with durations of 32\thinspace min and 23\thinspace min, resp., recorded close to the disk center of the Sun to study the propagation and excitation of solar acoustic oscillations. In the Doppler velocity data, both the standing acoustic waves and the short-lived, high-degree running waves are visible. The standing waves are visible as temporary enhancements of the amplitudes of the large-scale velocity field due to the stochastic superposition of the acoustic waves. We focus on the high-degree small-scale waves by suitable filtering in the Fourier domain. Investigating the propagation and excitation of $f$- and $p_1$-modes with wave numbers $k > 1.4$\thinspace 1/Mm we find that also exploding granules contribute to the excitation of solar $p$-modes in addition to the contribution of intergranular lanes.Comment: 12 pages, 4 figures, to appear in a special volume on Sunrise in Astrophysical Journal Letter

On the Moat-Penumbra Relation

Proper motions in a sunspot group with a delta-configuration and close to the solar disc center have been studied by employing local correlation tracking techniques. The analysis is based on more than one hour time series of G-band images. Radial outflows with a mean speed of 0.67 km s^{-1} have been detected around the spots, the well-known sunspots moats. However, these outflows are not found in those umbral core sides without penumbra. Moreover, moat flows are only found in those sides of penumbrae located in the direction marked by the penumbral filaments. Penumbral sides perpendicular to them show no moat flow. These results strongly suggest a relation between the moat flow and the well-known, filament aligned, Evershed flow. The standard picture of a moat flow originated from a blocking of the upward propagation of heat is commented in some detail.Comment: 4 pages, 4 figures, To appear in ApJ Letter

Fragment Dissolved molecular dynamics: A systematic and efficient method to locate binding sites.

Fragment-based drug discovery (FBDD) has been popular in the last decade, but some drawbacks, such as protein denaturation or ligand aggregation, have not yet clearly overcome in the framework of biomolecular simulations. In this work a systematic and semi-automatic method is presented as a novel proposal, named fragment dissolved Molecular Dynamics (fdMD), to improve research in future FBDD projects. Our method employs simulation boxes of solvated small fragments, adding a repulsive Lennard-Jones potential term to avoid aggregation, which can be easily used to solvate the object of interest. This method has the advantage of solvating the target with a low number of ligands, thus preventing this way denaturation of the target, while simultaneously generating a database of ligand-solvated boxes that can be used with other targets. A number of scripts are made available to analyze the results and obtain the descriptors proposed as a means of trustfully discard spurious binding sites. To test our method, four sets of different complexity have been solvated with ligand boxes and four molecular dynamics runs of 200 ns length have been run for each system, which have been extended up to 1 μs when needed. The reported results point that the selected number of replicas are enough to identify the correct binding sites irrespective of the initial structure, even in the case of proteins having several close binding sites for the same ligand. Among the proposed descriptors, average MMGBSA and average KDEEP energies emerge as the most robust ones

Bright points in the quiet Sun as observed in the visible and near-UV by the balloon-borne observatory Sunrise

Bright points (BPs) are manifestations of small magnetic elements in the solar photosphere. Their brightness contrast not only gives insight into the thermal state of the photosphere (and chromosphere) in magnetic elements, but also plays an important role in modulating the solar total and spectral irradiance. Here we report on simultaneous high-resolution imaging and spectropolarimetric observations of BPs using Sunrise balloon-borne observatory data of the quiet Sun at disk center. BP contrasts have been measured between 214 nm and 525 nm, including the first measurements at wavelengths below 388 nm. The histograms of the BP peak brightness show a clear trend toward broader contrast distributions and higher mean contrasts at shorter wavelengths. At 214 nm we observe a peak brightness of up to five times the mean quiet-Sun value, the highest BP contrast so far observed. All BPs are associated with a magnetic signal, although in a number of cases it is surprisingly weak. Most of the BPs show only weak downflows, the mean value being 240 m/s, but some display strong down- or upflows reaching a few km/s.Comment: Accepted for publication in The Astrophysical Journal Letters on September 08 201