On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts

Tewodros Amdeberhan and Armin Straub initiated the study of enumerating subfamilies of the set of (s,t)-core partitions. While the enumeration of (n+1,n+2)-core partitions into distinct parts is relatively easy (in fact it equals the Fibonacci number F_{n+2}), the enumeration of (n+1,n+2)-core partitions into odd parts remains elusive. Straub computed the first eleven terms of that sequence, and asked for a "formula," or at least a fast way, to compute many terms. While we are unable to find a "fast" algorithm, we did manage to find a "faster" algorithm, which enabled us to compute 23 terms of this intriguing sequence. We strongly believe that this sequence has an algebraic generating function, since a "sister sequence" (see the article), is OEIS sequence A047749 that does have an algebraic generating function. One of us (DZ) is pledging a donation of 100 dollars to the OEIS, in honor of the first person to generate sufficiently many terms to conjecture (and prove non-rigorously) an algebraic equation for the generating function of this sequence, and another 100 dollars for a rigorous proof of that conjecture. Finally, we also develop algorithms that find explicit generating functions for other, more tractable, families of (n+1,n+2)-core partitions.Comment: 12 pages, accompanied by Maple package. This version announces that our questions were all answered by Paul Johnson, and a donation to the OEIS, in his honor, has been mad

CD34 and CD105 Microvessels in Resected Bone Specimen May Implicate Wound Healing in MRONJ

Clinical treatment outcome of MRONJ (medication-related osteonecrosis of the jaw) surgery despite radical osseous removal and primary closure healing still shows differences in terms of outcome and disease recurrence. The study aims to assess the rate of angiogenesis of MRONJ lesions in order to understand the impact of angiogenesis and neoangiogenesis status on MRONJ surgical treatment outcome. This is the first study correlating microvessel density with prognosis in MRONJ surgically-treated patients. The immunohistochemical expression of CD34 and CD105 in MRONJ specimens obtained from surgically-treated patients was evaluated. The most vascularized areas detected by CD34 and CD105 were selected and the microvessel density value of the samples was registered. Samples were retrospectively divided according to the clinical outcome of MRONJ surgical treatment, dividing patients into two groups, “healed” and “not healed”. Statistical analysis was performed to assess if neovessels could influence treatment outcome in patients undergoing radical surgery. In the examined cohort, this value was highly predictive of better treatment outcome after radical surgery of MRONJ. Understanding of angiogenesis-dependent factors deserves further attention as a future target for MRONJ prevention and therapies

Diversity Assessment and DNA-Based Fingerprinting of Sicilian Hazelnut (Corylus avellana L.) Germplasm

The characterization of plant genetic resources is a precondition for genetic improvement and germplasm management. The increasing use of molecular markers for DNA-based genotype signature is crucial for variety identification and traceability in the food supply chain. We collected 75 Sicilian hazelnut accessions from private and public field collections, including widely grown varieties from the Nebrodi Mountains in north east Sicily (Italy). The germplasm was fingerprinted through nine standardized microsatellites (SSR) for hazelnut identification to evaluate the genetic diversity of the collected accessions, validating SSR discrimination power. We identified cases of homonymy and synonymy among acquisitions and the unique profiles. The genetic relationships illustrated by hierarchical clustering, structure, and discriminant analyses revealed a clear distinction between local and commercial varieties. The comparative genetic analysis also showed that the Nebrodi genotypes are significantly different from the Northern Italian, Iberian, and Turkish genotypes. These results highlight the need and urgency to preserve Nebrodi germplasm as a useful and valuable source for traits of interest employable for breeding. Our study demonstrates the usefulness of molecular marker analysis to select a reference germplasm collection of Sicilian hazelnut varieties and to implement certified plants’ production in the supply chain

Oral Secondary Syphilis in an HIV-Positive Transgender Patient: A Case Report and Review of the Literature

Background: Syphilis is a worldwide sexually transmitted infection caused by Treponema pallidum. In most cases, the oral manifestations of syphilis infection are associated with cutaneous involvement. However, the present case report is noteworthy since the oral lesions are the sole clinical sign in an HIV-positive transgender patient. Case presentations: We reported an uncommon case of secondary syphilis in a 37-year-old seropositive transgender male, whose diagnostic suspect was based only on oral mucosal lesions. The patient was referred to the Oral Medicine Unit for the presence of multiple undiagnosed painful oral lesions. The intraoral examination revealed the presence of white and red plaques on the right and the left buccal mucosa and several painful lesions localized on the upper and lower labial mucosa. No cutaneous lesions were observed. Considering the sexual history of the patient and clinical findings, secondary syphilis infection was suspected. The serologic analysis was conducted, and the diagnosis of syphilis was confirmed. Moreover, to exclude the presence of oral epithelial dysplasia or malignant disease, an incisional biopsy was performed. Discussion: Compared to the literature data, oral lesions as lone signs of secondary syphilis infection are uncommon, especially in HIV-positive patients. Syphilis and HIV coinfection create a concerning situation as they interact synergistically, leading to an increased risk of transmission and faster disease progression. Conclusions: This case report emphasizes the importance of considering syphilis as a diagnostic possibility, even when oral lesions are the only clinical manifestations, especially in HIV-positive patients. Comprehensive evaluation, including a detailed sexual history and careful oral examination, is essential for accurate diagnosis and appropriate management in such cases

Integrated Bayesian Approaches Shed Light on the Dissemination Routes of the Eurasian Grapevine Germplasm

The domestication and spreading of grapevine as well as the gene flow history had been described in many studies. We used a high-quality 7k SNP dataset of 1,038 Eurasian grape varieties with unique profiles to assess the population genetic diversity, structure, and relatedness, and to infer the most likely migration events. Comparisons of putative scenarios of gene flow throughout Europe from Caucasus helped to fit the more reliable migration routes around the Mediterranean Basin. Approximate Bayesian computation (ABC) approach made possible to provide a response to several questions so far remaining unsolved. Firstly, the assessment of genetic diversity and population structure within a well-covered dataset of ancient Italian varieties suggested the different histories between the Northern and Southern Italian grapevines. Moreover, Italian genotypes were shown to be distinguishable from all the other Eurasian populations for the first time. The entire Eurasian panel confirmed the east-to-west gene flow, highlighting the Greek role as a “bridge” between the Western and Eastern Eurasia. Portuguese germplasm showed a greater proximity to French varieties than the Spanish ones, thus being the main route for gene flow from Iberian Peninsula to Central Europe. Our findings reconciled genetic and archaeological data for one of the most cultivated and fascinating crops in the world

Sicilia—silicon carbide detectors for intense luminosity investigations and applications

Silicon carbide (SiC) is a compound semiconductor, which is considered as a possible alternative to silicon for particles and photons detection. Its characteristics make it very promising for the next generation of nuclear and particle physics experiments at high beam luminosity. Silicon Carbide detectors for Intense Luminosity Investigations and Applications (SiCILIA) is a project starting as a collaboration between the Italian National Institute of Nuclear Physics (INFN) and IMM-CNR, aiming at the realization of innovative detection systems based on SiC. In this paper, we discuss the main features of silicon carbide as a material and its potential application in the field of particles and photons detectors, the project structure and the strategies used for the prototype realization, and the first results concerning prototype production and their performance

Resistenza alla frattura di quattro materiali per protesi fissa provvisoria: valutazione comparativa in vitro.

Scopo del presente lavoro è stato quello di analizzare la resistenza alla frattura di quattro resine del commercio (Jet Kit, Duralay, Protemp 3 e Systempt C&B), usate per la fabbricazione di protesi parziali provvisorie fisse. Sono stati realizzati venti provini sperimentali di dimensioni standardizzate seguendo le istruzioni dei fabbricanti, suddivisi in quattro gruppi, uno per ciascuno dei quattro materiali testati. Cinque provini di ogni materiale sono stati inseriti in una macchina tipo T.E.M.A, bloccati tra due bracci, uno superiore ed uno inferiore, attraverso un sistema simile a quello di una morsa. La resistenza determinata dai provini sulla trazione esplicata dalla velocità di allontanamento (tre mm/min) effettuata dai bracci della macchina, veniva tradotta in Newton nel dispaly sul pannello di controllo; la prova di tensione si concludeva dopo la frattura del provino, identificando la forza registrata come ultimo carico di rottura. Una volta fratturato il provino, il carico ultimo di rottura veniva diviso per la nuova sezione della superficie, al fine di ottenere la “Tensione” del campione espressa in MPa. La stessa procedura è stata effettuata per tutti i provini. I risultati ottenuti sono stati esaminati con tests statistici per evidenziare eventuali differenze significative. Il Jet Kit è risultato il materiale più resistente alle prove di trazione con un valore elevato di carico di rottura. Nel Protemp le differenze di carico di rottura sono risultate minime in tutti i provini, a differenza del Systempt che presenta delle differenze significative. Tali dati evidenziano una buona resistenza alla trazione-pressione del Jet Kit dando prova dell’affidabilità del materiale

A tool in support of oral implantology

Il brevetto si riferisce ad un dispositivo che trova applicazione nella tecnica “flap-less” in chirurgia impiantare (inserimento di impianti senza esecuzione di lembo chirurgico), tecnica meno invasiva e traumatica per il paziente; esso consente di: - eseguire in modo diretto e preciso la rilevazione del profilo osseo esterno del sito impiantare - determinare l’angolazione ottimale dell’asse di foratura - guidare l’operazione di fresatura secondo l’asse prescelto Il dispositivo, grazie alla sua adattabilità e modularità è utilizzabile per eseguire siti implantari sia singoli che multipli ed è adattabile a tutte le variabili anatomiche che si possono presentare, è inoltre sterilizzabile e quindi riutilizzabile. Altre caratteristiche di rilievo sono la facilità d’uso e la semplicità costruttiva, che lo rendono competitivo rispetto ad altri sistemi più complessi e costosi presenti sul mercato