Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Nonchaotic Nonlinear Motion Visualized in Complex Nanostructures by Stereographic 4D Electron Microscopy

Direct electron imaging with sufficient time resolution is a powerful tool for visualizing the three-dimensional (3D) mechanical motion and resolving the four-dimensional (4D) trajectories of many different components of a nanomachine, e.g., a NEMS device. Here, we report a nanoscale nonchaotic motion of a nano- and microstructured NiTi shape memory alloy in 4D electron microscopy. A huge amplitude oscillatory mechanical motion following laser heating is observed repetitively, likened to a 3D motion of a conductor’s baton. By time-resolved 4D stereographic reconstruction of the motion, prominent vibrational frequencies (3.0, 3.8, 6.8, and 14.5 MHz) are fully characterized, showing evidence of nonlinear behavior. Moreover, it is found that a stress (fluence)−strain (displacement) profile shows nonlinear elasticity. The observed resonances of the nanostructure are reminiscent of classical molecular quasi-periodic behavior, but here both the amplitude and frequency of the motion are visualized using ultrafast electron microscopy

Application of Artificial Neural Network to Search for Gravitational-Wave Signals Associated with Short Gamma-Ray Bursts

We apply a machine learning algorithm, the artificial neural network, to the search for gravitational-wave signals associated with short gamma-ray bursts. The multi-dimensional samples consisting of data corresponding to the statistical and physical quantities from the coherent search pipeline are fed into the artificial neural network to distinguish simulated gravitational-wave signals from background noise artifacts. Our result shows that the data classification efficiency at a fixed false alarm probability is improved by the artificial neural network in comparison to the conventional detection statistic. Therefore, this algorithm increases the distance at which a gravitational-wave signal could be observed in coincidence with a gamma-ray burst. In order to demonstrate the performance, we also evaluate a few seconds of gravitational-wave data segment using the trained networks and obtain the false alarm probability. We suggest that the artificial neural network can be a complementary method to the conventional detection statistic for identifying gravitational-wave signals related to the short gamma-ray bursts.Comment: 30 pages, 10 figure

Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy

In this contribution, we report the development of ultrafast electron microscopy (UEM) with atomic-scale real-, energy-, and Fourier-space resolutions. This second-generation UEM provides images, diffraction patterns, and electron energy spectra, and here we demonstrate its potential with applications for nanostructured materials and organometallic crystals. We clearly resolve the separation between atoms in the direct images and the Bragg spots/Debye−Scherrer rings in diffraction and obtain the electronic structure and elemental energies in the electron energy loss spectra (EELS) and energy filtered transmission electron microscopy (EFTEM)

Reconstituting ring-rafts in bud-mimicking topography of model membranes.

During vesicular trafficking and release of enveloped viruses, the budding and fission processes dynamically remodel the donor cell membrane in a protein- or a lipid-mediated manner. In all cases, in addition to the generation or relief of the curvature stress, the buds recruit specific lipids and proteins from the donor membrane through restricted diffusion for the development of a ring-type raft domain of closed topology. Here, by reconstituting the bud topography in a model membrane, we demonstrate the preferential localization of cholesterol- and sphingomyelin-enriched microdomains in the collar band of the bud-neck interfaced with the donor membrane. The geometrical approach to the recapitulation of the dynamic membrane reorganization, resulting from the local radii of curvatures from nanometre-to-micrometre scales, offers important clues for understanding the active roles of the bud topography in the sorting and migration machinery of key signalling proteins involved in membrane budding