Extreme-Point-based Heuristics for the Three-Dimensional Bin Packing problem

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the proble

Steerable optical tweezers for ultracold atom studies

We report on the implementation of an optical tweezer system for controlled transport of ultracold atoms along a narrow, static confinement channel. The tweezer system is based on high-efficiency acousto-optical deflectors and offers two-dimensional control over beam position. This opens up the possibility for tracking the transport channel when shuttling atomic clouds along the guide, forestalling atom spilling. Multiple clouds can be tracked independently by time-shared tweezer beams addressing individual sites in the channel. The deflectors are controlled using a multichannel direct digital synthesizer, which receives instructions on a sub-microsecond time scale from a field-programmable gate array. Using the tweezer system, we demonstrate sequential binary splitting of an ultracold $\rm^{87}Rb$ cloud into $2^5$ clouds.Comment: 4 pages, 5 figures, 1 movie lin

Maximizing Maximal Angles for Plane Straight-Line Graphs

Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The incident angles of a vertex $p \in S$ of $G$ are the angles between any two edges of $G$ that appear consecutively in the circular order of the edges incident to $p$. A plane straight-line graph is called $\phi$-open if each vertex has an incident angle of size at least $\phi$. In this paper we study the following type of question: What is the maximum angle $\phi$ such that for any finite set $S\subset\R^2$ of points in general position we can find a graph from a certain class of graphs on $S$ that is $\phi$-open? In particular, we consider the classes of triangulations, spanning trees, and paths on $S$ and give tight bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that were omitted in the previous version are now include

Bounded-Angle Spanning Tree: Modeling Networks with Angular Constraints

We introduce a new structure for a set of points in the plane and an angle $\alpha$, which is similar in flavor to a bounded-degree MST. We name this structure $\alpha$-MST. Let $P$ be a set of points in the plane and let $0 < \alpha \le 2\pi$ be an angle. An $\alpha$-ST of $P$ is a spanning tree of the complete Euclidean graph induced by $P$, with the additional property that for each point $p \in P$, the smallest angle around $p$ containing all the edges adjacent to $p$ is at most $\alpha$. An $\alpha$-MST of $P$ is then an $\alpha$-ST of $P$ of minimum weight. For $\alpha < \pi/3$, an $\alpha$-ST does not always exist, and, for $\alpha \ge \pi/3$, it always exists. In this paper, we study the problem of computing an $\alpha$-MST for several common values of $\alpha$. Motivated by wireless networks, we formulate the problem in terms of directional antennas. With each point $p \in P$, we associate a wedge $W_p$ of angle $\alpha$ and apex $p$. The goal is to assign an orientation and a radius $r_p$ to each wedge $W_p$, such that the resulting graph is connected and its MST is an $\alpha$-MST. (We draw an edge between $p$ and $q$ if $p \in W_q$, $q \in W_p$, and $|pq| \le r_p, r_q$.) Unsurprisingly, the problem of computing an $\alpha$-MST is NP-hard, at least for $\alpha=\pi$ and $\alpha=2\pi/3$. We present constant-factor approximation algorithms for $\alpha = \pi/2, 2\pi/3, \pi$. One of our major results is a surprising theorem for $\alpha = 2\pi/3$, which, besides being interesting from a geometric point of view, has important applications. For example, the theorem guarantees that given any set $P$ of $3n$ points in the plane and any partitioning of the points into $n$ triplets, one can orient the wedges of each triplet {\em independently}, such that the graph induced by $P$ is connected. We apply the theorem to the {\em antenna conversion} problem

Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26

Comparative study on the uniform energy deposition achievable via optimized plasmonic nanoresonator distributions

Plasmonic nanoresonators of core-shell composition and nanorod shape were optimized to tune their absorption cross-section maximum to the central wavelength of a short pulse. Their distribution along a pulse-length scaled target was optimized to maximize the absorptance with the criterion of minimal absorption difference in between neighbouring layers. Successive approximation of layer distributions made it possible to ensure almost uniform deposited energy distribution up until the maximal overlap of two counter-propagating pulses. Based on the larger absorptance and smaller uncertainty in absorptance and energy distribution core-shell nanoresonators override the nanorods. However, optimization of both nanoresonator distributions has potential applications, where efficient and uniform energy deposition is crucial, including phase transitions and even fusion

Road traffic and landscape characteristics predict the occurrence of native halophytes on roadside verges

Road management practices, such as winter de-icing create ideal habitats and competitive advantage for salt-tolerant species. We aimed to map the occurrences of halophytes along roads in Hungary. Furthermore, we tested factors that might play a role in the roadside occurrences of five chosen native halophytes from rare to common, we encountered during our field surveys. These were Festuca pseudovina, Limonium gmelinii subsp. hungaricum, Podospermum canum, Puccinellia distans and Spergularia media. We found, that at least one halophyte species was documented in 71% of the total sampling points. Germination experiments indicated that substrate salt concentration significantly decreased germination rates in each of the five species, but in case of L. gmelinii subsp. hungaricum, or P. distans germination occurred on extremely high salt concentrations. Traffic intensity, the presence of other halophytes at the sampling point and the presence of a given species in the surrounding landscape had a significant positive effect on the occurrence of four of the five model species. Our results suggest that the studied species are mostly in the early stage of their roadside spread, colonizing roadsides close to their native distribution ranges. The possibility of a future range expansion along roads cannot be excluded

Realistic Earth escape strategies for solar sailing

With growing interest in solar sailing comes the requirement to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. Previously unexplained seasonal variations in sail escape times from Earth orbit are explained analytically and corroborated within a numerical trajectory model. Blended-sail control algorithms, explicitly independent of time, which providenear-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller, are then presented. These algorithms are investigated from a range of initial conditions and are shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the minimum sail characteristic acceleration required for escape from a polar orbit without traversing the Earth shadow cone increases exponentially as initial altitude is decreased

Uncertainties in Precipitation and Their Impacts on Runoff Estimates

Water balance calculations are becoming increasingly important for earth-system studies. Precipitation is one of the most critical input variables for such calculations because it is the immediate source of water for the land surface hydrological budget. Numerous precipitation datasets have been developed in the last two decades, but these datasets often show marked differences in their spatial and temporal distribution of this key hydrological variable. This paper compares six monthly precipitation datasets—Climate Research Unit of University of East Anglia (CRU), Willmott–Matsuura (WM), Global Precipitation Climate Center (GPCC), Global Precipitation Climatology Project (GPCP), Tropical Rainfall Measuring Mission (TRMM), and NCEP–Department of Energy (DOE) Atmospheric Model Intercomparison Project (AMIP-II) Reanalysis (NCEP-2)—to assess the uncertainties in these datasets and their impact on the terrestrial water balance. The six datasets tested in the present paper were climatologically averaged and compared by calculating various statistics of the differences. The climatologically averaged monthly precipitation estimates were applied as inputs to a water balance model to estimate runoff and the uncertainties in runoff arising directly from the precipitation estimates. The results of this study highlight the need for accurate precipitation inputs for water balance calculations. These results also demonstrate the need to improve precipitation estimates in arid and semiarid regions, where slight changes in precipitation can result in dramatic changes in the runoff response due to the nonlinearity of the runoff-generation processes