Structure formation in atom lithography using geometric collimation

Atom lithography uses standing wave light fields as arrays of lenses to focus neutral atom beams into line patterns on a substrate. Laser cooled atom beams are commonly used, but an atom beam source with a small opening placed at a large distance from a substrate creates atom beams which are locally geometrically collimated on the substrate. These beams have local offset angles with respect to the substrate. We show that this affects the height, width, shape, and position of the created structures. We find that simulated effects are partially obscured in experiments by substrate-dependent diffusion of atoms, while scattering and interference just above the substrate limit the quality of the standing wave lens. We find that in atom lithography without laser cooling the atom beam source geometry is imaged onto the substrate by the standing wave lens. We therefore propose using structured atom beam sources to image more complex patterns on subwavelength scales in a massively parallel way.     

Reconstructing polygons from x-rays

We present strategies for interactively reconstructing polygons from carefully chosen x-ray probes, generalizing previous results for convex polygons to a significantly larger class of objects. In particular, we show that n+h+2 parallel x-ray probes are sufficient to determine an n-gon P with h vertices on its convex hull, provided no three vertices of P are collinear. If given an upper bound n on the number of vertices of P, then 2n+2 parallel probes or 3n origin probes suffice. Further, we show that lg n–2 probes are necessary. Finally, we present verification strategies for arbitrary polygons. Interactive probing strategies have the potential to minimize radiation exposure in medical imaging.     

The Collatz conjecture and De Bruijn graphs

We study variants of the well-known Collatz graph, by considering the action of the 3n+1$3n+1$ function on congruence classes. For moduli equal to powers of 2, these graphs are shown to be isomorphic to binary De Bruijn graphs. Unlike the Collatz graph, these graphs are very structured, and have several interesting properties. We then look at a natural generalization of these finite graphs to the 2-adic integers, and show that the isomorphism between the resulting infinite graphs is exactly the conjugacy map previously studied by Bernstein and Lagarias. Finally, we show that for generalizations of the 3n+1$3n+1$ function, such as the family of an+b$an+b$ functions and Collatz-like functions, we get similar relations with 2-adic and p$p$-adic De Bruijn graphs respectively.     

Shifting representation search for hybrid flexible flowline problems

This paper considers the hybrid flexible flowline scheduling problem with a set of additional restrictions and generalizations that are common in practice. These include precedence constraints, sequence dependent setup times, time lags, machine eligibility and release times. There are many potential solution representations for this problem, ranging from simple and compact, to more complex and complete. Typically, when choosing the degree of detail of the solution representation, a tradeoff can be found between efficiency of the algorithm and the size of the search space. Several adaptations of existing methods are introduced (memetic algorithm, iterated local search, iterated greedy), as well as a novel algorithm called shifting representation search (SRS). This new method starts with an iterated greedy algorithm applied to a permutation version of the problem and at a given time, switches to an iterated local search on the full search space. As far as we know, this shift of the solution representation is new in the scheduling literature. Experimental results and statistical tests clearly prove the superiority of SRS compared with classical and existing methods.     

On Minimum Stars and Maximum Matchings

We discuss worst-case bounds on the ratio of maximum matching and minimum median values for finite point sets. In particular, we consider ``minimum stars,' which are defined by a center chosen from the given point set, such that the total geometric distance L <sub>S</sub> to all the points in the set is minimized. If the center point is not required to be an element of the set (i.e., the center may be a Steiner point), we get a ``minimum Steiner star' of total length L _SS . As a consequence of triangle inequality, the total length L _M of a maximum matching is a lower bound for the length L _SS of a minimum Steiner star, which makes the worst-case value ρ(SS,M) of the value L _SS /L _M interesting in the context of optimal communication networks. The ratio also appears as the duality gap in an integer programming formulation of a location problem by Tamir and Mitchell. In this paper we show that for a finite set that consists of an even number of points in the plane and Euclidean distances, the worst-case ratio ρ(S,M) cannot exceed . This proves a conjecture of Suri, who gave an example where this bound is achieved. For the case of Euclidean distances in two and three dimensions, we also prove upper and lower bounds for the worst-case value ρ(S,SS) of the ratio L _S /L _SS , and for the worst-case value ρ(S,M) of the ratio L _S /L _M . We give tight upper bounds for the case where distances are measured according to the Manhattan metric: we show that in three-dimensional space, ρ(SS,M) is bounded by 3/2, while in two-dimensional space L _SS =L _M , extending some independent observations by Tamir and Mitchell. Finally, we show that ρ(S,SS) is 3/2 in the two-dimensional case, and 5/3 in the three-dimensional case. Received January 1, 1999, and in revised form July 15, 1999.     

Variational Message Passing and Local Constraint Manipulation in Factor Graphs

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.     

ChemInform Abstract: Infrared Spectroscopy of Hydrated Bicarbonate Anion Clusters: HCO3‐(H2O)1‐10.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Supramolecular polymers: from scientific curiosity to technological reality

Supramolecular polymers^[1] are introduced as a new approach to come to materials in which the repeating units are not connected by covalent bonds but by specific secondary interactions. Self-complementary quadruple hydrogen bonded structures with high association constants are presented as easy to synthesize fragments in supramolecular polymers. Some of the many possibilities of equilibrium polymers are discussed, while it is shown that these supramolecular polymers can obtain materials properties normally only obtained with macromolecules.