Effect of Earth's rotation on the trajectories of free-fall bodies in Equivalence Principle Experiment

Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating sell. For the free-fall time of 40 seconds, the difference between the orbits of the two free-fall bodies is of the order of 10^{-9}cm which could be detected by a SQUID magnetometer owing to such a magnetometer can be used to measure displacements as small as 10^{-13} centimeters.Comment: 6 pages, 4 figure

Predictive Model Degrees of Freedom in Linear Regression

Overparametrized interpolating models have drawn increasing attention from machine learning. Some recent studies suggest that regularized interpolating models can generalize well. This phenomenon seemingly contradicts the conventional wisdom that interpolation tends to overfit the data and performs poorly on test data. Further, it appears to defy the bias-variance trade-off. As one of the shortcomings of the existing theory, the classical notion of model degrees of freedom fails to explain the intrinsic difference among the interpolating models since it focuses on estimation of in-sample prediction error. This motivates an alternative measure of model complexity which can differentiate those interpolating models and take different test points into account. In particular, we propose a measure with a proper adjustment based on the squared covariance between the predictions and observations. Our analysis with least squares method reveals some interesting properties of the measure, which can reconcile the "double descent" phenomenon with the classical theory. This opens doors to an extended definition of model degrees of freedom in modern predictive settings.Comment: 47 pages, 18 figure

NETWORK EXTERNALITY ON RETAILER AND SUPPLIER PRICING STRATEGIES FOR COMPETITIVE PRODUCTS

Network externality, which affects the value of many high-tech and Internet-related products, may have a critical impact on firm strategies. This paper focuses on the strategy selection of various players in a channel structure. We design a sequential game among two suppliers and a retailer. In the developed game and model, we provide two optional strategies to the retailer, whereas suppliers can impact retailer strategies with their own pricing. We found that (direct) network externality typically had a positive effect on firms. More important, we conclude that when the degree of product network externality from a weak supplier reaches a certain scale, a relatively stable state of competition is facilitated, which is more profitable compared with a collusion strategy. Otherwise, the two suppliers can still maintain a competition relationship. However, a collusion strategy may be more profitable than competition in the second case. In this article, we recommend an acquisition strategy as a sustainable and reasonable collusion strategy

Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester

Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester were studied in this paper. Von de Pol differencial item was introduced to interpret the hysteretic phenomena of piezoelectric ceramics, and then the nonlinear dynamic model of piezoelectric cantilever beam subjected to axial stochastic excitation was developed. The stochastic stability of the system was analyzed, and the steady-state probability density function and the joint probability density function of the dynamic response of the system were obtained, and then the conditions of stochastic Hopf bifurcation were analyzed. Numerical simulation shows that stochastic Hopf bifurcation appears when bifurcation parameter varies, which can increase vibration amplitude of cantilever beam system and improve the efficiency of piezoelectric energy harvester. Finally, the theoretical and numerical results were proved by experiments. The results of this paper are helpful to application of cantilevered piezoelectric energy harvester in engineering fields

FAT: An In-Memory Accelerator with Fast Addition for Ternary Weight Neural Networks

Convolutional Neural Networks (CNNs) demonstrate excellent performance in various applications but have high computational complexity. Quantization is applied to reduce the latency and storage cost of CNNs. Among the quantization methods, Binary and Ternary Weight Networks (BWNs and TWNs) have a unique advantage over 8-bit and 4-bit quantization. They replace the multiplication operations in CNNs with additions, which are favoured on In-Memory-Computing (IMC) devices. IMC acceleration for BWNs has been widely studied. However, though TWNs have higher accuracy and better sparsity than BWNs, IMC acceleration for TWNs has limited research. TWNs on existing IMC devices are inefficient because the sparsity is not well utilized, and the addition operation is not efficient. In this paper, we propose FAT as a novel IMC accelerator for TWNs. First, we propose a Sparse Addition Control Unit, which utilizes the sparsity of TWNs to skip the null operations on zero weights. Second, we propose a fast addition scheme based on the memory Sense Amplifier to avoid the time overhead of both carry propagation and writing back the carry to memory cells. Third, we further propose a Combined-Stationary data mapping to reduce the data movement of activations and weights and increase the parallelism across memory columns. Simulation results show that for addition operations at the Sense Amplifier level, FAT achieves 2.00X speedup, 1.22X power efficiency, and 1.22X area efficiency compared with a State-Of-The-Art IMC accelerator ParaPIM. FAT achieves 10.02X speedup and 12.19X energy efficiency compared with ParaPIM on networks with 80% average sparsity.Comment: 14 page

1-{(1Z)-1-[3-(2,4-Dichloro­phen­oxy)prop­oxy]-1-(2,4-difluoro­phen­yl)prop-1-en-2-yl}-1H-1,2,4-triazole

In the title compound, C20H17Cl2F2N3O2, the triazole ring makes dihedral angles of 28.0 (3) and 72.5 (2)° with the 2,4-dichloro­pheny and 2,4-difluoro­phenyl rings, respectively, and the mol­ecule adopts a Z-conformation about the C=C double bond. In the crystal, C—H⋯O and C—H⋯N hydrogen bonds link the mol­ecules