Legal Requirements for Admission to Public Schools

Advanced driver assistance systems for heavy duty vehicles, such as lookahead cruise and gearshift controllers, rely on high quality map data. Current digital maps do not offer the required level of road grade information. This contribution presents an algorithm for on-board road grade estimation based on fusion of GPS and vehicle sensor data with measurements from previous runs over the same road segment. An incremental update scheme is utilized to ensure that data storage requirements are independent of the number of measurement runs. Results of the implemented system based on six traversals of a known road with three different vehicles are presented.QC 20120216</p

Pure Gravities via Color-Kinematics Duality for Fundamental Matter

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.Comment: 48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal versio

Color-Kinematics Duality for QCD Amplitudes

We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.Comment: 33 pages + refs, 7 figures, 4 tables; v3 minor corrections, journal versio

Model reduction of networked passive systems through clustering

In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a reduced-order networked system that allows for a convenient physical interpretation. The identification of the subsystems to be clustered is performed through controllability and observability analysis of an associated edge system and it is shown that the property of synchronization (i.e., the convergence of trajectories of the subsystems to each other) is preserved during reduction. The results are illustrated by means of an example.Comment: 7 pages, 2 figures; minor changes in the final version, as accepted for publication at the 13th European Control Conference, Strasbourg, Franc

On the Exact Solution to a Smart Grid Cyber-Security Analysis Problem

This paper considers a smart grid cyber-security problem analyzing the vulnerabilities of electric power networks to false data attacks. The analysis problem is related to a constrained cardinality minimization problem. The main result shows that an $l_1$ relaxation technique provides an exact optimal solution to this cardinality minimization problem. The proposed result is based on a polyhedral combinatorics argument. It is different from well-known results based on mutual coherence and restricted isometry property. The results are illustrated on benchmarks including the IEEE 118-bus and 300-bus systems