Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Generalization of n-ary Nambu algebras and beyond

The aim of this paper is to introduce $n$-ary Hom-algebra structures generalizing the $n$-ary algebras of Lie type enclosing $n$-ary Nambu algebras, $n$-ary Nambu-Lie algebras, $n$-ary Lie algebras, and $n$-ary algebras of associative type enclosing $n$-ary totally associative and $n$-ary partially associative algebras. Also, we provide a way to construct examples starting from an $n$-ary algebra and an $n$-ary algebras endomorphism. Several examples could be derived using this process

On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Deep learning segmentation of fibrous cap in intravascular optical coherence tomography images

Thin-cap fibroatheroma (TCFA) is a prominent risk factor for plaque rupture. Intravascular optical coherence tomography (IVOCT) enables identification of fibrous cap (FC), measurement of FC thicknesses, and assessment of plaque vulnerability. We developed a fully-automated deep learning method for FC segmentation. This study included 32,531 images across 227 pullbacks from two registries. Images were semi-automatically labeled using our OCTOPUS with expert editing using established guidelines. We employed preprocessing including guidewire shadow detection, lumen segmentation, pixel-shifting, and Gaussian filtering on raw IVOCT (r,theta) images. Data were augmented in a natural way by changing theta in spiral acquisitions and by changing intensity and noise values. We used a modified SegResNet and comparison networks to segment FCs. We employed transfer learning from our existing much larger, fully-labeled calcification IVOCT dataset to reduce deep-learning training. Overall, our method consistently delivered better FC segmentation results (Dice: 0.837+/-0.012) than other deep-learning methods. Transfer learning reduced training time by 84% and reduced the need for more training samples. Our method showed a high level of generalizability, evidenced by highly-consistent segmentations across five-fold cross-validation (sensitivity: 85.0+/-0.3%, Dice: 0.846+/-0.011) and the held-out test (sensitivity: 84.9%, Dice: 0.816) sets. In addition, we found excellent agreement of FC thickness with ground truth (2.95+/-20.73 um), giving clinically insignificant bias. There was excellent reproducibility in pre- and post-stenting pullbacks (average FC angle: 200.9+/-128.0 deg / 202.0+/-121.1 deg). Our method will be useful for multiple research purposes and potentially for planning stent deployments that avoid placing a stent edge over an FC.Comment: 24 pages, 9 figures, 2 tables, 2 supplementary figures, 3 supplementary table

Deciphering the Clinical Behaviour of Invasive Lobular Carcinoma of the Breast Defines an Aggressive Subtype

Background: Invasive lobular carcinoma (ILC), the most common special type of breast cancer (BC), has unique clinical behaviour and is different from invasive ductal carcinoma of no special type (IDC-NST). However, ILC further comprises a diverse group of tumours with distinct features. This study aims to examine the clinicopathological and prognostic features of different variants of ILC, with a particular focus on characterising aggressive subtypes. Methods: A large (n = 7140) well-characterised and histologically reviewed BC cohort with treatment and long-term follow-up data was investigated. The cohort was classified based on the WHO classification of tumours into main histological subtypes, including ILC and IDC-NST. ILCs were further classified into variants. Clinicopathological parameters and patient outcomes in terms of BC-specific survival (BCSS) and disease-free survival (DFS) were evaluated. Results: ILC constituted 11% of the cohort. The most common non-classic ILC variants were pleomorphic (pILC) and solid (sILC), constituting 19% of ILC. Compared to classic and related variants (alveolar, trabecular, papillary, and tubulolobular; cILC), pILC and sILC variants were associated with aggressive tumour characteristics. The histologic grade of ILC was an important prognostic variable. The survival patterns identified an aggressive ILC subtype encompassing pILC and high-grade sILC. These tumours, which comprised 14% of the cases, were associated with clinicopathological characteristics of poor prognosis and had high BC-specific death and recurrence rates compared not only to cILC (p < 0.001) but also to IDC-NST (p = 0.02) patients. Contrasting this, cILC patients had significantly longer BCSS and DFS than IDC-NST patients in the first 10 to 15 years of follow-up. Adjuvant chemotherapy did not improve the outcome of patients with aggressive ILC subtypes. Conclusions: pILC and high-grade sILC variants comprise an aggressive ILC subtype associated with poor prognostic characteristics and a poor response to chemotherapy. These results warrant confirmation in randomised clinical trials

Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

The clinical and biological significance of estrogen receptor-low positive breast cancer

Estrogen Receptor (ER) status in breast cancer (BC) is determined using immunohistochemistry (IHC) with nuclear expression in ≥1% of cells defined as ER-positive. BC with 1-9% expression (ER-low positive), is a clinically and biologically unique subgroup. In this study, we hypothesized that ER-low positive BC represents a heterogeneous group with a mixture of ER-positive and ER-negative tumor, which may explain their divergent clinical behavior. A large BC cohort (n=8171) was investigated and categorized into three groups: ER-low positive (1-9%), ER-positive (≥10%) and ER-negative (<1%) where clinicopathological and outcome characteristics were compared. A subset of ER-low positive cases was further evaluated using IHC, RNAscope and RT-PCR. PAM50 subtyping and ESR1 mRNA expression levels were assessed in ER-low positive cases within The Cancer Genome Atlas dataset. The reliability of image analysis software in assessment of ER expression in the ER-low positive category was also assessed. ER-low positive tumors constituted <2% of BC cases examined and showed significant clinicopathological similarity to ER-negative tumors. Most of these tumors were non-luminal types showing low ESR1 mRNA expression. Further validation of ER status revealed that 45% of these tumors were ER-negative with repeated IHC staining and confirmed by RNAscope and RT-PCR. ER-low positive tumors diagnosed on needle core biopsy were enriched with false positive ER staining. BCs with 10% ER behaved similarly to ER-positive, rather than ER-negative or low positive BCs. Moderate concordance was found in assessment of ER-low positive tumors, and this was not improved by image analysis. Routinely diagnosed ER-low positive BC includes a proportion of ER-negative cases. We recommend repeat testing of BC showing 1-9% ER expression and using a cut-off ≥10% expression to define ER positivity to help better inform treatment decisions

Nanomaterial-based Sensors for the Study of DNA Interaction with Drugs

The interaction of drugs with DNA has been searched thoroughly giving rise to an endless number of findings of undoubted importance, such as a prompt alert to harmful substances, ability to explain most of the biological mechanisms, or provision of important clues in targeted development of novel chemotherapeutics. The existence of some drugs that induce oxidative damage is an increasing point of concern as they can cause cellular death, aging, and are closely related to the development of many diseases. Because of a direct correlation between the response, strength/ nature of the interaction and the pharmaceutical action of DNA-targeted drugs, the electrochemical analysis is based on the signals of DNA before and after the interaction with the DNA-targeted drug. Nowadays, nanoscale materials are used extensively for offering fascinating characteristics that can be used in designing new strategies for drug-DNA interaction detection. This work presents a review of nanomaterials (NMs) for the study of drug-nucleic acid interaction. We summarize types of drug-DNA interactions, electroanalytical techniques for evidencing these interactions and quantification of drug and/or DNA monitoring

Management of Hepatic Angiomyolipoma

Preoperative diagnosis of hepatic angiomyolipoma is difficult, and the treatment for it remains controversial. The aim of this study is to review our experience in the treatment of hepatic angiomyolipoma and to propose a treatment strategy for this disease. We retrospectively collected the clinical, imaging, and pathological features of patients with hepatic angiomyolipoma. Immunohistochemical studies with antibodies for HMB-45, actin, S-100, cytokeratin, vimentin, and c-kit were performed. Treatment experience and long-term follow-up results are summarized. During a period of 9 years, 10 patients with hepatic angiomyolipoma were treated at our hospital. There was marked female predominance (nine patients). Nine patients received surgical resection without complications. One patient received nonoperative management with biopsy and follow-up. One patient died 11 months after surgery because of recurrent disease. We propose all symptomatic patients should receive surgical resection for hepatic angiomyolipoma. Conservative management with close follow-up is suggested in patients with asymptomatic tumors and meet the following criteria: (1) tumor size smaller than 5 cm, (2) angiomyolipoma proved through fine needle aspiration biopsy, (3) patients with good compliance, and (4) not a hepatitis virus carrier