A Metrizable Topology on the Contracting Boundary of a Group

The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the contracting boundary. When the space is the Cayley graph of a finitely generated group we show that our new topology is metrizable.Comment: v1: 26 pages, 3 figures; v2: 44 pages, 6 figures, additional results; v3: 46 pages, 7 figures, minor change

Stellar Differential Rotation and Coronal Timescales

We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the geometric mean of the lap time and the surface diffusion timescale. In contrast, the lifetime of flux ropes are proportional to the lap time. With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than two days. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae

Electronic structure of periodic curved surfaces -- topological band structure

Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerene. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wavefunction interferes on a multiply-connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P- and D-surfaces) possess one-to-one correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to [email protected]

Towards gravitationally assisted negative refraction of light by vacuum

Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector. This conclusion suggests, inter alia, gravitationally assisted negative refraction by vacuum.Comment: 6 page

The structure of an LIM-only protein 4 (LMO4) and deformed epidermal autoregulatory factor-1 (DEAF1) complex reveals a common mode of binding to LMO4

LIM-domain only protein 4 (LMO4) is a widely expressed protein with important roles in embryonic development and breast cancer. It has been reported to bind many partners, including the transcription factor Deformed epidermal autoregulatory factor-1 (DEAF1), with which LMO4 shares many biological parallels. We used yeast two-hybrid assays to show that DEAF1 binds both LIM domains of LMO4 and that DEAF1 binds the same face on LMO4 as two other LMO4-binding partners, namely LIM domain binding protein 1 (LDB1) and C-terminal binding protein interacting protein (CtIP/RBBP8). Mutagenic screening analysed by the same method, indicates that the key residues in the interaction lie in LMO4LIM2 and the N-terminal half of the LMO4-binding domain in DEAF1. We generated a stable LMO4LIM2-DEAF1 complex and determined the solution structure of that complex. Although the LMO4-binding domain from DEAF1 is intrinsically disordered, it becomes structured on binding. The structure confirms that LDB1, CtIP and DEAF1 all bind to the same face on LMO4. LMO4 appears to form a hub in protein-protein interaction networks, linking numerous pathways within cells. Competitive binding for LMO4 therefore most likely provides a level of regulation between those different pathways.SJ was funded by an Australian Postgraduate Award (education.gov.au/australian-postgraduate-awards). JPM and JMM were awarded Senior Research Fellowships from the Australian National and Medical Research Council (www.nhmrc.gov.au). This project was funded by an Australian Research Council (www. arc.gov.au) Discovery Project Grant (DP110104332) to JMM and LC

Bayesian stochastic blockmodeling

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm

A Renormalization Group for Hamiltonians: Numerical Results

We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually simple, and allows for accurate numerical computations. In a numerical implementation, we find a nontrivial fixed point and determine the corresponding critical index and scaling. Our computed values for various universal constants are in good agreement with existing data for area-preserving maps. We also discuss the flow associated with the nontrivial fixed point.Comment: 11 Pages, 2 Figures. For future updates, check ftp://ftp.ma.utexas.edu/pub/papers/koch

Serine, but not glycine, supports one-carbon metabolism and proliferation of cancer cells

Previous work has shown that some cancer cells are highly dependent on serine/glycine uptake for proliferation. Although serine and glycine can be interconverted and either might be used for nucleotide synthesis and one-carbon metabolism, we show that exogenous glycine cannot replace serine to support cancer cell proliferation. Cancer cells selectively consumed exogenous serine, which was converted to intracellular glycine and one-carbon units for building nucleotides. Restriction of exogenous glycine or depletion of the glycine cleavage system did not impede proliferation. In the absence of serine, uptake of exogenous glycine was unable to support nucleotide synthesis. Indeed, higher concentrations of glycine inhibited proliferation. Under these conditions, glycine was converted to serine, a reaction that would deplete the one-carbon pool. Providing one-carbon units by adding formate rescued nucleotide synthesis and growth of glycine-fed cells. We conclude that nucleotide synthesis and cancer cell proliferation are supported by serine—rather than glycine—consumption

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Fast and flexible selection with a single switch

Selection methods that require only a single-switch input, such as a button click or blink, are potentially useful for individuals with motor impairments, mobile technology users, and individuals wishing to transmit information securely. We present a single-switch selection method, "Nomon," that is general and efficient. Existing single-switch selection methods require selectable options to be arranged in ways that limit potential applications. By contrast, traditional operating systems, web browsers, and free-form applications (such as drawing) place options at arbitrary points on the screen. Nomon, however, has the flexibility to select any point on a screen. Nomon adapts automatically to an individual's clicking ability; it allows a person who clicks precisely to make a selection quickly and allows a person who clicks imprecisely more time to make a selection without error. Nomon reaps gains in information rate by allowing the specification of beliefs (priors) about option selection probabilities and by avoiding tree-based selection schemes in favor of direct (posterior) inference. We have developed both a Nomon-based writing application and a drawing application. To evaluate Nomon's performance, we compared the writing application with a popular existing method for single-switch writing (row-column scanning). Novice users wrote 35% faster with the Nomon interface than with the scanning interface. An experienced user (author TB, with > 10 hours practice) wrote at speeds of 9.3 words per minute with Nomon, using 1.2 clicks per character and making no errors in the final text.Comment: 14 pages, 5 figures, 1 table, presented at NIPS 2009 Mini-symposi