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

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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

Effective age for application of orthopedic maxillary protraction

Abstract no. 1374published_or_final_versio

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

Construction of online catalog topologies using decision trees

Organization of a Web site is important to help users get the most out of the site. A good Web site should help visitors find the information they want easily. Visitors typically find information by searching for selected terms of interest or by following links from one Web page to another. The first approach is more useful if the visitor knows exactly what he is seeking, while the second approach is useful when the visitor has less of a preconceived notion about what he wants. The organization of a Web site is especially important in the latter case. Traditionally, Web site organization is done by hand. In this paper, we introduce the problem of automatic Web site construction and propose a solution for solving a major step of the problem based on decision tree algorithms. The solution is found to be useful in automatic construction of product catalogs.published_or_final_versio