For a class of stabilizing boundary controllers for nonlinear 1D parabolic PDEs introduced in a companion paper, we derive bounds for the gain kernels of our nonlinear Volterra controllers, prove the convergence of the series in the feedback laws, and establish the stability properties of the closed-loop system. We show that the state transformation is at least locally invertible and include an...

In the context of loop quantum gravity, we construct the phase-space of the isolated horizon with toroidal topology. Within the loop quantum gravity framework, this horizon is described by a torus with N punctures and the dimension of the corresponding phase-space is calculated including the toroidal cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting t...

In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by c...

Effective hadron models commonly require the computation of functional determinants. In the static case these are one–loop vacuum polarization energies, known as Casimir energies. In this talk I will present general methods to efficiently compute renormalized one–loop vacuum polarization energies and energy densities and apply these methods to construct soliton solutions within a variational ap...

We construct a phenomenological model describing aggregated spots and a loop structure. Our model is based on the Gray-Scott model which is supplemented with a global coupling term and advection terms. One of the species makes a field proportional to its concentration, which induces the advection. By numerically investigating the model, we show that the system has a transition from aggregated s...

We discuss the action of the configuration operators of loop quantum gravity. In particular, we derive the generalised eigenbasis for the Wilson loop operator and show that the transformation between this basis and the spinnetwork basis is given by an expansion in terms of Chebyshev polynomials. These results are used to construct states which approximate connections on the background 3-manifol...

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations ...

A constructive method for time-varying stabilization of smooth driftless controllable systems is developed. It provides time-varying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closed-loop system globally exponentially asymptotically stable if the control system is homogeneous with respect to a family of dilations and, using local homo...

We construct an extension of the MSSM in which scalar superpartners can naturally be as heavy as 1 TeV. In the MSSM, the most significant fine tuning stems from the logarithmically enhanced top-stop loop contribution to the soft Higgs mass. We combine supersymmetry with the “simplest little Higgs” to render this loop finite, thereby removing the large logarithm even in models in which superpart...

We present a technique for program termination analysis based on loop summarization. The algorithm relies on a library of abstract domains to discover well-founded transition invariants. In contrast to state-of-the-art methods it aims to construct a complete ranking argument for all paths through a loop at once, thus avoiding expensive enumeration of individual paths. Compositionality is used a...