Applications of Frobenius Algebras to Representation Theory of Schur Algebras

AbstractA Schur algebra is a subalgebra of the group algebraRGassociated to a partition ofG, whereGis a finite group andRis a commutative ring. For two classes of Schur algebras we study the relationship between indecomposable modules over the Schur algebra and overRG, but we discuss this problem in a more general context. Further we develop a character theory for Schur algebras; in particular, we express primitive central idempotents in terms of trace functions and we derive orthogonality relations for trace functions. These results are also presented in a more general context, namely for Frobenius algebras over rings. Moreover, we focus on class functions on Schur algebras

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property

Musculoskeletal models of a human and bonobo finger: parameter identification and comparison to in vitro experiments

Introduction: Knowledge of internal finger loading during human and non-human primate activities such as tool use or knuckle-walking has become increasingly important to reconstruct the behaviour of fossil hominins based on bone morphology. Musculoskeletal models have proven useful for predicting these internal loads during human activities, but load predictions for non-human primate activities are missing due to a lack of suitable finger models. The main goal of this study was to implement both a human and a representative non-human primate finger model to facilitate comparative studies on metacarpal bone loading. To ensure that the model predictions are sufficiently accurate, the specific goals were: (1) to identify species-specific model parameters based on in vitro measured fingertip forces resulting from single tendon loading and (2) to evaluate the model accuracy of predicted fingertip forces and net metacarpal bone loading in a different loading scenario. Materials & Methods: Three human and one bonobo (Pan paniscus) fingers were tested in vitro using a previously developed experimental setup. The cadaveric fingers were positioned in four static postures and load was applied by attaching weights to the tendons of the finger muscles. For parameter identification, fingertip forces were measured by loading each tendon individually in each posture. For the evaluation of model accuracy, the extrinsic flexor muscles were loaded simultaneously and both the fingertip force and net metacarpal bone force were measured. The finger models were implemented using custom Python scripts. Initial parameters were taken from literature for the human model and own dissection data for the bonobo model. Optimized model parameters were identified by minimizing the error between predicted and experimentally measured fingertip forces. Fingertip forces and net metacarpal bone loading in the combined loading scenario were predicted using the optimized models and the remaining error with respect to the experimental data was evaluated. Results. The parameter identification procedure led to minor model adjustments but considerably reduced the error in the predicted fingertip forces (root mean square error reduced from 0.53/0.69 N to 0.11/0.20 N for the human/bonobo model). Both models remained physiologically plausible after the parameter identification. In the combined loading scenario, fingertip and net metacarpal forces were predicted with average directional errors below 6◦ and magnitude errors below 12%. Conclusions. This study presents the first attempt to implement both a human and nonhuman primate finger model for comparative palaeoanthropological studies. The good agreement between predicted and experimental forces involving the action of extrinsic flexors—which are most relevant for forceful grasping—shows that the models are likely sufficiently accurate for comparisons of internal loads occurring during human and non-human primate manual activities

A horse’s locomotor signature: COP path determined by the individual limb

Introduction Ground reaction forces in sound horses with asymmetric hooves show systematic differences in the horizontal braking force and relative timing of break-over. The Center Of Pressure (COP) path quantifies the dynamic load distribution under the hoof in a moving horse. The objective was to test whether anatomical asymmetry, quantified by the difference in dorsal wall angle between the left and right forelimbs, correlates with asymmetry in the COP path between these limbs. In addition, repeatability of the COP path was investigated. Methods A larger group (n = 31) visually sound horses with various degree of dorsal hoof wall asymmetry trotted three times over a pressure mat. COP path was determined in a hoof-bound coordinate system. A relationship between correlations between left and right COP paths and degree of asymmetry was investigated. Results Using a hoof-bound coordinate system made the COP path highly repeatable and unique for each limb. The craniocaudal patterns are usually highly correlated between left and right, but the mediolateral patterns are not. Some patterns were found between COP path and dorsal wall angle but asymmetry in dorsal wall angle did not necessarily result in asymmetry in COP path and the same could be stated for symmetry. Conclusion This method is a highly sensitive method to quantify the net result of the interaction between all of the forces and torques that occur in the limb and its inertial properties. We argue that changes in motor control, muscle force, inertial properties, kinematics and kinetics can potentially be picked up at an early stage using this method and could therefore be used as an early detection method for changes in the musculoskeletal apparatus