Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

Tunable coupling in circuit quantum electrodynamics with a superconducting V-system

Recent progress in superconducting qubits has demonstrated the potential of these devices for the future of quantum information processing. One desirable feature for quantum computing is independent control of qubit interactions as well as qubit energies. We demonstrate a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independent control over the qubit energy and dipole coupling to a superconducting cavity. We demonstrate dynamic access to the strong coupling regime by tuning the coupling strength from less than 200 kHz to more than 40 MHz. This tunable coupling can be used to protect the qubit from cavity-induced relaxation and avoid unwanted qubit-qubit interactions in a multi-qubit system.Comment: 5 pages, 4 figure

Turbojet engine blade damping

The potentials of various sources of nonaerodynamic damping in engine blading are evaluated through a combination of advanced analysis and testing. The sources studied include material hysteresis, dry friction at shroud and root disk interfaces as well as at platform type external dampers. A limited seris of tests was conducted to evaluate damping capacities of composite materials (B/AL, B/AL/Ti) and thermal barrier coatings. Further, basic experiments were performed on titanium specimens to establish the characteristics of sliding friction and to determine material damping constants J and n. All the tests were conducted on single blades. Mathematical models were develthe several mechanisms of damping. Procedures to apply this data to predict damping levels in an assembly of blades are developed and discussed

Offer Price, Target Ownership Structure and IPO Performance

Although the choice of an IPO offer price level would seem to have little economic significance, firms do not decide this arbitrarily. Our findings suggest that firms select their IPO offer prices to target a desired ownership structure, which in turn has implications for underpricing and post-IPO performance. Higher priced IPOs are marketed by more reputed underwriters and attract a relatively larger institutional investment. These IPOs are relatively more underpriced, possibly as compensation for the monitoring and information benefits provided by institutional investors. IPOs whose offer prices are below the median level seem to be targeted towards a retail investor clientele. These IPOs are also relatively more underpriced, possibly as a cost of adverse selection. Our finding that long-run performance increases with offer price confirms that higher priced IPOs are better firms.Initial public offerings; share prices; share allocation

Is Share Price Related to Marketability? Evidence from Mutual Fund Share Splits

We examine the "marketability hypothesis," which states that stock splits enhance the attractiveness of shares to investors by restoring prices to a preferred trading range. We examine splits of mutual fund shares because they provide a clean testing ground for the marketability hypothesis, since the conventional rationales for common stock splits do not apply. We find that splitting funds experience significant increases (relative to non-splitting matched funds) in net assets and shareholders. Stock splits do appear to enhance marketability.

Dispersive Photon Blockade in a Superconducting Circuit

Mediated photon-photon interactions are realized in a superconducting coplanar waveguide cavity coupled to a superconducting charge qubit. These non-resonant interactions blockade the transmission of photons through the cavity. This so-called dispersive photon blockade is characterized by measuring the total transmitted power while varying the energy spectrum of the photons incident on the cavity. A staircase with four distinct steps is observed and can be understood in an analogy with electron transport and the Coulomb blockade in quantum dots. This work differs from previous efforts in that the cavity-qubit excitations retain a photonic nature rather than a hybridization of qubit and photon and provides the needed tolerance to disorder for future condensed matter experiments.Comment: 4 pages, 3 figure

Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system

A fiber taper waveguide is used to perform direct optical spectroscopy of a microdisk-quantum-dot system, exciting the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong coupling, the regime of coherent quantum interactions, is demonstrated through observation of vacuum Rabi splitting in the transmitted and reflected signals from the cavity. The fiber coupling method also allows the examination of the system's steady-state nonlinear properties, where saturation of the cavity-QD response is observed for less than one intracavity photon.Comment: adjusted references, added minor clarification