Zilber-Pink in Y(1)nY(1)^n: Beyond multiplicative degeneration

We establish Large Galois orbits conjectures for points of unlikely intersections of curves in $Y(1)^n$, upon assumptions on the intersection of such curves with the boundary $X(1)^n\backslash Y(1)^n$, in the Zilber-Pink setting. As a corollary, building on work of Habegger-Pila and Daw-Orr, we obtain new cases of the Zilber-Pink conjecture for curves in $Y(1)^n$.Comment: This content formerly appeared in arXiv:2310.04943v1, which has been split into two paper

Height bounds for certain exceptional points in some variations of Hodge structures

We consider smooth projective morphisms $f:X\rightarrow S$ of $K$-varieties with $S$ an open curve and $K$ a number field. We establish upper bounds of the Weil height $h(s)$ by $[K(s):K]$ at certain points $s\in S(\bar{K})$ that are "exceptional" with respect to the variation of Hodge structures R^n(f^{an})_{*}(\Q_{X^{an}_{\C}}), where $n=\dim X-1$. We work under the assumption that the generic special Mumford-Tate group of this variation is Sp(\mu,\Q), the variation degenerates in a strong fashion over some fixed point $s_0$ of a proper curve that contains $S$, the Hodge conjecture holds, and that what we define as a "good arithmetic model" exists for the morphism $f$ over the ring $\mathcal{O}_K$.Comment: Preliminary version, 80 pages. Comments are welcome

Repeated delivery of chlorhexidine chips for the treatment of peri‐implantitis: A multicenter, randomized, comparative clinical trial

BackgroundPeri‐implantitis is a challenging condition to manage and is frequently treated using non‐surgical debridement. The local delivery of antimicrobial agents has demonstrated benefit in mild to moderate cases of peri‐implantitis. This study compared the safety and efficacy of chlorhexidine gluconate 2.5 mg chip (CHX chips) as an adjunctive treatment to subgingival debridement in patients afflicted with peri‐implantitis.MethodsA multicenter, randomized, single‐blind, two‐arm, parallel Phase‐3 study was conducted. Peri‐implantitis patients with implant pocket depths (IPD) of 5‐8 mm underwent subgingival implant surface debridement followed by repeated bi‐weekly supragingival plaque removal and chlorhexidine chips application (ChxC group) for 12 weeks, or similar therapy but without application of ChxC (control group). All patients were followed for 24 weeks. Plaque and gingival indices were measured at every visit whereas IPD, recession, and bleeding on probing were assessed at 8, 12, 16, 24 week.ResultsA total of 290 patients were included: 146 in the ChxC group and 144 in the control. At 24 weeks, a significant reduction in IPD (P = 0.01) was measured in the ChxC group (1.76 ± 1.13 mm) compared with the control group (1.54 ± 1.13 mm). IPD reduction of ≥2 mm was found in 59% and 47.2% of the implants in the ChxC and control groups, respectively (P = 0.03). Changes in gingival recession (0.29 ± 0.68 mm versus 0.15 ± 0.55 mm, P = 0.015) and relative attachment gain (1.47 ± 1.32 mm and 1.39 ± 1.27 mm, P = 0.0017) were significantly larger in the ChxC group. Patients in the ChxC group that were < 65 years exhibited significantly better responses (P < 0.02); likewise, non‐smokers had similarly better response (P < 0.02). Both protocols were well tolerated, and no severe treatment‐related adverse events were recorded throughout the study.ConclusionsPatients with peri‐implantitis that were treated with an intensive treatment protocol of bi‐weekly supragingival plaque removal and local application of chlorhexidine chips had greater mean IPD reduction and greater percentile of sites with IPD reduction of ≥2 mm as compared with bi‐weekly supra‐gingival plaque removal.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166183/1/jper10672.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/166183/2/jper10672_am.pd