One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor

Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods

Motion and Trajectories of Particles Around Three-Dimensional Black Holes

The motion of relativistic particles around three dimensional black holes following the Hamilton-Jacobi formalism is studied. It follows that the Hamilton-Jacobi equation can be separated and reduced to quadratures in analogy with the four dimensional case. It is shown that: a) particles are trapped by the black hole independently of their energy and angular momentum, b) matter alway falls to the centre of the black hole and cannot understake a motion with stables orbits as in four dimensions. For the extreme values of the angular momentum of the black hole, we were able to find exact solutions of the equations of motion and trajectories of a test particle.Comment: Plain TeX, 9pp, IPNO-TH 93/06, DFTUZ 93/0

The human central nervous system transmits common synaptic inputs to distinct motor neuron pools during non-synergistic digit actions

KEY POINTS: Neural connectivity between distinct motor neuronal modules in the spinal cord is classically studied through electrical stimulation or multi-muscle EMG recordings. We quantified the strength of correlation in the activity of two distinct populations of motor neurons innervating the thenar and first dorsal interosseous muscles during tasks that required the two hand muscles to exert matched or un-matched forces in different directions. We show that when the two hand muscles are concurrently activated, synaptic input to the two motor neuron pools is shared across all frequency bandwidths (representing cortical and spinal input) associated with force control. The observed connectivity indicates that motor neuron pools receive common input even when digit actions do not belong to a common behavioural repertoire. ABSTRACT: Neural connectivity between distinct motor neuronal modules in the spinal cord is classically studied through electrical stimulation or multi-muscle EMG recordings. Here we quantify the strength of correlation in the activity of two distinct populations of motor neurons innervating the thenar and first dorsal interosseous muscles in humans during voluntary contractions. To remove confounds associated with previous studies, we used a task that required the two hand muscles to exert matched or un-matched forces in different directions. Despite the force production task consisting of uncommon digit force coordination patterns, we found that synaptic input to motor neurons is shared across all frequency bands, reflecting cortical and spinal inputs associated with force control. The coherence between discharge timings of the two pools of motor neurons was significant at the delta (0-5 Hz), alpha (5-15 Hz) and beta (15-35 Hz) bands (P < 0.05). These results suggest that correlated input to motor neurons of two hand muscles can occur even during tasks not belonging to a common behavioural repertoire and despite lack of common innervation. Moreover, we show that the extraction of activity from motor neurons during voluntary force control removes cross-talk associated with global EMG recordings, thus allowing direct in vivo interrogation of spinal motor neuron activity

Comparison between the degree of motor unit short-term synchronization and recurrence quantification analysis of the surface EMG in two human muscles

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Gene co-expression in the interactome: moving from correlation toward causation via an integrated approach to disease module discovery

In this study, we integrate the outcomes of co-expression network analysis with the human interactome network to predict novel putative disease genes and modules. We first apply the SWItch Miner (SWIM) methodology, which predicts important (switch) genes within the co-expression network that regulate disease state transitions, then map them to the human protein–protein interaction network (PPI, or interactome) to predict novel disease–disease relationships (i.e., a SWIM-informed diseasome). Although the relevance of switch genes to an observed phenotype has been recently assessed, their performance at the system or network level constitutes a new, potentially fascinating territory yet to be explored. Quantifying the interplay between switch genes and human diseases in the interactome network, we found that switch genes associated with specific disorders are closer to each other than to other nodes in the network, and tend to form localized connected subnetworks. These subnetworks overlap between similar diseases and are situated in different neighborhoods for pathologically distinct phenotypes, consistent with the well-known topological proximity property of disease genes. These findings allow us to demonstrate how SWIM-based correlation network analysis can serve as a useful tool for efficient screening of potentially new disease gene associations. When integrated with an interactome-based network analysis, it not only identifies novel candidate disease genes, but also may offer testable hypotheses by which to elucidate the molecular underpinnings of human disease and reveal commonalities between seemingly unrelated diseases