G-Gaussian random fields and stochastic quantization under nonlinear expectation

We construct a G-Gaussian random field parametrized by Hilbert space, which contains G-white noise as a special case. Using orthonormal expansion, we're able to study the distribution of this random field. Furthermore, we study G-spatial and G-spacetime white noise, infinite dimensional G-Brownian Motion and their respective stochastic integrals. Based on G-white noise analysis and Parisi-Wu's stochastic quantization, we generalize the scalar free field model to stochastic partial differential equations (SPDEs) driven by G-Gaussian random fields.Comment: 29 page

Design of New Oscillograph Based on FPGA

AbstractOscillograph is one of the necessary measurement instruments in modern electronic design field. A new type of Oscillograph based on FPGA is proposed and designed in this paper. It consists of oscillograph, logic analyzer and signal generator. The resolution of the oscillograph is 8 bit and the maximum value can reach 200Mbps with support of software based on windows operation system. That of the logic analyzer is 100 Msps with 16 channels. The resolution of signal generator is 140Msps with 10-bit

Design of New Oscillograph Based on FPGA

AbstractOscillograph is one of the necessary measurement instruments in modern electronic design field. A new type of Oscillograph based on FPGA is proposed and designed in this paper. It consists of oscillograph, logic analyzer and signal generator. The resolution of the oscillograph is 8 bit and the maximum value can reach 200Mbps with support of software based on windows operation system. That of the logic analyzer is 100 Msps with 16 channels. The resolution of signal generator is 140Msps with 10-bit

On the mod pp cohomology for GL2\mathrm{GL}_2: the non-semisimple case

Let $F$ be a totally real field unramified at all places above $p$ and $D$ be a quaternion algebra which splits at either none, or exactly one, of the infinite places. Let $\overline{r}:\mathrm{Gal}(\overline{F}/F)\rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a continuous irreducible representation which, when restricted to a fixed place $v|p$, is non-semisimple and sufficiently generic. Under some mild assumptions, we prove that the admissible smooth representations of $\mathrm{GL}_2(F_v)$ occurring in the corresponding Hecke eigenspaces of the mod $p$ cohomology of Shimura varieties associated to $D$ have Gelfand-Kirillov dimension $[F_v:\mathbb{Q}_p]$. We also prove that any such representation can be generated as a $\mathrm{GL}_2(F_v)$-representation by its subspace of invariants under the first principal congruence subgroup. If moreover $[F_v:\mathbb{Q}_p]=2$, we prove that such representations have length $3$, confirming a speculation of Breuil and Pa\v{s}k\=unas.Comment: Comments welcome

The optimality of (stochastic) veto delegation

We analyze the optimal delegation problem between a principal and an agent, assuming that the latter has state-independent preferences. Among all incentive-compatible direct mechanisms, the veto mechanisms -- in which the principal commits to mixing between the status quo option and another state-dependent option -- yield the highest expected payoffs for the principal. In the optimal veto mechanism, the principal uses veto (i.e., choosing the status quo option) only when the state is above some threshold, and both the veto probability and the state-dependent option increase as the state gets more extreme. Our model captures the aspect of many real-world scenarios that the agent only cares about the principal's final decision, and the result provides grounds for the veto delegation pervasive in various organizations.Comment: 47 pages including Appendi

Information transmission in monopolistic credence goods markets

We study a general credence goods model with N problem types and N treatments. Communication between the expert seller and the client is modeled as cheap talk. We find that the expert's equilibrium payoffs admit a geometric characterization, described by the quasiconcave envelope of his belief-based profits function under discriminatory pricing. We establish the existence of client-worst equilibria, apply the geometric characterization to previous research on credence goods, and provide a necessary and sufficient condition for when communication benefits the expert. For the binary case, we solve for all equilibria and characterize client's possible welfare among all equilibria.Comment: 34 page

Locality Preserving Projections for Grassmann manifold

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in more wide areas. In this research, we propose an unsupervised dimensionality reduction algorithm on Grassmann manifold based on the Locality Preserving Projections (LPP) criterion. LPP is a commonly used dimensionality reduction algorithm for vector-valued data, aiming to preserve local structure of data in the dimension-reduced space. The strategy is to construct a mapping from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability. The proposed method can be optimized as a basic eigenvalue problem. The performance of our proposed method is assessed on several classification and clustering tasks and the experimental results show its clear advantages over other Grassmann based algorithms.Comment: Accepted by IJCAI 201