An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators

In this article we investigate spectral properties of the coupling $H+V_\lambda$, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\mathbb R^3$, $m>0$ and $V_\lambda$ is an electrostatic shell potential (which depends on a parameter $\lambda\in\mathbb R$) located on the boundary of a smooth domain in $\mathbb R^3$. Our main result is an isoperimetric-type inequality for the admissible range of $\lambda$'s for which the coupling $H+V_\lambda$ generates pure point spectrum in $(-m,m)$. That the ball is the unique optimizer of this inequality is also shown. Regarding some ingredients of the proof, we make use of the Birman-Schwinger principle adapted to our setting in order to prove some monotonicity property of the admissible $\lambda$'s, and we use this to relate the endpoints of the admissible range of $\lambda$'s to the sharp constant of a quadratic form inequality, from which the isoperimetric-type inequality is derived.Comment: 21 page

Accuracy of liquid-based brush cytology and HPV detection for the diagnosis and management of patients with oropharyngeal and oral cancer.

Objectives This study aims to evaluate the usefulness of liquid-based brush cytology for malignancy diagnosis and HPV detection in patients with suspected oropharyngeal and oral carcinomas, as well as for the diagnosis of tumoral persistence after treatment. Material and methods Seventy-five patients with suspicion of squamous cell carcinoma of the oropharynx or oral cavity were included. Two different study groups were analyzed according to the date of the sample collection: (1) during the first endoscopy exploration and (2) in the first control endoscopy after treatment for squamous cell carcinoma. Sensitivity, specificity, positive predictive value, negative predictive value, and accuracy for malignancy diagnosis as well as for HPV-DNA detection on brush cytologies were assessed. Results Before treatment, the brush cytology showed a sensitivity of 88%, specificity of 100%, and accuracy of 88%. After treatment, it showed a sensitivity of 71%, specificity of 77%, and accuracy of 75%. HPV-DNA detection in cytology samples showed a sensitivity of 85%, specificity of 100%, and accuracy of 91% before treatment and an accuracy of 100% after treatment. Conclusions Liquid-based brush cytology showed good accuracy for diagnosis of oropharyngeal and oral squamous cell carcinoma before treatment, but its value decreases after treatment. Nevertheless, it is useful for HPV-DNA detection, as well as to monitor the patients after treatment. Clinical relevance Brush cytology samples are reliable for the detection of HPV-DNA before and after treatment and may be a useful method to incorporate in the HPV testing guidelines

P53 in Penile Squamous Cell Carcinoma : A Pattern-Based Immunohistochemical Framework with Molecular Correlation

Penile squamous cell carcinomas harbouring mutations of TP53 have an increased risk of lymph node metastases and an impaired prognosis, but the mutational analysis of the TP53 gene is not available in many pathology laboratories. Although p53 immunohistochemistry (IHC) has been proposed as an alternative to the molecular analysis, the current method of evaluation of p53 IHC has many inaccuracies. The aim of our study was to determine, in a series of 40 penile tumours, if a recently described pattern-based framework of p53 IHC evaluation correlates better than the classical method with the TP53 mutational status. Our results show that the new method has a very good correlation with TP53 mutations (95% sensitivity; 92% specificity), higher than that of the classical method, and can be considered as a reliable surrogate of the TP53 mutational status. This new framework can help clinicians to better define risk groups and refine treatment strategies. p53 immunohistochemistry (IHC) has been proposed as a surrogate for TP53 mutations in penile squamous cell carcinomas (PSCC). We aimed to evaluate the performance of a pattern-based evaluation of p53 IHC in PSCC. Human papilloma virus (HPV) DNA testing, p16 and p53 IHC, and whole exome sequencing were performed in a series of 40 PSCC. p53 IHC was evaluated following a pattern-based framework and conventional p53 IHC evaluation. Out of 40 PSCC, 12 (30.0%) were HPV-associated, and 28 (70.0%) were HPV-independent. The agreement between the p53 IHC pattern-based evaluation and TP53 mutational status was almost perfect (k = 0.85). The sensitivity and accuracy of the pattern-based framework for identifying TP53 mutations were 95.5% and 92.5%, respectively, which were higher than the values of conventional p53 IHC interpretation (54.5% and 70.0%, respectively), whereas the specificity was the same (88.9%). In conclusions, the pattern-based framework improves the accuracy of detecting TP53 mutations in PSCC compared to the classical p53 IHC evaluation

Positive association of the hepatic lipase gene polymorphism c.514C > T with estrogen replacement therapy response

<p>Abstract</p> <p>Background</p> <p>Hepatic lipase (HL), an enzyme present in the hepatic sinusoids, is responsible for the lipolysis of lipoproteins. Human HL contains four polymorphic sites: G-250A, T-710C, A-763G, and C-514T single-nucleotide polymorphism (SNPs). The last polymorphism is the focus of the current study. The genotypes associated with the C-514T polymorphism are CC (normal homozygous - W), CT (heterozygous - H), and TT (minor-allele homozygous - M). HL activity is significantly impaired in individuals of the TT and CT genotypes. A total of 58 post-menopausal women were studied. The subjects were hysterectomized women receiving hormone replacement therapy consisting of 0.625 mg of conjugated equine estrogen once a day. The inclusion criteria were menopause of up to three years and normal blood tests, radiographs, cervical-vaginal cytology, and densitometry. DNA was extracted from the buccal and blood cells of all 58 patients using a commercially available kit (GFX^®- Amersham-Pharmacia, USA).</p> <p>Results</p> <p>Statistically significant reductions in triglycerides (t = 2.16; n = 58; p = 0.03) but not in total cholesterol (t = 0.14; n = 58; p = 0.89) were found after treatment. This group of good responders were carriers of the T allele; the CT and TT genotypes were present significantly more frequently than in the group of non-responders (p = 0.02 or p = 0.07, respectively). However, no significant difference in HDL-C (t = 0.94; n = 58; p = 0.35) or LDL-C (t = -0.83; n = 58; p = 0.41) was found in these patients.</p> <p>Conclusions</p> <p>The variation in lipid profile associated with the C-514T polymorphism is significant, and the T allele is associated with the best response to ERT.</p

Shell interactions for Dirac operators: on the point spectrum and the confinement

Spectral properties and the confinement phenomenon for the couplingH+Varestudied, whereH=-ia·¿+mßis the free Dirac operator inR3andVis a measure-valuedpotential. The potentialsVunder consideration are given in terms of surface measures onthe boundary of bounded regular domains inR3.A criterion for the existence of point spectrum is given, with applications to electrostaticshell potentials. In the case of the sphere, an uncertainty principle is developed and itsrelation with some eigenvectors of the coupling is shown.Furthermore, a criterion for generating confinement is given. As an application, someknown results about confinement on the sphere for electrostatic plus Lorentz scalar shellpotentials are generalized to regular surfaces.Peer Reviewe

Eigenvalue curves for generalized MIT bag models

We study spectral properties of Dirac operators on bounded domains O¿R3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter t¿R; the case t=0 corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of t, and we exploit this monotonicity to study the limits as t¿±8. We prove that if O is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all t large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as t¿-8, and we also analyze its first order asymptotics.Peer ReviewedPostprint (author's final draft

PD-L1 Expression in Non-Small Cell Lung Cancer: Data from a Referral Center in Spain

Anti-programmed cell death (PD1)/ligand-1 (PD-L1) checkpoint inhibitors have improved the survival of non-small cell lung cancer (NSCLC) patients. Additionally, PD-L1 has emerged as a predictive biomarker of response. Our goal was to examine the histological features of all PD-L1 cases of NSCLC analyzed in our center between 2017 and 2020, as well as to correlate the expression values of the same patient in different tested samples. PD-L1 immunohistochemistry (IHC) was carried out on 1279 external and internal samples: 482 negative (tumor proportion score, TPS &lt; 1%; 37.7%), 444 low-expression (TPS 1–49%; 34.7%) and 353 high-expression (TPS ≥ 50%; 27.6%). Similar results were observed with samples from our institution (N = 816). Significant differences were observed with respect to tumor histological type (p = 0.004); squamous carcinoma was positive in a higher proportion of cases than other histological types. There were also differences between PD-L1 expression and the type of sample analyzed (surgical, biopsy, cytology; p &lt; 0.001), with a higher frequency of negative cytology. In addition, there were cases with more than one PD-L1 determination, showing heterogeneity. Our results show strong correlation with the literature data and reveal heterogeneity between tumors and samples from the same patient, which could affect eligibility for treatment with immunotherapy