Graded Lie algebras with finite polydepth

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and if the orbits of H_*(\Omega Y) acting in the homology of the homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite then either L is solvable and UL grows at most polynomially or else for some integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some $k(r)$

Political Competition and Mirrleesian Income Taxation: A First Pass

We study Downsian competition in a Mirrleesian model of income taxation. The competing politicians may differ in competence. If politicians engage in vote-share maximization, the less competent politician’s policy proposals are attractive to the minority of rich agents, whereas those of the competent politician are attractive to the majority of poor agents. The less competent politician wins with positive probability, which gives rise to a political failure in the sense of Besley and Coate (1998). Political failures are avoided if politicians maximize winning probabilities. Nevertheless, the two equilibria cannot be Pareto-ranked, the minority may be better off under vote-share maximization.electoral competition, non-linear income taxation, candidate quality

What is the Shell Around R Coronae Borealis?

The hydrogen-deficient, carbon-rich R Coronae Borealis (RCB) stars are known for being prolific producers of dust which causes their large iconic declines in brightness. Several RCB stars, including R CrB, itself, have large extended dust shells seen in the far-infrared. The origin of these shells is uncertain but they may give us clues to the evolution of the RCB stars. The shells could form in three possible ways. 1) they are fossil Planetary Nebula (PN) shells, which would exist if RCB stars are the result of a final, helium-shell flash, 2) they are material left over from a white-dwarf merger event which formed the RCB stars, or 3) they are material lost from the star during the RCB phase. Arecibo 21-cm observations establish an upper limit on the column density of H I in the R CrB shell implying a maximum shell mass of $\lesssim$0.3 M$_{\odot}$. A low-mass fossil PN shell is still a possible source of the shell although it may not contain enough dust. The mass of gas lost during a white-dwarf merger event will not condense enough dust to produce the observed shell, assuming a reasonable gas-to-dust ratio. The third scenario where the shell around R CrB has been produced during the star's RCB phase seems most likely to produce the observed mass of dust and the observed size of the shell. But this means that R CrB has been in its RCB phase for $\sim$10$^{4}$ yr.Comment: 5 pages, 2 figures, 2 tables, Accepted for publication in A

Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation

We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves in space time with corresponding interface condition, followed by a correction step. Using a Laplace transform argument, for a particular relaxation parameter, we prove convergence of both algorithms in a finite number of steps for finite time intervals. The number of steps depends on the size of the subdomains and the time window length on which the algorithms are employed. We illustrate the performance of the algorithms with numerical results, and also show a comparison with classical and optimized Schwarz WR methods.Comment: 8 pages, 6 figures, presented in 22nd International conference on Domain Decomposition Methods, to appear in Domain Decomposition in Science and Engineering XXII, LNCSE, Springer-Verlag 201

A Universal Live Cell Barcoding-Platform for Multiplexed Human Single Cell Analysis.

Single-cell barcoding enables the combined processing and acquisition of multiple individual samples as one. This maximizes assay efficiency and eliminates technical variability in both sample preparation and analysis. Remaining challenges are the barcoding of live, unprocessed cells to increase downstream assay performance combined with the flexibility of the approach towards a broad range of cell types. To that end, we developed a novel antibody-based platform that allows the robust barcoding of live human cells for mass cytometry (CyTOF). By targeting both the MHC class I complex (beta-2-microglobulin) and a broadly expressed sodium-potassium ATPase-subunit (CD298) with platinum-conjugated antibodies, human immune cells, stem cells as well as tumor cells could be multiplexed in the same single-cell assay. In addition, we present a novel palladium-based covalent viability reagent compatible with this barcoding strategy. Altogether, this platform enables mass cytometry-based, live-cell barcoding across a multitude of human sample types and provides a scheme for multiplexed barcoding of human single-cell assays in general

Low-field microwave absorption and magnetoresistance in iron nanostructures grown by electrodeposition on n-type lightly-doped silicon substrates

In this study we investigate magnetic properties, surface morphology and crystal structure in iron nanoclusters electrodeposited on lightly-doped (100) n-type silicon substrates. Our goal is to investigate the spin injection and detection in the Fe/Si lateral structures. The samples obtained under electric percolation were characterized by magnetoresistive and magnetic resonance measurements with cycling the sweeping applied field in order to understand the spin dynamics in the as-produced samples. The observed hysteresis in the magnetic resonance spectra, plus the presence of a broad peak in the non-saturated regime confirming the low field microwave absorption (LFMA), were correlated to the peaks and slopes found in the magnetoresistance curves. The results suggest long range spin injection and detection in low resistive silicon and the magnetic resonance technique is herein introduced as a promising tool for analysis of electric contactless magnetoresistive samples.Comment: 12 pages, 5 figure

Supermodes of Hexagonal Lattice Waveguide Arrays

We present a semi-analytical formulation for calculating the supermodes and corresponding Bloch factors of light in hexagonal lattice photonic crystal waveguide arrays. We then use this formulation to easily calculate dispersion curves and predict propagation in systems too large to calculate using standard numerical methods.Comment: Accepted by J. Opt. Soc. Am. B, DocID:160522. http://www.opticsinfobase.org/abstract.cfm?msid=16052

Optimal stochastic modelling with unitary quantum dynamics

Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of future trajectories whilst using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of causal simulation with a unitary quantum circuit. We show that the resulting constructions can display advantages over previous state-of-art methods - both in the amount of information they need to store about the past, and in the minimal memory dimension they require to store this information. Moreover, we find that these two features are generally competing factors in optimisation - leading to an ambiguity in what constitutes the optimal model - a phenomenon that does not manifest classically. Our results thus simultaneously offer new quantum advantages for stochastic simulation, and illustrate further qualitative differences in behaviour between classical and quantum notions of complexity.Comment: 9 pages, 5 figure