Kodaira-Spencer formality of products of complex manifolds

We shall say that a complex manifold $X$ is emph{Kodaira-Spencer formal} if its Kodaira-Spencer differential graded Lie algebra $A^{0,*}_X(Theta_X)$ is formal; if this happen, then the deformation theory of $X$ is completely determined by the graded Lie algebra $H^*(X,Theta_X)$ and the base space of the semiuniversal deformation is a quadratic singularity.. Determine when a complex manifold is Kodaira-Spencer formal is generally difficult and we actually know only a limited class of cases where this happen. Among such examples we have Riemann surfaces, projective spaces, holomorphic Poisson manifolds with surjective anchor map $H^*(X,Omega^1_X) o H^*(X,Theta_X)$ and every compact K"{a}hler manifold with trivial or torsion canonical bundle. In this short note we investigate the behavior of this property under finite products. Let $X,Y$ be compact complex manifolds; we prove that whenever $X$ and $Y$ are K"{a}hler, then $X imes Y$ is Kodaira-Spencer formal if and only if the same holds for $X$ and $Y$. A revisit of a classical example by Douady shows that the above result fails if the K"{a}hler assumption is droppe

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Dynamics of drag and force distributions for projectile impact in a granular medium

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show that the probability distribution function of forces on grains is time-independent during a projectile's penetration of the medium. At all times the force distribution function decreases exponentially for large forces.Comment: 4 page

Discovery of a Wide Substellar Companion to a Nearby Low-Mass Star

We report the discovery of a wide (135+/-25 AU), unusually blue L5 companion 2MASS J17114559+4028578 to the nearby M4.5 dwarf G 203-50 as a result of a targeted search for common proper motion pairs in the Sloan Digital Sky Survey and the Two Micron All Sky Survey. Adaptive Optics imaging with Subaru indicates that neither component is a nearly equal mass binary with separation > 0.18", and places limits on the existence of additional faint companions. An examination of TiO and CaH features in the primary's spectrum is consistent with solar metallicity and provides no evidence that G 203-50 is metal poor. We estimate an age for the primary of 1-5 Gyr based on activity. Assuming coevality of the companion, its age, gravity and metallicity can be constrained from properties of the primary, making it a suitable benchmark object for the calibration of evolutionary models and for determining the atmospheric properties of peculiar blue L dwarfs. The low total mass (M_tot=0.21+/-0.03 M_sun), intermediate mass ratio (q=0.45+/-0.14), and wide separation of this system demonstrate that the star formation process is capable of forming wide, weakly bound binary systems with low mass and BD components. Based on the sensitivity of our search we find that no more than 2.2% of early-to-mid M dwarfs (9.0 0.06 M_sun.Comment: 24 pages, 5 figures, accepted for publication in Ap

Quantum motion of a neutron in a wave-guide in the gravitational field

We study theoretically the quantum motion of a neutron in a horizontal wave-guide in the gravitational field of the Earth. The wave-guide in question is equipped with a mirror below and a rough absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are mainly determined by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing wave-guide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in the Earth's gravitational field

Quantum Statistical Calculations and Symplectic Corrector Algorithms

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher order splitting will result in a higher order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Greens function. Since diffusion cannot be simulated backward in time, the splitting must maintain the positivity of all intermediate time steps. However, since the trace is invariant under similarity transformations of the propagator, one can use this freedom to "correct" the split propagator to higher order. This use of similarity transforms classically give rises to symplectic corrector algorithms. The split propagator is the symplectic kernel and the similarity transformation is the corrector. This work proves a generalization of the Sheng-Suzuki theorem: no positive time step propagators with only kinetic and potential operators can be corrected beyond second order. Second order forward propagators can have fourth order traces only with the inclusion of an additional commutator. We give detailed derivations of four forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket

Surface effects on the orbital order in the single layered manganite La0.5Sr1.5MnO4

We report the first observation of `orbital truncation rods' -- the scattering arising from the termination of bulk orbital order at the surface of a crystal. The x-ray measurements, performed on a cleaved, single-layered perovskite, La0.5Sr1.5MnO4, reveal that while the crystallographic surface is atomically smooth, the orbital `surface' is much rougher, with an r.m.s. deviation from the average `surface' of ~0.7nm. The temperature dependence of this scattering shows evidence of a surface-induced second order transition.Comment: 13 pages, 4 figure