Let (M, g, σ) be a compact Riemannian surface equipped with a spin structure σ. For any metric ḡ onM , we denote by ΣḡM the spinor bundle associated to ḡ. We let ∆ḡ be the Laplace-Beltrami operator acting on smooth functions of M and Dḡ be the Dirac operator acting on smooth spinor fields with respect to the metric ḡ. We also denote by μ1(ḡ) (resp. λ1(ḡ)) the smallest positive eigenvalue of ∆ḡ ...

In 1556 Georgius Agricola I wrote, in his De Re Metallica, about the "colour of fumes" from various types of ores. This may be the earliest record available in which the color of a flame-excited metal sample was used to identify a substance. If so, it represents the start of flame spectroscopy as an analytical tool. For several hundred years thereafter, development in this field was very slow. ...

There is a need to empirically validate theoretical Machine Learning research. This can be di cult because the algorithms being tested often require large amounts of training data. Softbots provide a unique solution to this problem. Softbots or software robots are intelligent agents that interact with software environments. By attaching the agent directly to the training environment, it is poss...