13,366 research outputs found
Equations of motion of test particles for solving the spin-dependent Boltzmann-Vlasov equation
A consistent derivation of the equations of motion (EOMs) of test particles
for solving the spin-dependent Boltzmann-Vlasov equation is presented. The
resulting EOMs in phase space are similar to the canonical equations in
Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg
picture of quantum mechanics. Considering further the quantum nature of spin
and choosing the direction of total angular momentum in heavy-ion reactions as
a reference of measuring nucleon spin, the EOMs of spin-up and spin-down
nucleons are given separately. The key elements affecting the spin dynamics in
heavy-ion collisions are identified. The resulting EOMs provide a solid
foundation for using the test-particle approach in studying spin dynamics in
heavy-ion collisions at intermediate energies. Future comparisons of model
simulations with experimental data will help constrain the poorly known
in-medium nucleon spin-orbit coupling relevant for understanding properties of
rare isotopes and their astrophysical impacts.Comment: 5 page
DFedADMM: Dual Constraints Controlled Model Inconsistency for Decentralized Federated Learning
To address the communication burden issues associated with federated learning
(FL), decentralized federated learning (DFL) discards the central server and
establishes a decentralized communication network, where each client
communicates only with neighboring clients. However, existing DFL methods still
suffer from two major challenges: local inconsistency and local heterogeneous
overfitting, which have not been fundamentally addressed by existing DFL
methods. To tackle these issues, we propose novel DFL algorithms, DFedADMM and
its enhanced version DFedADMM-SAM, to enhance the performance of DFL. The
DFedADMM algorithm employs primal-dual optimization (ADMM) by utilizing dual
variables to control the model inconsistency raised from the decentralized
heterogeneous data distributions. The DFedADMM-SAM algorithm further improves
on DFedADMM by employing a Sharpness-Aware Minimization (SAM) optimizer, which
uses gradient perturbations to generate locally flat models and searches for
models with uniformly low loss values to mitigate local heterogeneous
overfitting. Theoretically, we derive convergence rates of and in the non-convex setting for DFedADMM and
DFedADMM-SAM, respectively, where represents the spectral gap of the
gossip matrix. Empirically, extensive experiments on MNIST, CIFAR10 and
CIFAR100 datesets demonstrate that our algorithms exhibit superior performance
in terms of both generalization and convergence speed compared to existing
state-of-the-art (SOTA) optimizers in DFL.Comment: 24 page
(E)-Ethyl 3-(3-bromophenyl)-2-cyanoacrylate
The title molecule, C12H10BrNO2, adopts an E configuration with respect to the C=C bond of the acrylate unit. In the crystal structure, molecules are connected by a pair of intermolecular C—H⋯O hydrogen bonds, forming a centrosymmetric dimer
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