An alternative inference tool to total probability formula and its applications

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some traditional results in statistical inference. However, as far as the authors know, there is no work on this subject, except [1]. The results of this paper can be extended to other branches of probability and statistics. In Section 2 total probability formula based on median is defined and its basic properties are proved. A few applications of this new tool are given in Section 3.Comment: Presented at the 23th Int. worskhop on Bayesian and Maximum Entropy methods (MaxEnt23), Aug. 3-7, 2003, Jackson Hole, US

Planck-Scale Corrections to Friedmann Equation

Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde's proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to \emph{quantum gravity} such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde's proposal and two known models of GUPs, we obtain modifications to Newton's law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the $p=\omega \rho$ equation of state.Comment: 15 pages, no figure, to appear in Central Eur.J.Phys. arXiv admin note: text overlap with arXiv:1301.350

Minimal Length, Friedmann Equations and Maximum Density

Inspired by Jacobson's thermodynamic approach[gr-qc/9504004], Cai et al [hep-th/0501055,hep-th/0609128] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar--Cai derivation [hep-th/0609128] of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure $p(\rho,a)$ leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature $k$. As an example we study the evolution of the equation of state $p=\omega \rho$ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.Comment: 15 pages, 1 figure, minor revisions, To appear in JHE

Bayesian segmentation of hyperspectral images

In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.Comment: 8 pages, 2 figures, presented at MaxEnt 2004, Inst. Max Planck, Garching, German

PDE–Based Modelling and Control Strategies for Manufacturing Processes

This work aims to design boundary control strategies to solve demand tracking and backlog problems for manufacturing systems in terms of conservation laws coupled with ODEs in different network topologies. The OCPs are investigated in the dispersing and the merging networks. The problems are optimized utilizing open-loop optimal control based on the direct and the indirect approaches. The proposed approaches enable the solution of the OCPs. All of the approaches, in general, reach a local minima with similar behaviour that leads to the steady-state. The results analysis reveals that each method has its own distinct characteristics. The indirect methodology is characterized by excellent accuracy and minimal processing burden; yet, due to the information necessary to compute the gradient, it is a sensitive method. The ease of use and flexibility to any problem distinguishes the direct method. However, this approach takes substantially longer to achieve a solution when compared to the indirect method. Also, the AMPC was introduced to investigate demand tracking and backlog problems in the context of the complex network of production systems. The addressed network includes structures that are dispersing and merging. Furthermore, the appropriate way to handle the parameters of the AMPC for both control and prediction horizons is addressed. Moreover, the proposed AMPC provides for the solutions of demand tracking and backlog problems. In general, AMPC and traditional MPC attain local minima with similar behaviour that leads to steady-state convergence. When compared to a typical MPC, the AMPC's performance shows a considerable reduction in computational time. Additionally, because it provides a mathematical insight into the method's structure, the AMPC allows for great accuracy of optimal solutions. Finally, the AMPC is characterized by its robustness according to perturbation effects