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Fractional Brownian motion (fBm) features both randomness and strong scale-free correlations, challenging generative models to reproduce the intrinsic memory characterizing the underlying stochastic process. Here we examine a zoo of diffusion-based inpainting methods on a specific dataset of corrupted images, which represent incomplete Euclidean distance matrices (EDMs) of fBm at various memory exponents $H$. Our dataset implies uniqueness of the data imputation in the regime of low missing ratio, where the remaining partial graph is rigid, providing the ground truth for the inpainting. We find that the conditional diffusion generation readily reproduces the built-in correlations of fBm paths in different memory regimes (i.e., for sub-, Brownian and super-diffusion trajectories), providing a robust tool for the statistical imputation at high missing ratio. Furthermore, while diffusion models have been recently shown to memorize samples from the training database, we demonstrate that diffusion behaves qualitatively different from the database search and thus generalize rather than memorize the training dataset. As a biological application, we apply our fBm-trained diffusion model for the imputation of microscopy-derived distance matrices of chromosomal segments (FISH data) - incomplete due to experimental imperfections - and demonstrate its superiority over the standard approaches used in bioinformatics.

We propose a new approach to the optimal placement of sensors for the problem of reconstructing geophysical fields from sparse measurements. Our method consists of two stages. In the first stage, we estimate the variability of the physical field as a function of spatial coordinates by approximating its information entropy through the Conditional PixelCNN network. To calculate the entropy, a new ordering of a two-dimensional data array (spiral ordering) is proposed, which makes it possible to obtain the entropy of a physical field simultaneously for several spatial scales. In the second stage, the entropy of the physical field is used to initialize the distribution of optimal sensor locations. This distribution is further optimized with the Concrete Autoencoder architecture with the straight-through gradient estimator and adversarial loss to simultaneously minimize the number of sensors and maximize reconstruction accuracy. Our method scales linearly with data size, unlike commonly used Principal Component Analysis. We demonstrate our method on the two examples: (a) temperature and (b) salinity fields around the Barents Sea and the Svalbard group of islands. For these examples, we compute the reconstruction error of our method and a few baselines. We test our approach against two baselines (1) PCA with QR factorization and (2) climatology. We find out that the obtained optimal sensor locations have clear physical interpretation and correspond to the boundaries between sea currents., Comment: 18 pages, 6 figures

We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions over a space of external parameters and approximating the metric field by a Hessian of a convex function. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP without any a priori knowledge about microscopic rules of the models. We also demonstrate how our approach can be used to visualize the latent space of StyleGAN models and evaluate the variability of the generated images., Comment: 20 pages, 9 figures, plus appendix with additional figures

We report on the neutrino mass measurement result from the first four-week science run of the Karlsruhe Tritium Neutrino experiment KATRIN in spring 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are energy analyzed by a high-resolution MAC-E filter. A fit of the integrated electron spectrum over a narrow interval around the kinematic endpoint at 18.57 keV gives an effective neutrino mass square value of $(-1.0^{+0.9}_{-1.1})$ eV$^2$. From this we derive an upper limit of 1.1 eV (90$\%$ confidence level) on the absolute mass scale of neutrinos. This value coincides with the KATRIN sensitivity. It improves upon previous mass limits from kinematic measurements by almost a factor of two and provides model-independent input to cosmological studies of structure formation.

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. The strong magnetic field that guides the beta-electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips has been deployed and was tested during the commissioning of the spectrometer. In this paper the configuration, the commissioning with bake-out at 300{\deg}C, and the performance of this system are presented in detail. The vacuum system has to maintain a pressure in the 10^{-11} mbar range. It is demonstrated that the performance of the system is already close to these stringent functional requirements for the KATRIN experiment, which will start at the end of 2016., Comment: submitted for publication in JINST, 39 pages, 15 figures

An electron antineutrino mass has been measured in tritium beta-decay in the "Troitsk nu-mass" experiment. The setup consists of a windowless gaseous tritium source and an electrostatic electron spectrometer. The whole data set acquired from 1994 to 2004 was reanalysed. A thorough selection of data with the reliable experimental conditions has been performed. We checked every known systematic effect and got the following experimental estimate for neutrino mass squared m_{nu}^{2}=-0.67+/- 2.53 {eV}^{2}. This gives an experimental upper sensitivity limit of m_{nu}<2.2 eV and upper limit estimates m_{nu}<2.12 eV, 95% C.L. for Bayesian statistics and m_{nu}<2.05 eV, 95% C.L. for the Feldman and Cousins approach., Comment: 9 pages, 6 figures and 1 table

The search for CP violating forces between nucleons in the so-called axion window of force ranges lam between 2x10^-5 m and 0.02 m is interesting because only little experimental information is available there. Axion-like particles would induce a pseudo-magnetic field for neutrons close to bulk matter. A laboratory search investigates neutron spin precession close to a heavy mirror using ultracold neutrons in a magnetic resonance spectrometer. From the absence of a shift of the magnetic resonance we established new constraints on the coupling strength of axion-like particles in terms of the product gs x gp of scalar and pseudo-scalar dimensionless constants, as a function of the force range lam, gs x gp x lam^2 <= 2x10-21 [cm^2] (C.L.95%) for 10^-4 cm < lam < 1 cm. For 0.1 cm < lam < 1 cm previous limits are improved by 4 to 5 orders of magnitude., Comment: 10 pages, 3 figures

An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known estimates for the total number of the bound states in the same potential for various dimensionality. Coincidence with some known exact results is demonstrated. The effective number is used for constructing the periodical system of the atomic electron shells., Comment: RevTeX, 9 pages with 1 Postscript figure