Music-stylized hierarchical dance synthesis with user control

Background Synthesizing dance motions to match musical inputs is a significant challenge in animation research.Compared to functional human motions,such as locomotion,dance motions are creative and artistic,often influenced by music,and can be independent body language expressions.Dance choreography requires motion content to follow a general dance genre,whereas dance performances under musical influence are infused with diverse impromptu motion styles.Considering the high expressiveness and variations in space and time,providing accessible and effective user control for tuning dance motion styles remains an open problem.Methods In this study,we present a hierarchical framework that decouples the dance synthesis task into independent modules.We use a high-level choreography module built as a Transformer-based sequence model to predict the long-term structure of a dance genre and a low-level realization module that implements dance stylization and synchronization to match the musical input or user preferences.This novel framework allows the individual modules to be trained separately.Because of the decoupling,dance composition can fully utilize existing high-quality dance datasets that do not have musical accompaniments,and the dance implementation can conveniently incorporate user controls and edit motions through a decoder network.Each module is replaceable at runtime,which adds flexibility to the synthesis of dance sequences.Results Synthesized results demonstrate that our framework generates high-quality diverse dance motions that are well adapted to varying musical conditions and user controls.

COMPONENTWISE CONDITION NUMBERS FOR GENERALIZED MATRIX INVERSION AND LINEAR LEAST SQUARES

We present componentwise condition numbers for the problems of MoorePenrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.

Enumeration Order Equivalence in Rational Numbers

The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way.

A Monte Carlo Enhanced PSO Algorithm for Optimal QoM in Multi-Channel Wireless Networks

In wireless monitoring networks, wireless sniffers are distributed in a region to monitor the activities of users. It can be used for fault diagnosis, resource management and critical path analysis. Due to hardware limitations, wireless sniffers typically can only collect information on one channel at a time. Therefore, it is a key topic to optimize the channel selection for sniffers to maximize the information collected, so as to maximize the quality of monitoring （QoM） of the network. In this paper, a particle swarm optimization （PSO）-based solution is proposed to achieve the optimal channel selection. A 2D mapping particle coding and its moving scheme are devised. Monte Carlo method is incorporated to revise the solution and significantly improve the convergence of the algorithm. The extensive simulations demonstrate that the Monte Carlo enhanced PSO （MC-PSO） algorithm outperforms the related algorithms evidently with higher monitoring quality, lower computation complexity, and faster convergence. The practical experiment also shows the feasibility of this algorithm.

A Nearly Analytical Discrete Method for Wave-Field Simulations in 2D Porous Media

The nearly analytic discrete method(NADM)is a perturbation method originally proposed by Yang et al.(2003)[26]for acoustic and elastic waves in elastic media.This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used.In the present work,we apply the NADM to simulating acoustic and elastic wave propagations in 2D porous media.Our method enables wave propagation to be simulated in 2D porous isotropic and anisotropic media.Numerical experiments show that the error of the NADM for the porous case is less than those of the conventional finite-difference method(FDM)and the so-called Lax-Wendroff correction(LWC)schemes.The three-component seismic wave fields in the 2D porous isotropic medium are simulated and compared with those obtained by using the LWC method and exact solutions.Several characteristics of wave propagating in porous anisotropic media,computed by the NADM,are also reported in this study.Promising numerical results illustrate that the NADM provides a useful tool for large-scale porous problems and it can suppress effectively numerical dispersions.

CONDITION NUMBER FOR WEIGHTED LINEAR LEAST SQUARES PROBLEM

In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem： minx ｜｜Ax- b｜｜2, where A is an m-by-n （m ≥ n） rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm ｜｜ [AT,βb] ｜｜F of the data A and b, where T is a positive diagonal matrix and β is a positive scalar. We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.