Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The cash flow bundle is the associated vector bundle. The zero eigenspace of its connection Laplacian parameterizes all risk-neutral measures equivalent to the statistical one. A market satisfies the No-Free-Lunch-with-Vanishing-Risk (NFLVR) condition if and only if 0 is in the discrete spectrum of the Laplacian. The Jarrow–Protter–Shimbo theory of asset bubbles and their classification and decomposition extend to markets not satisfying the NFLVR. Euler’s characteristic of the asset nominal space and non-vanishing of the homology group of the cash flow bundle are both topological obstructions to NFLVR.

Determination of Tensile Properties for Twisted Fibre Bundles of Oil Palm Empty Fruit Bunch at Different Diameters

The potential use of natural fibre extracted from oil palm empty fruit bunches has gained wide attention among researchers. This natural fibre comes from fibrous strands which form fibre bundle after shredding process at a mill. The measurement of tensile properties is important to understand the mechanical performance of this fibre bundle. This study was undertaken to determine the tensile properties of the fibre bundle from oil palm empty fruit bunch (OPEFB). Fibrous strands of the OPEFB extracted from shredded empty fruit bunches were twisted to form fibre bundle specimens at different diameters varying from 1 to 5 mm. The tensile properties measured in this study including tensile strength, tensile load and tensile modulus. The measurements were performed using Instron Universal Test Machine (IUTM) model 5000. From the results, it was found that the specimens at 1 and 5 mm in diameter required 71.25 and 429.68 N of the tensile load to break, respectively. The specimen with 1 mm in diameter recorded the highest tensile strength of 90.72 MPa while the specimen with 5 mm in diameter recorded only 21.88 MPa. The highest tensile modulus with value of 662.50 MPa was obtained from the specimen with 1 mm in diameter while the specimen with 5 mm in diameter had the tensile modulus value of 157.47 MPa. It was also found that the tensile strength and tensile modulus decreased when the diameter of the specimens increased. The findings reported in this study can serve as an engineering basis for the design specification in the development of the future in-silo composting machine.

A generic form of fibre bundle models for root reinforcement of soil

Purpose The mechanical contribution of plant roots to the soil shear strength is commonly modelled using fibre bundle models (FBM), accounting for sequential breakage of roots. This study provides a generic framework, able to includes the many different existing approaches, to quantify the effect of various model assumptions. Methods The framework uses (1) a single model parameter determining how load is shared between all roots, (2) a continuous power-law distribution of root area ratio over a range of root diameters, and (3) power-law relationships between root diameters and biomechanical properties. A new load sharing parameter, closely resembling how roots mobilise strength under landslide conditions, is proposed. Exact analytical solutions were found for the peak root reinforcement, thus eliminating the current need for iterative algorithms. Model assumptions and results were validated against existing biomechanical and root reinforcement data. Results Root reinforcements proved very sensitive to the user-defined load sharing parameter. It is shown that the current method of discretising all roots in discrete diameter classes prior to reinforcement calculations leads to significant overestimations of reinforcement. Addition of a probabilistic distribution of root failure by means of Weibull survival functions, thus adding a second source of sequential mobilisation, further reduced predicted reinforcements, but only when the reduction due to load sharing was limited. Conclusion The presented solutions greatly simplify root reinforcement calculations while maintaining analytical exactness as well as clarity in the assumptions made. The proposed standardisation of fibre bundle-type models will greatly aid comparison and exchange of data.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

Functional Anatomy of the Craniolateral and Caudomedial Bundles of the Caudal Cruciate Ligament in Beagle Dogs

Objective The aim of this study was to investigate functional anatomy of the craniolateral bundle (CrLB) and caudomedial bundle (CdMB) of caudal cruciate ligament in normal Beagles. Materials and Methods Twelve stifle joints of 12 Beagle cadavers that were euthanatized for reasons other than musculoskeletal disease were used. Anatomical characteristics of femoral and tibial attachment regions of the caudal cruciate ligament were described, and location and area of the footprints of the CrLB and CdMB were objectively determined. The CrLB was artificially divided into two equal fibre bundle units and the CdMB was artificially divided into four equal bundle units. Changes in the fibre arrangement were recorded during stifle range of motion, and the tension of each fibre bundle unit at various stifle joint angles was objectively measured. Results The CrLB was attached to the intercondylar fossa of the femur, and the CdMB was attached to the medial surface of the medial condyle of the femur. The centre of the CrLB attachment site was located craniomedial to that of the CdMB on the tibia. During stifle range of motion, each divided fibre bundle unit in the CrLB and CdMB was twisted externally. The tension of entire CdMB tended to be higher than that of entire CrLB at 180 to 135 degrees of the stifle angles. In full extension angle, the tension of entire CdMB was 1.55 times higher than that of entire CrLB. Clinical Significance This study contributes to understanding of the biomechanics and the function of the caudal cruciate ligament, which help to elucidate the pathophysiology of caudal cruciate ligament tear and to develop stifle joint stabilization surgery.

The Holonomy Groupoids of Singularly Foliated Bundles

We define a notion of connection in a fibre bundle that is compatible with a singular foliation of the base. Fibre bundles equipped with such connections are in plentiful supply, arising naturally for any Lie groupoid-equivariant bundle, and simultaneously generalising regularly foliated bundles in the sense of Kamber-Tondeur and singular foliations. We define hierarchies of diffeological holonomy groupoids associated to such bundles, which arise from the parallel transport of jet/germinal conservation laws. We show that the groupoids associated in this manner to trivial singularly foliated bundles are quotients of Androulidakis-Skandalis holonomy groupoids, which coincide with Androulidakis-Skandalis holonomy groupoids in the regular case. Finally we prove functoriality of all our constructions under appropriate morphisms.

The Principal Fibre Bundle on Lorentzian Almost R-para Contact Structure

The purpose of this paper is to study the principal fibre bundle ( P , M , G , π p ) with Lie group G , where M admits Lorentzian almost paracontact structure ( Ø , ξ p , η p , g ) satisfying certain condtions on (1, 1) tensor field J , indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

Modeling the Deformation and the Failure Process of Glass Woven Fabrics Based on the Fibre-Bundle-Cells Theory

In this study, we modeled the deformation and failure behavior of different glass woven fabrics under uni-axial tension using the Fibre Bundle Cells-modeling method. The difference between the analytical, phenomenological model curve and the mean curve calculated from the measurement results was classified by the relative mean squared error (RMSE), which is closely related to the coefficient of determination. This value was less than 3.6% in all the examined cases, which indicated good modeling.