We show that a self-tuning mechanism of the cosmological constant could work in 5D non-compact space with Z 2 symmetry with scalar kinetic energy term. The standard model matter fields live only on the 4 dimensional (4D) brane. The change of vacuum energy on the brane (brane cosmological constant) by, for instance, electroweak and QCD phase transitions, just gives rise to dynamical shifts of th...

We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar is a recursive compact set. A further result on the case that the ...

A self-avoiding walk (saw) is a path on a lattice that does not pass through the same point twice. Though mathematicians have studied saws for over fifty years, the number of n-step saws is unknown. This paper examines a special case of this problem, finding the number of nstep “up-side” saws (ussaws), saws restricted to moving up and sideways. It presents formulas for the number of n-step ussa...

An old problem raised independently by Jacobson and Schönheim asks to determine the maximum s for which every graph with m edges contains a pair of edge-disjoint isomorphic subgraphs with s edges. In this paper we determine this maximum up to a constant factor. We show that every m-edge graph contains a pair of edge-disjoint isomorphic subgraphs with at least c(m logm) edges for some absolute c...

Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind (which can be obtained from dimensional considerations and is invariantly characterized by the existence of a homothetic vector in perfect fluid spacetimes) and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of rel...

We present a method of combining a self-stabilizing algorithm with a hierarchical structure to construct a self-stabilizing algorithm with improved stabilization time complexity and fault-containment features. As a case study, a self-stabilizing spanning-tree algorithm is presented which in favorable settings has logarithmic stabilization time complexity.

Self-similar properties of proton structure in the kinematic region of low Bjorken x are introduced and studied numerically. A description of the proton structure function F 2 (x, Q 2) reflecting self-similarity is proposed with a few parameters which are fitted to recent HERA data. The specific parameterisation provides an excellent description of the data which cover a region of four momentum...

Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system, adversary and resilience in operational terms, based on transition systems and observations. While the general problem of proving systems to be behaviourall...

Statistical analysis of high-resolution traffic measurements from a wide range of working packet networks (e.g., Ethernet LANs, WANs, CCSN/SS7, ISDN and VBR video over ATM) have convincingly shown the presence of fractal or self-similar properties in both local area and wide area traffic traces [2, 3, 5, 15, 19]. That means that similar statistical patterns may occur over different time scales ...

The foveated patch distance was shown to be a valuable feature for the assessment of nonlocal self-similarity in image filtering. The Foveated NL-means [1], which modifies the classical nonlocal means denoising filter (NL-means) [2] by computing the averaging weights based on the foveated patch distance instead of the conventional windowed patch distance, leads to a consistent improvement in th...