Joining Spacetimes on Fractal Hypersurfaces

The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in understanding stochastic process and fractal dynamics. In this paper, we apply the techniques of fractional calculus to study some specific modifications of the geometry of submanifolds. Our generalisation is applied to extend the Israel formalism which is used to glue together two spacetimes across a timelike, spacelike or a null hypersurface. In this context, we show that the fractional extrapolation leads to some striking new results. More precisely we demonstrate that, in contrast to the original Israel formalism, where many spacetimes can only be joined together through an intermediate thin hypersurface of matter satisfying some non- standard energy conditions, the fractional generalisation allows these spacetimes to be smoothly sewed together without any such requirements on the stress tensor of the matter fields. We discuss the ramifications of these results for spacetime structure and the possible implications for gravitational physics.Comment: 22 pages, 2 figure

Automatic Generation of Personalized Recommendations in eCoaching

Denne avhandlingen omhandler eCoaching for personlig livsstilsstøtte i sanntid ved bruk av informasjons- og kommunikasjonsteknologi. Utfordringen er å designe, utvikle og teknisk evaluere en prototyp av en intelligent eCoach som automatisk genererer personlige og evidensbaserte anbefalinger til en bedre livsstil. Den utviklede løsningen er fokusert på forbedring av fysisk aktivitet. Prototypen bruker bærbare medisinske aktivitetssensorer. De innsamlede data blir semantisk representert og kunstig intelligente algoritmer genererer automatisk meningsfulle, personlige og kontekstbaserte anbefalinger for mindre stillesittende tid. Oppgaven bruker den veletablerte designvitenskapelige forskningsmetodikken for å utvikle teoretiske grunnlag og praktiske implementeringer. Samlet sett fokuserer denne forskningen på teknologisk verifisering snarere enn klinisk evaluering.publishedVersio

Linear Inverse Problem (LIP) Optimisation for Remote Sensing Applications - Spectral Reconstruction

3MT presented at the 2018 Defence and Security Doctoral Symposium.Remote sensing applications like classification and target detection, particularly for high demanded applications such as the detection of difficult targets from cluttered scene, depends on relevant wavelengths of information. While multispectral imagery in airborne or spaceborne platforms consists of a few wavelengths far apart from each other (usually less than 20 bands), which is found not sufficient enough. This project explores new concepts for using not only spatial/spectral information, but also to extract new information from the few bands in the input data for an enhanced spectral mixture analysis.Dst

Kalb-Ramond field interactions in a braneworld scenario

Electromagnetic and (linearized) gravitational interactions of the Kalb-Ramond (KR) field, derived from an underlying ten dimensional heterotic string in the zero slope limit, are studied in a five dimensional background Randall-Sundrum I spacetime with standard model fields confined to the visible brane having negative tension. The warp factor responsible for generating the gauge hierarchy in the Higgs sector is seen to appear inverted in the KR field couplings, when reduced to four dimensions. This leads to dramatically enhanced rotation, {\it far beyond observational bounds}, of the polarization plane of electromagnetic and gravitational waves, when scattered by a homogeneous KR background. Possible reasons for the conflict between theory and observation are discussed.Comment: 13 pages Latex, no figures, discussion and acknowledgements adde

On a given iteration during training, which pixel should we select?

On a given training iteration, visualise yourself physically standing on a residual error map. Assume (i) the pixel with the smallest residual error is likely the most learned material. And, (ii) the pixel with the maximum error is probably the least learned material. Simultaneous orthogonal marching pursuit (SOMP) residue is a way to estimate the residual error rapidly with dictionary atoms. In a real scene, there is noise and outliers. However, by selecting the pixels with the maximum SOMP residue at each iteration, one can learn both background and trace materials blindly. Learning trace materials is critical for essential applications like target detection. (IEEE Letters of the Computer Society publication DOI: 10.1109/LOCS.2019.2938446, pre-print available from Cranfield CERES)DST

Hawking radiation from dynamical horizons

In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.Comment: 5 Page