Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$.Comment: 9 pages, 3 figure

Cephalometric comparisons of Chinese and Caucasian surgical class III patients

published_or_final_versio

Effective age for application of orthopedic maxillary protraction

Abstract no. 1374published_or_final_versio

Reviewer Integration and Performance Measurement for Malware Detection

We present and evaluate a large-scale malware detection system integrating machine learning with expert reviewers, treating reviewers as a limited labeling resource. We demonstrate that even in small numbers, reviewers can vastly improve the system's ability to keep pace with evolving threats. We conduct our evaluation on a sample of VirusTotal submissions spanning 2.5 years and containing 1.1 million binaries with 778GB of raw feature data. Without reviewer assistance, we achieve 72% detection at a 0.5% false positive rate, performing comparable to the best vendors on VirusTotal. Given a budget of 80 accurate reviews daily, we improve detection to 89% and are able to detect 42% of malicious binaries undetected upon initial submission to VirusTotal. Additionally, we identify a previously unnoticed temporal inconsistency in the labeling of training datasets. We compare the impact of training labels obtained at the same time training data is first seen with training labels obtained months later. We find that using training labels obtained well after samples appear, and thus unavailable in practice for current training data, inflates measured detection by almost 20 percentage points. We release our cluster-based implementation, as well as a list of all hashes in our evaluation and 3% of our entire dataset.Comment: 20 papers, 11 figures, accepted at the 13th Conference on Detection of Intrusions and Malware & Vulnerability Assessment (DIMVA 2016

Light atom quantum oscillations in UC and US

High energy vibrational scattering in the binary systems UC and US is measured using time-of-flight inelastic neutron scattering. A clear set of well-defined peaks equally separated in energy is observed in UC, corresponding to harmonic oscillations of the light C atoms in a cage of heavy U atoms. The scattering is much weaker in US and only a few oscillator peaks are visible. We show how the difference between the materials can be understood by considering the neutron scattering lengths and masses of the lighter atoms. Monte Carlo ray tracing is used to simulate the scattering, with near quantitative agreement with the data in UC, and some differences with US. The possibility of observing anharmonicity and anisotropy in the potentials of the light atoms is investigated in UC. Overall the observed data is well accounted for by considering each light atom as a single atom isotropic quantum harmonic oscillator.Comment: 10 pages, 8 figure

Optimal Income Transfers and Tariffs.

This paper investigates the optimality of international income transfers in a two-country model in which each country engages in non-cooperative trade policy behaviour. It is shown that unconditional income transfers can never be optimal for the donor country, which not only suffers the loss of income but is harmed as the recipient responds optimally by raising tariffs. It is further shown that it is possible for the donor to attach carefully designed conditionality rules to the aid package to ensure that the recipient will agree to the package and that the donor's welfare is improved. In fact, the use of conditional income transfers is shown to result in a Pareto efficient equilibrium.