How Does a Dipolar Bose-Einstein Condensate Collapse?

We emphasize that the macroscopic collapse of a dipolar Bose-Einstein condensate in a pancake-shaped trap occurs through local density fluctuations, rather than through a global collapse to the trap center. This hypothesis is supported by a recent experiment in a chromium condensate.Comment: Proceedings of 17th International Laser Physics Worksho

Subgraphs and network motifs in geometric networks

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in abstract spaces such as multivariate biological or economic datasets and models of social networks. These networks often display network motifs: subgraphs that recur in the network much more often than in randomized networks. To understand the origin of the network motifs in these networks, it is important to study the subgraphs and network motifs that arise solely from geometric constraints. To address this, we analyze geometric network models, in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes. We present analytical solutions for the numbers of all 3 and 4-node subgraphs, in both directed and non-directed geometric networks. We also analyze geometric networks with arbitrary degree sequences, and models with a field that biases for directed edges in one direction. Scaling rules for scaling of subgraph numbers with system size, lattice dimension and interaction range are given. Several invariant measures are found, such as the ratio of feedback and feed-forward loops, which do not depend on system size, dimension or connectivity function. We find that network motifs in many real-world networks, including social networks and neuronal networks, are not captured solely by these geometric models. This is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information-processing functions.Comment: 9 pages, 6 figure

Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate

We report on measurements of the excitation spectrum of a strongly interacting Bose-Einstein condensate. A magnetic-field Feshbach resonance is used to tune atom-atom interactions in the condensate and to reach a regime where quantum depletion and beyond mean-field corrections to the condensate chemical potential are significant. We use two-photon Bragg spectroscopy to probe the condensate excitation spectrum; our results demonstrate the onset of beyond mean-field effects in a gaseous Bose-Einstein condensate

Various quantum nonlocality tests with a simple 2-photon entanglement source

Nonlocality is a fascinating and counterintuitive aspect of Nature, revealed by the violation of a Bell inequality. The standard and easiest configuration in which Bell inequalities can be measured has been proposed by Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can also be carried out. In particular, Bell inequalities requiring multiple measurement settings can provide deeper fundamental insights about quantum nonlocality as well as offering advantages in the presence of noise and detection inefficiency. In this article we show how these nonlocality tests can be performed using a commercially available source of entangled photon pairs. We report the violation of a series of these nonlocality tests (I3322, I4422 and chained inequalities). With the violation of the chained inequality with 4 settings per side we put an upper limit at 0.49 on the local content of the states prepared by the source (instead of 0.63 attainable with CHSH). We also quantify the amount of true randomness that has been created during our experiment (assuming fair sampling of the detected events).Comment: 8 pages, 5 figure

Identifying the favored mutation in a positive selective sweep.

Most approaches that capture signatures of selective sweeps in population genomics data do not identify the specific mutation favored by selection. We present iSAFE (for "integrated selection of allele favored by evolution"), a method that enables researchers to accurately pinpoint the favored mutation in a large region (∼5 Mbp) by using a statistic derived solely from population genetics signals. iSAFE does not require knowledge of demography, the phenotype under selection, or functional annotations of mutations

Toward a script theory of guidance in computer-supported collaborative learning

This article presents an outline of a script theory of guidance for computer-supported collaborative learning (CSCL). With its four types of components of internal and external scripts (play, scene, role, and scriptlet) and seven principles, this theory addresses the question how CSCL practices are shaped by dynamically re-configured internal collaboration scripts of the participating learners. Furthermore, it explains how internal collaboration scripts develop through participation in CSCL practices. It emphasizes the importance of active application of subject matter knowledge in CSCL practices, and it prioritizes transactive over non-transactive forms of knowledge application in order to facilitate learning. Further, the theory explains how external collaboration scripts modify CSCL practices and how they influence the development of internal collaboration scripts. The principles specify an optimal scaffolding level for external collaboration scripts and allow for the formulation of hypotheses about the fading of external collaboration scripts. Finally, the article points towards conceptual challenges and future research questions

Coarse-Graining and Self-Dissimilarity of Complex Networks

Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units (CGU) as connectivity patterns which can serve as the nodes of a coarse-grained network, and present algorithms to detect them. We use this approach to systematically reverse-engineer electronic circuits, forming understandable high-level maps from incomprehensible transistor wiring: first, a coarse-grained version in which each node is a gate made of several transistors is established. Then, the coarse-grained network is itself coarse-grained, resulting in a high-level blueprint in which each node is a circuit-module made of multiple gates. We apply our approach also to a mammalian protein-signaling network, to find a simplified coarse-grained network with three main signaling channels that correspond to cross-interacting MAP-kinase cascades. We find that both biological and electronic networks are 'self-dissimilar', with different network motifs found at each level. The present approach can be used to simplify a wide variety of directed and nondirected, natural and designed networks.Comment: 11 pages, 11 figure

Classical Scattering in 1+11+1 Dimensional String Theory

We find the general solution to Polchinski's classical scattering equations for $1+1$ dimensional string theory. This allows efficient computation of scattering amplitudes in the standard Liouville $\times$ $c=1$ background. Moreover, the solution leads to a mapping from a large class of time-dependent collective field theory backgrounds to corresponding nonlinear sigma models. Finally, we derive recursion relations between tachyon amplitudes. These may be summarized by an infinite set of nonlinear PDE's for the partition function in an arbitrary time-dependent background.Comment: 15 p

Three-body interactions with cold polar molecules

We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.Comment: 8 pages, 4 figure

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi--Yau manifolds. Our results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.Comment: 44 pages plus 3 tables using harvma