Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model

Global optimisation for a developed price discrimination model:A signomial geometric programming-based approach

This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer objective is to maximize the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set up costs and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions

Global optimisation for a developed price discrimination model:A signomial geometric programming-based approach

This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer objective is to maximize the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set up costs and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions

Extremal holomorphic maps and the symmetrised bidisc

We introduce the class of $n$-extremal holomorphic maps, a class that generalises both finite Blaschke products and complex geodesics, and apply the notion to the finite interpolation problem for analytic functions from the open unit disc into the symmetrised bidisc $\Gamma$. We show that a well-known necessary condition for the solvability of such an interpolation problem is not sufficient whenever the number of interpolation nodes is 3 or greater. We introduce a sequence $\mathcal{C}_\nu, \nu \geq 0,$ of necessary conditions for solvability, prove that they are of strictly increasing strength and show that $\mathcal{C}_{n-3}$ is insufficient for the solvability of an $n$-point problem for $n\geq 3$. We propose the conjecture that condition $\mathcal{C}_{n-2}$ is necessary and sufficient for the solvability of an $n$-point interpolation problem for $\Gamma$ and we explore the implications of this conjecture. We introduce a classification of rational $\Gamma$-inner functions, that is, analytic functions from the disc into $\Gamma$ whose radial limits at almost all points on the unit circle lie in the distinguished boundary of $\Gamma$. The classes are related to $n$-extremality and the conditions $\mathcal{C}_\nu$; we prove numerous strict inclusions between the classes.Comment: 40 page

Inferring cognitive heterogeneity from aggregate choices

Theories of bounded rationality often assume a rich dataset of choices from many overlapping menus, limiting their practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset that consists of aggregate choice shares from a single menu, and includes no observable covariates of any kind. With homogeneous preferences, we find that “consideration capacity” and “consideration probability” distributions can both be recovered effectively if the menu is sufficiently large. This remains true generically when tastes are heterogeneous with a known distribution. When the taste distribution is unknown, we show that joint choice share data from three “occasions” are generically sufficient for full identification of the cognitive distribution, and also provide substantial information about tastes

Estimation of muscle torque impulses and ability to predict high-risk knee joint mechanics during landing maneuvers

This research first examined the validity of net knee joint moment estimations, calculated as the difference between quadriceps and hamstrings torques estimated using either an isometric or angle and action specific sEMG/Torque ratio calculated during calibration actions, during the impact phase of the initial landing of a drop jump maneuver. Second, this research investigated the extent to which the torque impulses of the medial and lateral aspects of the quadriceps and hamstrings, estimated during the impact phase of the initial landing of a drop jump maneuver using an angle and action specific sEMG/Torque ratio predicted knee joint mechanics associated with ACL injury risk, in the three planes of motion. Forty healthy active females, between the ages of 18 and 25, participated in the study. Participants performed maximal calibration actions on an isokinetic dynamometer (eccentric and isometric quadriceps, concentric and isometric hamstrings) while surface electromyographic (sEMG) data were collected from the vastus lateralis, vastus medialis, bicep femoris and semitendinous. Subsequently, a drop jump maneuver was performed while three dimensional biomechanical data as well as sEMG data from the above mentioned muscles were collected. Based on the calibration actions, individualized isometric as well as angle and action specific (eccentric quadriceps, concentric hamstrings) sEMG/Torque ratios (sEMG amplitude divided by half of the torque produced) were computed for each of the four muscles, from full extension to 90 degrees of knee flexion. Using the knee flexion data during the landing maneuver, the sEMG/Torque ratio was then estimated for the impact phase of the drop jump maneuver. It was then divided by the concurrently acquired sEMG to estimate torques for the four afore mentioned muscles during the impact phase of landing. Muscle torques were resolved into a net joint moment as the difference between the sum of the extensors and flexors, and the impulses were then calculated for each of the muscle torques and for the net joint moments. High risk knee joint mechanics, in the three planes of motion, were observed during the impact phase of the initial landing of the drop jump. A RMANOVA tested differences between the net joint moments estimated based on isometric or angle and action specific measurements and inverse dynamics analysis. Regression models assessed the extent to which the muscle torque impulses, estimated using the angle and action specific sEMG/Torque ratio during the impact phase of the initial landing of a drop jump maneuver, predicted each of the seven variables identified as high risk knee joint mechanics. First, the results revealed that net knee joint moment based on the angle and action specific sEMG/Torque ratio provided a closer estimation of the net knee joint moment calculated using an inverse dynamics analysis than the net knee joint moment based on the isometric sEMG/Torque ratio. Second, muscle torque impulses, estimated using the angle and action specific sEMG/Torque ratio, were significantly predictive of only frontal and transverse moments about the knee. Secondary analyses revealed that when including simple ground contact kinematic variables and impact phase duration into the regression models, muscle torques predictivity of high risk knee joint biomechanics often increased. Hence, it was concluded that the angle and action specific sEMG/Torque ratio provides a better estimation of sagittal joint moments than the traditional isometric approach to sEMG normalization. Future studies should investigate the factors influencing ground contact knee joint kinematics and impact phase duration during the initial landing of a drop jump maneuver

Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions

This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link between the highly damped modes and black hole thermodynamics. The third chapter is related to the topic of multiplication of tensorial distributions.Comment: PhD thesis, 207 page

Photoelectron recoil in CO in the x-ray region up to 7 keV

Carbon 1s photoelectron spectra of CO molecules in gas phase were recorded in the tender x-ray energy range, from 2.3 to 6.9 keV. The intensity ratios of individual peaks from nu = 0 to 3 within the vibrational progression of the C 1s photoelectron spectrum were determined at the various photon energies and are shown to be strongly affected by the photoelectron recoil effect. The experimental vibrational intensity ratios are compared with theoretical predictions at different levels of accuracy. Developments of the recoil model, using generalized Franck-Condon factors, rovibrational coupling, Morse potential energy curves, and accurate angular averaging are presented and applied to the analysis of the experimental results