It is known that a Bank–Laine function
E
is a product of two normalized solutions of the second order differential equation
f
′
′
+
A
f
=
0
(
†
)
, where
A
=
A
(
z
)
is an entire function. By using ...Bergweiler and Eremenko’s method of constructing transcendental entire function
A
(
z
) by gluing certain meromorphic functions with infinitely many times, we show that, for each
λ
∈
1
,
∞
)
and each
δ
∈
0
,
1
, there exists a Bank–Laine function
E
such that
E
=
f
1
f
2
with
f
1
and
f
2
being two entire functions such that
λ
(
f
1
)
=
δ
λ
and
λ
(
f
2
)
=
λ
, respectively. We actually provide a complete construction of the Bank–Laine functions given by Bergweiler and Eremenko.
Let
p
(
z
) be a non-constant polynomial and
β
(
z
)
be a small entire function of
e
p
(
z
)
in the sense of Nevanlinna. We describe the growth behavior of the entire function
H
(
z
)
:
=
e
p
(
z
)
∫
...0
z
β
(
t
)
e
-
p
(
t
)
d
t
in the complex plane
C
. As an application, we find entire solutions of the Tumura–Clunie type differential equation
f
(
z
)
n
+
P
(
z
,
f
)
=
b
1
(
z
)
e
p
1
(
z
)
+
b
2
(
z
)
e
p
2
(
z
)
, where
b
1
(
z
)
and
b
2
(
z
)
are non-zero polynomials,
p
1
(
z
)
and
p
2
(
z
)
are two polynomials of the same degree
k
≥
1
and
P
(
z
,
f
) is a differential polynomial in
f
of degree at most
n
-
1
with meromorphic functions of order less than
k
as coefficients. These results allow us to determine all solutions with relatively few zeros of the second-order differential equation
f
′
′
-
b
1
(
z
)
e
p
1
(
z
)
+
b
2
(
z
)
e
p
2
(
z
)
+
b
3
(
z
)
f
=
0
, where
b
3
(
z
)
is a polynomial. We also prove a theorem on certain first-order linear differential equations related to complex dynamics.
It is shown that if the equation
f
(
z
+
1
)
n
=
R
(
z
,
f
)
,
where
R
(
z
,
f
) is rational in both arguments and
deg
f
(
R
(
z
,
f
)
)
≠
n
, has a transcendental meromorphic solution, then the ...equation above reduces into one out of several types of difference equations where the rational term
R
(
z
,
f
) takes particular forms. Solutions of these equations are presented in terms of Weierstrass or Jacobian elliptic functions, exponential type functions or functions which are solutions to a certain autonomous first-order difference equation having meromorphic solutions with preassigned asymptotic behavior. These results complement our previous work on the case
deg
f
(
R
(
z
,
f
)
)
=
n
of the equation above and thus provide a complete difference analogue of Steinmetz’ generalization of Malmquist’s theorem.
Embodied theories of semantic cognition predict that brain regions involved in motion perception are engaged when people comprehend motion concepts expressed in language. Left lateral ...occipitotemporal cortex (LOTC) is implicated in both motion perception and motion concept processing but prior studies have produced mixed findings on which parts of this region are engaged by motion language. We scanned participants performing semantic judgements about sentences describing motion events and static events. We performed univariate analyses, multivariate pattern analyses (MVPA) and psychophysiological interaction (PPI) analyses to investigate the effect of motion on activity and connectivity in different parts of LOTC. In multivariate analyses that decoded whether a sentence described motion or not, the middle and posterior parts of LOTC showed above-chance level performance, with performance exceeding that of other brain regions. Univariate ROI analyses found the middle part of LOTC was more active for motion events than static ones. Finally, PPI analyses found that when processing motion events, the middle and posterior parts of LOTC (overlapping with motion perception regions), increased their connectivity with cognitive control regions. Taken together, these results indicate that the more posterior parts of LOTC, including motion perception cortex, respond differently to motion vs. static events. These findings are consistent with embodiment accounts of semantic processing, and suggest that understanding verbal descriptions of motion engages areas of the occipitotemporal cortex involved in perceiving motion.
In this paper, we propose a novel design of human visual system (HVS) response in a convolutional filter form to decompose meaningful features that are closely tied with image sharpness level. ...No-reference (NR) image sharpness assessment (ISA) techniques have emerged as the standard of image quality assessment in diverse imaging applications. Despite their high correlation with subjective scoring, they are challenging for practical considerations due to high computational cost and lack of scalability across different image blurs. We bridge this gap by synthesizing the HVS response as a linear combination of finite impulse response derivative filters to boost the falloff of high band frequency magnitudes in natural imaging paradigm. The numerical implementation of the HVS filter is carried out with MaxPol filter library that can be arbitrarily set for any differential orders and cutoff frequencies to balance out the estimation of informative features and noise sensitivities. Utilized by the HVS filter, we then design an innovative NR-ISA metric called "HVS-MaxPol" that 1) requires minimal computational cost, 2) produces high correlation accuracy with image sharpness level, and 3) scales to assess the synthetic and natural image blur. Specifically, the synthetic blur images are constructed by blurring the raw images using a Gaussian filter, while natural blur is observed from real-life application such as motion, out-of-focus, and luminance contrast. Furthermore, we create a natural benchmark database in digital pathology for validation of image focus quality in whole slide imaging systems called "FocusPath" consisting of 864 blurred images. Thorough experiments are designed to test and validate the efficiency of HVS-MaxPol across different blur databases and the state-of-the-art NR-ISA metrics. The experiment result indicates that our metric has the best overall performance with respect to speed, accuracy, and scalability.
Quantifying a species thermal tolerance is critical to assessing biological impacts of anticipated increases in temperature (e.g., climate change). Although many studies have documented the critical ...thermal maximum (CTₘₐₓ) of fish, there is a paucity of research on thermal biology of sturgeon. The shortnose sturgeon (Acipenser brevirostrum LeSueur, 1818) is a threatened species that exists along the eastern coast of North America. They can be exposed to temperatures ranging from freezing to above 25 °C. Using a heating rate of 6 °C/h, CTₘₐₓ and the associated hematological responses of shortnose sturgeon acclimated to 10, 15, and 20 °C were determined. There was a significant positive relationship between CTₘₐₓ and body mass, and CTₘₐₓ increased significantly with increases in acclimation temperature (Tₐ). In general, hematology of thermally stressed fish was modified relative to control (nonstressed) fish. Hematocrit, plasma lactate, and plasma Na⁺ and Cl– of fish were all significantly influenced by thermal stress and Tₐ. Glucose and K⁺ were only significantly influenced by thermal stress. Future studies should address the importance of other stressors, such as salinity and toxicants, on thermal relationships of sturgeon.
In a continuous downhill section of a mountain highway, factors such as road alignment, roadside environment, and other visual characteristics will impact the slope illusion drivers experience and ...engage in unsafe driving behaviors. To improve the negative consequences of slope illusion and driving safety in continuous downhill sections, the effects of plant spacing, height, roadside distance, and color on driving behavior were all studied by simulating the plant landscape in a virtual environment. A driving simulator and UC-win/road software were used to conduct an indoor driving simulation experiment, and parameters such as speed and lateral position offset were used as the evaluation indices of driving stability to reflect the driver’s speed perception ability with subjective equivalent speeds. The results show that a plant landscape with appropriate plant spacing, height, roadside separation, and color is conducive to improving driving stability. Furthermore, a landscape with a height of 3 m, spacing of 10 m, roadside spacing of 0.75 m, and appropriate color matching can enhance the slope perception ability and speed perception ability of drivers, which is conducive to improving the driving safety of continuous downhill sections.
Purpose
Periarticular infiltration analgesia (PIA) is widely used to control postoperative pain in patients who underwent total knee arthroplasty (TKA). This study aimed to evaluate the efficacy of ...adding corticosteroids to the PIA cocktail for pain management in patients who underwent TKA.
Methods
The patients were randomized to the corticosteroid or control group (double-blind). The patients in the corticosteroid group received a periarticular infiltration of an analgesic cocktail of ropivacaine, epinephrine, and dexamethasone. Dexamethasone was omitted from the cocktail in the control group. The primary outcomes were postoperative pain assessed using a visual analog scale (VAS), time until the administration of first rescue analgesia, morphine consumption, and postoperative inflammatory biomarkers C-reactive protein (CRP) and interleukin-6 (IL-6). The secondary outcomes were functional recovery, assessed by the range of knee motion, quadriceps strength, and daily ambulation distance. The tertiary outcomes included postoperative adverse effects.
Results
The patients in the corticosteroid group had significantly lower resting VAS scores at 6 and 12 h after surgery, lower VAS scores during motion up to 24 h after surgery, and lower levels of inflammatory biomarkers. All the differences in the VAS scores between the two groups did not reach the point to be considered clinically significant. The additional use of corticosteroid significantly prolonged analgesic effects and led to lower rescue morphine consumption. The patients in the corticosteroid group had significantly better functional recovery on the first day after surgery. The two groups had a similar occurrence of adverse effects.
Conclusions
Adding corticosteroids to an analgesic cocktail for PIA could lightly improve early pain relief and accelerate recovery in the first 24 h after TKA.
Level of evidence
Randomized controlled trial, Level I.
It is shown that if
f
(
z
+
1
)
n
=
R
(
z
,
f
)
,
where
R
(
z
,
f
) is rational in
f
with meromorphic coefficients and
deg
f
(
R
(
z
,
f
)
)
=
n
, has an admissible meromorphic solution, then either
...f
satisfies a difference linear or Riccati equation with meromorphic coefficients, or the equation above can be transformed into one in a list of ten equations with certain meromorphic or algebroid coefficients. In particular, if
f
(
z
+
1
)
n
=
R
(
z
,
f
)
, where the assumption
deg
f
(
R
(
z
,
f
)
)
=
n
has been discarded, has rational coefficients and a transcendental meromorphic solution
f
of hyper-order
<
1
, then either
f
satisfies a difference linear or Riccati equation with rational coefficients, or the equation above can be transformed into one in a list of five equations which consists of four difference Fermat equations and one equation which is a special case of the symmetric QRT map. Solutions to all of these equations are presented in terms of Weierstrass or Jacobi elliptic functions, or in terms of meromorphic functions that are solutions to a difference Riccati equation. This provides a natural difference analogue of Steinmetz’ generalization of Malmquist’s theorem.
To systematically evaluate several factors of persistent human papillomavirus (HPV) infection following conization in patients with cervical intraepithelial neoplasia (CIN).
PubMed, EMBASE and the ...Cochrane Library were searched from January 1, 1998 to September 10, 2021. Random-effects models for meta-analyses were used and pooled relative risks with 95% confidence intervals were reported. Literature screening, data extraction, and assessment of the risk of bias in the included studies were conducted independently by two researchers. Data analysis was performed with Stata software, version 12.0.
A total of 28 studies were included in this study. Meta-analysis revealed that surgical margin and residual disease were positively correlated with persistent HPV infection after conization. Compared with patients infected with other types of HPV, CIN patients with HPV 16 had a higher persistent infection rate (OR = 1.967, 95% CI (1.232-3.140), P < 0.05).
CIN patients who are postmenopausal, have positive surgical margins and residual lesions, and are positive for HPV 16 are prone to persistent HPV infection after conization.
PDF
