Computing indicators of Radford algebras

We compute higher Frobenius-Schur indicators of Radford algebras in positive characteristic and find minimal polynomials of these linearly recursive sequences. As a result of Kashina, Montgomery and Ng, we obtain gauge invariants for the monoidal categories of representations of Radford algebras.Comment: Accepted for publication by Involve, a journal of mathematics. The results in this paper were partially obtained from an undergraduate research projec

ReNN: Rule-embedded Neural Networks

The artificial neural network shows powerful ability of inference, but it is still criticized for lack of interpretability and prerequisite needs of big dataset. This paper proposes the Rule-embedded Neural Network (ReNN) to overcome the shortages. ReNN first makes local-based inferences to detect local patterns, and then uses rules based on domain knowledge about the local patterns to generate rule-modulated map. After that, ReNN makes global-based inferences that synthesizes the local patterns and the rule-modulated map. To solve the optimization problem caused by rules, we use a two-stage optimization strategy to train the ReNN model. By introducing rules into ReNN, we can strengthen traditional neural networks with long-term dependencies which are difficult to learn with limited empirical dataset, thus improving inference accuracy. The complexity of neural networks can be reduced since long-term dependencies are not modeled with neural connections, and thus the amount of data needed to optimize the neural networks can be reduced. Besides, inferences from ReNN can be analyzed with both local patterns and rules, and thus have better interpretability. In this paper, ReNN has been validated with a time-series detection problem.Comment: poster paper in ICPR, 6 pages, 4 figures, and 1 Tabl

A 28/37/39GHz Multiband Linear Doherty Power Amplifier in Silicon for 5G Applications

This paper presents the first multiband mm-wave linear Doherty PA in silicon for broadband 5G applications. We introduce a new transformer-based on-chip Doherty power combiner, which can reduce the impedance transformation ratio in power back-off (PBO) and thus improve the bandwidth and power-combining efficiency. We also devise a "driver-PA co-design" method, which creates power-dependent uneven feeding in the Doherty PA and enhances the Doherty operation without any hardware overhead or bandwidth compromise. For the proof of concept, we implement a 28/37/39-GHz PA fully integrated in a standard 130-nm SiGe BiCMOS process, which occupies 1.8mm2. The PA achieves a 52% -3-dB small-signal S21 bandwidth and a 40% -1-dB large-signal saturated output power (Psat) bandwidth. At 28/37/39GHz, the PA achieves +16.8/+17.1/+17-dBm Psat, +15.2/+15.5/+15.4-dBm P1dB, and superior 1.72/1.92/1.62 times efficiency enhancement over class-B operation at 5.9/6/6.7-dB PBO. Moreover, the PA demonstrates multi-Gb/s data rates with excellent efficiency and linearity for 64QAM in all the three 5G bands. This PA advances the state of the art for Doherty, wideband, and 5G silicon PAs in mm-wave bands. It supports drop-in upgrade for current PAs in existing mm-wave systems and opens doors to compact system solutions for future multiband 5G massive MIMO and phased-array platforms

Strong Solutions to the Three-Dimensional Compressible Viscoelastic Fluids

The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates on the density and the deformation gradient are also obtained

Formation of singularity for compressible viscoelasticity

The formation of singularity and breakdown of classical solutions to the three-dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solutions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions

Mass-Dependent Baryon Acoustic Oscillation Signal and Halo Bias

We characterize the baryon acoustic oscillations (BAO) feature in halo two-point statistics using N-body simulations. We find that nonlinear damping of the BAO signal is less severe for halos in the mass range we investigate than for dark matter. The amount of damping depends weakly on the halo mass. The correlation functions show a mass-dependent drop of the halo clustering bias below roughly 90 Mpc/h, which coincides with the scale of the BAO trough. The drop of bias is 4% for halos with mass M>10^{14} Msun/h and reduces to roughly 2% for halos with mass M>10^{13} Msun/h. In contrast, halo biases in simulations without BAO change more smoothly around 90 Mpc/h. In Fourier space, the bias of M>10^{14} Msun/h halos decreases smoothly by 11% from wavenumber k = 0.012 h/Mpc to 0.2 h/Mpc, whereas that of M>10^{13} Msun/h halos decreases by less than 4% over the same range. By comparing the halo biases in pairs of otherwise identical simulations, one with and the other without BAO, we also observe a modulation of the halo bias. These results suggest that precise calibrations of the mass-dependent BAO signal and scale-dependent bias on large scales would be needed for interpreting precise measurements of the two-point statistics of clusters or massive galaxies in the future.Comment: 5 Pages, 4 Figures, accepted for publication in the Astrophysical Journal Letter

Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the uniqueness viscosity solution of the related HJBI equation

Reversible "triple-Q" elastic field structures in a chiral magnet

The analytical solution of the periodic elastic field in chiral magnets caused by presence of periodically distributed eigenstrains is obtained. For the skyrmion phase, both the periodic displacement field and the stress field are composed of three "triple-Q" structures with different wave numbers. We find that for increasing external magnetic field, one type of "triple-Q" displacement structure and stress structure undergo a configurational reversal, where the initial and the final field configuration share similar pattern but with opposite direction of all the field vectors. This result is enlightening for designing novel skyrmion-based data-storage devices and microwave applications. The solution obtained is of fundamental significance for understanding the emergent mechanical properties of skyrmions in chiral magnets.Comment: 20 pages, 4 figure

A note on the strong consistency of M-estimates in linear models

We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions

Asymptotics for stochastic Burgers equation with jumps

For one-dimensional stochastic Burgers equation driven by Brownian motion and Poisson process, we study the $\psi$-uniformly exponential ergodicity with $\psi(x)=1+\|x\|$, the moderate deviation principle and the large deviation principle for the occupation measures