Some notions of subharmonicity over the quaternions

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.Comment: 16 page

On commuting polynomial automorphisms of C2

We characterize the commuting polynomial automorphisms of $\mathbb{C}^2$, using their meromorphic extension to $\mathbb{P}^2$ and looking at their dynamics on the line at infinity

Engineering the Mosquito Symbiont Pantoea agglomerans to secrete Anti-Plasmodium Inhibitory Proteins

The disease malaria originates from the transmission of the parasite Plasmodium to humans by female anopheline mosquitoes. Estimates put the number of deaths at 1-3 million people annually and this number will increase without the establishment of new control strategies. There is currently no vaccine and the effectiveness of insecticides and drugs are thwarted by the gain of resistances for both the insect and parasite. An alternative genetic engineering approach to combating malaria is presented here. The bacterial mosquito symbiont Pantoea agglomerans, which resides in the mosquito gut, was chosen to express anti-Plasmodium effector gene products that are known to inhibit Plasmodium development. A caveat is finding an appropriate protein secretion signal for export of the effectors from the cell. A two-pronged approach to finding a secretion signal involved identifying and testing a native secreted protein signal in P. agglomerans, and also testing heterologous secretion signals shown to work previously in related species. Proteomic analysis of native secreted proteins in spent growth medium followed by the identification of the corresponding genes revealed the best native candidate for trials was the secreted protein FliC/Flagellin. Various constructs involving the fliC 5\u27 UTR and the fliC ORF were used for secretion of a test protein (an anti-BSA scFv) in P. agglomerans and found to not be a sufficient secretion signal. The heterologous PelB (from Erwinia carotovora), and OmpA, TolB, and HlyA (all from E. coli) signals were also used in secretion trials with the anti-BSA scFv. The PelB and HlyA signals were shown to secrete the scFv in P. agglomerans, however it was only active in the case of PelB-induced secretion. In addition, four anti-Plasmodium effector proteins (SM1, Anti-Pbs21, PLA2, and CEL-III) were available for testing in constructs containing the heterologous secretion signals. Varying success was observed with the different combinations of signals and effector genes. The OmpA and TolB signals were not functional in P. agglomerans. P. agglomerans was able to secrete Anti-Pbs21-HlyA and PLA2 H67N-HlyA fusions and these strains are now available for testing inside malaria-infected anophelines for the inhibition of Plasmodium development

Regular vs. classical M\"obius transformations of the quaternionic unit ball

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular M\"obius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular M\"obius transformations and the Poincar\'e metric of B, which is preserved by the classical M\"obius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page

Chemical bond and electronic states in the CaF2-Si(111) and Ca-Si(111) interfaces

The first stage of formation of the CaF2-Si(111) and Ca-Si(111) interfaces is studied through the employment of the surface linear-muffin-tin-orbital approach in the atomic-sphere approximation. The interfaces are simulated by monolayers of F-Ca and Ca on Si(111), respectively. Both valence- and core-electron states have been calculated: their analysis gives important information about the nature of the Ca-Si and Ca-F bonds. These results are successfully compared with the available experimental data. The importance of considering the Madelung contribution in the interpretation of surface-core-level shifts is pointed out

Schwannoma vestibular (neurinoma do acústico) imitando desordens temporomandibulares: um relato de caso

Aproximadamente 6 a 16% dos pacientes com sintomas de neuralgia trigeminal apresentam tumores intracranianos, sendo mais comum o schwannoma vestibular (neurinoma do acústico). Alguns sintomas relatados pelos pacientes são perda da audição, zumbido, dores de cabeça, vertigens e distúrbios trigeminais. Uma resposta muscular aumentada na musculatura associada da cabeça e do pescoço também pode ser observada, o que pode mimetizar sinais e sintomas de desordens temporomandibulares. Nestes casos é de grande valia o uso de imagem de ressonância magnética (IRM) para detecção de tumores. É importante, também, a diferenciação de dores miofasciais e neurálgicas, pois ambas podem apresentar características semelhantes, mas com origens e tratamentos diferentes. O objetivo desse trabalho foi demonstrar através de relato de caso clínico a associação entre sintomas de neuralgia trigeminal, tumores intracranianos e disfunção temporomandibular.Approximately 6 to 16% of patients with trigeminal neuralgia symptoms present intracranial tumors, the most common being the vestibular schwannoma (acoustic neuroma). Some symptoms reported by patients include hearing loss, tinnitus, headaches, vertigo and trigeminal disturbances. An increased muscle response in the surrounding head and neck musculature may also be observed, which mimics signs and symptoms of temporomandibular disorders. In these cases, magnetic resonance imaging (MRI) has proved to be a useful tool in tumor diagnosis. The differential diagnosis between myofascial and neuralgic pain is important, as both may present similar characteristics, while being of different origin, and demanding special treatment approaches. The purpose of this paper is to demonstrate the relationship among trigeminal neuralgia symptoms, intracranial tumors and temporomandibular dysfunction by presenting a clinical case

Strong Convergence towards homogeneous cooling states for dissipative Maxwell models

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogenous cooling state present in the literature implies the strong convergence in Sobolev norms and in the $L^1$ norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the $L^1$ distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.Comment: 2 figure

Modulations of Cortical Power and Connectivity in Alpha and Beta Bands during the Preparation of Reaching Movements

Planning goal-directed movements towards different targets is at the basis of common daily activities (e.g., reaching), involving visual, visuomotor, and sensorimotor brain areas. Alpha (8-13 Hz) and beta (13-30 Hz) oscillations are modulated during movement preparation and are implicated in correct motor functioning. However, how brain regions activate and interact during reaching tasks and how brain rhythms are functionally involved in these interactions is still limitedly explored. Here, alpha and beta brain activity and connectivity during reaching preparation are investigated at EEG-source level, considering a network of task-related cortical areas. Sixty-channel EEG was recorded from 20 healthy participants during a delayed center-out reaching task and projected to the cortex to extract the activity of 8 cortical regions per hemisphere (2 occipital, 2 parietal, 3 peri-central, 1 frontal). Then, we analyzed event-related spectral perturbations and directed connectivity, computed via spectral Granger causality and summarized using graph theory centrality indices (in degree, out degree). Results suggest that alpha and beta oscillations are functionally involved in the preparation of reaching in different ways, with the former mediating the inhibition of the ipsilateral sensorimotor areas and disinhibition of visual areas, and the latter coordinating disinhibition of the contralateral sensorimotor and visuomotor areas

Tanaka Theorem for Inelastic Maxwell Models

We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like caricature. This property is as a generalization of the Tanaka theorem to inelastic interactions. Consequences are drawn on the asymptotic behavior of solutions in terms only of the Euclidean Wasserstein distance