Scale Invariance

The concept of distance between two compositions is important in the statistical analysis of compo-sitional data, particularly in such activities as cluster analysis and multidimensional scaling. This paper exposes the fallacies in a recent criticism of logratio-based distance ...

Template Matching is one of the most basic techniques in computer vision, where the algorithm should search for a template image T in an image to analyze I. It is heavily used in signal, image and video processing. A lot of applications are based on template matching in object detection, superresolution, image denoising and image compression. In this thesis, the rotation, scale, brightness and contrast invariant grayscale template matching problem is considered. An algorithm is proposed that uses a sufficient condition for distinguishing between candidate matching positions and other positions that cannot provide a better degree of match with respect to the current best candidate. The proposed algorithm is compared with eight existing state-of-the-art techniques. Theoretical analysis and experiments on eight image datasets show that the proposed algorithm, under some conditions, can maintain exhaustive accuracy while providing a significant speedup over state-of-the-art techniques with over than one order of magnitude in some cases.

We construct a multi-field inflationary model consisting of multiple K\"ahler moduli derived from type IIB string compactification in the large volume limit. The model consists of both heavy and light fields, with the former being frozen during the inflationary period and the latter acting as the inflaton(s). We study the evolution of all the fields during and after inflation until the preheating era when all the fields oscillate around their vacuum expectation values. Our numerical analysis shows that the curvature perturbations have an almost scale invariant power spectrum with $n_s \simeq 0.96$.

We find successful models of D-brane/anti-brane inflation within a string context. We work within the GKP-KKLT class of type IIB string vacua for which many moduli are stabilized through fluxes, as recently modified to include `realistic' orbifold sectors containing standard-model type particles. We allow all moduli to roll when searching for inflationary solutions and find that inflation is not generic inasmuch as special choices must be made for the parameters describing the vacuum. But given these choices inflation can occur for a reasonably wide range of initial conditions for the brane and antibrane. We find that D-terms associated with the orbifold blowing-up modes play an important role in the inflationary dynamics. Since the models contain a standard-model-like sector after inflation, they open up the possibility of addressing reheating issues. We calculate predictions for the CMB temperature fluctuations and find that these can be consistent with observations, but are generically not deep within the scale-invariant regime and so can allow appreciable values for $dn_s/d\ln k$ as well as predicting a potentially observable gravity-wave signal. It is also possible to generate some admixture of isocurvature fluctuations.

This paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of all particle species that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or CDM+HDM models (including a possible cosmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been either ignored or approximated crudely in previous works. Isentropic initial conditions on super-horizon scales are derived. The coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric and ...