Noise reduction in photon counting by exploiting spatial correlations

Joint photocount distributions of a weak twin beam acquired by an iCCD camera are analyzed with respect to the beam spatial correlations. A method for extracting these correlations from the experimental joint photocount distributions is suggested using a suitable statistical model that quantifies the contribution of spatial correlations to the joint photocount distributions. In detail, the profile of twin-beam intensity spatial cross-correlation function is revealed from the curve that gives the genuine mean photon-pair number (both photons from a pair are detected) as a function of the extent of the detection area. Also, the principle of reducing the noise in photon-number-resolving detection by using spatial correlations is experimentally demonstrated.Comment: 12 pages, 16 figure

Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions

The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations can only convey spatial information implicitly when coupled with powerful decoders. In this work, we propose spatial VAEs that use feature maps of larger size as latent variables to explicitly capture spatial information. This is achieved by allowing the latent variables to be sampled from matrix-variate normal (MVN) distributions whose parameters are computed from the encoder network. To increase dependencies among locations on latent feature maps and reduce the number of parameters, we further propose spatial VAEs via low-rank MVN distributions. Experimental results show that the proposed spatial VAEs outperform original VAEs in capturing rich structural and spatial information.Comment: Accepted by SDM2019. Code is publicly available at https://github.com/divelab/sva

Velocity and spatial biases in CDM subhalo distributions

We present a statistical study of substructure within a sample of LCDM clusters and galaxies simulated with up to 25 million particles. With thousands of subhalos per object we can accurately measure their spatial clustering and velocity distribution functions and compare these with observational data. The substructure properties of galactic halos closely resembles those of galaxy clusters with a small scatter in the mass and circular velocity functions. The velocity distribution function is non-Maxwellian and flat topped with a negative kurtosis of about -0.7. Within the virial radius the velocity bias $b=\sigma_{\rm sub}/\sigma_{\rm DM}\sim 1.12 \pm 0.04$, increasing to b > 1.3 within the halo centers. Slow subhalos are much less common, due to physical disruption by gravitational tides early in the merging history. This leads to a spatially anti-biased subhalo distribution that is well fitted by a cored isothermal. Observations of cluster galaxies do not show such biases which we interpret as a limitation of pure dark matter simulations - we estimate that we are missing half of the halo population which has been destroyed by physical overmerging. High resolution hydrodynamical simulations are required to study these issues further. If CDM is correct then the cluster galaxies must survive the tidal field, perhaps due to baryonic inflow during elliptical galaxy formation. Spirals can never exist near the cluster centers and the elliptical galaxies there will have little remaining dark matter. This implies that the morphology-density relation is set {\it before} the cluster forms, rather than a subsequent transformation of disks to S0's by virtue of the cluster environment.Comment: MNRAS accepted version. Due to an error in the initial conditions these simulations have a lower sigma_8 than the published value, 0.7 instead of 0.9. We thank Mike Kuhlen who helped us finding this mistake. See the erratum at http://www-theorie.physik.unizh.ch/~diemand/suberr.pdf . Images and movies available at http://www-theorie.physik.unizh.ch/~diemand/clusters

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys.

Magneto-sensitive elastomers in a homogeneous magnetic field: a regular rectangular lattice model

A theory of mechanical behaviour of the magneto-sensitive elastomers is developed in the framework of a linear elasticity approach. Using a regular rectangular lattice model, different spatial distributions of magnetic particles within a polymer matrix are considered: isotropic, chain-like and plane-like. It is shown that interaction between the magnetic particles results in the contraction of an elastomer along the homogeneous magnetic field. With increasing magnetic field the shear modulus for the shear deformation perpendicular to the magnetic field increases for all spatial distributions of magnetic particles. At the same time, with increasing magnetic field the Young's modulus for tensile deformation along the magnetic field decreases for both chain-like and isotropic distributions of magnetic particles and increases for the plane-like distribution of magnetic particles.Comment: 38 pages, 15 figure