In a quantum world, reference frames are ultimately systems too -- but what does it mean to "jump into the perspective of particle"? this work, we show that frame (QRF) transformations appear naturally as symmetries simple physical systems. This allows us rederive and generalize known QRF within an alternative, operationally transparent framework, shed new light on their structure interpretatio...

The Arnowitt–Deser–Misner (ADM) evolution equations for the induced metric and the extrinsic-curvature tensor of the spacelike surfaces which foliate the space-time manifold in canonical general relativity are a first-order system of quasi-linear partial differential equations, supplemented by the constraint equations. Such equations are here mapped into another first-order system. In particula...

Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of Lagrangian Relaxation and the semi...

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one in this note when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewis...

This paper studies matrix completion under a general sampling model using the max-norm as a convex relaxation for the rank of the matrix. The optimal rate of convergence is established for the Frobenius norm loss. It is shown that the max-norm constrained minimization method is rate-optimal and it yields a more stable approximate recovery guarantee, with respect to the sampling distributions, t...

The occurrence of unphysical negative concentrations in solutions to diffusion equations is a well known and severe problem. Especially in three dimensions finite element discretizations give qualitatively very poor results, while finite volume discretizations are much more stable. We investigate the cause of these instabilities and trace them back to constraints on the mesh. It turns out that ...

Abstract. This paper considers the problem of optimizing the ratio Tr [W T AW ]/Tr [W T BW ] over all unitary matrices W with p columns, where A, B are two positive definite matrices. This problem is common in supervised learning techniques. However, because its numerical solution is typically expensive it is often replaced by the simpler optimization problem which consists of optimizing Tr [W ...

Small transistors and high clock frequency have resulted in high power density, which makes temperature a strong constraint in today’s microprocessor design. For maximizing performance, the thermal design power must be set according to average, instead of worst case, conditions. Consequently, current processors feature temperature sensors and throttling mechanisms to keep the chip temperature a...