2,435 research outputs found
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
Generation multiple vector light modes using beam displacers
Complex vector light modes, characterized by a non-uniform transverse
polarization distribution, have pervaded a wide range of research fields. In
this study, we propose a novel approach that enables the simultaneous
generation of multiple vector beams based on a spatially-segmented digital
hologram and two or more cascaded beam displacers. More precisely, an input
beam is separated into multiple parallel copies spatially separated, which are
then sent to the center of each segmented hologram, enabling independent
modulation of each beam. The modulated beams are then judiciously recombined
with a beam displacer to generate multiple vector modes in a simultaneous way.
We demonstrated our technique with two arbitrary vector modes but the technique
can be easily extended to more by inserting additional beam dispalcers. To
assess the quality of the generated vector modes, we employed Stokes
polarimetry to reconstruct their transverse polarisation distribution and to
measure their degree of non-separability. We envision that this technique will
find significant applications in various fields, including optical
communications, optical sensing, optical tweezers to mention a few
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