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In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called 'basis rhombicity' which is the sum of the absolute val ...
In recent years, the conjecture on the instability of Anti-de Sitter spacetime, put forward by Dafermos-Holzegel (Dynamic instability of solitons in 4 + 1 dimesnional gravity with negative cosmological constant, 2006. https://www.dpmms.cam.ac.uk/similar to ...
We present constraints on extensions of the minimal cosmological models dominated by dark matter and dark energy, Lambda CDM and wCDM, by using a combined analysis of galaxy clustering and weak gravitational lensing from the first-year data of the Dark Ene ...
We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...
We find the conditions under which scale-invariant Einstein-Cartan gravity with scalar matter fields leads to an approximate conformal invariance of the flat space particle theory up to energies of the order of the Planck mass. In the minimal setup, these ...
Quantum field theories (QFTs) are the backbone upon which the edifice of modern physics is built. In this thesis we explore the S-matrix bootstrap which is a non-perturbative method that constrains the vast space of QFTs by using consistency conditions tha ...
We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...
In summarization, automatic evaluation metrics are usually compared based on their ability to correlate with human judgments. Unfortunately, the few existing human judgment datasets have been created as by-products of the manual evaluations performed durin ...
The integration of new materials mediating light-matter interaction in nanoscale devices is a persistent goal in nanophotonics. One of these materials is Gallium phosphide, which offers an attractive combination of a high refractive index (n=3.05 at a wave ...
