Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

The first occurrence of the Order Mormonilloida (Copepoda) in the Tropical Southwest Atlantic Ocean

This communication is the first report of the occurrence of the order Mormonilloida (Mormonilla phasma) in the tropical Southwestern Atlantic Ocean. Female individuals were found in surface waters from the shelf break state of Rio Grande do Norte (Northeastern Brazil) and between depths of 60 and 100 m in the epipelagic layer around the St. Peter and St. Paul Archipelago (equatorial Atlantic). This finding extends the vertical limits for this species

Impulses of activation but not motor modules are preserved in the locomotion of subacute stroke patients

Gizzi L, Nielsen JF, Felici F, Ivanenko YP, Farina D. Impulses of activation but not motor modules are preserved in the locomotion of subacute stroke patients. J Neurophysiol 106: 202-210, 2011. First published April 20, 2011; doi:10.1152/jn.00727.2010.-It has been hypothesized that the coordinated activation of muscles is controlled by the central nervous system by means of a small alphabet of control signals (also referred to as activation signals) and motor modules (synergies). We analyzed the locomotion of 10 patients recently affected by stroke (maximum of 20 wk) and compared it with that of healthy controls. The aim was to assess whether the walking of subacute stroke patients is based on the same motor modules and/or activation signals as healthy subjects. The activity of muscles of the lower and upper limb and the trunk was measured and used for extracting motor modules. Four modules were sufficient to explain the majority of variance in muscle activation in both controls and patients. Modules from the affected side of stroke patients were different from those of healthy controls and from the unaffected side of stroke patients. However, the activation signals were similar between groups and between the affected and unaffected side of stroke patients, and were characterized by impulses at specific time instants within the gait cycle, underlying an impulsive controller of gait. In conclusion, motor modules observed in healthy subjects during locomotion are different from those used by subacute stroke patients, despite similar impulsive activation signals. We suggest that this pattern is consistent with a neuronal network in which the timing of activity generated by central pattern generators is directed to the motoneurons via a premotor network that distributes the activity in a task-dependent manner determined by sensory and descending control information