Conflict-Free Coloring Made Stronger

In FOCS 2002, Even et al. showed that any set of $n$ discs in the plane can be Conflict-Free colored with a total of at most $O(\log n)$ colors. That is, it can be colored with $O(\log n)$ colors such that for any (covered) point $p$ there is some disc whose color is distinct from all other colors of discs containing $p$. They also showed that this bound is asymptotically tight. In this paper we prove the following stronger results: \begin{enumerate} \item [(i)] Any set of $n$ discs in the plane can be colored with a total of at most $O(k \log n)$ colors such that (a) for any point $p$ that is covered by at least $k$ discs, there are at least $k$ distinct discs each of which is colored by a color distinct from all other discs containing $p$ and (b) for any point $p$ covered by at most $k$ discs, all discs covering $p$ are colored distinctively. We call such a coloring a {\em $k$-Strong Conflict-Free} coloring. We extend this result to pseudo-discs and arbitrary regions with linear union-complexity. \item [(ii)] More generally, for families of $n$ simple closed Jordan regions with union-complexity bounded by $O(n^{1+\alpha})$, we prove that there exists a $k$-Strong Conflict-Free coloring with at most $O(k n^\alpha)$ colors. \item [(iii)] We prove that any set of $n$ axis-parallel rectangles can be $k$-Strong Conflict-Free colored with at most $O(k \log^2 n)$ colors. \item [(iv)] We provide a general framework for $k$-Strong Conflict-Free coloring arbitrary hypergraphs. This framework relates the notion of $k$-Strong Conflict-Free coloring and the recently studied notion of $k$-colorful coloring. \end{enumerate} All of our proofs are constructive. That is, there exist polynomial time algorithms for computing such colorings

Monolithic optoelectronic integration of a GaAlAs laser, a field-effect transistor, and a photodiode

A low threshold buried heterostructure laser, a metal-semiconductor field-effect transistor, and a p-i-n photodiode have been integrated on a semi-insulating GaAs substrate. The circuit was operated as a rudimentary optical repeater. The gain bandwidth product of the repeater was measured to be 178 MHz

High-speed GaAlAs/GaAs p-i-n photodiode on a semi-insulating GaAs substrate

A high-speed, high-responsivity GaAlAs/GaAs p-i-n photodiode has been fabricated on a GaAs semi-insulating substrate. The 75-µm-diam photodiode has a 3-dB bandwidth of 2.5 GHz and responsivity of 0.45 A/W at 8400 Å (external quantum efficiency of 65%). The diode is suitable for monolithic integration with other optoelectronic devices

Gallium Aluminum Arsenide/Gallium Arsenide Integrated Optical Repeater

A low threshold buried heterostructure laser, a metal-semiconductor field effect transistor (MESFET), and a photodiode, have for the first time, been monolithically integrated on a semi-insulating GaAs substrate. This integrated optoelectronic circuit (IOEC) was operated as a rudimentary optical repeater. The incident optical signal is detected by the photodiode, amplified by the MESFET, and converted back to light by the laser. The gain bandwidth product of the repeater was measured to be 178 MHz

Direct amplitude modulation of short-cavity GaAs lasers up to X-band frequencies

Experimental and theoretical studies indicate that a high-frequency laser with bandwidths up to X-band frequencies (~> 10 GHz) should be one having a short cavity with a window structure, and preferably operating at low temperatures. These designs would accomplish the task of shortening the photon lifetime, increasing the intrinsic optical gain, and increasing the internal photon density without inflicting mirror damage. A modulation bandwidth of >8 GHz has been achieved using a 120-µm laser without any special window structure at room temperature

Superluminescent damping of relaxation resonance in the modulation response of GaAs lasers

It is demonstrated experimentally that the intrinsic modulation response of injection lasers can be modified by reducing mirror reflectivities, which leads to suppression of relaxation oscillation resonance and a reduction of nonlinear distortions up to multi-GHz frequencies. A totally flat response with a 3-dB bandwidth of 5 GHz was obtained using antireflection coated buried heterostructure lasers fabricated on a semi-insulating substrate. Harmonic distortions were below 40 dB within the entire 3-dB bandwidth. These results are in accord with theoretical predictions based on an analysis which include the effects of superluminescence in the laser cavity

Globular: an online proof assistant for higher-dimensional rewriting

This article introduces Globular, an online proof assistant for the formalization and veri cation of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their construction with a point-and- click interface, and performs type checking to prevent incorrect rewrites. Hosted on the web, it has a low barrier to use, and allows hyperlinking of formalized proofs directly from research papers. It allows the formalization of proofs from logic, topology and algebra which are not formalizable by other methods, and we give several examples

Monolithic integration of a very low threshold GaInAsP laser and metal-insulator-semiconductor field-effect transistor on semi-insulating InP

Monolithic integration of 1.3-µm groove lasers and metal-insulator-semiconductor field-effect transistors (MISFET) is achieved by a simple single liquid phase epitaxy (LPE) growth process. Laser thresholds as low as 14 mA for 300-µm cavity length are obtained. MIS depletion mode FET's with n channels on LPE grown InP layer show typical transconductance of 5–10 mmho. Laser modulation by the FET current is demonstrated at up to twice the threshold current

Ultralow threshold graded-index separate-confinement heterostructure single quantum well (Al,Ga)As lasers

Broad area graded‐index separate‐confinement heterostructure single quantum well lasers grown by molecular‐beam epitaxy (MBE) with threshold current density as low as 93 A/cm^2 (520 μm long) have been fabricated. Buried lasers formed from similarly structured MBE material with liquid phase epitaxy regrowth had threshold currents at submilliampere levels when high reflectivity coatings were applied to the end facets. A cw threshold current of 0.55 mA was obtained for a laser with facet reflectivities of ∼80%, a cavity length of 120 μm, and an active region stripe width of 1 μm. These devices driven directly with logic level signals have switch‐on delays <50 ps without any current prebias. Such lasers permit fully on–off switching while at the same time obviating the need for bias monitoring and feedback control

Infrared coronal emission lines and the possibility of their maser emission in Seyfert nuclei

Energetic emitting regions have traditionally been studied via x-ray, UV and optical emission lines of highly ionized intermediate mass elements. Such lines are often referred to as 'coronal lines' since the ions, when produced by collisional ionization, reach maximum abundance at electron temperatures of approx. 10(exp 5) - 10(exp 6) K typical of the sun's upper atmosphere. However, optical and UV coronal lines are also observed in a wide variety of Galactic and extragalactic sources including the Galactic interstellar medium, nova shells, supernova remnants, galaxies and QSOs. Infrared coronal lines are providing a new window for observation of energetic emitting regions in heavily dust obscured sources such as infrared bright merging galaxies and Seyfert nuclei and new opportunities for model constraints on physical conditions in these sources. Unlike their UV and optical counterparts, infrared coronal lines can be primary coolants of collisionally ionized plasmas with 10(exp 4) less than T(sub e)(K) less than 10(exp 6) which produce little or no optical or shorter wavelength coronal line emission. In addition, they provide a means to probe heavily dust obscured emitting regions which are often inaccessible to optical or UV line studies. In this poster, we provide results from new model calculations to support upcoming Infrared Space Observatory (ISO) and current ground-based observing programs involving infrared coronal emission lines in AGN. We present a complete list of infrared (lambda greater than 1 micron) lines due to transitions within the ground configurations 2s(2)2p(k) and 3s(2)3p(k) (k = 1 to 5) or the first excited configurations 2s2p and 3s3p of highly ionized (x greater than or equal to 100 eV) astrophysically abundant (n(X)/n(H) greater than or equal to 10(exp -6)) elements. Included are approximately 74 lines in ions of O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, and Ni spanning a wavelength range of approximately 1 - 280 microns. We present new results from detailed balance calculations, new critical densities for collisional de-excitation, intrinsic photon rates, branching ratios, and excitation temperatures for the majority of the compiled transitions. The temperature and density parameter space for dominant cooling via infrared coronal lines is presented, and the relationship of infrared to optical coronal lines is discussed