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

Effective age for application of orthopedic maxillary protraction

Abstract no. 1374published_or_final_versio

Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain

The formation of Stationary Localized states due to a nonlinear dimeric impurity embedded in a perfect 1-d chain is studied here using the appropriate Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper ansatz for the Localized state is introduced in the appropriate Hamiltonian of the system to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, $\beta = \phi_1/\phi_0$ which is the ratio of stationary amplitudes at impurity sites. Relevant equations for Localized states are obtained from the fixed point of the reduced dynamical system. $|\beta|$ = 1 is always a permissible solution. We also find solutions for which $|\beta| \ne 1$. Complete phase diagram in the $(\chi, \sigma)$ plane comprising of both cases is discussed. Several critical lines separating various regions are found. Maximum number of Localized states is found to be six. Furthermore, the phase diagram continuously extrapolates from one region to the other. The importance of our results in relation to solitonic solutions in a fully nonlinear system is discussed.Comment: Seven figures are available on reques

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.

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

Cephalometric comparisons of Chinese and Caucasian surgical class III patients

published_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