Orthogonal packing of identical rectangles within isotropic convex regions

A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.

Analysis of designed beta-hairpin peptides: molecular conformation and packing in crystals

The crystal structures of several designed peptide hairpins have been determined in order to establish features of molecular conformations and modes of aggregation in the crystals. Hairpin formation has been induced using a centrally positioned (D)Pro-Xxx segment (Xxx = (L)Pro, Aib, Ac(6)c, Ala; Aib = alpha-aminoisobutyric acid; Ac(6)c = 1-aminocyclohexane-1-carboxylic acid). Structures of the peptides Boc-Leu-Phe-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (1), Boc-Leu-Tyr-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (2, polymorphic forms labeled as 2a and 2b), Boc-Leu-Val-Val-(D)Pro-(L)Pro-Leu-Val-Val-OMe (3), Boc-Leu-Phe-Val-(D)Pro-Aib-Leu-Phe-Val-OMe (4, polymorphic forms labeled as 4a and 4b), Boc-Leu-Phe-Val-(D)Pro-Ac(6)c-Leu-Phe-Val-OMe (5) and Boc-Leu-Phe-Val-(D)Pro-Ala-Leu-Phe-Val-OMe (6) are described. All the octapeptides adopt type II' beta-turn nucleated hairpins, stabilized by three or four cross-strand intramolecular hydrogen bonds. The angle of twist between the two antiparallel strands lies in the range of -9.8 degrees to -26.7 degrees. A detailed analysis of packing motifs in peptide hairpin crystals is presented, revealing three broad modes of association: parallel packing, antiparallel packing and orthogonal packing. An attempt to correlate aggregation modes in solution with observed packing motifs in crystals has been made by indexing of crystal faces in the case of three of the peptide hairpins. The observed modes of hairpin aggregation may be of relevance in modeling multiple modes of association, which may provide insights into the structure of insoluble polypeptide aggregates.

Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Local densities orthogonal to beta-sheet amide planes: patterns of packing in globular proteins.

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions predominate over hydrogen bonding and solvent interactions. We observed considerable variability in packing densities within these regions, confirming that the interior packing of a protein does not result in uniform occupation of the available space. Patterns of fluctuation in packing density suggest that the regular backbone-to-backbone network of hydrogen bonds is not likely to be interrupted to maximize van der Waals interactions. However, high-density packing tends to occur toward the ends of beta-structure strands where hydrogen bonds are more likely to involve nonpolar side-chain groups or solvent molecules. These features result in internal protein folding with a central low-density core surrounded by a higher-density subsurface shell, consistent with our previous calculations regarding overall protein packing density.

A Cyclotomic Lattice Based Quasi-Orthogonal STBC for Eight Transmit Antennas

In this letter, we propose a lattice-based full diversity design for rate-one quasi-orthogonal space time block codes (QSTBC) to obtain an improved diversity product for eight transmit antennas where the information bits are mapped into 4-D lattice points instead of the common modulation constellations. Particularly, the diversity product of the proposed code is directly determined by the minimum Euclidean distance of the used lattice and can be improved by using the lattice packing. We show analytically and by using simulation results that the proposed code achieves a larger diversity product than the rate-one QSTBCs reported previously.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Automatic grading and packing of prawns

Prawns are a substantial Australian resource but presently are processed in a very labour-intensive manner. A prototype system has been developed for automatically grading and packing prawns into single-layer 'consumer packs' in which each prawn is approximately straight and has the same orientation. The novel technology includes a machine vision system that has been specially programmed to calculate relevant parameters at high speed and a gripper mechanism that can acquire, straighten and place prawns of various sizes. The system can be implemented on board a trawler or in an onshore processing facility. © 1993.

Distributed orthogonal space-time block codes with adaptive diversity gain

In this paper we present a novel distributed coding protocol for multi-user cooperative networks. The proposed distributed coding protocol exploits the existing orthogonal space-time block codes to achieve higher diversity gain by repeating the code across time and space (available relay nodes). The achievable diversity gain depends on the number of relay nodes that can fully decode the signal from the source. These relay nodes then form space-time codes to cooperatively relay to the destination using number of time slots. However, the improved diversity gain is archived at the expense of the transmission rate. The design principles of the proposed space-time distributed code and the issues related to transmission rate and diversity trade off is discussed in detail. We show that the proposed distributed space-time coding protocol out performs existing distributed codes with a variable transmission rate.

Multiphase experiments with at least one later laboratory phase. I. orthogonal designs

The paper provides a systematic approach to designing the laboratory phase of a multiphase experiment, taking into account previous phases. General principles are outlined for experiments in which orthogonal designs can be employed. Multiphase experiments occur widely, although their multiphase nature is often not recognized. The need to randomize the material produced from the first phase in the laboratory phase is emphasized. Factor-allocation diagrams are used to depict the randomizations in a design and the use of skeleton analysis-of-variance (ANOVA) tables to evaluate their properties discussed. The methods are illustrated using a scenario and a case study. A basis for categorizing designs is suggested. This article has supplementary material online.

Ideal threshold schemes from orthogonal arrays

The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.

λ-orthogonal pericyclic macromolecular photoligation

A photochemical strategy enabling λ-orthogonal reactions is introduced to construct macromolecular architectures and to encode variable functional groups with site-selective precision into a single molecule by the choice of wavelength. λ-Orthogonal pericyclic reactions proceed independently of one another by the selection of functional groups that absorb light of specific wavelengths. The power of the new concept is shown by a one-pot reaction of equimolar quantities of maleimide with two polymers carrying different maleimide-reactive endgroups, that is, a photoactive diene (photoenol) and a nitrile imine (tetrazole). Under selective irradiation at λ=310–350 nm, any maleimide (or activated ene) end-capped compound reacts exclusively with the photoenol functional polymer. After complete conversion of the photoenol, subsequent irradiation at λ=270–310 nm activates the reaction of the tetrazole group with functional enes. The versatility of the approach is shown by λ-orthogonal click reactions of complex maleimides, functional enes, and polymers to the central polymer scaffold.

Pentacene on Ni(111): room-temperature molecular packing and temperature-activated conversion to graphene

We investigate, using scanning tunnelling microscopy, the adsorption of pentacene on Ni(111) at room temperature and the behaviour of these monolayer films with annealing up to 700 °C. We observe the conversion of pentacene into graphene, which begins from as low as 220 °C with the coalescence of pentacene molecules into large planar aggregates. Then, by annealing at 350 °C for 20 minutes, these aggregates expand into irregular domains of graphene tens of nanometers in size. On surfaces where graphene and nickel carbide coexist, pentacene shows preferential adsorption on the nickel carbide phase. The same pentacene to graphene transformation was also achieved on Cu(111), but at a higher activation temperature, producing large graphene domains that exhibit a range of moiré superlattice periodicities.