Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector fields.Comment: 20 pages, 25 figure

Closed-Loop Control of Local Magnetic Actuation for Robotic Surgical Instruments

We propose local magnetic actuation (LMA) as an approach to robotic actuation for surgical instruments. An LMA actuation unit consists of a pair of diametrically magnetized single-dipole cylindrical magnets, working as magnetic gears across the abdominal wall. In this study, we developed a dynamic model for an LMA actuation unit by extending the theory proposed for coaxial magnetic gears. The dynamic model was used for closed-loop control, and two alternative strategies-using either the angular velocity at the motor or at the load as feedback parameter-were compared. The amount of mechanical power that can be transferred across the abdominal wall at different intermagnetic distances was also investigated. The proposed dynamic model presented a relative error below 7.5% in estimating the load torque from the system parameters. Both the strategies proposed for closed-loop control were effective in regulating the load speed with a relative error below 2% of the desired steady-state value. However, the load-side closed-loop control approach was more precise and allowed the system to transmit larger values of torque, showing, at the same time, less dependence from the angular velocity. In particular, an average value of 1.5 mN·m can be transferred at 7 cm, increasing up to 13.5 mN·m as the separation distance is reduced down to 2 cm. Given the constraints in diameter and volume for a surgical instrument, the proposed approach allows for transferring a larger amount of mechanical power than what would be possible to achieve by embedding commercial dc motors

Cartografía geomorfológica y procesos de activos en la cuenca media-alta del río Eria mediante técnicas de SIG.( Provincia de León, España)

El objetivo es la elaboración de la cartografía geomorfológica y de procesos geológicos activos de un tramo del curso medio de la cuenca del río Eria, en el sector suroccidental de la provincia de León utilizando técnicas de SIG. El trabajo se ha basado en la fotointerpretación de fotos aéreas en visión estereoscópica, estudio bibliográfico y aplicación de técnicas de SIG para el análisis de modelos digitales de terreno y mapas derivados (pendientes, alturas…) y para la representación cartográfica. Como resultado se distinguen tres dominios de relieve caracterizados por diferentes procesos geológicos: dominio de los relieves sobre sustrato paleozoico, dominio de los relieves de origen fluvial y dominio de las formas de origen antrópico. En el primero tienen gran relevancia las formas del relieve relacionadas con la estructura geológica hercínica, en donde aparecen procesos activos ligados a procesos gravitacionales, originando formas del relieve como canchales, coluviones, depósitos de piedemonte y. Debido a lo escarpado de este dominio, apenas existen infraestructuras humanas, por lo que la interferencia de los procesos activos con las mismas es baja. En el segundo dominio aparecen formas del relieve originadas por procesos activos relacionados con el encajamiento de la red fluvial y de sedimentación, pudiendo afectar a infraestructuras humanas. En el tercero aparecen actuaciones susceptibles de interferir con los procesos activos naturales, provocando efectos adversos para la población. La información cartográfica obtenida supone la base para un análisis de susceptibilidad espacial de los distintos peligros de origen geológico, útil para la planificación territorial.The aim of this work is to represent by means of GIS techniques the geomorphological and active geological processes map of the middle course of the Eria river, located in the southwestern León province, Spain. This study is based on aerial photointerpretation, bibliographic analysis of previous works, and on the application of GIS techniques. These techniques were used for the representation of the mapping units, and for analyzing a DTM and derived maps (slop, aspect, etc.), creating a spatial and attribute database.Three main relief domains were differentiated based on the predominant active geological processes: the domain of landforms developed on the Palaeozoic metamorphic rocks, the domain of fluvial landforms, and the domain of anthropogenic landforms. The first one is mainly related to active gravitational processes, but because of the low human occupation, the interaction with human infrastructures is almost negligible. The second one is mainly related to incision and sedimentation of the drainage network, interacting with some human infrastructures developed on the floodplains, alluvial fans and close to the river side. The third one is formed by human elements affecting and modifying at different levels the strength of the active geological processes. The resulting map act as a basis for further spatial susceptibility for geological hazards analysis, which is useful for land use planning

Absence of RNA-binding protein FXR2P prevents prolonged phase of kainate-induced seizures.

Status epilepticus (SE) is a condition in which seizures are not self-terminating and thereby pose a serious threat to the patient's life. The molecular mechanisms underlying SE are likely heterogeneous and not well understood. Here, we reveal a role for the RNA-binding protein Fragile X-Related Protein 2 (FXR2P) in SE. Fxr2 KO mice display reduced sensitivity specifically to kainic acid-induced SE. Immunoprecipitation of FXR2P coupled to next-generation sequencing of associated mRNAs shows that FXR2P targets are enriched in genes that encode glutamatergic post-synaptic components. Of note, the FXR2P target transcriptome has a significant overlap with epilepsy and SE risk genes. In addition, Fxr2 KO mice fail to show sustained ERK1/2 phosphorylation induced by KA and present reduced burst activity in the hippocampus. Taken together, our findings show that the absence of FXR2P decreases the expression of glutamatergic proteins, and this decrease might prevent self-sustained seizures

Transverse Wave Propagation in Relativistic Two-fluid Plasmas in de Sitter Space

We investigate transverse electromagnetic waves propagating in a plasma in the de Sitter space. Using the 3+1 formalism we derive the relativistic two-fluid equations to take account of the effects due to the horizon and describe the set of simultaneous linear equations for the perturbations. We use a local approximation to investigate the one-dimensional radial propagation of Alfv\'en and high frequency electromagnetic waves and solve the dispersion relation for these waves numerically.Comment: 19 pages, 12 figure

Numerical Solutions of ideal two-fluid equations very closed to the event horizon of Schwarzschild black hole

The 3+1 formalism of Thorne, Price and Macdonald has been used to derive the linear two-fluid equations describing transverse and longitudinal waves propagating in the two-fluid ideal collisionless plasmas surrounding a Schwarzschild black hole. The plasma is assumed to be falling in radial direction toward the event horizon. The relativistic two-fluid equations have been reformulate, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here a WKB approximation is used to derive the local dispersion relation for these waves and solved numerically for the wave number k.Comment: 16 pages, 15 figures. arXiv admin note: text overlap with arXiv:0902.3766, arXiv:0807.459

Design, synthesis and evaluation of benzothiazole derivatives as multifunctional agents

Oxidative stress is the product or aetiology of various multifactorial diseases; on the other hand, the development of multifunctional compounds is a recognized strategy for the control of complex diseases. To this end, a series of benzothiazole derivatives was synthesized and evaluated for their multifunctional effectiveness as antioxidant, sunscreen (filter), antifungal and antiproliferative agents. Compounds were easily synthesized via condensation reaction between 2-aminothiophenols and different benzaldehydes. SAR study, particularly in position 2 and 6 of benzothiazoles, led to the identification of 4g and 4k as very interesting potential compounds for the design of multifunctional drugs. In particular, compound 4g is the best blocker of hERG potassium channels expressed in HEK 293 cells exhibiting 60.32% inhibition with IC50 = 4.79 μM

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

A7. SITUAZIONE NAZIONALE: CORPI IDRICI INTERESSATI DA CIANOBATTERI TOSSICI

I cianobatteri sono diffusi in moltissimi ambienti acquatici, dove possono produrre cianotossine con diversi profili tossicologici. Il presente rapporto riporta le linee guida per la gestione delle fioriture di cianobatteri nelle acque di balneazione, elaborate da un gruppo di esperti. La prima parte sintetizza le attuali conoscenze scientifiche su vari aspetti, fra cui la loro presenza nei laghi italiani, le caratteristiche chimiche e tossicologiche delle varie cianotossine, gli effetti osservati sulla salute dell\u2019uomo e la valutazione del rischio. La seconda parte definisce le linee guida per prevenire effetti dannosi per la salute dei bagnanti e gestire il rischio associato alle fioriture. Vengono fornite indicazioni per pianificare attivit\ue0 di monitoraggio ambientale e sorveglianza sanitaria nelle aree a maggiore criticit\ue0. Viene inoltre presentato un sistema di reportistica, ambientale e sanitario, anche allo scopo di uniformare le informazioni a livello nazionale. Il rapporto \ue8 completato dalle indicazioni tecniche rivolte alle strutture territoriali preposte.Cyanobacteria thrive in many aquatic environments, where they can produce cyanotoxins with different toxicological profiles. This report provides the guidelines for the management of cyanobacterial blooms in bathing water, put together by a group of experts. The first part summarizes the current scientific knowledge on various aspects, including their presence in the Italian lakes, chemical and toxicological characteristics of different cyanotoxins, the observed effects on human health and the risk assessment. The second part defines the guidelines to prevent harmful effects on the health of bathers and manage the risk associated with blooms. It provides recommendations for planning environmental monitoring activities and a health surveillance system in most critical areas. It also introduces an environmental and health reporting system, with the purpose to standardize the information at national level too. The report is supplemented by technical information aimed at territorial authorities in charge

Escape Rates and Physically Relevant Measures for Billiards with Small Holes

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure