Title: Weak lensing cosmology with convolutional neural networks on noisy data

Weak gravitational lensing is one of the most promising cosmological probes
of the late universe. Several large ongoing (DES, KiDS, HSC) and planned
(LSST, EUCLID, WFIRST) astronomical surveys attempt to collect even deeper
and larger scale data on weak lensing. Due to gravitational collapse, the
distribution of dark matter is non-Gaussian on small scales. However,
observations are typically evaluated through the two-point correlation
function of galaxy shear, which does not capture non-Gaussian features of
the lensing maps. Previous studies attempted to extract non-Gaussian
information from weak lensing observations through several higher-order
statistics such as the three-point correlation function, peak counts or
Minkowski-functionals. Deep convolutional neural networks (CNN) emerged in
the field of computer vision with tremendous success, and they offer a new
and very promising framework to extract information from 2 or 3-dimensional
astronomical data sets, confirmed by recent studies on weak lensing. We
show that a CNN is able to yield significantly stricter constraints of
(σ8,Ωm) cosmological parameters than the power spectrum using convergence
maps generated by full N-body simulations and ray-tracing, at angular
scales and shape noise levels relevant for future observations. In a
scenario mimicking LSST or Euclid, the CNN yields 2.4-2.8 times smaller
credible contours than the power spectrum, and 3.5-4.2 times smaller at
noise levels corresponding to a deep space survey such as WFIRST. We also
show that at shape noise levels achievable in future space surveys the CNN
yields 1.4-2.1 times smaller contours than peak counts, a higher-order
statistic capable of extracting non-Gaussian information from weak lensing
maps.

Recently an incredible progress has been achieved in the hardware implementation of artificial neural networks utilizing resistive switching memory (RRAM) technology relying on the voltage induced formation and degradation of conducting filaments within an insulator matrix. As an example, 128x64 memristor crossbar arrays were built and successfully applied for efficient image processing and machine learning tasks. The active volume of such devices is much smaller than in conventional semiconductor architectures, it can even reach the ultimate, atomic size-scales. In the talk I will review the recent progress in RRAM research, along with our results on the physical understanding of atomic-sized artificial synapses.

Title: "Accurate Numerical Calculations for Strongly Correlated Ultracold Few-Fermion Systems with the Transcorrelated Approach"

Abstract:

"In the description of the ultracold few-fermion systems, the exact diagonalization approach is frequently applied in order to achieve reliability and accuracy in theoretical calculations. In this approach, the energies and the wave functions are obtained by diagonalizing the Hamiltonian in a many-body Fock basis. As the size of Hilbert space combinatorially increases with the size of the system, most of the calculations are limited to the intermediate interaction strength. Therefore, understanding and improving convergence properties is crucial in order to make the approach more widely applicable.

The rate of convergence of physical observables with increasing basis size is determined, for the most part, by the nature of the particle-particle interaction itself. In ultracold atoms, the interaction potential is usually modeled by a zero-range pseudopotential, which introduces a singularity in the wave function at the particle-particle coalescence point. This singularity causes painfully slow convergence in one spatial dimension whereas in two or three dimensions it can lead to pathologic behavior.

We improve the exisiting exact diagonaliyzation approach with two distinguished steps. First, we apply the Full Configuration Interaction Quantum Monte Carlo, which introducing a stochastic sampling in the wave function significantly descreases the memory requirements and accelerates the numerical calculations compare to the exact diagonalization approach. Then, we also apply the transcorrelated approach, where the wave function is considered as a product of a Jastrow-type two-particle function and a linear combination of Fock basis states. The Jastrow factor, which contains the singularity of the wave function, is folded into the Hamiltonian by a similarity transformation. Thus the singularity is removed from the Fock-space expansion to leading order. The transformation thus smoothes out the singularity of the original zero-range pseudopotential, which significantly improves the convergence rate of the transcorrelated eigenfunction in the Fock basis states.

We will present numerical examples for the few-fermion sytems at strong interactions in one dimension and for few-fermion systems in three dimensions at unitarity. In one dimension the transcorrelated approach improves the convergence of the energy error from M^{−1} to M^{−3}, where M is the number of the single-particle basis functions. In three dimensions due to the pathological zero-range pseudopotential, the exact diagonalization of the original Hamiltonian is not possible. The transcorrelated transformation eliminates the pathological nature of the Hamiltonian and yields a M^{-1} convergence, which is a significant improvement compared to the standard renormalization approach, M^{-1/3}."