The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and (...) angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories. (shrink)

In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach , Oxford University Press, Oxford, 1996, pp. 225–260) to analyze Cheney's simplification 189) of Jackson's original proof 320) of the uniqueness of the best L1-approximation of continuous functions fC[0,1] by polynomials pPn of degree n. Cheney's (...) proof is non-effective in the sense that it is based on classical logic and on the non-computational principle WKL . The result of our analysis provides the first effective uniform modulus of uniqueness . Moreover, the extracted modulus has the optimal ε-dependency as follows from Kroó 331). The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed fC[0,1] with arbitrary precision. The second author uses this result to give a complexity upper bound on the computation of the best L1-approximation in Oliva 66–77). (shrink)

In this paper I take a sceptical view of the standard cosmological model and its variants, mainly on the following grounds: (i) The method of mathematical modelling that characterises modern natural philosophy-as opposed to Aristotle's-goes well with the analytic, piecemeal approach to physical phenomena adopted by Galileo, Newton and their followers, but it is hardly suited for application to the whole world. (ii) Einstein's first cosmological model (1917) was not prompted by the intimations of experience but by a desire to (...) satisfy Mach's Principle. (iii) The standard cosmological model-a Friedmann-Lematre-Robertson-Walker spacetime expanding with or without end from an initial singularity-is supported by the phenomena of redshifted light from distant sources and very nearly isotropic thermal background radiation provided that two mutually inconsistent physical theories are jointly brought to bear on these phenomena, viz the quantum theory of elementary particles and Einstein's theory of gravity. (iv) While the former is certainly corroborated by high-energy experiments conducted under conditions allegedly similar to those prevailing in the early world, precise tests of the latter involve applications of the Schwarzschild solution or the PPN formalism for which there is no room in a Friedmann-Lematre-Robertson-Walker spacetime. (shrink)

Background: Treating medication-refractory freezing of gait in Parkinson’s disease remains challenging despite several trials reporting improvements in motor symptoms using subthalamic nucleus or globus pallidus internus deep brain stimulation. Pedunculopontine nucleus region DBS has been used for medication-refractory FoG, with mixed findings. FoG, as a paroxysmal phenomenon, provides an ideal framework for the possibility of closed-loop DBS.Methods: In this clinical trial, five subjects with medication-refractory FoG underwent bilateral GPi DBS implantation to address levodopa-responsive PD symptoms with open-loop stimulation. Additionally, PPN (...) DBS leads were implanted for CL-DBS to treat FoG. The primary outcome of the study was a 40% improvement in medication-refractory FoG in 60% of subjects at 6 months when “on” PPN CL-DBS. Secondary outcomes included device feasibility to gauge the recruitment potential of this four-lead DBS approach for a potentially larger clinical trial. Safety was judged based on adverse events and explantation rate.Findings: The feasibility of this approach was demonstrated as we recruited five subjects with both “on” and “off” medication freezing. The safety for this population of patients receiving four DBS leads was suboptimal and associated with a high explantation rate of 40%. The primary clinical outcome in three of the five subjects was achieved at 6 months. However, the group analysis of the primary clinical outcome did not reveal any benefit.Interpretation: This study of a human PPN CL-DBS trial in medication-refractory FoG showed feasibility in recruitment, suboptimal safety, and a heterogeneous clinical effect in FoG outcomes. (shrink)

Deformation of ground during tunnelling projects is one of the complex issues that is required to be monitored carefully to avoid the unexpected damages and human losses. Accurate prediction of ground settlement is a crucial concern for tunnelling problems, and the adequate predictive model can be a vital tool for tunnel designers to simulate the ground settlement accurately. This study proposes relatively new hybrid artificial intelligence models to predict the ground settlement of earth pressure balance shield tunnelling in the Bangkok (...) MRTA project. The predictive models were various nature-inspired frameworks, such as differential evolution, particle swarm optimization, genetic algorithm, and ant colony optimizer to tune the adaptive neuro-fuzzy inference system. To obtain the accurate and reliable results, the modeling procedure is established based on four different dataset scenarios including preprocessed and normalized, preprocessed and nonnormalized, non-preprocessed and normalized, and non-preprocessed and nonnormalized datasets. Results indicated that PPN dataset scenario significantly affected the prediction models in terms of their perdition accuracy. Among all the developed hybrid models, ANOFS-PSO model achieved the best predictability performance. In quantitative terms, PPN-ANFIS-PSO model attained the least root mean square error value of 7.98 and a correlation coefficient value of 0.83. Overall, the attained results confirmed the superiority of the explored hybrid AI models as robust predictive model for ground settlement of earth pressure balance shield tunnelling. (shrink)