Hadamard Products of Symbolic Powers and Hadamard Fat Grids

In this paper we address the question if, for points P, Q ? P-2, I(P)I-m(*)(Q)(n) = I(P(*)Q)(m+n-1 )and we obtain different results according to the number of zero coordinates in P and Q. Successively, we use our results to define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicities. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed

From green-energy to green-logistics: a pilot study in an Italian port area

Abstract An ongoing two-year research is performing with the general objective to assess the feasibility of a system integrating the production of green-energy and its consumption inside and close to port areas for mobility services. The system is composed by two elements: (a) a "sea-to-grid" technological component harvesting and producing electrical energy from sea waves; and (b) a "green" logistic service based on the use of Fully Electric Vehicles (FEVs). A pilot study will be conducted near an Italian port area supporting passengers and freight mobility between a port and a backward (sub)-urban area. The proposed system is within the environmental goals set by the EU (Europe 2020 Strategy) and the Italian Government (National Energy Masterplan). Indeed, the energy-producing technology reduces dependence from traditional energy sources (coal, gas, oil) and consequently reduces their negative effects (greenhouse gases, air pollution, etc.). Considering that the energy is produced by sea waves, the system transfers the entire amount of produced (green) energy to the electric vehicles. The system will be experimented in a medium size urbanized area and the energy will be produced in a small size port

Enamel interproximal reduction during treatment with clear aligners: digital planning versus OrthoCAD analysis

Background The aim of the study was to compare the amount of interproximal enamel reduction (IPR) provided on ClinCheck software with the amount of IPR carried out by the orthodontist during treatment with clear aligners. Methods 30 subjects (14 males, 16 females; mean age of 24.53 +/- 13.41 years) randomly recruited from the Invisalign account of the Department of Orthodontics at the University of Rome "Tor Vergata" from November 2018 to October 2019, were collected according to the following inclusion criteria: mild to moderate dento-alveolar discrepancy (1.5-6.5 mm); Class I canine and molar relationship; full permanent dentition (excluding third molars); both arches treated only using Comprehensive Package by Invisalign system; treatment plan including IPR. Pre- (T0) and post-treatment (T1) digital models (.stl files), created from an iTero scan, were collected from all selected patients. The OrthoCAD digital software was used to measure tooth mesiodistal width in upper and lower arches before (T0) and at the end of treatment (T1) before any refinement. The widest mesio-distal diameter was measured for each tooth excluding molars by "Diagnostic" OrthoCAD tool. The total amount of IPR performed during treatment was obtained comparing the sum of mesio-distal widths of all measured teeth at T0 and T1. Significant T1-T0 differences were tested with dependent sample t-test (P < 0.05). Results In the upper arch, IPR was digitally planned on average for 0.62 mm while in the lower arch was on average for 1.92 mm. As for the amount of enamel actually removed after IPR performing, it was on average 0.62 mm in the maxillary arch. In the mandibular arch, the mean of IPR carried out was 1.93 mm. The difference between planned IPR and performed IPR is described: this difference was on average 0.00 mm in the upper arch and 0.01 in the lower arch. Conclusions The amount of enamel removed in vivo corresponded with the amount of IPR planned by the Orthodontist using ClinCheck software

The algebraic Bethe ansatz for open vertex models

We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A^{(2)}_{2n},A^{(2)}_{2n-1},B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ Lie algebras. By the method, we solve these models with the trivial K matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the $B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ models with some non-trivial diagonal K-matrices (one free parameter case) by the algebraic Bethe ansatz.Comment: Latex, 35 pages, new content and references are added, minor revisions are mad

On the Uq[sl(2)]{\cal{U}}_{q}[sl(2)] Temperley-Lieb reflection matrices

This work concerns the boundary integrability of the spin-s ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented. It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free parameters. Moreover, some particular solutions are discussed.Comment: LaTex 17 page

Case Report: Filling Defect in Posterior Semicircular Canal on MRI With Balanced Steady-State Gradient-Echo Sequences After Labyrinthine Ischemia in the Common Cochlear Artery Territory as an Early Sign of Fibrosis

We describe a rare case of posterior semicircular canal (PSC) fibrosis following acute labyrinthine ischemia in the territory supplied by the common cochlear artery (CCA) and review the relevant literature. A 71-year-old man with multiple vascular risk factors presented 12 days after the onset of acute vertigo and profound left-sided hearing loss. Right-beating spontaneous nystagmus with downbeat components elicited by mastoid vibrations and headshaking was detected. The video head impulse test (vHIT) revealed an isolated hypofunction of the left PSC, whereas vestibular evoked myogenic potentials (VEMPs) showed ipsilateral saccular loss. The clinical presentation and instrumental picture were consistent with acute ischemia in the territory supplied by left CCA. Compared to previous imaging, a new MRI of the brain with 3D-FIESTA sequences highlighted a filling defect in the left PSC, consistent with fibrosis. Hearing function exhibited mild improvement after steroid therapy and hyperbaric oxygen sessions, whereas vHIT abnormalities persisted over time. To the best of our knowledge, this is the only case in the literature reporting a filling defect on MRI, consistent with semicircular canal fibrosis following acute labyrinthine ischemia. Moreover, PSC fibrosis was related with poor functional outcome. We therefore suggest using balanced steady-state gradient-echo sequences a few weeks following an acute lesion of inner ear sensors to detect signal loss within membranous labyrinth consistent with post-ischemic fibrosis. Besides addressing the underlying etiology, signal loss might also offer clues on the functional behavior of the involved sensor over time. In cases of acute loss of inner ear function, a careful bedside examination supplemented by instrumental assessments, including vHIT and VEMPs, of vestibular receptors and afferents may be completed by MRI with balanced steady-state gradient-echo sequences at a later time to confirm the diagnosis and address both etiology and functional outcome

On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary

Motivated by a study of the crossing symmetry of the `gemini' representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to the Yang--Baxter equation satisfying the crossing condition (that is, integrable quantum spin chains). We show that every crossing representation of the Temperley--Lieb algebra appears in this construction, and in particular that this construction builds new representations. We extend these to new representations of the blob algebra, which build new solutions to the Boundary Yang--Baxter equation (i.e. open spin chains with integrable boundary conditions). We prove that the open spin chain Hamiltonian derived from Sklyanin's commuting transfer matrix using such a solution can always be expressed as the representation of an element of the blob algebra, and determine this element. We determine the representation theory (irreducible content) of the new representations and hence show that all such Hamiltonians have the same spectrum up to multiplicity, for any given value of the algebraic boundary parameter. (A corollary is that our models have the same spectrum as the open XXZ chain with nondiagonal boundary -- despite differing from this model in having reference states.) Using this multiplicity data, and other ideas, we investigate the underlying quantum group symmetry of the new Hamiltonians. We derive the form of the spectrum and the Bethe ansatz equations.Comment: 43 pages, multiple figure

Aurora Kinase A expression predicts platinum-resistance and adverse outcome in high-grade serous ovarian carcinoma patients

High-Grade Serous Ovarian Carcinoma (HGSOC) is the predominant histotype of epithelial ovarian cancer (EOC), characterized by advanced stage at diagnosis, frequent TP53 mutation, rapid progression, and high responsiveness to platinum-based-chemotherapy. To date, standard first-line-chemotherapy in advanced EOC includes platinum salts and paclitaxel with or without bevacizumab. The major prognostic factor is the response duration from the end of the platinum-based treatment (platinum-free interval) and about 10-0 % of EOC patients bear a platinum-refractory disease or develop early resistance (platinum-free interval shorter than 6 months). On these bases, a careful selection of patients who could benefit from chemotherapy is recommended to avoid unnecessary side effects and for a better disease outcome. In this retrospective study, an immunohistochemical evaluation of Aurora Kinase A (AURKA) was performed on 41 cases of HGSOC according to platinum-status. Taking into account the number and intensity of AURKA positive cells we built a predictive score able to discriminate with high accuracy platinum-sensitive patients from platinum-resistant patients (p < 0.001). Furthermore, we observed that AURKA overexpression correlates to worse overall survival (p = 0.001; HR 0.14). We here suggest AURKA as new effective tool to predict the biological behavior of HGSOC. Particularly, our results indicate that AURKA has a role both as predictor of platinum-resistance and as prognostic factor, that deserves further investigation in prospective clinical trials. Indeed, in the era of personalized medicine, AURKA could assist the clinicians in selecting the best treatment and represent, at the same time, a promising new therapeutic target in EOC treatment