Pattern evocation and geometric phases in mechanical systems with symmetry

This paper is concerned with the relation between the dynamics of a given Hamiltonian system with a given symmetry group and its reduced dynamics. We illustrate the process of visualization of reduced orbits using the double spherical pendulum. In this process of visualization, one sees certain patterns when the dynamics is viewed relative to rotating frames with certain critical angular velocities. By using the reduced dynamics, we also explain these patterns. We show that if the motion on the phase space reduced by a continuous symmetry group at a given momentum level is periodic, then there is a uniformly rotating frame, that is, a one-parameter group motion, relative to which the unreduced trajectory is periodic with the same period. If the continuous symmetry group of the system is Abelian, which corresponds to the system having cyclic variables, we derive an explicit expression for the required angular velocity in terms of the dynamic phase (an average of the mechanical connection) and the geometric phase (the holonomy of the mechanical connection). We show that one can also find such a frame if the reduced orbit is quasi-periodic and a KAM (Kolmogorov-Arnold-Moser) condition is satisfied The almost periodic case is also discussed. An important aspect of this procedure is how to use it in the presence of discrete symmetries. We show that, under appropriate conditions, the visualized orbit has, relative to a suitable uniformly rotating frame, the same temporal behavior and discrete symmetries as the reduced orbit. Since these spatio-temporal patterns are not apparent with repect to most frames, we call the phenomenon pattern evocation     

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and inter-annually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R² = 0.80 and R² = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages.     

Review of 23 patients affected by the stiff man syndrome: clinical subdivision into stiff trunk (man) syndrome, stiff limb syndrome, and progressive encephalomyelitis with rigidity

OBJECTIVE: To investigate whether the stiff limb syndrome may be separated from the stiff man syndrome and progressive encephalomyelitis with rigidity on simple clinical grounds, and whether such a distinction has implications for aetiology, treatment, and prognosis. METHODS: Twenty three patients referred over a 10 year period with rigidity and spasms in association with continuous motor unit activity, but without evidence of neuromyotonia, extrapyramidal or pyramidal dysfunction or focal lesions of the spinal cord were reviewed. The patients were divided into those with an acute or subacute illness, leading to death within 1 year, and those with a chronic course. The latter were divided into those in whom rigidity and spasms dominated in the axial muscles, or in one or more distal limbs, at the time of their first assessment. RESULTS: This simple division identified three distinct groups of patients. (1) Progressive encephalomyelitis with rigidity: two patients had a rapidly progressive condition characterised by widespread rigidity which resulted in death within 6 and 16 weeks. One patient had negative anti-GAD and anti-neuronal antibodies, but had markedly abnormal CSF and widespread denervation. The principal pathological findings in this case were a subacute encephalomyelitis which primarily affected the grey matter. In the remaining patient anti-GAD antibodies were not tested, and postmortem was refused. (2) Stiff man syndrome: eight patients had rigidity and painful spasms of the lumbar paraspinal, abdominal, and occasionally proximal leg muscles associated with a lumbar hyperlordosis. There was no involvement of the upper limbs, distal lower limbs, sphincters or cranial nerves. Seven had anti-GAD antibodies and most had additional evidence of autoimmune disease. Neurophysiologically there was continuous motor unit activity with abnormal exteroceptive reflexes, but a normal interference pattern during spasms. The patients all responded to baclofen/diazepam and remained ambulant. (3) Stiff limb syndrome: thirteen patients had rigidity, painful spasm, and abnormal postures of the distal limb, ususphincter or brainstem involvement. Generalised myoclonic jerks were not a feature. Only two had truncal rigidity, and another two had anti-GAD antibodies. Most had no evidence of autoimmune disease. Neurophysiologically they had continuous motor unit activity in the affected limb, abnormal exteroceptive reflexes, and abnormally segmented EMG activity during spasms. The disease ran a protracted course, and most patients had only a partial response to baclofen or diazepam. About half became wheelchair bound. CONCLUSIONS: The stiff limb syndrome seems distinct from the stiff man syndrome or progressive encephalomyelitis with rigidity, and is an important cause of rigidity and spasm in the setting of continuous motor unit activity.     

Toward Empowered Design

Pragmatic design requires no radical alterations to the existing digital ecology and has successfully provided many viable solutions. Given the skills limitations within the developing world, however, developers also need a new design focus that views the user as designer.