Global Analytic Solutions for the Nonlinear Schr\"odinger Equation

We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$, hence it is the unique solution obtained by Huh and Oh

Model studies of fluctuations in the background for jets in heavy ion collisions

Jets produced in high energy heavy ion collisions are quenched by the production of the quark gluon plasma. Measurements of these jets are influenced by the methods used to suppress and subtract the large, fluctuating background and the assumptions inherent in these methods. We compare the measurements of the background in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV by the ALICE collaboration to calculations in TennGen (a data-driven random background generator) and PYTHIA Angantyr. The standard deviation of the energy in random cones in TennGen is approximately in agreement with the form predicted in the ALICE paper, with deviations of 1-6 $\%$. The standard deviation of energy in random cones in Angantyr exceeds the same predictions by approximately 40 $\%$. Deviations in both models can be explained by the assumption that the single particle $d^2N/dydp_T$ is a Gamma distribution in the derivation of the prediction. This indicates that model comparisons are potentially sensitive to the treatment of the background

Neural Networks Architecture Evaluation in a Quantum Computer

In this work, we propose a quantum algorithm to evaluate neural networks architectures named Quantum Neural Network Architecture Evaluation (QNNAE). The proposed algorithm is based on a quantum associative memory and the learning algorithm for artificial neural networks. Unlike conventional algorithms for evaluating neural network architectures, QNNAE does not depend on initialization of weights. The proposed algorithm has a binary output and results in 0 with probability proportional to the performance of the network. And its computational cost is equal to the computational cost to train a neural network