Witten deformation for non-Morse functions and gluing formula for analytic torsions

In this paper, we introduce a coupling technique and analyze Witten deformation for a family of non-Morse functions parametrized by $T\in \mathbb{R}_+$, resulting in a novel purely analytic proof of gluing formula for analytic torsion in complete generality. Intriguingly, the gluing formula in this article could be reformulated as the Bismut-Zhang theorem for non-Morse functions, and from the perspective of Vishik's theory of moving boundary problems, the deformation parameter $T$ parametrizes a family of boundary conditions. Our proof also makes use of an interesting connection between small eigenvalues of Witten Laplacians and Mayer-Vietoris sequences. Lastly, in subsequent work, the techniques above are extended to analytic torsion forms.Comment: 41 pages. Some Typos are corrected. Certain proofs have been made simpler. Any comments are welcome

A new proof of gluing formula for analytic torsion forms

By extending the author's prior work to the family case, this paper presents a new proof of the gluing formula for the analytic torsion forms, considerably simplifying the proof given by Puchol-Zhang-Zhu.Comment: 41 pages. Some typos are corrected. Any comments are welcome! Text overlap with arXiv:2301.0199

Calabi-Yau/Landau-Ginzburg Correspondence for Weil-Peterson Metrics and tt∗tt^* Structures

The aim of this paper is to rigorously establish the Calabi-Yau/Landau-Ginzburg (CY/LG) correspondence for the $tt^*$ geometry structure--a generalized version of variation of Hodge structures. Although it is well-known that there exists a map between Hodge structures on the LG and CY's sides that preserves the Hodge filtration and bilinear form, it remains unclear whether the real structures are also preserved. In our paper, we conduct a detailed analysis of two period integrals on the LG's side. Based on this analysis, we modify the real structure proposed by Cecotti on LG's side, and show that the aforementioned map is also preserved under the modified real structure. As a result, we establish full CY/LG correspondence for $tt^*$ structures.Comment: 34 page

The Impact of Intracerebral Hemorrhage on the Progression of White Matter Hyperintensity

Objective: The exact relationship between white matter hyperintensity (WMH) and intracerebral hemorrhage (ICH) after ICH remains unclear. In this retrospective study, we investigated whether patients with ICH had more severe WMH progression.Patients and Methods: A total of 2,951 patients aged ≥40 years with ICH who received brain computed tomography (CT) imaging within 12 h of ICH symptom onset were screened. Ninety patients with two fluid-attenuated inversion recovery (FLAIR) magnetic resonance imaging (MRI) assessments, including 36 patients with Lobar ICH, 40 with basal ganglia region ICH and 14 with ICH at other sites, were included in the final study. We selected 90 age- and gender-matched healthy individuals with two MRI scans as the control group. The WMH volumes at baseline and follow-up were assessed using the FLAIR image by MRICRON and ITK-SNAP software, while the hematoma volumes were calculated based on the CT images using ITK-SNAP software.Results: The annual progression rate of WMH was significantly higher in the ICH group compared with the control group (p < 0.05). Furthermore, WMH progression was associated with the ICH volume. The largest ICH volume (>30 mL) was associated with the highest annual progression rate of WMH (p < 0.05). In contrast, no trend toward an association between ICH location and the annual progression rate of WMH was observed (p > 0.05).Conclusions: Our results showed that ICH patients had more severe WMH progression and that larger ICH volume was related to greater progression of WMH after ICH. These results could provide important prognostic information about patients with ICH

Giant superficial angiomyxoma of the male perineum: A case report

Superficial angiomyxoma (SA) is a rare benign tumor that occurs either in the superficial dermis or subcutaneously. It often occurs in the trunk, neck, or limbs, and grows slowly. The diameter of the tumor is usually less than 5 cm. A giant SA of the perineum in men is very rare. We detailed the diagnosis and treatment of male patients with perineal SA and performed a literature review. We report a case of a 42-year-old male patient. He was admitted to hospital with a perineal mass found more than 1 year previously. A pelvic contrast-enhanced computed tomography scan in our hospital suggests that a round slightly hypointense foci of about 6.0 cm × 8.6 cm × 4.5 cm in size with still clear borders was seen below the penile corpus cavernosum in the perineum. We performed a perineal mass excision under continuous epidural anesthesia. A postoperative pathology report diagnosed perineal SA. There was no recurrence at follow-up for 27 months up to May 2022. Perineal SA is rare and should be combined with patient history and imaging to ensure complete excision of the mass margins. Adherence to long-term postoperative follow-up is the key to curing this case

A common MET polymorphism harnesses HER2 signaling to drive aggressive squamous cell carcinoma.

c-MET receptors are activated in cancers through genomic events like tyrosine kinase domain mutations, juxtamembrane splicing mutation and amplified copy numbers, which can be inhibited by c-MET small molecule inhibitors. Here, we discover that the most common polymorphism known to affect MET gene (N375S), involving the semaphorin domain, confers exquisite binding affinity for HER2 and enables METN375S to interact with HER2 in a ligand-independent fashion. The resultant METN375S/HER2 dimer transduces potent proliferative, pro-invasive and pro-metastatic cues through the HER2 signaling axis to drive aggressive squamous cell carcinomas of the head and neck (HNSCC) and lung (LUSC), and is associated with poor prognosis. Accordingly, HER2 blockers, but not c-MET inhibitors, are paradoxically effective at restraining in vivo and in vitro models expressing METN375S. These results establish METN375S as a biologically distinct and clinically actionable molecular subset of SCCs that are uniquely amenable to HER2 blocking therapies

A common MET polymorphism harnesses HER2 signaling to drive aggressive squamous cell carcinoma.

c-MET receptors are activated in cancers through genomic events like tyrosine kinase domain mutations, juxtamembrane splicing mutation and amplified copy numbers, which can be inhibited by c-MET small molecule inhibitors. Here, we discover that the most common polymorphism known to affect MET gene (N375S), involving the semaphorin domain, confers exquisite binding affinity for HER2 and enables METN375S to interact with HER2 in a ligand-independent fashion. The resultant METN375S/HER2 dimer transduces potent proliferative, pro-invasive and pro-metastatic cues through the HER2 signaling axis to drive aggressive squamous cell carcinomas of the head and neck (HNSCC) and lung (LUSC), and is associated with poor prognosis. Accordingly, HER2 blockers, but not c-MET inhibitors, are paradoxically effective at restraining in vivo and in vitro models expressing METN375S. These results establish METN375S as a biologically distinct and clinically actionable molecular subset of SCCs that are uniquely amenable to HER2 blocking therapies