We develop a systematic approach to the discovery of parallel iterative schemes for solving the shape-from-shading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shape-from-shading problem is known to be mathematically equivalent to a nonlinear first-order partial differential equation in surface elevation. To ...

We derive the fixed-$\mathrm{\ensuremath{\Lambda}}$ and unimodular propagators using path integral formalism as applied to Einstein-Cartan action. The simplicity of action (which is linear in lapse function) allows for an exact integration starting from function enforcement Hamiltonian constraint, leading a product Chern-Simons states if connection fixed at endpoints. No saddle point approximat...

Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler – DeWitt constraint equations in terms of a single Master Equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding con...

We carry out the Hamiltonian formulation of the three-dimensional gravitational teleparallelism without imposing the time gauge condition, by rigorously performing the Legendre transform. Definition of the gravitational angular momentum arises by suitably interpreting the integral form of the constraint equation Γik = 0 as an angular momentum equation. The gravitational angular momentum is eval...

For linear systems, we show that the constraint known as Bode’s sensitivity integral has an information theoretic interpretation in terms of the difference in the entropy rates between the input and output of the systems. We use this interpretation to show that, if the open loop system is globally exponentially stable, this difference is zero. For nonlinear systems that are not stable, we start...

Robust stability of linear systems in presence of bounded uncertain time-varying time delays is studied. The time delay robustness problem is treated in the Integral Quadratic Constraint (IQC) framework. The stability criterion is formulated as frequency dependent linear matrix inequalities. The criterion can be equivalently formulated as a Semi-Definite Program (SDP) by applying KalmanYakubovi...

Various issues about integral processes with dead time controlled by a PI controller are discussed. First, the region of the control parameters to guarantee the system stability is characterised. Then, the control parameters to achieve the given gain and/or phase margins (GPM) are determined. Furthermore, the constraint on achievable GPM is derived. These results are obtained on the basis of th...

Stability of a data network topology, in which a source updates its data transmission rate based on delayed congestion information on its own path only, is examined. Delays associated with feedback information are taken to be known constants and bounded uncertainty is associated with feedback information. Use of linear matrix inequality (LMI) and integral quadratic constraint (IQC) techniques t...