On the Jacobi-Metric Stability Criterion

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure

Ion channels and neuronal excitability in polyglutamine neurodegenerative diseases

Abstract Polyglutamine (polyQ) diseases are a family composed of nine neurodegenerative inherited disorders (NDDs) caused by pathological expansions of cytosine-adenine-guanine (CAG) trinucleotide repeats which encode a polyQ tract in the corresponding proteins. CAG polyQ repeat expansions produce neurodegeneration via multiple downstream mechanisms; among those the neuronal activity underlying the ion channels is affected directly by specific channelopathies or indirectly by secondary dysregulation. In both cases, the altered excitability underlies to gain- or loss-of-function pathological effects. Here we summarize the repertoire of ion channels in polyQ NDDs emphasizing the biophysical features of neuronal excitability and their pathogenic role. The aim of this review is to point out the value of a deeper understanding of those functional mechanisms and processes as crucial elements for the designing and targeting of novel therapeutic avenues

Functionally different PIN proteins control auxin flux during bulbil development in Agave tequilana

In Agave tequilana, reproductive failure or inadequate flower development stimulates the formation of vegetative bulbils at the bracteoles, ensuring survival in a hostile environment. Little is known about the signals that trigger this probably unique phenomenon in agave species. Here we report that auxin plays a central role in bulbil development and show that the localization of PIN1-related proteins is consistent with altered auxin transport during this process. Analysis of agave transcriptome data led to the identification of the A. tequilana orthologue of PIN1 (denoted AtqPIN1) and a second closely related gene from a distinct clade reported as ‘Sister of PIN1’ (denoted AtqSoPIN1). Quantitative real-time reverse transcription–PCR (RT-qPCR) analysis showed different patterns of expression for each gene during bulbil formation, and heterologous expression of the A. tequilana PIN1 and SoPIN1 genes in Arabidopsis thaliana confirmed functional differences between these genes. Although no free auxin was detected in induced pedicel samples, changes in the levels of auxin precursors were observed. Taken as a whole, the data support the model that AtqPIN1 and AtqSoPIN1 have co-ordinated but distinct functions in relation to auxin transport during the initial stages of bulbil formation

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation

Multiscale reduction of discrete nonlinear Schroedinger equations

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.Comment: 12 page

On the Integrability of the Discrete Nonlinear Schroedinger Equation

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.Comment: 4 pages, accepted in EP

Closing the dark photon window to thermal dark matter

The nature of dark matter remains a central question in particle physics, cosmology, and astrophysics. The prevailing hypothesis postulates that dark matter consists of particles that interact only weakly with Standard Model particles. However, the knowledge of dark matter properties beyond these interactions is limited. This study explores a scenario involving a dark photon as a mediator between dark matter and the Standard Model, akin to the photon's role in electromagnetism. Recent cosmological and experimental evidence impose constraints on this scenario, focusing on results from direct detection experiments such as PICO-60, XENON-1T, and PANDAX-4T. The results reveal severe constraints, effectively closing the window for laboratory searches for dark photons as mediators between the Standard Model and the dark sector (dark electrons) in the secluded dark matter scenario. The findings underscore the need for alternative explanations and offer fresh perspectives on the ongoing quest to understand dark matter and its interactions since they are nearly independent of the dark electron fraction content for the total dark matter. This analysis significantly narrows down the parameter space for thermal dark matter scenarios involving a dark photon portal, reinforcing the urgency of exploring alternative models and designing new experiments to unravel the mysteries surrounding the nature of dark matter.Comment: 11 pages, 5 figure

3D Printable Conducting and Biocompatible PEDOT-graft-PLA Copolymers by Direct Ink Writing

Tailor-made polymers are needed to fully exploit the possibilities of additive manufacturing, constructing complex, and functional devices in areas such as bioelectronics. In this paper, the synthesis of a conducting and biocompatible graft copolymer which can be 3D printed using direct melting extrusion methods is shown. For this purpose, graft copolymers composed by conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) and a biocompatible polymer polylactide (PLA) are designed. The PEDOT-g-PLA copolymers are synthesized by chemical oxidative polymerization between 3,4-ethylenedioxythiophene and PLA macromonomers. PEDOT-g-PLA copolymers with different compositions are obtained and fully characterized. The rheological characterization indicates that copolymers containing below 20 wt% of PEDOT show the right complex viscosity values suitable for direct ink writing (DIW). The 3D printing tests using the DIW methodology allows printing different parts with different shapes with high resolution (200\ua0\ub5m). The conductive and biocompatible printed patterns of PEDOT-g-PLA show excellent cell growth and maturation of neonatal cardiac myocytes cocultured with fibroblasts