Information-Theoretic Multi-Server PIR with Global Preprocessing

We propose a new unified framework to construct multi-server, information-theoretic Private Information Retrieval (PIR) schemes that leverage global preprocesing to achieve sublinear computation per query. Despite a couple earlier attempts, our understanding of PIR schemes in the global preprocessing model remains limited, and so far, we only know a few sparse points in the broad design space. Our framework not only unifies earlier results in this space, but leads to several new results. First, we can improve the server space of the state-of-the-art scheme by a polynomial factor. Second, we can broaden the parameter space of known results, allowing a smooth tradeoff between bandwidth and computation. Third, while earlier schemes achieve better per-server bandwidth and computation as we add more servers, the server space actually grows w.r.t. the number of servers. We offer a new scalable family of schemes where the per-server bandwidth, computation, and space all decrease as we add more servers. This scalable family of schemes also implies the so-called ``doubly efficient\u27\u27 PIR scheme with any super-constant number of servers, achieving $n^{1+o(1)}$ server space and preprocessing cost, and $n^{o(1)}$ bandwidth and computation per query

Study and Simulation of Deformation Mechanics Modeling of Flexible Workpiece Processing by Rayleigh-Ritz Method

This paper discusses the calculation problems of bending deformation of FWP processing. Take three axis CNC machining as an example, to establish mechanics model of flexible workpiece processing process. The flexible workpiece balance equation is a two-dimensional partial differential equation, to solve the problem of flexible workpiece bending deformation using Rayleigh-Ritz method and designing the test function of bending deformation of flexible workpiece. By satisfying the minimum potential energy condition of FWP processing to work out the approximate solution of bending deformation of flexible workpiece, find out the relationship between material properties of flexible piece, acting force Fz, and deformation value. Finally, the rectangle flexible workpiece which is made up of polyurethane sponge is selected as an experiment subject. The results show that the average relative deviation between theoretical value and observed value is only 5.51%. It is proved that the bending deformation test function satisfies the actual deformation calculation requirements

Electronic structure and direct observation of ferrimagnetism in multiferroic hexagonal YbFeO3

The magnetic interactions between rare-earth and Fe ions in hexagonal rare-earth ferrites (h-RFeO3), may amplify the weak ferromagnetic moment on Fe, making these materials more appealing as multiferroics. To elucidate the interaction strength between the rare-earth and Fe ions as well as the magnetic moment of the rare-earth ions, element-specific magnetic characterization is needed. Using x-ray magnetic circular dichroism, we have studied the ferrimagnetism in h-YbFeO3 by measuring the magnetization of Fe and Yb separately. The results directly show antialignment of magnetization of Yb and Fe ions in h-YbFeO3 at low temperature, with an exchange field on Yb of about 17 kOe. The magnetic moment of Yb is about 1.6μB at low temperature, significantly reduced compared with the 4.5 μB moment of a free Yb3+. In addition, the saturation magnetization of Fe in h-YbFeO3 has a sizable enhancement compared with that in h-LuFeO3. These findings directly demonstrate that ferrimagnetic order exists in h-YbFeO3; they also account for the enhancement of magnetization and the reduction of coercivity in h-YbFeO3 compared with those in h-LuFeO3 at low temperature, suggesting an important role for the rare-earth ions in tuning the multiferroic properties of h-RFeO3