Stable Hamiltonian structures in dimension three are supported by open books

We prove that every stable Hamiltonian structure on a closed oriented three-manifold is stably homotopic to one which is supported (with suitable signs) by an open book.Comment: 30 pages, 6 figure

Nature of phase transitions in a probabilistic cellular automaton with two absorbing states

We present a probabilistic cellular automaton with two absorbing states, which can be considered a natural extension of the Domany-Kinzel model. Despite its simplicity, it shows a very rich phase diagram, with two second-order and one first-order transition lines that meet at a tricritical point. We study the phase transitions and the critical behavior of the model using mean field approximations, direct numerical simulations and field theory. A closed form for the dynamics of the kinks between the two absorbing phases near the tricritical point is obtained, providing an exact correspondence between the presence of conserved quantities and the symmetry of absorbing states. The second-order critical curves and the kink critical dynamics are found to be in the directed percolation and parity conservation universality classes, respectively. The first order phase transition is put in evidence by examining the hysteresis cycle. We also study the "chaotic" phase, in which two replicas evolving with the same noise diverge, using mean field and numerical techniques. Finally, we show how the shape of the potential of the field-theoretic formulation of the problem can be obtained by direct numerical simulations.Comment: 19 pages with 7 figure

Early-Life Critical Windows of Susceptibility to Manganese Exposure and Sex-Specific Changes in Brain Connectivity in Late Adolescence

Background: Early-life environmental exposures during critical windows (CWs) of development can impact life course health. Exposure to neuroactive metals such as manganese (Mn) during prenatal and early postnatal CWs may disrupt typical brain development, leading to persistent behavioral changes. Males and females may be differentially vulnerable to Mn, presenting distinctive CWs to Mn exposure. Methods: We used magnetic resonance imaging to investigate sex-specific associations between early-life Mn uptake and intrinsic functional connectivity in adolescence. A total of 71 participants (15-23 years old; 53% female) from the Public Health Impact of Manganese Exposure study completed a resting-state functional magnetic resonance imaging scan. We estimated dentine Mn concentrations at prenatal, postnatal, and early childhood periods using laser ablation-inductively coupled plasma-mass spectrometry. We performed seed-based correlation analyses to investigate the moderating effect of sex on the associations between Mn and intrinsic functional connectivity adjusting for age and socioeconomic status. Results: We identified significant sex-specific associations between dentine Mn at all time points and intrinsic functional connectivity in brain regions involved in cognitive and motor function: 1) prenatal: dorsal striatum, occipital/frontal lobes, and middle frontal gyrus; 2) postnatal: right putamen and cerebellum; and 3) early childhood: putamen and occipital, frontal, and temporal lobes. Network associations differed depending on exposure timing, suggesting that different brain networks may present distinctive CWs to Mn. Conclusions: These findings suggest that the developing brain is vulnerable to Mn exposure, with effects lasting through late adolescence, and that females and males are not equally vulnerable to these effects. Future studies should investigate cognitive and motor outcomes related to these associations

Intravitreal triamcinolone with photodynamic therapy for subfoveal choroidal neovascularisation in age related macular degeneration

Aims: To report the effects of intravitreal triamcinolone acetonide (iTAAC) injections as an adjunctive treatment to photodynamic therapy (PDT) with verteporfin for new subfoveal choroidal neovascularisation (CNV) in age related macular degeneration (AMD). Methods: We retrospectively reviewed the records of all AMD patients who had iTAAC within 6 weeks of their first PDT and had a follow up of one year or longer. The proportion of eyes after one year follow up that lost or gained ⩾15 and ⩾30 ETDRS letters, baseline and one year lesion greatest linear dimension (GLD), number of PDTs, and side effects were assessed. Results: Fourteen patients were evaluated. Eleven received one initial combined treatment and three received an additional combined treatment after 6 months. Median follow up was 18 months (range 12 to 25 months). Overall, 7% gained ⩾30 letters, 50% maintained stable vision, 14% lost 15–29 letters, and 29% lost ⩾30 letters. Overall, mean GLD increased from 2580 (SD 1088) µm to 3946 (SD 1503) µm (p = 0.01). The mean number of PDTs during the first year was 2.57. Side effects were mild intraocular pressure elevation in 28.5% and cataract progression in 50% of phakic eyes. Conclusions: iTAAC with PDT in AMD was found to be relatively safe and had reasonable results for lesions with some classic component