Mutual information of spin systems from autoregressive neural networks

We describe a new direct method to estimate bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It allows studying arbitrary geometries of subsystems and can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply-connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning

Hierarchical autoregressive neural networks for statistical systems

It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational approximators to assess extensive properties of statistical systems, like free energy, and also as neural samplers used in Monte Carlo simulations. The practical application of this approach is unfortunately limited by its unfavourable scaling both of the numerical cost required for training, and the memory requirements with the system size. This is due to the fact that the original proposition involved a neural network of width which scaled with the total number of degrees of freedom, e.g. $L^{2}$ in case of a two dimensional L x L lattice. In this work we propose a hierarchical association of physical degrees of freedom, for instance spins, to neurons which replaces it with the scaling with the linear extent L of the system. We demonstrate our approach on the two-dimensional Ising model by simulating lattices of various sizes up to 128 x 128 spins, with time benchmarks reaching lattices of size 512 x 512. We observe that our proposal improves the quality of neural network training, i.e. the approximated probability distribution is closer to the target that could be previously achieved. As a consequence, the variational free energy reaches a value closer to its theoretical expectation and, if applied in a Markov Chain Monte Carlo algorithm, the resulting autocorrelation time is smaller. Finally, the replacement of a single neural network by a hierarchy of smaller networks considerably reduces the memory requirements

Mutual information of spin systems from autoregressive neural networks

We describe a direct approach to estimate bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It allows studying arbitrary geometries of subsystems and can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply-connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.Comment: 11 pages, 8 figure

Vacuum Insertion Method from Chiral Nc \to \infty Approach for the \Delta S = 1 Effective Hamiltonian

We check to what extent the assumptions of the vacuum insertion method, as used in the theory o f K —* tttt decays, can be derived from the high N c approximation to the chiral perturbation theory. We find that, besides the well-known problem of Fierz terms, only the assumption for the K 13 formfactor ( /_ = 0) does not follow. This assumption, however, affects the penguin contributions by less than four per cent and the nonpenguin contributions by less than two percent[…

Effect of Fe3+Fe^{3+} ions present in the structure of poly(acrylic acid) / montmorillonite composites on their thermal decomposition

Poly(acrylic acid)/montmorillonite (MMT) composites with various polymer contents were synthesized by in situ polymerization technique. The structure of obtained materials was characterized by powder X-ray dif- fraction and infrared spectroscopy (FTIR). It was found that only a limited amount of hydrogel could be introduced between the clay layers. The remaining part of polymer was deposited on the external surface of clay particles. The introduction of the polymer modifier significantly increased the adsorption capacity of MMT in the elimination of $Fe^{3+}$ ions from aqueous solution. The thermal behavior of the samples before and after the $Fe^{3+}$ adsorption was examined by thermogravimetry and differential thermal analysis. Moreover, the composition of gaseous products evolved during decomposition was determined by FTIR. The mate- rials after $Fe^{3+}$ adsorption exhibited different thermal sta- bility in oxidizing atmosphere than the fresh samples. $Fe^{3+}$ cations, forming $FeO_x$ species during thermal treatment, appeared to be effective catalysts of polymer oxidation

Simulating first-order phase transition with hierarchical autoregressive networks

We apply the Hierarchical Autoregressive Neural (HAN) network sampling algorithm to the two-dimensional $Q$-state Potts model and perform simulations around the phase transition at $Q=12$. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pre-training. It allows to train some neural networks using smaller system sizes and then employing them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of $10^{-7}$ for the former and $10^{-3}$ for the latter based on a statistics of $10^6$ configurations.Comment: 14 pages, 12 figure

Simulating the J-PET detector on NVidia ray tracing hardware

In this contribution, we present preliminary results of using graphic card with hardware support for ray tracing for physics simulation of a positron emission tomography (PET) scanner. On our simplistic setup, we notice an impressive (about 350 times) speedup compared to Geant4 code running on modern multicore CPU. We expect this speedup to come down but remain substantial also for other more complicated scenarios

GPU-Accelerated and CPU SIMD Optimized Monte Carlo Simulation of φ4 Model

In this contribution we describe an efficient GPU implementation of the Monte-Carlo simulation of the Ginzburg-Landau model. We achieve the performance close to 50 % of the peak performance of the used GPU. We compare this performance with a parallelized and vectorized CPU code and discuss the observed differences

Gonadotropina kosmówkowa – czego nie mierzą komercyjne testy

Measurements of human chorionic gonadotropin (hCG) synthesized by trophoblast cells is a powerful tool of pregnancy monitoring. It was showed that similarly to pregnancy also trophoblastic and nontrophoblastic malignancies produce variety of hCG molecules. In urine and serum of both pregnant women and tumors patients a fifteen various forms of hCG, such as: regular hCG, hyperglycosylated hCG and predominant hyperglycosylated hCG free β, were identified. These forms might be useful in order to recognize between physiological and pathological pregnancies as well as cancers. Even the presence of these different hormone variants is well documented the commercially available biochemical tests detecting hCG failed to identified and distinguish among these forms. Especially hard is to identify glycan chains linked to heterodimer. Thus, a detailed analysis of hCG-related molecules produced during physiological and pathological condition, together with a new tests development are needed.Wykrywanie ludzkiej gonadotropiny kosmówkowej (hCG) produkowanej przez komórki trofoblastu jest wykorzystywane do wykrywania i monitorowania rozwijającej się ciąży. Oprócz ciąży szereg nowotworów pochodzenia zarówno trofoblastycznego jak i nietrofoblastycznego cechuje synteza i wydzielanie różnych form gonadotropiny kosmówkowej. Dotychczas w surowicy i moczu kobiet ciężarnych oraz u osób z chorobami nowotworowymi zidentyfikowano piętnaście różnych form hCG. Najczęściej występującymi cząsteczkami są: regularna hCG, hiperglikozylowana hCG i hiperglikozylowana wolna podjednostka beta. Cząsteczki te mogą być wykorzystane do rozróżnienia pomiędzy ciążą fizjologiczną a patologiczną, czy rozpoznania nowotworu rakiem Niestety dostępne na rynku testy diagnostyczne nie są wstanie wykryć i rozróżnić poszczególnych form hCG. Szczególnie trudne w identyfikacji są reszty cukrowcowe związane z hormonem. Szczegółowa analiza cząsteczek hCG produkowanych w określonych warunkach fizjologicznych jak i patologicznych powinna pozwolić na opracowanie nowych testów pozwalających na ich identyfikację

Partition of energy for a dissipative quantum oscillator

We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems. Both mean kinetic energy Ek and mean potential energy Ep of the oscillator are expressed as Ek = 〈εk〉 and Ep = 〈εp〉, where 〈εk〉 and 〈εp〉 are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too. The symbol 〈...〉 denotes two-fold averaging: (i) over the Gibbs canonical state for the thermostat and (ii) over thermostat oscillators frequencies ω which contribute to Ek and Ep according to the probability distribution [Formula: see text] and [Formula: see text], respectively. The role of the system-thermostat coupling strength and the memory time is analysed for the exponentially decaying memory function (Drude dissipation mechanism) and the algebraically decaying damping kernel