Cyclic derangements

A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem to enumerating derangements in the wreath product of any finite cyclic group with the symmetric group. We also give q- and (q, t)-analogs for cyclic derangements, generalizing results of Brenti and Gessel.Comment: 14 page

Dual equivalence graphs I: A new paradigm for Schur positivity

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for establishing the symmetry and Schur positivity of quasisymmetric functions.Comment: 24 pages, 27 figures, to appear in Forum of Mathematics, Sigma. arXiv admin note: substantial text overlap with arXiv:1005.375

Extinction of metastable stochastic populations

We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n=0. In scenario B there is an intermediate repelling point n=n_1 between the attracting point n=0 and another attracting point n=n_2 in the vicinity of which the metastable population resides. The crux of the theory is WKB method which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasi-stationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasi-stationary master equation at small n and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multi-step processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.Comment: 19 pages, 7 figure

Antiferromagnetic phase of the gapless semiconductor V3Al

Discovering new antiferromagnetic compounds is at the forefront of developing future spintronic devices without fringing magnetic fields. The antiferromagnetic gapless semiconducting D03 phase of V3Al was successfully synthesized via arc-melting and annealing. The antiferromagnetic properties were established through synchrotron measurements of the atom-specific magnetic moments, where the magnetic dichroism reveals large and oppositely-oriented moments on individual V atoms. Density functional theory calculations confirmed the stability of a type G antiferromagnetism involving only two-third of the V atoms, while the remaining V atoms are nonmagnetic. Magnetization, x-ray diffraction and transport measurements also support the antiferromagnetism. This archetypal gapless semiconductor may be considered as a cornerstone for future spintronic devices containing antiferromagnetic elements.Comment: Accepted to Physics Review B on 02/23/1

A coral-on-a-chip microfluidic platform enabling live-imaging microscopy of reef-building corals

Coral reefs, and the unique ecosystems they support, are facing severe threats by human activities and climate change. Our understanding of these threats is hampered by the lack of robust approaches for studying the micro-scale interactions between corals and their environment. Here we present an experimental platform, coral-on-a-chip, combining micropropagation and microfluidics to allow direct microscopic study of live coral polyps. The small and transparent coral micropropagates are ideally suited for live-imaging microscopy, while the microfluidic platform facilitates long-term visualization under controlled environmental conditions. We demonstrate the usefulness of this approach by imaging coral micropropagates at previously unattainable spatio-temporal resolutions, providing new insights into several micro-scale processes including coral calcification, coral-pathogen interaction and the loss of algal symbionts (coral bleaching). Coral-on-a-chip thus provides a powerful method for studying coral physiology in vivo at the micro-scale, opening new vistas in coral biology

High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator

The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic field. The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon as the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism.Here we report the experimental observation of the QAH state in V-doped (Bi,Sb)2Te3 films with the zero-field longitudinal resistance down to 0.00013+-0.00007h/e2 (~3.35+-1.76 ohm), Hall conductance reaching 0.9998+-0.0006e2/h and the Hall angle becoming as high as 89.993+-0.004degree at T=25mK. Further advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field (Hc>1.0T) and a relative high Curie temperature. This realization of robust QAH state in hard FMTIs is a major step towards dissipationless electronic applications without external fields.Comment: 16 pages, 4 figures, this is the final version, accepted by Nature Materials, forthcomin

The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples

We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples. The observed sample consists of 10 X-ray selected clusters at redshifts z ~ 0.2 imaged with HST by Smith et al. The simulated dataset is produced by lensing the Hubble Deep Field, which serves as a background source image, with 150 realizations (different projections and shifts) of five simulated z = 0.2 clusters from a LambdaCDM N-body simulation. The real and simulated clusters have similar masses, the real photometric redshift is used for each background source, and all the observational effects influencing arc detection in the real dataset, including light from cluster galaxies, are simulated in the artificial dataset. We develop, and apply to both datasets, an objective automatic arc-finding algorithm. We find consistent arc statistics in the real and in the simulated sample, with an average of ~ 1 detected giant (length to width ratio >= 10) arc per cluster and ~ 0.2 giant luminous (R<22.3 mag) arc per cluster. Thus, taking into account a realistic source population and observational effects, the clusters predicted by LambdaCDM have the same arc-production efficiency as the observed clusters. If, as suggested by other studies, there is a discrepancy between the predicted and the observed total number of arcs on the sky, it must be the result of differences between the redshift dependent cluster mass functions, and not due to differences in the lensing efficiency of the most massive clusters.Comment: 13 pages, Accepted by ApJ, High resolution version of the paper can be found at: ftp://wise3.tau.ac.il/pub/assafh/horesh_arcs_stat_2005.ps.gz, Arc-finding algorithm available at: http://wise-obs.tau.ac.il/~assafh/ ; A comment was added ; A missing x-axis label in Fig. 7 was adde