The generalized fractional Brownian motion (GFBM)
X
:
=
{
X
(
t
)
}
t
≥
0
with parameters
γ
∈
0
,
1
)
and
α
∈
-
1
2
+
γ
2
,
1
2
+
γ
2
is a centered Gaussian
H
-self-similar process introduced by ...Pang and Taqqu (2019) as the scaling limit of power-law shot noise processes, where
H
=
α
-
γ
2
+
1
2
∈
(
0
,
1
)
. When
γ
=
0
,
X
is the ordinary fractional Brownian motion. When
γ
∈
(
0
,
1
)
, GFBM
X
does not have stationary increments, and its sample path properties such as Hölder continuity, path differentiability/non-differentiability, and the functional law of the iterated logarithm (LIL) have been investigated recently by Ichiba et al. (J Theoret Probab 10.1007/s10959-020-01066-1, 2021). They mainly focused on sample path properties that are described in terms of the self-similarity index
H
(e.g., LILs at infinity or at the origin). In this paper, we further study the sample path properties of GFBM
X
and establish the exact uniform modulus of continuity, small ball probabilities, and Chung’s laws of iterated logarithm at any fixed point
t
>
0
. Our results show that the local regularity properties away from the origin and fractal properties of GFBM
X
are determined by the index
α
+
1
2
instead of the self-similarity index
H
. This is in contrast with the properties of ordinary fractional Brownian motion whose local and asymptotic properties are determined by the single index
H
.
This paper is concerned with sample path properties of real-valued isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local ...nondeterminism of an isotropic Gaussian field and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.
•An advanced model for calculating air flowing through deeply buried tunnel is proposed.•The new model can calculate the three-step cooling and dehumidifying process of air.•The formula of minimum ...relative humidity of condensation is fitted.•The new model greatly improves the accuracy of results during the condensation stage.
Earth-air tunnel heat exchanger (EATHE) system is a potential passive cooling/heating air conditioning technology to pre-treat the ventilation air. Predicting the heat and mass transfer is critically important to ensure sufficient ventilation for occupational safety, while the existing method calculates it without the unsaturated condensation process. In this paper, the description failure of dehumidifying process of unsaturated air is attempted by proposing an advanced model for a deeply buried underground tunnel. Based on the experimental results, the minimum relative humidity of condensation was fitted with air flow rate, equivalent radius of tunnel, inner wall temperature, air temperature and relative humidity. Then, the advanced model was validated with the measured data and good agreement was achieved. Finally, comparisons between new model and existing model were conducted. The results show that the advanced model can calculate the unsaturated condensation process. Besides, the new model has higher calculation accuracy. Specifically, the relative error of temperature and relative humidity of condensation period is reduced by 50% when compared to the existing model.
Cardiac hypertrophy is an adaptive enlargement of the myocardium in response to overload pressure of heart. From abundant studies, a conclusion is drawn that many microRNAs (miRNAs) are associated ...with cardiac hypertrophy and heart failure. To investigate the role of microRNA-497 (miR-497) in myocardial hypertrophy, two models were established in this study from cell level to integral level. Cardiac hypertrophy was induced by using angiotensin Ⅱ (Ang Ⅱ) in vitro and was created by transverse abdominal aortic constriction (TAC) in vivo. There was a significant decrease expression of miR-497 in cardiac hypertrophy models. Moreover, overexpression of miR-497 inhibited myocardial hypertrophy both in vitro and in vivo without heart function variation. In addition, luciferase reporter assays demonstrated that Sirt4 was a direct target gene of miR-497. Taking together, our study indicates that miR-497 modulates cardiac hypertrophy by targeting Sirt4 and may serve as a potential therapeutic substance in the course.
We prove uniform Hausdorff and packing dimension results for the inverse images of a large class of real-valued symmetric Lévy processes. Our main result for the Hausdorff dimension extends that of ...Kaufman (C R Acad Sci Paris Sér I Math 300:281–282, 1985) for Brownian motion and that of Song et al. (Electron Commun Probab 23:10, 2018) for
α
-stable Lévy processes with
1
<
α
<
2
. Along the way, we also prove an upper bound for the uniform modulus of continuity of the local times of these processes.
Let
(
X
,
B
,
μ
,
T
,
d
)
be a measure-preserving dynamical system with exponentially mixing property, and let
μ
be an Ahlfors
s
-regular probability measure. The dynamical covering problem concerns ...the set
E
(
x
) of points which are covered by the orbits of
x
∈
X
infinitely many times. We prove that the Hausdorff dimension of the intersection of
E
(
x
) and any regular fractal
G
with
dim
H
G
>
s
-
α
equals
dim
H
G
+
α
-
s
, where
α
=
dim
H
E
(
x
)
μ
–a.e. Moreover, we obtain the packing dimension of
E
(
x
)
∩
G
and an estimate for
dim
H
(
E
(
x
)
∩
G
)
for any analytic set
G
.
In recent years, with the rapid development of metro tunnels, many scholars have paid attention to the serious dust environment during blasting construction. To efficiently alleviate the dust ...pollution in working zone and reduce the ventilation time after blasting, this study adopted the CFD numerical simulation method to investigate the effect of supply airflow angle on the dust removal performance of 3 m breathing height within the working zone in an entrance and exit metro tunnel. The supply airflow angle corresponding to the optimal dust removal performance and minimum ventilation energy consumption was determined after in-depth analysis of four kinds of supply airflow angles. The simulation results showed that when the supply airflow angle was 30°, the minimum ventilation time was obtained in the breathing zone 5 m away from the driving face; while in the breathing zone 10 m, 15 m and 20 m away from the driving face, the minimum ventilation time was achieved when the supply airflow angle was 10°. From the view of the weighted average dust concentration and ventilation time in the working zone, the supply airflow angle of 10° could obtain the optimal dust removal performance and minimum ventilation energy consumption, with dust removal performance improved by 67.6% and ventilation energy consumption reduced by 20.46%.
We determine the Hausdorff dimension of the set of
k
-multiple points for a symmetric operator semistable Lévy process
X
=
{
X
(
t
)
,
t
∈
R
+
}
in terms of the eigenvalues of its stability exponent. ...We also give a necessary and sufficient condition for the existence of
k
-multiple points. Our results extend to all
k
≥
2
the recent work (Luks and Xiao in J Theor Probab 30(1):297–325,
2017
) where the set of double points
(
k
=
2
)
was studied in the symmetric operator stable case.
Kalman filter is a commonly used method in the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated navigation system, in which the process noise covariance matrix ...has a significant influence on the positioning accuracy and sometimes even causes the filter to diverge when using the process noise covariance matrix with large errors. Though many studies have been done on process noise covariance estimation, the ability of the existing methods to adapt to dynamic and complex environments is still weak. To obtain accurate and robust localization results under various complex and dynamic environments, we propose an adaptive Kalman filter navigation algorithm (which is simply called RL-AKF), which can adaptively estimate the process noise covariance matrix using a reinforcement learning approach. By taking the integrated navigation system as the environment, and the opposite of the current positioning error as the reward, the adaptive Kalman filter navigation algorithm uses the deep deterministic policy gradient to obtain the most optimal process noise covariance matrix estimation from the continuous action space. Extensive experimental results show that our proposed algorithm can accurately estimate the process noise covariance matrix, which is robust under different data collection times, different GNSS outage time periods, and using different integration navigation fusion schemes. The RL-AKF achieves an average positioning error of 0.6517 m within 10 s GNSS outage for GNSS/INS integrated navigation system and 14.9426 m and 15.3380 m within 300 s GNSS outage for the GNSS/INS/Odometer (ODO) and the GNSS/INS/Non-Holonomic Constraint (NHC) integrated navigation systems, respectively.
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