Truncation quantization in the edge calculus Schulze, B.-Wolfgang; Seiler, Jörg
Journal of pseudo-differential operators and applications,
12/2023, Letnik:
14, Številka:
4
Journal Article
Odprti dostop
Pseudodifferential operators on the half-space associated with classical symbols of order zero without transmission property are shown to belong to the so-called edge algebra.
The following essay aims at elaborating some aspects of the genre grammar of linguistic practices embodied in folk narratives. It starts from the idea that linguistic practices like narratives are ...controlled by a corresponding genre-knowledge just as it holds for most types of human actions in general. Individual linguistic practices are thus sequenced and arranged according to a corresponding knowledge frame that is related to the situationally activated genre. The term
is used to denote this sequence of situationally and interactionally coherent linguistic practices that are construed according to the
of a ‘genre in action’. A
will be understood as a semiotic unit whose
corresponds to a set of types of lexical and grammatical patterns ultimately represented by the micro-structure of the text. Its
will be interpreted as a text world model (TWM) that is internally invoked by the functionality, semantics, and quantification of the types of construction that occur in a text together with their syntax as well as by corresponding world knowledge. The essay first discusses some theoretical aspects of a genre-based approach to one kind of linguistic practices, namely narratives before turning to an illustration of the approach by referring to some selected aspects of two folk narratives, one taken from Grimms’ collection of folk narratives, the other stemming from the Udi community in the Eastern Caucasus (Northwestern Azerbaijan).
Analysis on Regular Corner Spaces Chang, Der-Chen; Khalil, Sara; Schulze, Bert-Wolfgang
The Journal of geometric analysis,
09/2021, Letnik:
31, Številka:
9
Journal Article
Recenzirano
We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in ...terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel’s calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11–51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective
2
×
2
operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11–51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
Abstract
STUDY QUESTION
Is it possible to induce in vitro reorganization of primary human testis cells from testicular sperm extraction (TESE) biopsies, maintain their long-term cultivation in a 2D ...system and identify cellular compositions?
SUMMARY ANSWER
In vitro reorganization of primary human testis cells from TESE biopsies and their long-term cultivation on uncoated cell culture dishes is feasible and the cellular compositions can be uncovered through gene expression and microscopic analyses.
WHAT IS KNOWN ALREADY
It has been shown in the rodent model that mixtures of testicular cell types are able to reassemble into clusters when cultivated on different kinds of surfaces or three-dimensional matrices. Two recent publications demonstrated the ability of primary human testicular cells to assemble into testicular organoids and their cultivation for a period of 3–4 weeks.
STUDY DESIGN SIZE, DURATION
Primary human testis cells from TESE biopsies from 16 patients were reorganized in vitro and the clusters were cultivated long term on uncoated cell culture dishes, providing a solid ground for in vitro spermatogenesis. Gene expression analysis as well as fluorescence/transmission electron microscopy (TEM) were employed to uncover the cellular composition of the clusters.
PARTICIPANTS/MATERIALS, SETTING, METHODS
Testis biopsies from adult, normogonadotropic patients displaying full spermatogenesis (n = 11), hypospermatogenesis (n = 2), predominantly full spermatogenesis with some hypospermatogenic tubules (n = 1), meiotic arrest (n = 1) or mixed atrophy (n = 1) were enzymatically digested and dispersed cells were cultivated on 96-well plates or chamber dishes as aggregate-free cell suspensions. Time-lapse imaging of cluster formation was performed over a period of 48 h. For receptor tyrosine kinase inhibition of cluster formation, cells were treated twice with K252a within 2–3 days. Immunofluorescence staining and confocal microscopy was carried out on clusters after 1–3 weeks of cultivation to identify the presence of Sertoli cells (SC) (SOX9), peritubular myoid cells (SMA), Leydig cells (LC) (STAR), undifferentiated spermatogonia (FGFR3), differentiating spermatogonia/spermatocytes (DDX4) and postmeiotic germ cells (PRM1). Single clusters from four patients and a pool of eight larger clusters from another patient were manually picked and subjected to quantitative real-time PCR to evaluate the presence of SC (SOX9, AR), LC (INSL3, STAR, HSD3B1), peritubular myoid cells (ACTA2), fibroblasts (FSP1), endothelial cells (CD34), macrophages (CD68), undifferentiated spermatogonia (FGFR3), differentiating spermatogonia/spermatocytes (DDX4) and postmeiotic germ cells (PRM1). Finally, an ultrastructural investigation was conducted based on TEM of clusters from six different patients, among them 3-month cultivated large clusters from two patients.
MAIN RESULTS AND THE ROLE OF CHANCE
Quantitative PCR-based analysis of single-picked testicular cell clusters identified SC, peritubular myoid cells, endothelial cells, fibroblasts, macrophages, spermatids and LC after 1, 2 or 3 weeks or 3 months of cultivation. Immunofluorescence positivity for SC and peritubular myoid cells corroborated the presence of these two kinds of testis niche cells. In addition, round as well as elongated spermatids were frequently encountered in 1 and 2 weeks old clusters. Transmission electron microscopical classification confirmed all these cell types together with a few spermatogonia. Macrophages were found to be of the proinflammatory M1 subtype, as revealed by CD68+/CD163−/IL6+ expression. Time-lapse imaging uncovered the specific dynamics of cluster fusion and enlargement, which could be prevented by addition of protein kinase inhibitor K252a.
LARGE SCALE DATA
N/A.
LIMITATIONS REASON FOR CAUTION
Cell composition of the clusters varied based on the spermatogenic state of the TESE patient. Although spermatids could be observed with all applied methods, spermatogonia were only detected by TEM in single cases. Hence, a direct maintenance of these germ cell types by our system in its current state cannot be postulated. Moreover, putative dedifferentiation and malignant degeneration of cells in long-term cluster cultivation needs to be investigated in the future.
WIDER IMPLICATIONS OF THE FINDINGS
This work demonstrates that the reorganization of testicular cells can be achieved with TESE biopsies obtained from men enroled in a standard clinical assisted reproduction program. The formed clusters can be cultivated for at least 3 months and are composed, to a large extent, of the most important somatic cell types that are essential to support spermatogenesis. These findings may provide the cellular basis for advances in human in vitro spermatogenesis and/or the possibility for propagation of spermatogonia within a natural stem cell niche-like environment.
STUDY FUNDING AND COMPETING INTERESTS
The project was funded by a DFG grant to K.v.K. (KO 4769/2-1). The authors declare they have no conflicts of interest.
Corner Operators with Symbol Hierarchies Chang, Der-Chen; Khalil, Sara; Schulze, Bert-Wolfgang
Advances in applied Clifford algebras,
07/2021, Letnik:
31, Številka:
3
Journal Article
Recenzirano
This paper outlines an approach for studying operators on stratified spaces
M
∈
M
k
with regular singularities of higher order
k
. Smoothness corresponds to
k
=
0
.
Manifolds with smooth boundaries ...belong to the category
M
1
.
The case
k
=
1
generally indicates conical or edge singularities. Boutet de Monvel’s algebra of boundary value problems (BVPs) with the transmission property at the boundary may be interpreted as a special singular operator calculus for
k
=
1
.
Also, BVPs
A
with violated transmission properties belong to edge calculus and are controlled by pairs
{
σ
j
(
A
)
}
j
=
0
,
1
,
consisting of interior and boundary symbols. Singularities of
M
∈
M
k
for higher order
k
give rise to a sequence of strata
s
(
M
)
=
{
s
j
(
M
)
}
j
=
0
,
…
,
k
,
where
s
j
(
M
)
∈
M
0
.
Operators
A
in corresponding algebras of operators (corner-degenerate in stretched variables) are determined by a hierarchy of symbols
σ
(
A
)
=
{
σ
j
(
A
)
}
j
=
0
,
…
,
k
,
modulo lower order terms. Those express ellipticity and parametrices
A
(
-
1
)
in weighted corner Sobolev spaces, containing sequences of real weights
γ
j
.
Components
σ
j
(
A
)
for
j
>
0
,
depending on variables and covariables in
T
∗
(
s
j
(
M
)
)
\
0
,
act as operator families on infinite straight cones with compact singular links in
M
j
-
1
,
and
σ
0
(
A
)
is the standard principal symbol on
T
∗
(
s
0
(
M
)
)
\
0
.
Abstract
Background and study aims
Endoscopic negative pressure therapy (ENPT) has been developed to treat gastrointestinal leakages. Up to now, ENPT has usually been performed with open-pore ...polyurethane foam drains (OPD). A big disadvantage of the OPDs is their large diameter. We have developed a new, small-bore open-pore film drainage (OFD). Herein we report our first experience in a case series of 16 patients.
Patients and methods
OFD is constructed with a drainage tube and a very thin double-layered open-pore drainage film (Suprasorb CNP, Drainage Film, Lohmann & Rauscher International, Germany). The distal end of the tube is wrapped with only one layer of film. OFD is placed into the gastrointestinal leakage site with common endoscopic techniques. The tube is connected to an electronic vacuum device and continuous negative pressure of –125 mmHg applied.
Results
From 2013 to 2016, 16 patients were treated with the new OFD device. In 10 patients, transmural intestinal defects (4 esophageal, 4 rectum/colon, 1 duodenal, 1 pancreatic cyst) were closed with ENPT in median time of 12 days (range 3 – 34 days). Five of the 10 patients were treated solely with OFD devices. In five patients ENPT started with ODP and changed to OFD when the cavity was shrunken to a channel with a small opening. In four patients postoperative gastric reflux was eliminated for 5 to 16 days.
Conclusions
Small-bore OFD opens up promising new treatment options within ENPT. OFD can be used in endoscopic closure management of intestinal leakages in the upper and lower gastrointestinal tract. Gastric reflux can be eliminated in an active manner. OFD can be inserted nasally. OFD may be an adequate substitute for OPD, especially when placement of the larger OPD is difficult.
Meeting presentations: The authorsʼ experience was first reported in an oral presentation at the 46th Kongress der Deutschen Gesellschaft für Endoskopie und Bildgebende Verfahren in Mannheim (DGE-BV), 17. – 19.03.2016.
BACKGROUND A key step in studying the biology of spermatogonia is to determine their global gene expression profile. However, disassociation of these cells from the testis may alter their profile to ...a considerable degree. To characterize the molecular phenotype of human spermatogonia, including spermatogonial stem cells (SSCs), within their cognate microenvironment, a rare subtype of human defective spermatogenesis was exploited in which spermatogonia were the only germ cell type. METHODS The global expression profile of these samples was assessed on the Affymetrix microarray platform and compared with tissues showing homogeneous Sertoli-cell-only appearance; selected genes were validated by quantitative real-time PCR and immunohistochemistry on disparate sample sets. RESULTS Highly significant differences in gene expression levels correlated with the appearance of spermatogonia, including 239 best candidates of human spermatogonially expressed genes. Specifically, fibroblast growth factor receptor 3 (FGFR3), desmoglein 2 (DSG2), E3 ubiquitin ligase c-CBL (casitas B-cell lymphoma), cancer/testis antigen NY-ESO-1 (CTAG1A/B), undifferentiated embryonic cell transcription factor 1 (UTF1) and synaptosomal-associated protein, 91 kDa homolog (SNAP91) were shown to represent specific biomarkers of human spermatogonia. CONCLUSIONS These biomarkers, specifically the surface markers FGFR3 and DSG2, may facilitate the isolation and enrichment of human stem and/or progenitor spermatogonia and thus lay a foundation for studies of long-term maintenance of human SSCs/progenitor cells, spermatogonial self-renewal, clonal expansion and differentiation.
Human spermatogonia (Spg) and their fetal precursors express fibroblast growth factor receptor 3 (FGFR3). To further elucidate the role of FGFR3 in the control of Spg self-renewal, proliferation, ...and/or differentiation, and to narrow down the FGFR3-positive cell type(s) in the normal adult human testis, tissue sections and whole mount preparations of seminiferous tubules were analyzed combining immunofluorescence and confocal fluorescence microscopy. FGFR3 protein was chiefly observed in cellular membranes and cytoplasmic vesicles of a subpopulation of type A Spg, which comprised the chromatin rarefaction zone-containing type A
dark
. Cytoplasmic expression of FGFR3 and nuclear expression of proliferation-associated antigen KI-67 were mutually exclusive. Similarly, FGFR3-positive Spg were negative for
Doublesex
and
Mab
-
3
related transcription factor 1 (DMRT1). By contrast, undifferentiated embryonic cell transcription factor 1 (UTF1) and survival time-associated PHD finger in ovarian cancer 1 protein (SPOC1) were co-expressed in the nuclei of FGFR3-positive Spg. Whole mounted seminiferous tubules illustrated the clonogenic arrangement of the FGFR3/UTF1 double-positive Spg, which mainly occurred as pairs or quadruplets and, different from the KIT-positive Spg, showed no overlap with KI-67 labeled clusters. Taken together, in the adult human testis, FGFR3 expression is a feature of small clones of rarely dividing type A Spg which resemble “undifferentiated” Spg, including the spermatogonial stem cells.
Throughout spermatogenesis multiplication, maturation and differentiation of germ cells results in the formation of the male gamete. The understanding of spermatogenesis needs detailed informations ...about the organization of the germinal epithelium, the structure and function of different types of germ cells, endocrine and paracrine cells and mechanisms, intratesticular and extratesticular regulation of spermatogenesis. Normal germ cells must be discriminated from malformed, apoptotic and degenerating germ cells and tumor cells. Identification of the border line between normal and disturbed spermatogenesis substantiate the diagnosis of impaired male fertility. The profound knowledge of the complicate process of spermatogenesis and all cells or cell systems involved with is the prerequisite to develop concepts for therapy of male infertility or to handle germ cells in the management of assisted reproduction.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Human spermatozoal RNA features special characteristics such as a significantly reduced quantity within spermatozoa compared with somatic cells is described as being devoid of ribosomal RNAs and is ...difficult to isolate due to a massive excess of genomic DNA in the lysates. Using a novel two-round column-based protocol for human ejaculates delivering highly purified spermatozoal RNA, we uncovered a heterogeneous, but specific banding pattern in microelectrophoresis with 28S ribosomal RNA being indicative for the amount of round cell contamination. Ejaculates with different round cell quantities and density-purified spermatozoa revealed that 18S rRNA but not 28S rRNA is inherent to a pure spermatozoal fraction. Transmission electron microscopy showed monoribosomes and polyribosomes in spermatozoal cytoplasm, while immunohistochemical results suggest the presence of proteins from small and large ribosomal subunits in retained spermatozoal cytoplasm irrespective of 28S rRNA absence.
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