oundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties

We consider the six-vertex model with the rational weights on an s by N square lattice with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are imposed. For a finite lattice, it can be computed by the quantum inverse scattering method in terms of determinants. In the large N limit, the result boils down to an explicit terminating series in the parameter of the weights. Using the saddle-point method for an equivalent integral representation, we show that as s next tends to infinity, the one-point function demonstrates a step-wise behavior; at the vicinity of the step it scales as the error function. We also show that the asymptotic expansion of the one-point function can be computed from a second-order ordinary differential equation.

Deep Reinforcement Learning Boosted Partial Domain Adaptation

Domain adaptation is critical for learning transferable features that effectively reduce the distribution difference among domains. In the era of big data, the availability of large-scale labeled datasets motivates partial domain adaptation (PDA) which deals with adaptation from large source domains to small target domains with less number of classes. In the PDA setting, it is crucial to transfer relevant source samples and eliminate irrelevant ones to mitigate negative transfer. In this paper, we propose a deep reinforcement learning based source data selector for PDA, which is capable of eliminating less relevant source samples automatically to boost existing adaptation methods. It determines to either keep or discard the source instances based on their feature representations so that more effective knowledge transfer across domains can be achieved via filtering out irrelevant samples. As a general module, the proposed DRL-based data selector can be integrated into any existing domain adaptation or partial domain adaptation models. Extensive experiments on several benchmark datasets demonstrate the superiority of the proposed DRL-based data selector which leads to state-of-the-art performance for various PDA tasks.

Numerical simulation of characteristics of propagation of symmetric waves in microwave circular shielded waveguide with a radially inhomogeneous dielectric filling

The paper presents a numerical simulation of the propagation characteristics of symmetric E-type and H-type waves in microwave circular shielded waveguide with radially inhomogeneous dielectric filling. Using the modified Galerkin method, the calculation of a circular two-layer shielded waveguide was carried out, as a result of which the distribution of the electromagnetic field of the waveguide with linear and parabolic distribution of permeability was determined. The results obtained using the modified Galerkin method were compared with the results obtained using the classical partial domain method, which agree well enough.