Singularity points for first passage percolation

Let $0<a<b<\infty$ be fixed scalars. Assign independently to each edge in the lattice $\mathbb{Z}^2$ the value $a$ with probability $p$ or the value $b$ with probability $1-p$. For all $u,v\in\mathbb{Z}^2$, let $T(u,v)$ denote the first passage time between $u$ and $v$. We show that there are points $x\in\mathbb{R}^2$ such that the ``time constant'' in the direction of $x$, namely, $\lim_{n\to\infty}n^{-1}\mathbf{E}_p[T(\mathbf{0},nx)],$ is not a three times differentiable function of $p$.Comment: Published at http://dx.doi.org/10.1214/009117905000000819 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Intrinsically Motivated Learning of Visual Motion Perception and Smooth Pursuit

We extend the framework of efficient coding, which has been used to model the development of sensory processing in isolation, to model the development of the perception/action cycle. Our extension combines sparse coding and reinforcement learning so that sensory processing and behavior co-develop to optimize a shared intrinsic motivational signal: the fidelity of the neural encoding of the sensory input under resource constraints. Applying this framework to a model system consisting of an active eye behaving in a time varying environment, we find that this generic principle leads to the simultaneous development of both smooth pursuit behavior and model neurons whose properties are similar to those of primary visual cortical neurons selective for different directions of visual motion. We suggest that this general principle may form the basis for a unified and integrated explanation of many perception/action loops.Comment: 6 pages, 5 figure

Self force in 2+1 electrodynamics

The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincar\'e invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like charge acting upon itself plus a non-local term which provides finiteness of the self-action.Comment: 20 pages, 3 figure

Diastereoselective three-component synthesis of beta-amino carbonyl compounds using diazo compounds, boranes, and acyl imines under catalyst-free conditions

Diazo compounds, boranes, and acyl imines undergo a three-component Mannich condensation reaction under catalyst-free conditions to give the anti β-amino carbonyl compounds in high diastereoselectivity. The reaction tolerates a variety of functional groups, and an asymmetric variant was achieved using the (−)-phenylmenthol as chiral auxiliary in good yield and selectivity. These β-amino carbonyl compounds are valuable intermediates, which can be transformed to many potential bioactive molecules.We gratefully acknowledge Philip N. Moquist for editorial review of the manuscript. Preliminary experiments were performed by Y.L. at Boston University. Completion of the work was accomplished under the direction of G.W. at the University of Science and Technology Beijing, China. S.E.S. and Y.L. gratefully acknowledge the NIH for support (NIGMS R01 GM078240). Y.L., J.Y., and G.W. thank the Innovative Foundation from China National Petroleum Corporation (Grant No. 2012D-5006-0504) for financial support. Y.L. also thanks the Beijing Natural Science Foundation (Grant No. 2144052) and China Postdoctoral Science Foundation (2013M540859) for financial support. (NIGMS R01 GM078240 - NIH; 2012D-5006-0504 - Innovative Foundation from China National Petroleum Corporation; 2144052 - Beijing Natural Science Foundation; 2013M540859 - China Postdoctoral Science Foundation)Published versio

Kilohertz QPO Frequency and Flux Decrease in AQL X-1 and Effect of Soft X-ray Spectral Components

We report on an RXTE/PCA observation of Aql X-1 during its outburst in March 1997 in which, immediately following a Type-I burst, the broad-band 2-10 keV flux decreased by about 10% and the kilohertz QPO frequency decreased from 813+-3 Hz to 776+-4 Hz. This change in kHz QPO frequency is much larger than expected from a simple extrapolation of a frequency-flux correlation established using data before the burst. Meanwhile a very low frequency noise (VLFN) component in the broad-band FFT power spectra with a fractional root-mean-square (rms) amplitude of 1.2% before the burst ceased to exist after the burst. All these changes were accompanied by a change in the energy spectral shape. If we characterize the energy spectra with a model composed of two blackbody (BB) components and a power law component, almost all the decrease in flux was in the two BB components. We attribute the two BB components to the contributions from a region very near the neutron star or even the neutron star itself and from the accretion disk, respectively.Comment: 12 pages with 4 figures, accepted for publication in ApJ Letters, typos corrected and references update