3D face tracking and multi-scale, spatio-temporal analysis of linguistically significant facial expressions and head positions in ASL

Essential grammatical information is conveyed in signed languages by clusters of events involving facial expressions and movements of the head and upper body. This poses a significant challenge for computer-based sign language recognition. Here, we present new methods for the recognition of nonmanual grammatical markers in American Sign Language (ASL) based on: (1) new 3D tracking methods for the estimation of 3D head pose and facial expressions to determine the relevant low-level features; (2) methods for higher-level analysis of component events (raised/lowered eyebrows, periodic head nods and head shakes) used in grammatical markings—with differentiation of temporal phases (onset, core, offset, where appropriate), analysis of their characteristic properties, and extraction of corresponding features; (3) a 2-level learning framework to combine lowand high-level features of differing spatio-temporal scales. This new approach achieves significantly better tracking and recognition results than our previous methods

A stochastic control problem arising from relaxed wealth tracking with a monotone benchmark process

This paper studies a nonstandard stochastic control problem motivated by the optimal consumption in an incomplete market with wealth tracking of a non-decreasing benchmark process. In particular, the monotone benchmark is modelled by the running maximum of a drifted Brownian motion. We consider a relaxed tracking formulation using capital injection such that the wealth compensated by the injected capital dominates the benchmark process at all times. The stochastic control problem is to maximize the expected utility on consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied such that the singular control of capital injection and the floor constraint can be hidden. To tackle the HJB equation with two Neumann boundary conditions, we establish the existence of a unique classical solution to the dual PDE in a separation form using some novel probabilistic representations involving the dual reflected processes and the local time. The proof of the verification theorem on the optimal feedback control can be carried out by some technical stochastic flow analysis of the dual reflected processes and estimations of the optimal control.Comment: Keywords: Non-decreasing benchmark, capital injection, optimal consumption, Neumann boundary conditions, probabilistic representation, reflected diffusion processe

An extended Merton problem with relaxed benchmark tracking

This paper studies a Merton's optimal portfolio and consumption problem in an extended formulation incorporating the tracking of a benchmark process described by a geometric Brownian motion. We consider a relaxed tracking formulation such that that the wealth process compensated by a fictitious capital injection outperforms the external benchmark at all times. The fund manager aims to maximize the expected utility of consumption deducted by the cost of the capital injection, where the latter term can also be regarded as the expected largest shortfall with reference to the benchmark. By introducing an auxiliary state process with reflection, we formulate and tackle an equivalent stochastic control problem by means of the dual transform and probabilistic representation, where the dual PDE can be solved explicitly. On the strength of the closed-form results, we can derive and verify the feedback optimal control in the semi-analytical form for the primal control problem, allowing us to observe and discuss some new and interesting financial implications on portfolio and consumption decision making induced by the additional risk-taking in capital injection and the goal of tracking.Comment: Keywords: Benchmark tracking, capital injection, expected largest shortfall, consumption and portfolio choice, Neumann boundary conditio

Cell-Wall Mechanical Properties of Bamboo Investigated by In-Situ Imaging Nanoindentation

A novel in-situ imaging nanoindentation technique was used to investigate the cell-wall mechanical properties of bamboo fibers and parenchyma cells. In-situ imaging confirmed neither "piling up" nor "sinking in" occurred around the indentations in the cell walls. The load-displacement curves revealed different deformation mechanisms of the cell walls when indented, respectively, in the longitudinal and transverse direction of bamboo fibers. There existed significant differences in MOE between longitudinal (16.1 GPa) and transverse direction (5.91 GPa) for the cell walls of bamboo fibers, while no differences were significant in hardness. Furthermore, the measured longitudinal MOE and hardness of parenchyma cell walls were 5.8 GPa and 0.23 GPa. This corresponds to 33% and 63% of the corresponding value of bamboo fibers. It was found that the longitudinal MOE of the cells of bamboo fibers remained almost constant from the outer portion to the inner portion of bamboo culms, while hardness showed a decreasing tendency. It was concluded that the nanoindentation technique was capable of effectively characterizing the mechanical properties of bamboo at the cellular level, though it might underestimate the real longitudinal MOE of the cell walls. The results highlighted the extreme importance of locating indentations at the nano scale for the mechanical characterization of complicated natural biomaterials such as wood and bamboo

Centralized systemic risk control in the interbank system: Relaxed control and Gamma-convergence

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply for the interbank system with borrowing and lending activities. Facing both heterogeneity among banks and the common noise, the central bank aims to find an optimal strategy to minimize the average distance between log-monetary reserves and some prescribed capital levels for all banks. A relaxed control approach is adopted, and an optimal randomized control can be obtained in the system with finite banks by applying Ekeland's variational principle. As the number of banks grows large, we further prove the convergence of optimal strategies using the Gamma-convergence arguments, which yields an optimal relaxed control in the mean field model. It is shown that the limiting optimal relaxed control is linked to a solution of a stochastic Fokker-Planck-Kolmogorov (FPK) equation. The uniqueness of the solution to the stochastic FPK equation is also established under some mild conditions.Comment: Keywords: Systemic risk; interbank system; relaxed control; mean field model; stochastic FPK equation; Gamma-convergenc