Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit ($R_{ISCO}$), the rotation frequency $\Omega\equiv\frac{d\phi}{dt}$ and the epicyclic frequencies $\Omega_{\rho},\;\Omega_z$. Finally we present some results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity (NEB XIII), corrected typo in $M_4$ of eq. 5 of the published versio

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star that has been constructed numerically in the former coordinates with an axially symmetric stationary metric that is given through an analytical form in the latter coordinates. Since a stationary metric associated with an isolated object that is built numerically partly refers to a non-vacuum solution (interior of the star) the transformation of its coordinates to Weyl-Papapetrou coordinates, which are usually used to describe vacuum axisymmetric and stationary solutions of Einstein equations, is not straightforward in the non-vacuum region. If this point is \textit{not} taken into consideration, one may end up to erroneous conclusions about how well a specific analytical metric matches the metric around the star, due to fallacious coordinate transformations.Comment: 18 pages, 2 figure

Correlating decoherence in transmon qubits: Low frequency noise by single fluctuators

We report on long-term measurements of a highly coherent, non-tunable superconducting transmon qubit, revealing low-frequency burst noise in coherence times and qubit transition frequency. We achieve this through a simultaneous measurement of the qubit's relaxation and dephasing rate as well as its resonance frequency. The analysis of correlations between these parameters yields information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our results are consistent with a small number of microscopic two-level systems located at the edges of the superconducting film, which is further confirmed by a spectral noise analysis.Comment: 10 Pages, 6 figure

Fair Robust Assignment Using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298

Fair Robust Assignment Using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298

Thermally induced magnetic relaxation in square artificial spin ice

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice - we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.Comment: 15 pages, 5 figure