Computing the Largest Empty Rectangle

We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones used by Bentley [1] and introduces a new notion of Voronoi diagram along with a method for efficient computation of certain functions over paths of a tree

Performance analysis of an orbital angular momentum multiplexed amplify-and-forward radio relay chain with inter-modal crosstalk

The end-to-end spectral efficiency and bit error rate (BER) of an amplify-and-forward (AF) radio relay chain employing orbital angular momentum (OAM) multiplexing is presented. The inherent divergence of a beam carrying OAM is overcome by means of a lens. Modelled and measured inter-modal crosstalk levels are incorporated into the analysis. The results show that an end-to-end spectral efficiency of up to 8 bits s−1 Hz−1 is achievable using four OAM modes to multiplex four parallel data streams over 20 hops, provided that the detrimental effects of inter-modal crosstalk are mitigated. The spectral efficiency is expected to scale further by using more OAM modes. The BER profile along the relay chain is analysed for each of the four OAM modes

Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Drosophila tan Encodes a Novel Hydrolase Required in Pigmentation and Vision

Many proteins are used repeatedly in development, but usually the function of the protein is similar in the different contexts. Here we report that the classical Drosophila melanogaster locus tan encodes a novel enzyme required for two very different cellular functions: hydrolysis of N-β-alanyl dopamine (NBAD) to dopamine during cuticular melanization, and hydrolysis of carcinine to histamine in the metabolism of photoreceptor neurotransmitter. We characterized two tan-like P-element insertions that failed to complement classical tan mutations. Both are inserted in the 5′ untranslated region of the previously uncharacterized gene CG12120, a putative homolog of fungal isopenicillin-N N-acyltransferase (EC 2.3.1.164). Both P insertions showed abnormally low transcription of the CG12120 mRNA. Ectopic CG12120 expression rescued tan mutant pigmentation phenotypes and caused the production of striking black melanin patterns. Electroretinogram and head histamine assays indicated that CG12120 is required for hydrolysis of carcinine to histamine, which is required for histaminergic neurotransmission. Recombinant CG12120 protein efficiently hydrolyzed both NBAD to dopamine and carcinine to histamine. We conclude that D. melanogaster CG12120 corresponds to tan. This is, to our knowledge, the first molecular genetic characterization of NBAD hydrolase and carcinine hydrolase activity in any organism and is central to the understanding of pigmentation and photoreceptor function

Experimental evaluation of 3D printed spiral phase plates for enabling an orbital angular momentum multiplexed radio system

This paper evaluates the performance of three-dimensionally (3D) printed spiral phase plates (SPPs) for enabling an orbital angular momentum (OAM) multiplexed radio system. The design and realization of the SPPs by means of additive manufacturing exploiting a high-permittivity material is described. Modes 1 and 2 SPPs are then evaluated at 15 GHz in terms of 3D complex radiation pattern, mode purity and beam collimation by means of a 3D printed dielectric lens. The results with the lens yield a crosstalk of −8 dB for between modes 1 and −1, and −11.4 dB for between modes 2 and −2. We suggest a mode multiplexer architecture that is expected to further reduce the crosstalk for each mode. An additional loss of 4.2 dB is incurred with the SPPs inserted into the communication link, which is undesirable for obtaining reliable LTE-based communications. Thus, we suggest: using lower loss materials, seeking ways to reduce material interface reflections or alternative ways of OAM multiplexing to realize a viable OAM multiplexed radio system

Comparison of toxic product yields of burning cables in bench and large-scale experiments

Toxic product yields from five commercial cables obtained from a steady state tube furnace (SSTF) method (lEC 60695-7-50, Purser furnace) are compared with results from a large-scale test, which uses the physical fire model in the proposed prEN50399-2-2 test, with the addition of effluent gas analysis, using Fourier transform infrared (FTIR), and for further comparison, a static tube furnace method (NF X 70-100). This work represents one of the first attempts to establish a relationship between bench- and large-scale toxic product yields for burning cables. This is difficult because the cables have been formulated for low flammability, and therefore do not burn consistently. The tube furnace burns the cable completely, whereas the large-scale test effluent is the result of a combination of flame spread and toxic product yields, both of which are fire scenario dependant. There is significant differentiation between cable types based on composition, and arising because only a portion of the cables burn in the large-scale test, accompanied by possible decomposition of hydrate sheaths. The fire stage of the large-scale test appears to have been replicated in an appropriate manner, given the correspondence of the CO2/CO ratios. The yields of CO2, CO, HCl and smoke show reasonable agreement, given the differences in the extent of burning, and the accuracy of the mass-loss data available for the large-scale test. The yields and extent of burning have been combined to demonstrate the estimation of toxic hazard for a particular fire scenario based around the large-scale test, which shows only marginal sensitivity to the differences in toxic product yield between the SSTF and the large-scale test. (c) 2007 Elsevier Ltd. All rights reserved

Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump

The small size (58 residues) and simple structure of the B domain of staphylococcal protein A (BdpA) have led to this domain being a paradigm for theoretical studies of folding. Experimental studies of the folding of BdpA have been limited by the rapidity of its folding kinetics. We report the folding kinetics of a fluorescent mutant of BdpA (G29A F13W), named F13W*, using nanosecond laser-induced temperature jump experiments. Automation of the apparatus has permitted large data sets to be acquired that provide excellent signal-to-noise ratio over a wide range of experimental conditions. By measuring the temperature and denaturant dependence of equilibrium and kinetic data for F13W*, we show that thermodynamic modeling of multidimensional equilibrium and kinetic surfaces is a robust method that allows reliable extrapolation of rate constants to regions of the folding landscape not directly accessible experimentally. The results reveal that F13W* is the fastest-folding protein of its size studied to date, with a maximum folding rate constant at 0 M guanidinium chloride and 45°C of 249,000 (s-1). Assuming the single-exponential kinetics represent barrier-limited folding, these data limit the value for the preexponential factor for folding of this protein to at least ≈2 x 10(6) s(-1)

Global DNA methylation and cognitive and behavioral outcomes at 4 years of age: A cross‐sectional study

Background Accumulating evidence suggests that breastfeeding exclusivity and duration are positively associated with child cognition. This study investigated whether DNA methylation, an epigenetic mechanism modified by nutrient intake, may contribute to the link between breastfeeding and child cognition. The aim was to quantify the relationship between global DNA methylation and cognition and behavior at 4 years of age. Methods Child behavior and cognition were measured at age 4 years using the Wechsler Preschool and Primary Scale of Intelligence, third version (WPPSI‐III), and Child Behavior Checklist (CBC). Global DNA methylation (%5‐methylcytosines (%5mC)) was measured in buccal cells at age 4 years, using an enzyme‐linked immunosorbent assay (ELISA) commercial kit. Linear regression models were used to quantify the statistical relationships. Results Data were collected from 73 children recruited from the Women and Their Children's Health (WATCH) study. No statistically significant associations were found between global DNA methylation levels and child cognition or behavior (p > .05), though the estimates of effect were consistently negative. Global DNA methylation levels in males were significantly higher than in females (median %5mC: 1.82 vs. 1.03, males and females, respectively, (p < .05)). Conclusion No association was found between global DNA methylation and child cognition and behavior; however given the small sample, this study should be pooled with other cohorts in future meta‐analyses

The Suaineadh Project : a stepping stone towards the deployment of large flexible structures in space

The Suaineadh project aims at testing the controlled deployment and stabilization of space web. The deployment system is based on a simple yet ingenious control of the centrifugal force that will pull each of the four daughters sections apart. The four daughters are attached onto the four corners of a square web, and will be released from their initial stowed configuration attached to a central hub. Enclosed in the central hub is a specifically designed spinning reaction wheel that controls the rotational speed with a closed loop control fed by measurements from an onboard inertial measurement sensor. Five other such sensors located within the web and central hub provide information on the surface curvature of the web, and progression of the deployment. Suaineadh is currently at an advanced stage of development: all the components are manufactured with the subsystems integrated and are presently awaiting full integration and testing. This paper will present the current status of the Suaineadh project and the results of the most recent set of tests. In particular, the paper will cover the overall mechanical design of the system, the electrical and sensor assemblies, the communication and power systems and the spinning wheel with its control system