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Ran Duan

Publications and source records attributed to Ran Duan.

42 records · Page 3Linked to original sources
arXiv2016

Improved distance sensitivity oracles via tree partitioning

We introduce an improved structure of distance sensitivity oracle (DSO). The task is to pre-process a non-negatively weighted graph so that a data structure can quickly answer replacement path length for every triple of source, terminal and failed vertex. The previous best algorithm constructs in time $\tilde{O}(mn)$ a distance sensitivity oracle of size $O(n^2\log n)$ that processes queries in $O(1)$ time. As an improvement, our oracle takes up $O(n^2)$ space, while preserving $O(1)$ query efficiency and $\tilde{O}(mn)$ preprocessing time. One should notice that space complexity and query time of our novel data structure are asymptotically optimal.

cs.DS↗
arXiv2012

Status of MUSIC, the MUltiwavelength Sub/millimeter Inductance Camera

We present the status of MUSIC, the MUltiwavelength Sub/millimeter Inductance Camera, a new instrument for the Caltech Submillimeter Observatory. MUSIC is designed to have a 14', diffraction-limited field-of-view instrumented with 2304 detectors in 576 spatial pixels and four spectral bands at 0.87, 1.04, 1.33, and 1.98 mm. MUSIC will be used to study dusty star-forming galaxies, galaxy clusters via the Sunyaev-Zeldovich effect, and star formation in our own and nearby galaxies. MUSIC uses broadband superconducting phased-array slot-dipole antennas to form beams, lumped-element on-chip bandpass filters to define spectral bands, and microwave kinetic inductance detectors to senseincoming light. The focal plane is fabricated in 8 tiles consisting of 72 spatial pixels each. It is coupled to the telescope via an ambient temperature ellipsoidal mirror and a cold reimaging lens. A cold Lyot stop sits at the image of the primary mirror formed by the ellipsoidal mirror. Dielectric and metal mesh filters are used to block thermal infrared and out-of-band radiation. The instrument uses a pulse tube cooler and 3He/3He/4He closed-cycle cooler to cool the focal plane to below 250 mK. A multilayer shield attenuates Earth's magnetic field. Each focal plane tile is read out by a single pair of coaxes and a HEMT amplifier. The readout system consists of 16 copies of custom-designed ADC/DAC and IF boards coupled to the CASPER ROACH platform. We focus on recent updates on the instrument design and results from the commissioning of the full camera in 2012.

astro-ph.IM↗
arXiv2012

Rayleigh-Taylor instability for compressible rotating flows

In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational field. First we construct the Rayleigh-Taylor steady-state solutions with a denser fluid lying above the free interface with the second fluid, then we turn to an analysis of the equations obtained from linearization around such a steady state. In the presence of uniform rotation, there is no natural variational framework for constructing growing mode solutions to the linearized problem. Using the general method of studying a family of modified variational problems introduced in \cite{Y-I2}, we construct normal mode solutions that grow exponentially in time with rate like $e^{t\sqrt{c|ξ|-1}}$, where $ξ$ is the spatial frequency of the normal mode and the constant $c$ depends on some physical parameters of the two layer fluids. A Fourier synthesis of these normal mode solutions allows us to construct solutions that grow arbitrarily quickly in the Sobolev space $H^k$, and lead to an ill-posedness result for the linearized problem. Moreover, from the analysis we see that rotation diminishes the growth of instability. Using the pathological solutions, we then demonstrate the ill-posedness for the original non-linear problem in some sense.

math.GM↗
arXiv2012

A readout for large arrays of Microwave Kinetic Inductance Detectors

Microwave Kinetic Inductance Detectors (MKIDs) are superconducting detectors capable of counting single photons and measuring their energy in the UV, optical, and near-IR. MKIDs feature intrinsic frequency domain multiplexing (FDM) at microwave frequencies, allowing the construction and readout of large arrays. Due to the microwave FDM, MKIDs do not require the complex cryogenic multiplexing electronics used for similar detectors, such as Transition Edge Sensors (TESs), but instead transfer this complexity to room temperature electronics where they present a formidable signal processing challenge. In this paper we describe the first successful effort to build a readout for a photon counting optical/near-IR astronomical instrument, the ARray Camera for Optical to Near-infrared Spectrophotometry (ARCONS). This readout is based on open source hardware developed by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER). Designed principally for radio telescope backends, it is flexible enough to be used for a variety of signal processing applications.

astro-ph.IM↗
arXiv2011

Scaling algorithms for approximate and exact maximum weight matching

The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and vertices.) In this article we demonstrate that this "$m\sqrt{n}$ barrier" is extremely fragile, in the following sense. For any $ε>0$, we give an algorithm that computes a $(1-ε)$-approximate maximum weight matching in $O(mε^{-1}\logε^{-1})$ time, that is, optimal {\em linear time} for any fixed $ε$. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new {\em exact} maximum weight matching algorithm for integer-weighted bipartite graphs that runs in time $O(m\sqrt{n}\log N)$. This improves on the $O(Nm\sqrt{n})$-time and $O(m\sqrt{n}\log(nN))$-time algorithms known since the mid 1980s, for $1\ll \log N \ll \log n$. Here $N$ is the maximum integer edge weight.

cs.DS↗