807 research outputs found
Birational Geometry of Singular Moduli Spaces of O'Grady Type
Following Bayer and Macr\`{i}, we study the birational geometry of singular
moduli spaces of sheaves on a K3 surface which admit symplectic
resolutions. More precisely, we use the Bayer-Macr\`{i} map from the space of
Bridgeland stability conditions to the cone of movable
divisors on to relate wall-crossing in to birational
transformations of . We give a complete classification of walls in
and show that every birational model of obtained by
performing a finite sequence of flops from appears as a moduli space of
Bridgeland semistable objects on . An essential ingredient of our proof is
an isometry between the orthogonal complement of a Mukai vector inside the
algebraic Mukai lattice of and the N\'{e}ron-Severi lattice of which
generalises results of Yoshioka, as well as Perego and Rapagnetta. Moreover,
this allows us to conclude that the symplectic resolution of is deformation
equivalent to the 10-dimensional irreducible holomorphic symplectic manifold
found by O'Grady.Comment: Final versio
Weak solutions for forward--backward SDEs--a martingale problem approach
In this paper, we propose a new notion of Forward--Backward Martingale
Problem (FBMP), and study its relationship with the weak solution to the
forward--backward stochastic differential equations (FBSDEs). The FBMP extends
the idea of the well-known (forward) martingale problem of Stroock and
Varadhan, but it is structured specifically to fit the nature of an FBSDE. We
first prove a general sufficient condition for the existence of the solution to
the FBMP. In the Markovian case with uniformly continuous coefficients, we show
that the weak solution to the FBSDE (or equivalently, the solution to the FBMP)
does exist. Moreover, we prove that the uniqueness of the FBMP (whence the
uniqueness of the weak solution) is determined by the uniqueness of the
viscosity solution of the corresponding quasilinear PDE.Comment: Published in at http://dx.doi.org/10.1214/08-AOP0383 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Creativity: Generating Diverse Questions using Variational Autoencoders
Generating diverse questions for given images is an important task for
computational education, entertainment and AI assistants. Different from many
conventional prediction techniques is the need for algorithms to generate a
diverse set of plausible questions, which we refer to as "creativity". In this
paper we propose a creative algorithm for visual question generation which
combines the advantages of variational autoencoders with long short-term memory
networks. We demonstrate that our framework is able to generate a large set of
varying questions given a single input image.Comment: Accepted to CVPR 201
Surface chemistry and growth of oxide supported metal nanoparticles
A model heterogeneous catalyst inspired by a real catalyst is synthesized for the purpose of understanding how it works. To make such model catalysts, we choose to evaporate metal atoms on metal oxide single crystals and measure them under UHV conditions. The study of model catalysts could advance the understandings of fundamental catalytic properties of real catalysts and helps to optimize or redesign industrial catalysts. In our experiments, many ultra-high vacuum (UHV) techniques have been employed to investigate the atomic and electronic structure of the surface as well as the interface of the prepared samples. In particular, the surface-sensitive tools such as electron energy loss spectra (EELS) and low energy ion scattering (LEIS) spectra provide us detailed information of the surface modification. In this dissertation, we confine our attention to three popular catalysts: Cu on ZnO, Au on ZnO and Cu on TiO2, which play primary roles on modern methanol industry. For instance, Au on ZnO and Cu on ZnO are important catalysts for methanol synthesis, water-shift reaction and methanol-steam reforming, while Cu on TiO2 possesses a high photocatalytic activity for photoreduction of CO2 into methanol. It becomes important for us to develop an understanding of which factors determine the functions of the prepared samples. Different metal growth models are observed for the above samples, due to the varied metal-oxide interactions. At the high substrate temperature, full encapsulation of metal nanoparticles takes place to all of the above samples, which dramatically changes the adsorption behavior and catalytic performance. It provides a strong indication that these thin encapsulation layers are very different from their bulk materials in both geometric and electronic sides. The charge transfer in the interface may be responsible for the modification of geometric and electronic structure of surface, and results in high-thermal stability of these ultra-thin films. The above reconstruction leads to an exceptional catalytic activity of CO oxidation through a different reaction kinetics and mechanism. The CO oxidation experiments show a direct relation between encapsulation rate and reaction rate, which indicates the active sites should be localized at these thin oxide films rather than the metal nanoparticles
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