Singular hypersurfaces characterizing the Lefschetz properties

In the paper untitled "Laplace equations and the Weak Lefschetz Property" the authors highlight the link between rational varieties satisfying a Laplace equation and artinian ideals that fail the Weak Lefschetz property. Continuing their work we extend this link to the more general situation of artinian ideals failing the Strong Lefschetz Property. We characterize the failure of SLP (that includes WLP) by the existence of special singular hypersurfaces (cones for WLP). This characterization allows us to solve three problems posed by Migliore and Nagel and to give new examples of ideals failing the SLP. Finally, line arrangements are related to artinian ideals and the unstability of the associated derivation bundle is linked with the failure of SLP. Moreover we reformulate the so-called Terao's conjecture for free line arrangements in terms of artinian ideals failing the SLP

Laplace equations, Lefschetz properties and line arrangements

In this note we generalize the main result in the previous work on JLMS on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimally generation of ideals generated by power of linear forms by the conguration of their dual points in the projective plane. Finally we show the equivalence among failing SLP, Laplace equations and unexpected curves

On varieties with higher osculating defect

In this paper, using the method of moving frames, we generalise some of Terracini's results on varieties with tangent defect. In particular, we characterise varieties with higher order osculating defect in terms of Jacobians of higher fundamental forms and moreover we characterise varieties with "small" higher fundamental forms as contained in scrolls.Comment: AMS-LaTeX; 17 pages. To appear in Revista Matem\'atica Iberoam\'erican

Companion varieties for root systems and Fermat arrangements

Unexpected hypersurfaces are a brand name for some special linear systems. They were introduced around 2017 and are a field of intensive study since then. They attracted a lot of attention because of their close tights to various other areas of mathematics including vector bundles, arrangements of hyperplanes, geometry of projective varieties. Our research is motivated by the what is now known as the BMSS duality, which is a new way of deriving projective varieties out of already constructed. The last author coined the concept of companion surfaces in the setting of unexpected curves admitted by the $B_3$ root system. Here we extend this construction in various directions. We revisit the configurations of points associated to either root systems or to Fermat arrangements and we study the geometry of the associated varieties and their companions.Comment: 22 pages, collaboration started at the Oberwolfach workshop on Lefschetz Properties in Algebra, Geometry and Combinatorics held in September/October 202

Perioperative characterization of anastomotic doughnuts with high-resolution probe-based confocal laser endomicroscopy in colorectal cancer surgery: a feasibility study.

BACKGROUND: Confocal laser enables in vivo real-time histopathology of the mucosa layer of gastrointestinal tract. The aim of this study was to assess the feasibility and the role of probe-based confocal laser endomicroscopy in extemporary examination of staple rings of patients with colorectal cancer. METHODS: This was a prospective, single-center pilot study. Patients who underwent end-to-end stapled surgical resection for colorectal cancer were included. Confocal imaging was analyzed with great attention to image quality evaluation of cellular morphology and cellular structures of the serosal, muscular, and mucosal layers of the doughnuts than comparing results with definitive histopathology. RESULTS: Twenty-six doughnuts were analyzed. Real-time video sequences were obtained in all patients, with a total of 204 mosaic images. For each doughnut, most of the images were adequate for evaluation of cellular morphology and cellular structure of the serosal, muscular, and mucosal layers. CONCLUSIONS: Perioperative assessment of doughnut tissues in patients with colorectal cancer by confocal laser endomicroscopy is feasible and safe. Prospective studies are warranted for further evaluation of the clinical impact of this technology during surgery

The proliferation marker Chromatin Assembly Factor-1 is of clinical value in predicting the biological behaviour of salivary gland tumours.

Salivary gland tumours (SGT) constitute a diagnostically challenging group of neoplasms with frequently unpredictable clinical outcome. The proliferation rate facilitates the identification of aggressive SGT. The Chromatin Assembly Factor-1 (CAF-1) is a major epigenetic regulator of nuclear chromatin organization during DNA replication. It plays a critical function in human tumourigenesis and has been proposed as a new proliferation and prognostic marker for some malignancies. This study focused on the role of CAF-1/p60 protein as a marker of clinical value for SGT. The expression of CAF-1/p60 was evaluated by immunohistochemistry on a retrospective series of 362 surgically excised benign and malignant SGT with different histogenesis and, when available, on fine-needle pre-surgical cytological biopsies. The resulting data were compared with traditional prognostic parameters, including the expression of the routine proliferation marker ki67/MIB1. CAF-1/p60 was detectable in all SGT, with highest degree of expression in metastasizing malignant tumours. Moreover, the cases of benign tumours which progressed to carcinoma during the follow-up, showed significantly higher CAF-1/p60 expression than non-progressing benign SGT, both on histological sections and cytological smears of the primary tumour. Cox's multiple regression analysis selected CAF-1/p60 expression as the best independent predictor of cancer development for benign SGT (p<0.0001), and the best independent predictor of metastasis onset for malignant tumours (p<0.0004). Overexpression of CAF-1/p60, on histological and/or cytological samples, characterizes malignant SGT with aggressive behaviour, irrespective of their specific histotype, and allows the early diagnosis of progression toward malignancy of morphologically benign tumours

The disruption of the CCDC6 - PP4 axis induces a BRCAness like phenotype and sensitivity to PARP inhibitors in high-grade serous ovarian carcinoma

Treatment with PARP inhibitors (PARPi) is primarily effective against high-grade serous ovarian cancers (HGSOC) with BRCA1/2 mutations or other deficiencies in homologous recombination (HR) repair mechanisms. However, resistance to PARPi frequently develops, mostly as a result of BRCA1/2 reversion mutations. The tumour suppressor CCDC6 is involved in HR repair by regulating the PP4c phosphatase activity on γH2AX. In this work, we reported that in ovarian cancer cells, a physical or functional loss of CCDC6 results synthetic lethal with the PARP-inhibitors drugs, by affecting the HR repair. We also unravelled a role for CCDC6 as predictive marker of PARPi sensitivity in ovarian cancer, and the impact of CCDC6 downregulation in overcoming PARPi resistance in these tumours

Retrospective observational multicenter study on patients treated with a non-animal origin cross-linked hyaluronic acid with different molecular weights for nasolabial folds

Background: According to the American Academy of Aesthetic Plastic Surgeons, more than 11 million cosmetic surgical and nonsurgical procedures were performed by board-certified plastic surgeons, dermatologists and otolaryngologists in the United States, totaling more than 12 billion dollars. Of that total, more than 7 billion was spent on surgical procedures and more than 5 billion was spent on nonsurgical procedures. More than 1,872,172 people received Hyaluronic Acid (HA) injections in 2013. Moreover, filler treatments are the most popular procedures performed by dermatologists. Objective: Evaluate, with a new imaging system, durability, efficacy and safety of a nasolabial fold treatment with a cross-linked HA of non-animal origin with different molecular weights. Material and methods: A cross-linked HA (25 mg/ml, 1000-2000 kDa, 23 ± 3 Newton [N] extrusion force, 1,4-Butanediol Diglycidyl Ether (BDDE) content < 0.1 ppm) was used in order to perform the treatment. The product is commercially available with the trademark Aliaxin®GP (Global Performance) and distributed by IBSA Farmaceutici Italia Srl. 25 female subjects aged 40 and 60 years with a photoageing level III according Rubin or type III according Glogau were recruited for the treatment and 0.5 ml of the product were injected for single nasolabial fold. The aesthetic result and the duration of the aesthetic correction were evaluated by the analysis of the skin microreliefs through confocal microscopy and by Glogau's Scale. Additionally, pictures of each patient were collected by Canon PowerShot G10 Digital Camera (14.7 megapixels) before and after treatment. Below the description of the experimental schedule: T0: Baseline, evaluation and treatment; T1: second visit, 4 months after the treatment; T2: third visit, 6 months after the treatment. Results: From 25 patients, 150 silicone casts were obtained: 75 casts of the right nasolabial fold and 75 casts of the left nasolabial fold. Roughness arithmetical average (Ra) was assessed by profilometry. This parameter represents the arithmetic mean deviation of the profile points compared to the average value. The Ra of the right fold at T2 decreased by 50% versus T0 and by 40% compared to T1; Ra of the left fold at T2 decreased by the 45% versus T0 and by 35% compared to T1. No side effects were reported during the observation period beyond mild symptoms (pain, sensation of heat, reddening in the injection site) also described by the product technical sheet. Conclusion: The results proved the efficacy and safety of the nasolabial folds treatment with the tested product and the durability of the aesthetic correction