Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice

Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $\nu$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the lowtemperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer casewith finite chemical potential $\mu$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $\nu-T$ and $\mu-T$ . Moreover, for the noninteracting monomer-dimer model (setting $\mu = \nu = 0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant $h_2$) as $f=-0.662\, 798\, 972\, 833\, 746$ with the dimer density $n=0.638\, 123\, 109\, 228\, 547$, both of 15 correct digits.Comment: 8 pages, 15 figure

Accelerating federated learning via momentum gradient descent

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this article, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence properties of MFL and derive an upper bound on MFL convergence rate. Comparing the upper bounds on MFL and FL convergence rates, we provide conditions in which MFL accelerates the convergence. For different machine learning models, the convergence performance of MFL is evaluated based on experiments with MNIST and CIFAR-10 datasets. Simulation results confirm that MFL is globally convergent and further reveal significant convergence improvement over FL

Stochastic Calculus for Markov Processes Associated with Non-symmetric Dirichlet Forms

Nakao's stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. Ito's formula in terms of the extended stochastic integrals is obtained.Comment: An additional note has been added between the Acknowledgments part and the References part on page 1