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

Vertical field-effect transistors in III-V semiconductors

Vertical metal-semiconductor field-effect transistors in GaAs/GaAlAs and vertical metal-oxide-semiconductor field-effect transistors (MOSFET's) in InP/GaInPAs materials have been fabricated. These structures make possible short channel devices with gate lengths defined by epitaxy rather than by submicron photolithography processes. Devices with transconductances as high as 280 mS/mm in GaAs and 60 mS/mm (with 100-nm gate oxide) for the InP/GaInPAs MOSFET's were observed

Phased arrays of buried-ridge InP/InGaAsP diode lasers

Phase-locked arrays of buried-ridge InP/InGaAsP lasers, emitting at 1.3 µm, were grown by liquid phase epitaxy. The arrays consist of index-guided, buried-ridge lasers which are coupled via their evanescent optical fields. This index-guided structure makes it possible to avoid the occurrence of lower gain in the interchannel regions. As a result, the buried-ridge arrays oscillate mainly in the fundamental supermode, which yields single lobed, narrow far-field patterns. Single lobed beams less than 4° in width were obtained from buried-ridge InP/InGaAsP phased arrays up to more than twice the threshold current

Phase-locking characteristics of coupled ridge-waveguide InP/InGaAsP diode lasers

The phase-locking characteristics of two coupled, ridge waveguide InP/InGaAsP diode lasers emitting at 1.2 µm were investigated experimentally. The phase locking of the lasers was verified by the observation of phase-locked modes (supermodes) in the spectrally resolved near fields and distinct diffraction patterns in the far field. By independent control of the laser currents it was possible to vary continuously the mutual phase shift between the two phase-locked lasers and thus steer the far-field diffraction lobes. In addition, the separate current control could be utilized to obtain single longitudinal mode oscillation of the phase-locked lasers. Variation in one of the laser currents resulted then in tuning of the wavelength of this single mode over a range of 90 Å

Cd diffused mesa-substrate buried heterostructure InGaAsP/InP laser

A new type of buried heterostructure InGaAsP/InP lasers grown by a single-step liquid phase epitaxy on Cd diffused mesa substrate is described. These lasers exhibit excellent current and optical confinement. Threshold currents as low as 15 mA are achieved for a laser with a 2-µm-wide active region

Short cavity InGaAsP/InP lasers with dielectric mirrors

Short cavity length (38 µm) lasers have been fabricated using a recently developed microcleavage technique. SiO2-amorphous Si multilayer coatings have been evaported on the lasers to obtain high reflectivity mirrors. The lasers have current thresholds as low as 3.8 mA with 85% reflecting front mirror and high reflectivity rear mirror and 2.9 mA with two high reflectivity mirrors. Single longitudinal mode operation is observed over a wide range of driving currents and temperatures

Chemical Force Microscopy of Chemical and Biological Interactions

Interactions between chemical functionalities define outcomes of the vast majority of important events in chemistry, biology and materials science. Chemical Force Microscopy (CFM)--a technique that uses direct chemical functionalization of AFM probes with specific functionalities--allows researchers to investigate these important interactions directly. We review the basic principles of CFM, some examples of its application, and theoretical models that provide the basis for understanding the experimental results. We also emphasize application of modern kinetic theory of non-covalent interactions strength to the analysis of CFM data

Bimodal information increases spontaneous interpersonal synchronization of goal directed upper limb movements

When interacting with each other, people often synchronize spontaneously their movements, e.g. during pendulum swinging, chair rocking[5], walking [4][7], and when executing periodic forearm movements[3].Although the spatiotemporal information that establishes the coupling, leading to synchronization, might be provided by several perceptual systems, the systematic study of different sensory modalities contribution is widely neglected. Considering a) differences in the sensory dominance on the spatial and temporal dimension[5] , b) different cue combination and integration strategies [1][2], and c) that sensory information might provide different aspects of the same event, synchronization should be moderated by the type of sensory modality. Here, 9 naïve participants placed a bottle periodically between two target zones, 40 times, in 12 conditions while sitting in front of a confederate executing the same task. The participant could a) see and hear, b) see , c) hear the confederate, d) or audiovisual information about the movements of the confederate was absent. The couple started in 3 different relative positions (i.e., in-phase, anti-phase, out of phase). A retro-reflective marker was attached to the top of the bottles. Bottle displacement was captured by a motion capture system. We analyzed the variability of the continuous relative phase reflecting the degree of synchronization. Results indicate the emergence of spontaneous synchronization, an increase with bimodal information, and an influence of the initial phase relation on the particular synchronization pattern. Results have theoretical implication for studying cue combination in interpersonal coordination and are consistent with coupled oscillator models.Fundação Bial (Grant 77/12) and Fundação para a Ciência e Tecnologia - FCT: SFRH/BD/8839 6/2012; EXPL/MHC - PCN/0162/2013; FCOMP - 01 - 0124 - FEDER - 022674 and PEst - C/CTM/U10264/2011; FCOMP - 01 - 0124 - FEDER - 037281 and PEst - C/EEI/LA0014/2013. This work was financed by FEDER grants through the Operational Competitiveness Program – COMPET