Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

In Vivo Neuromechanics: Decoding Causal Motor Neuron Behavior with Resulting Musculoskeletal Function.

Human motor function emerges from the interaction between the neuromuscular and the musculoskeletal systems. Despite the knowledge of the mechanisms underlying neural and mechanical functions, there is no relevant understanding of the neuro-mechanical interplay in the neuro-musculo-skeletal system. This currently represents the major challenge to the understanding of human movement. We address this challenge by proposing a paradigm for investigating spinal motor neuron contribution to skeletal joint mechanical function in the intact human in vivo. We employ multi-muscle spatial sampling and deconvolution of high-density fiber electrical activity to decode accurate α-motor neuron discharges across five lumbosacral segments in the human spinal cord. We use complete α-motor neuron discharge series to drive forward subject-specific models of the musculoskeletal system in open-loop with no corrective feedback. We perform validation tests where mechanical moments are estimated with no knowledge of reference data over unseen conditions. This enables accurate blinded estimation of ankle function purely from motor neuron information. Remarkably, this enables observing causal associations between spinal motor neuron activity and joint moment control. We provide a new class of neural data-driven musculoskeletal modeling formulations for bridging between movement neural and mechanical levels in vivo with implications for understanding motor physiology, pathology, and recovery

Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group $G=${\bf O}$_3\otimes${\bf U}$_1\times$. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial $G$-invariant free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table II

Neuro-Musculoskeletal Mapping for Man-Machine Interfacing.

We propose a myoelectric control method based on neural data regression and musculoskeletal modeling. This paradigm uses the timings of motor neuron discharges decoded by high-density surface electromyogram (HD-EMG) decomposition to estimate muscle excitations. The muscle excitations are then mapped into the kinematics of the wrist joint using forward dynamics. The offline tracking performance of the proposed method was superior to that of state-of-the-art myoelectric regression methods based on artificial neural networks in two amputees and in four out of six intact-bodied subjects. In addition to joint kinematics, the proposed data-driven model-based approach also estimated several biomechanical variables in a full feed-forward manner that could potentially be useful in supporting the rehabilitation and training process. These results indicate that using a full forward dynamics musculoskeletal model directly driven by motor neuron activity is a promising approach in rehabilitation and prosthetics to model the series of transformations from muscle excitation to resulting joint function

The problem of political science and practical politics

Copyright @ 2006 The AuthorsWe reflect on the reasons why there is not a greater and more fruitful relationship between those who seek to understand policy and the political process from academia and those with a similar task in ‘practical politics’. We attribute this lack of engagement to three core factors: (1) from without, instrumental government visions of political science perpetuate the view that the discipline exists to serve those with power; (2) from within, scientism and abstraction diminish the discipline's stock of ‘usable’ product for ‘practical politics’; and (3) where relevant research exists, its uptake is hampered by limited communication between these spheres

Kinematics of the 1991 Randa rockslides (Valais, Switzerland)

International audienceAbout 22 mio m3 of rock fell from a cliff near the village of Randa (10 km north of Zermatt, Switzerland) on 18 April 1991. A second retrogressive rockslide of about 7 mio m3 followed on 9 May 1991. At present, a rock mass situated above the scarp is still slowly moving toward the valley, involving several mio m 3 of rock. A kinematic approach to study of this well-documented rockslide was made "a posteriori" in order to identify the parameters relevant to the detection of such failures involving large volumes of rock. A 3-D model of the pre-rockslide geometry is presented, and is used to interpret the geostructural, hydrogeological, and chronological data. The steepness of the cliff, the massive lithology (mainly orthogneiss), the location on a topographic ridge outcropping at the confluence between a glacial cirque and the main valley, and the existence of previous events of instability were the preexisting field conditions that affected the stability of the area. The structural cause of instability was a 30 dipping, more than 500-m-long, persistent fault, which cut the base of the rock face. Together with a steeply dipping set of persistent joints, this basal discontinuity delimited a 20- mio-m 3 rock block, with a potential sliding direction approximately parallel to the axis of the valley. To the North, the fractures delimiting the unstable mass were less persistent and separated by rock bridges; this rock volume acted as key block. This topographic and structural configuration was freed from glacier support about 15 000 years BP. The various mechanisms of degradation that led to the final loss of equilibrium required various amounts of time. During the late-and post-glacial periods, seismic activity and weathering of the orthogneiss along the fissure network due to infiltration of meteoric water, joined to reduce the mechanical resistance of the sliding surfaces and the rocks bridges. In addition, crystallisation of clay minerals due to mineralogical alteration of the fault gouge accumulated along the sliding surface, reducing its angle of internal friction, and sealing the surface against water circulation. Once this basal fracture began to act as an aquiclude, the seasonal increase of the hydraulic head in the fissures promoted hydraulic fracturing on the highly stressed edges of the key block. Acceleration of this mechanical degradation occurred during the 20-year period before the 1991 rockslides, giving rise to an increasing rockfall activity, that constituted a forewarning sign. The final triggering event corresponded to a snow-melt period with high water table, leading to fracturation around the key block. On 18 April 1991, the key block finally failed, allowing subsidiary orthogneiss blocks to slide. They fell in turn over a period of several hours. The 9 May 1991, rockslide was the first of a series of expected future retrogressive reequilibrium stages of the very fractured and decompressed paragneisses, which lie on the orthogneiss base cut by the 18 April event