67 research outputs found
Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise
Motivated by porous medium equations with randomly perturbed velocity field,
this paper considers a class of nonlinear degenerate diffusion equations with
nonlinear conservative noise in bounded domains. The existence, uniqueness and
-stability of non-negative entropy solutions under the homogeneous
Dirichlet boundary condition are proved. The approach combines Kruzhkov's
doubling variables technique with a revised strong entropy condition that is
automatically satisfied by the solutions of approximate equations.Comment: 33 page
Quantum multipartite maskers vs quantum error-correcting codes
Since masking of quantum information was introduced by Modi et al. in [PRL
120, 230501 (2018)], many discussions on this topic have been published. In
this paper, we consider relationship between quantum multipartite maskers
(QMMs) and quantum error-correcting codes (QECCs). We say that a subset of
pure states of a system can be masked by an operator into a
multipartite system \H^{(n)} if all of the image states of states
in have the same marginal states on each subsystem. We call such
an a QMM of . By establishing an expression of a QMM, we obtain a
relationship between QMMs and QECCs, which reads that an isometry is a QMM of
all pure states of a system if and only if its range is a QECC of any
one-erasure channel. As an application, we prove that there is no an isometric
universal masker from \C^2 into \C^2\otimes\C^2\otimes\C^2 and then the
states of \C^3 can not be masked isometrically into
\C^2\otimes\C^2\otimes\C^2. This gives a consummation to a main result and
leads to a negative answer to an open question in [PRA 98, 062306 (2018)].
Another application is that arbitrary quantum states of \C^d can be
completely hidden in correlations between any two subsystems of the tripartite
system \C^{d+1}\otimes\C^{d+1}\otimes\C^{d+1}, while arbitrary quantum states
cannot be completely hidden in the correlations between subsystems of a
bipartite system [PRL 98, 080502 (2007)].Comment: This is a revision about arXiv:2004.14540. In the present version,
and old Eq. (2.2) have been exchanged and the followed three
equations have been correcte
Extremely large magnetoresistance in topologically trivial semimetal -WP
Extremely large magnetoresistance (XMR) was recently discovered in many
non-magnetic materials, while its underlying mechanism remains poorly
understood due to the complex electronic structure of these materials. Here, we
report an investigation of the -phase WP, a topologically trivial
semimetal with monoclinic crystal structure (C2/m), which contrasts to the
recently discovered robust type-II Weyl semimetal phase in -WP. We
found that -WP exhibits almost all the characteristics of XMR
materials: the near-quadratic field dependence of MR, a field-induced up-turn
in resistivity following by a plateau at low temperature, which can be
understood by the compensation effect, and high mobility of carriers confirmed
by our Hall effect measurements. It was also found that the normalized MRs
under different magnetic fields has the same temperature dependence in
-WP, the Kohler scaling law can describe the MR data in a wide
temperature range, and there is no obvious change in the anisotropic parameter
value with temperature. The resistance polar diagram has a peanut
shape when field is rotated in plane, which can be understood by
the anisotropy of Fermi surface. These results indicate that both
field-induced-gap and temperature-induced Lifshitz transition are not the
origin of up-turn in resistivity in the -WP semimetal. Our findings
establish -WP as a new reference material for exploring the XMR
phenomena.Comment: 18 pages, 12 figure
EVD Surgical Guidance with Retro-Reflective Tool Tracking and Spatial Reconstruction using Head-Mounted Augmented Reality Device
Augmented Reality (AR) has been used to facilitate surgical guidance during
External Ventricular Drain (EVD) surgery, reducing the risks of misplacement in
manual operations. During this procedure, the pivotal challenge is the accurate
estimation of spatial relationship between pre-operative images and actual
patient anatomy in AR environment. In this research, we propose a novel
framework utilizing Time of Flight (ToF) depth sensors integrated in
commercially available AR Head Mounted Devices (HMD) for precise EVD surgical
guidance. As previous studies have proven depth errors for ToF sensors, we
first conducted a comprehensive assessment for the properties of this error on
AR-HMDs. Subsequently, a depth error model and patient-specific model parameter
identification method, is introduced for accurate surface information. After
that, a tracking procedure combining retro-reflective markers and point clouds
is proposed for accurate head tracking, where head surface is reconstructed
using ToF sensor data for spatial registration, avoiding fixing tracking
targets rigidly on the patient's cranium. Firstly, ToF
sensor depth value error was revealed on human skin, indicating the
significance of depth correction. Our results showed that the ToF sensor depth
error was reduced by over using proposed depth correction method on head
phantoms in different materials. Meanwhile, the head surface reconstructed with
corrected depth data achieved sub-millimeter accuracy. Experiment on a sheep
head revealed reconstruction error. Furthermore, a user study was
conducted for the performance of proposed framework in simulated EVD surgery,
where 5 surgeons performed 9 k-wire injections on a head phantom with virtual
guidance. Results of this study revealed translational
accuracy and orientational accuracy
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