bluuebunny/crossref_metadata_2025_split huggingface dataset:
Ordinary Differential Equations
Authors: Seifert Christian , Trostorff Sascha , Waurick Marcus 
Published: February 2022

AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem. It is also called existence and uniqueness theorem for initial value problems for ordinary differential equations as well as Cauchy–Lipschitz theorem). We shall furthermore see that the abstract theory developed here also allows for more general differential equations to be considered. In particular, we will have a look at so-called delay differential equations with finite or infinite delay; neutral differential equations are considered in the exercises section.
The Fourier–Laplace Transformation and Material Law Operators
Authors: Seifert Christian , Trostorff Sascha , Waurick Marcus 
Published: February 2022

AbstractIn this chapter we introduce the Fourier–Laplace transformation and use it to define operator-valued functions of ∂t,ν; the so-called material law operators. These operators will play a crucial role when we deal with partial differential equations. In the equations of classical mathematical physics, like the heat equation, wave equation or Maxwell’s equation, the involved material parameters, such as heat conductivity or permeability of the underlying medium, are incorporated within these operators. Hence, these operators are also called “material law operators”. We start our chapter by defining the Fourier transformation and proving Plancherel’s theorem in the Hilbert space-valued case, which states that the Fourier transformation defines a unitary operator on
$$L_2(\mathbb {R};H)$$

L

2

(
ℝ
;
H
)
.
Causality and a Theorem of Paley and Wiener
Authors: Seifert Christian , Trostorff Sascha , Waurick Marcus 
Published: February 2022

AbstractIn this chapter we turn our focus back to causal operators. In Chap. 10.1007/978-3-030-89397-2_5 we found out that material laws provide a class of causal and autonomous bounded operators. In this chapter we will present another proof of this fact, which rests on a result which characterises functions in
$$L_2(\mathbb {R};H)$$

L

2

(
ℝ
;
H
)
with support contained in the non-negative reals; the celebrated Theorem of Paley and Wiener. With the help of this theorem, which is interesting in its own right, the proof of causality for material laws becomes very easy. At a first glance it seems that holomorphy of a material law is a rather strong assumption. In the second part of this chapter, however, we shall see that in designing autonomous and causal solution operators, there is no way of circumventing holomorphy.
Initial Value Problems and Extrapolation Spaces
Authors: Seifert Christian , Trostorff Sascha , Waurick Marcus 
Published: February 2022

AbstractUp until now we have dealt with evolutionary equations of the form
$$\displaystyle \big (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\big )U=F $$

(

∂

t
,
ν

M
(

∂

t
,
ν

)
+
A

¯

)

U
=
F
for some given
$$F\in L_{2,\nu }(\mathbb {R};H)$$

F
∈

L

2
,
ν

(
ℝ
;
H
)
for some Hilbert space H, a skew-selfadjoint operator A in H and a material law M defined on a suitable half-plane satisfying an appropriate positive definiteness condition with
$$\nu \in \mathbb {R}$$

ν
∈
ℝ
chosen suitably large. Under these conditions, we established that the solution operator, "Equation missing", is eventually independent of ν and causal; that is, if F = 0 on
$$\left (-\infty ,a\right ]$$

−
∞
,
a

for some
$$a\in \mathbb {R}$$

a
∈
ℝ
, then so too is U.
Kinematic singularities of Feynman integrals and principal A-determinants
Authors: Klausen René Pascal 
Published: February 2022

AbstractWe consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and $$ \mathcal{A} $$
A
-hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigorous description of the singular locus, also known as Landau variety, via principal A-determinants. We also comprise a description of the various second type singularities. Moreover, by the Horn-Kapranov-parametrization we give a very efficient way to calculate a parametrization of Landau varieties. We furthermore present a new approach to study the sheet structure of multivalued Feynman integrals by the use of coamoebas.
Global Wave Front Sets in Ultradifferentiable Classes
Authors: Asensio Vicente , Boiti Chiara , Jornet David , Oliaro Alessandro 
Published: February 2022

AbstractWe introduce a global wave front set using Weyl quantizations of pseudodifferential operators of infinite order in the ultradifferentiable setting. We see that in many cases it coincides with the Gabor wave front set already studied by the last three authors of the present work. In this sense, we also extend, to the ultradifferentiable setting, previous work by Rodino and Wahlberg. Finally, we give applications to the study of propagation of singularities of pseudodifferential operators.
Reopening schools in a context of low COVID-19 contagion: consequences for teachers, students and their parents
Authors: Godøy Anna , Grøtting Maja Weemes , Hart Rannveig Kaldager 
Published: February 2022

AbstractKnowing how school reopenings affect the spread of COVID-19 is crucial when balancing children’s right to schooling with contagion management. This paper considers the effects on COVID-19 testing prevalence and the positive test rate of reopening Norwegian schools after a 6-week closure aimed at reducing contagion. We estimate the effects of school reopening on teachers, parents and students using an event study/difference-in-differences design that incorporates comparison groups with minimal exposure to in-person schooling. We find no evidence that COVID-19 incidence increased following reopening among students, parents or teachers pooled across grade levels. We find some suggestive evidence that infection rates among upper secondary school teachers increased; however, the effects are small and transitory. At low levels of contagion, schools can safely be reopened when other social distancing policies remain in place.
Posteriorly positioned femoral grafts decrease long-term failure in anterior cruciate ligament reconstruction, femoral and tibial graft positions did not affect long-term reported outcome
Authors: de Mees Tim T. C. R. , Reijman Max , Waarsing Jan Hendrik , Meuffels Duncan E. 
Published: February 2022

Abstract
Purpose
To investigate the effect that femoral and tibial tunnel positions have on long-term reported and clinical outcome and to identify a safe zone based on favourable outcome.

Methods
Seventy-eight patients from a previous randomised controlled trial were included and were followed with a mean follow-up of 11.4 years. All patients had primary trans-tibial anterior cruciate ligament reconstruction performed. The femoral and tibial tunnel positions were visualised and translated in percentages with three-dimensional computed tomography post-operatively. There were 3 separate outcome variables: patient-reported outcome measured with the IKDC Subjective Knee Form, overall failure, and radiographic osteoarthritis. The correlation between tunnel aperture positions and outcome was determined with multivariate regression. The area with best outcome was defined as the safe zone and was determined with Youden’s index in conjunction with receiver operating characteristics.

Results
No significant relationship was found between tunnel aperture positions and IKDC Subjective Knee Form at 10-year follow-up. The posterior-to-anterior femoral tunnel aperture position parallel to Blumensaat line showed a significant relationship (p = 0.03) to overall failure at 10-year follow-up. The mean posterior-to-anterior tunnel position of the group that did not fail was 37.7% compared to 44.1% in the overall failure group. Femoral tunnel apertures placed further anteriorly had more overall failures at long-term. The cut-off point lies at 35.0% from posterior-to-anterior parallel to Blumensaat. Of the 16 overall failures, 15 (93.8%) were placed further anteriorly than the cut-off point. No significant relationship was found between tunnel aperture positions and radiographic osteoarthritis.

Conclusion
Femoral and tibial tunnel positions were not associated with long-term patient-reported outcome and radiographic osteoarthritis. Long-term overall failure was more frequently seen in patients with a more anteriorly placed femoral tunnel. This study identified a safe zone located at the most posterior 35% of the femoral condyle parallel to Blumensaat. This knowledge offers guidance to surgeons to operate more precisely and accurately and reconstruct a long-lasting graft.

Level of evidence

Level III.
A combined analytical-chemometric approach for the in vitro determination of polyphenol bioaccessibility by simulated gastrointestinal digestion
Authors: Gómez-Mejía Esther , Rosales-Conrado Noelia , León-González María Eugenia , Valverde Alejandro , Madrid Yolanda 
Published: February 2022

AbstractIn this study, an integrated characterisation through polyphenol and caffeine content and antioxidant activity was combined with chemometric analysis to assess the effects of simulated in vitro gastrointestinal digestion on the bioaccessibility of these bioactive compounds from nine different tea infusions. Tea infusions were characterised based on total flavonoids, total polyphenols and antioxidant activity, together with the determination of individual polyphenol content. Fourteen phenolic compounds, including phenolic acids, stilbenes and flavonoids, were selected based on their reported bioactivity and high accessibility, attributed to their low molecular weight. Both polyphenols and caffeine were initially monitored in raw tea infusions and through the different digestion stages (salivary, gastric and duodenal) by capillary high performance liquid chromatography coupled to diode array detection (cHPLC-DAD) and/or HPLC coupled to a triple quadrupole mass analyser (HPLC–MS/MS). Multivariate analysis of the studied bioactives, using principal component analysis and cluster analysis, revealed that the decaffeination process seems to increase the stability and concentration of the compounds evaluated during digestion. The greatest transformations occurred mainly in the gastric and duodenal stages, where low bioactivity indices (IVBA) were shown for resveratrol and caffeic acid (IVBA = 0%). In contrast, the polyphenols gallic acid, chlorogenic acid and quercetin gave rise to their availability in white, green and oolong infusion teas (IVBA > 90%). Furthermore, highly fermented black and pu-erh varieties could be designated as less bioaccessible environments in the duodenum with respect to the tested compounds.
Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-Mixing Nonuniformly Hyperbolic Maps
Authors: Fleming-Vázquez Nicholas 
Published: February 2022

AbstractConsider a nonuniformly hyperbolic map $$ T:M\rightarrow M $$

T
:
M
→
M

modelled by a Young tower with tails of the form $$ O(n^{-\beta }) $$

O
(

n

-
β

)

, $$ \beta >2 $$

β
>
2

. We prove optimal moment bounds for Birkhoff sums $$ \sum _{i=0}^{n-1}v\circ T^i $$

∑

i
=
0

n
-
1

v
∘

T
i

and iterated sums $$ \sum _{0\le i<j<n}v\circ T^i\, w\circ T^j $$

∑

0
≤
i
<
j
<
n

v
∘

T
i

w
∘

T
j

, where $$ v,w:M\rightarrow {{\mathbb {R}}} $$

v
,
w
:
M
→
R

are (dynamically) Hölder observables. Previously iterated moment bounds were only known for $$ \beta >5$$

β
>
5

. Our method of proof is as follows; (i) prove that $$ T$$
T
satisfies an abstract functional correlation bound, (ii) use a weak dependence argument to show that the functional correlation bound implies moment estimates. Such iterated moment bounds arise when using rough path theory to prove deterministic homogenisation results. Indeed, by a recent result of Chevyrev, Friz, Korepanov, Melbourne & Zhang we have convergence to an Itô diffusion for fast-slow systems of the form $$\begin{aligned} x^{(n)}_{k+1}=x_k^{(n)}+n^{-1}a(x_k^{(n)},y_k)+n^{-1/2}b(x_k^{(n)},y_k) , \quad y_{k+1}=Ty_k \end{aligned}$$

x

k
+
1

(
n
)

=

x
k

(
n
)

+

n

-
1

a

(

x
k

(
n
)

,

y
k

)

+

n

-
1
/
2

b

(

x
k

(
n
)

,

y
k

)

,

y

k
+
1

=
T

y
k

in the optimal range $$ \beta >2$$

β
>
2

.
Automated segmentation of magnetic resonance bone marrow signal: a feasibility study
Authors: von Brandis Elisabeth , Jenssen Håvard B. , Avenarius Derk F. M. , Bjørnerud Atle , Flatø Berit , Tomterstad Anders H. , Lilleby Vibke , Rosendahl Karen , Sakinis Tomas , Zadig Pia K. K. , Müller Lil-Sofie Ording 
Published: February 2022

Abstract
Background
Manual assessment of bone marrow signal is time-consuming and requires meticulous standardisation to secure adequate precision of findings.

Objective
We examined the feasibility of using deep learning for automated segmentation of bone marrow signal in children and adolescents.

Materials and methods
We selected knee images from 95 whole-body MRI examinations of healthy individuals and of children with chronic non-bacterial osteomyelitis, ages 6–18 years, in a longitudinal prospective multi-centre study cohort. Bone marrow signal on T2-weighted Dixon water-only images was divided into three color-coded intensity-levels: 1 = slightly increased; 2 = mildly increased; 3 = moderately to highly increased, up to fluid-like signal. We trained a convolutional neural network on 85 examinations to perform bone marrow segmentation. Four readers manually segmented a test set of 10 examinations and calculated ground truth using simultaneous truth and performance level estimation (STAPLE). We evaluated model and rater performance through Dice similarity coefficient and in consensus.

Results
Consensus score of model performance showed acceptable results for all but one examination. Model performance and reader agreement had highest scores for level-1 signal (median Dice 0.68) and lowest scores for level-3 signal (median Dice 0.40), particularly in examinations where this signal was sparse.

Conclusion
It is feasible to develop a deep-learning-based model for automated segmentation of bone marrow signal in children and adolescents. Our model performed poorest for the highest signal intensity in examinations where this signal was sparse. Further improvement requires training on larger and more balanced datasets and validation against ground truth, which should be established by radiologists from several institutions in consensus.
Unboxing the black box—one step forward to understand the soil microbiome: A systematic review
Authors: Mishra Apurva , Singh Lal , Singh Dharmesh 
Published: February 2022

AbstractSoil is one of the most important assets of the planet Earth, responsible for maintaining the biodiversity and managing the ecosystem services for both managed and natural ecosystems. It encompasses large proportion of microscopic biodiversity, including prokaryotes and the microscopic eukaryotes. Soil microbiome is critical in managing the soil functions, but their activities have diminutive recognition in few systems like desert land and forest ecosystems. Soil microbiome is highly dependent on abiotic and biotic factors like pH, carbon content, soil structure, texture, and vegetation, but it can notably vary with ecosystems and the respective inhabitants. Thus, unboxing this black box is essential to comprehend the basic components adding to the soil systems and supported ecosystem services. Recent advancements in the field of molecular microbial ecology have delivered commanding tools to examine this genetic trove of soil biodiversity. Objective of this review is to provide a critical evaluation of the work on the soil microbiome, especially since the advent of the NGS techniques. The review also focuses on advances in our understanding of soil communities, their interactions, and functional capabilities along with understanding their role in maneuvering the biogeochemical cycle while underlining and tapping the unprecedented metagenomics data to infer the ecological attributes of yet undiscovered soil microbiome. This review focuses key research directions that could shape the future of basic and applied research into the soil microbiome. This review has led us to understand that it is difficult to generalize that soil microbiome plays a substantiated role in shaping the soil networks and it is indeed a vital resource for sustaining the ecosystem functioning. Exploring soil microbiome will help in unlocking their roles in various soil network. It could be resourceful in exploring and forecasting its impacts on soil systems and for dealing with alleviating problems like rapid climate change.
Occupancy times for time-dependent stage-structured models
Authors: Chappelle George , Hastings Alan , Rasmussen Martin 
Published: February 2022

AbstractDuring their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in a recent paper by Roth and Caswell for cases where the environmental conditions are constant. However, it is truly important to consider the case where environments are changing randomly or in directional way through time, so the transition probabilities between different states change over time, motivating the use of time-dependent stage-structured models. Using absorbing inhomogenous Markov chains and the discrete-time McKendrick–von Foerster equation, we derive explicit formulas for the occupancy time, its expectation, and its higher-order moments for stage-structured models with time-dependent transition rates. The results provide insights into the dynamics of long lived plant or animal populations where individuals transition in both directions between reproductive and non reproductive stages. We apply our approach to study a specific time-dependent model of the Southern Fulmar, and obtain insights into how the number of breeding attempts depends on external conditions that vary through time.
Depressive symptoms in youth with ADHD: the role of impairments in cognitive emotion regulation
Authors: Mayer Jutta S. , Brandt Geva A. , Medda Juliane , Basten Ulrike , Grimm Oliver , Reif Andreas , Freitag Christine M. 
Published: February 2022

AbstractYouth with attention-deficit/hyperactivity disorder (ADHD) are at increased risk to develop co-morbid depression. Identifying factors that contribute to depression risk may allow early intervention and prevention. Poor emotion regulation, which is common in adolescents, is a candidate risk factor. Impaired cognitive emotion regulation is a fundamental characteristic of depression and depression risk in the general population. However, little is known about cognitive emotion regulation in youth with ADHD and its link to depression and depression risk. Using explicit and implicit measures, this study assessed cognitive emotion regulation in youth with ADHD (N = 40) compared to demographically matched healthy controls (N = 40) and determined the association with depressive symptomatology. As explicit measure, we assessed the use of cognitive emotion regulation strategies via self-report. As implicit measure, performance in an ambiguous cue-conditioning task was assessed as indicator of affective bias in the processing of information. Compared to controls, patients reported more frequent use of maladaptive (i.e., self-blame, catastrophizing, and rumination) and less frequent use of adaptive (i.e., positive reappraisal) emotion regulation strategies. This pattern was associated with the severity of current depressive symptoms in patients. In the implicit measure of cognitive bias, there was no significant difference in response of patients and controls and no association with depression. Our findings point to depression-related alterations in the use of cognitive emotion regulation strategies in youth with ADHD. The study suggests those alterations as a candidate risk factor for ADHD-depression comorbidity that may be used for risk assessment and prevention strategies.
Morphological characterization and clinical effects of stromal alterations after intracorneal ring segment implantation in keratoconus
Authors: Hamon Loïc , Schlötzer-Schrehardt Ursula , Flockerzi Fidelis A. , Seitz Berthold , Daas Loay 
Published: February 2022

Abstract

Purpose
To analyze the histological and (ultra)structural stromal tissue changes after femtosecond (Fs) laser–assisted intracorneal ring segment (ICRS) implantation and their refractive and topographic effects in patients with keratoconus.

Methods
This monocentric retrospective case series included 15 consecutive patients with clinical peri-segmental lamellar channel deposits after treatment with Fs-ICRS implantation for keratoconus. The stromal changes were investigated using in vivo confocal microscopy. Two patients underwent a penetrating keratoplasty after the Fs-ICRS implantation; the explanted corneas were processed for histopathology and transmission electron microscopy (TEM). Refractive and topographic effects were investigated comparing the uncorrected (UDVA) and corrected (CDVA) distance visual acuity, spherical equivalent (SE), flat (K1), steep (K2), and steepest (Kmax) keratometry before and after detection of lamellar channel deposits.

Results
In vivo confocal microscopy revealed diffuse linear and focal granular hyperreflective structures. Histologically, there was mild proliferation of fibroblasts and fibrosis. TEM demonstrated focal accumulations of degenerated keratocytes with cytoplasmic lipid inclusions. There were no significant changes for UDVA (Δ = 0.0 ± 0.2 logMAR; p = 0.67), CDVA (Δ = 0.0 ± 0.1 logMAR; p = 0.32), SE (Δ 0.1 ± 0.9 D; p = 0.22), K1 (Δ = 0.3 ± 1.0 D; p = 0.28), K2 (Δ = 0.1 ± 0.9 D; p = 0.51), and Kmax (Δ = 0.3 ± 1.5 D; p = 0.17).

Conclusions
Two types of structural stromal changes were identified: (1) diffuse peri-segmental fibrosis and (2) lamellar channel deposits. These structural changes showed no evidence of a relevant refractive or topographic effect.
Limitations of laparoscopy to assess the peritoneal cancer index and eligibility for cytoreductive surgery with HIPEC in peritoneal metastasis
Authors: Yurttas Can , Überrück Lisa , Nadiradze Giorgi , Königsrainer Alfred , Horvath Philipp 
Published: February 2022

Abstract
Purpose
We aimed to determine the value of laparoscopy to assess the intra-abdominal tumor extent and predict complete cytoreduction.

Methods
All patients at our department in the period from 2017 to 2021 that underwent laparoscopy to assess peritoneal metastasis and subsequent open exploration with the intention to perform cytoreductive surgery (CRS) with HIPEC were retrospectively identified in a continuously maintained database.

Results
Forty-three patients were analyzed. Peritoneal cancer index (PCI) determination by laparoscopy compared to open surgery was overestimated in five patients (11.6%), identical in eleven patients (25.6%), and underestimated in 27 patients (62.8%). PCI differences were independent of surgeons, tumor entities, and prior chemotherapy. Thirty-four patients (79.1%) were determined eligible for CRS with HIPEC during open exploration, whereas nine patients (20.9%) underwent a non-therapeutic laparotomy. Complete or almost complete cytoreduction was achieved in 33 patients (76.7%). In one patient, completeness of cytoreduction was not documented.

Conclusions
We demonstrate a moderate agreement according to weighted Cohen’s kappa analysis of PCI values calculated during laparoscopy and subsequent open exploration for CRS with HIPEC. Uncertainty of PCI assessment should therefore be kept in mind when performing laparoscopy in patients with peritoneal metastasis.