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We construct the partition function of small spin ½ systems defined on Ci, (Ci is a circle where are sitting the 2N spin variables. The spins interact with two body ferromagnetic interactions and are immersed in a magnetic field a one body interaction) and compare them with a polynomial truncation of the Riemann ξ function, the idea being to use some rigorous results on the zeros of the spin systems to obtain some information about the possible \"non negativity\" property of the Li-Keiper coefficients. The analysis is carried out up to 2N = 12 spin systems and a numerical experiment is performed up to 2N = 56. (For simplicity, only for the case where all the two body interaction strengths are equal is considered, i.e., the case where X(i, j)= X= e(-2K) for all (i, j); the magnetic field variable is given by z = e(-2h)). The zeros of the truncated ξ function are then on the unit circle but the associated values of the first few Li-Keiper coefficients so obtained holds only for a maximum value of N. A non zero lower bound to the values of the coefficients in the form of a conjecture is also presented. Possible developments are also indicated.

The aim of this work is to describe a new formula relating the nontrivial zeros of the Riemann Zeta function to the energy levels of the harmonic oscillator, which we call the \"Riemann wave,\" whose nodes are located at the height of the non-trivial zeros (on the Riemann Hypothesis, RH). We illustrate the formula by means of various Figures, and we present a calculation up to relatively \"high\" heights. Then, we propose formally an \"operator\" in agreement to the Polya's idea, which involves here the Lambert W function. We call it the \"Quantum Riemann Wave.\" Some approximations of the implicit equation for this operator, as well as a special interesting approximation (with the use of the Montgomery bound on the fluctuations S(t) and an additional factor), are also discussed and illustrated with some numerical experiments and Figures.

We develop an expression for the Li-Keiper coefficients λn in terms of k-blocks partitions, to begin with, for low values of n. The k-blocks partitions are given in terms of our cluster functions φn and the main point of this work lies in the emergence of an alternating sequence of values converging toward values of λn near the true values, i.e., increasing the index k of the blocks one obtains an increasing range of positivity of the Li-Keiper coefficients. With the contribution of k = 1 and k = 2 blocks, positivity of the λn is reached already until n = 26-27. The treatment is given here until k = 4 blocks up to n = 30. λn are all found to be positive.

In connection with the binomial transform, we establish a concrete asymptotic expression for the (trend, tiny part and complete) Li-Keiper coefficients in terms of elementary functions. The tiny fluctuations are computed up to n=5000 and a careful numerical analysis allows the derivation of an asymptotic formula using the extreme values of such fluctuations which is correct up to n=100000. Such an asymptotic expression - do not assume - but it is in agreement with the assumption of the truth of the Riemann Hypothesis.

Patients with mantle cell lymphoma (MCL) that fail induction treatment represent a difficult-to-treat population, where no standard therapy exists. We evaluated outcomes in patients with first relapsed-refractory (r/r) MCL after upfront high dose cytarabine including standard regimens. Overall survival (OS-2) and progression-free survival (PFS-2) were estimated from the time of salvage therapy. The previously described threshold of 24 months was used to define patients as early- or late-progressors (POD). Overall, 261 r/r MCL patients were included. Second-line regimens consisted of rituximab-bendamustine (R-B, 21%), R-B and cytarabine (R-BAC, 29%), ibrutinib (19%), and others (31%). The four groups were balanced in terms of clinicopathological features. Adjusting for age and early/late-POD, patients treated with R-BAC had significantly higher complete remission (63%) than comparators. Overall, Ibrutinib and R-BAC were associated with improved median PFS-2 [24 and 25 months, respectively], compared to R-B (13) or others (7). In patients with early-POD ( n  = 127), ibrutinib was associated with inferior risk of death than comparators (HR 2.41 for R-B, 2.17 for others, 2.78 for R-BAC). In patients with late-POD ( n  = 134), no significant differences were observed between ibrutinib and bendamustine-based treatments. Ibrutinib was associated with improved outcome in early-POD patients.

Recently, loss-of-function variants in TLR7 were identified in two families in which COVID-19 segregates like an X-linked recessive disorder environmentally conditioned by SARS-CoV-2. We investigated whether the two families represent the tip of the iceberg of a subset of COVID-19 male patients. This is a nested case-control study in which we compared male participants with extreme phenotype selected from the Italian GEN-COVID cohort of SARS-CoV-2-infected participants (<60 y, 79 severe cases versus 77 control cases). We applied the LASSO Logistic Regression analysis, considering only rare variants on young male subsets with extreme phenotype, picking up TLR7 as the most important susceptibility gene. Overall, we found TLR7 deleterious variants in 2.1% of severely affected males and in none of the asymptomatic participants. The functional gene expression profile analysis demonstrated a reduction in TLR7-related gene expression in patients compared with controls demonstrating an impairment in type I and II IFN responses. Young males with TLR7 loss-of-function variants and severe COVID-19 represent a subset of male patients contributing to disease susceptibility in up to 2% of severe COVID-19. Funded by private donors for the Host Genetics Research Project, the Intesa San Paolo for 2020 charity fund, and the Host Genetics Initiative. NCT04549831.

The Palatal Rugae are considered a useful human identification marker for both orthodontists and forensic personnel. The principal aim of the present study was to evaluate the stability of palatal rugae with a 3D-3D superimposition procedure following Slow Maxillary Expansion (SME), in order to assess whether they kept their uniqueness and validity for human identification, even after a specific dental treatment. For this purpose, a sample of 27 digital dental models - belonging to growing patients (13 males and 14 females), aged between 8.5 and 15 years, who underwent SME therapy - was retrospectively studied and compared with a control group of 27 untreated subjects - (13 males and 14 females). Digital dental models were obtained pre-treatment and at device removal; both were processed by means of an intraoral scanner. A superimposition procedure was thus performed to reach the minimum point-to-point distance between two models of palatal rugae. Intra- and inter-observer differences were statistically analyzed by paired Wilcoxon test and Intra-class Correlation coefficient (ICC), showing values larger than 0.93. There was no difference in Root-Mean-Square (RMS) values between untreated control subjects and subjects treated with Leaf Expander (p = 0.062). A RMS value of 0.43 was the threshold to distinguish the pooled group (“Untreated” and “Leaf”) from any mismatch. According to the obtained results, this study failed to reject the null hypothesis and presented no differences between the RMS values of the Test group and the RMS values of the untreated control group. This work highlighted the usefulness of 3D superimposition procedure for purposes of human identification, in subjects undergoing dental treatment. However, keeping in sight the forensic use of this technique as a helpful probation element in court, further studies should be performed to confirm these findings.

Collagen-based skin-like scaffolds (CBSS) are promising alternatives to skin grafts to repair wounds and injuries. In this work, we propose that the common marine invertebrate sea urchin represents a promising and eco-friendly source of native collagen to develop innovative CBSS for skin injury treatment. Sea urchin food waste after gonad removal was here used to extract fibrillar glycosaminoglycan (GAG)-rich collagen to produce bilayer (2D + 3D) CBSS. Microstructure, mechanical stability, permeability to water and proteins, ability to exclude bacteria and act as scaffolding for fibroblasts were evaluated. Our data show that the thin and dense 2D collagen membrane strongly reduces water evaporation (less than 5% of water passes through the membrane after 7 days) and protein diffusion (less than 2% of BSA passes after 7 days), and acts as a barrier against bacterial infiltration (more than 99% of the different tested bacterial species is retained by the 2D collagen membrane up to 48 h), thus functionally mimicking the epidermal layer. The thick sponge-like 3D collagen scaffold, structurally and functionally resembling the dermal layer, is mechanically stable in wet conditions, biocompatible in vitro (seeded fibroblasts are viable and proliferate), and efficiently acts as a scaffold for fibroblast infiltration. Thus, thanks to their chemical and biological properties, CBSS derived from sea urchins might represent a promising, eco-friendly, and economically sustainable biomaterial for tissue regenerative medicine.

Microbial colonization and biofilm formation drive infection persistence and the spread of antimicrobial resistance, particularly under flow conditions typical of medical and natural environments. Here, we combine spontaneously buckled wrinkled topographies with microfluidic platforms to investigate the adhesion of Pseudomonas aeruginosa and Staphylococcus aureus across shear rates of 0.4-200 s −1 . Wrinkled surfaces with tunable wavelengths (0.5-20 μ m) are fabricated and characterized using optical, atomic force, and scanning electron microscopy. Sinusoidal wrinkles with a 2 μ m wavelength reduce bacterial colonization by over 70% when oriented perpendicular to flow, while folded wrinkles of 5 μ m achieve more than 90% reduction across broader shear regimes and suppress biofilm formation by over 85% relative to flat controls. These topographies retain antifouling performance under pulsatile flow. This work demonstrates a scalable, chemical-free strategy for passive biofilm control through geometric surface design, enabling durable antimicrobial materials for biomedical and industrial applications. Microbial colonization and biofilm formation drive persistent infections on medical devices, often under fluid flow. Here, the authors engineer buckling-induced wrinkled and folded patterns with precisely defined geometries, integrate them into microfluidic channels, and show how wrinkling instabilities can be exploited to mitigate bacterial colonization under dynamic conditions.

In December 2019, an initial cluster of interstitial bilateral pneumonia emerged in Wuhan, China. A human-to-human transmission was assumed and a previously unrecognized entity, termed coronavirus disease-19 (COVID-19) due to a novel coronavirus (SARS-CoV-2) was described. The infection has rapidly spread out all over the world and Italy has been the first European country experiencing the endemic wave with unexpected clinical severity in comparison with Asian countries. It has been shown that SARS-CoV-2 utilizes angiotensin converting enzyme 2 (ACE2) as host receptor and host proteases for cell surface binding and internalization. Thus, a predisposing genetic background can give reason for interindividual disease susceptibility and/or severity. Taking advantage of the Network of Italian Genomes (NIG), here we mined whole-exome sequencing data of 6930 Italian control individuals from five different centers looking for ACE2 variants. A number of variants with a potential impact on protein stability were identified. Among these, three more common missense changes, p.(Asn720Asp), p.(Lys26Arg), and p.(Gly211Arg) were predicted to interfere with protein structure and stabilization. Rare variants likely interfering with the internalization process, namely p.(Leu351Val) and p.(Pro389His), predicted to interfere with SARS-CoV-2 spike protein binding, were also observed. Comparison of ACE2 WES data between a cohort of 131 patients and 258 controls allowed identifying a statistically significant (P value < 0.029) higher allelic variability in controls compared with patients. These findings suggest that a predisposing genetic background may contribute to the observed interindividual clinical variability associated with COVID-19, allowing an evidence-based risk assessment leading to personalized preventive measures and therapeutic options.