Uniqueness for a Stochastic Inviscid Dyadic Model

For the deterministic dyadic model of turbulence, there are examples of initial conditions in $l^2$ which have more than one solution. The aim of this paper is to prove that uniqueness, for all $l^2$-initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.Comment: 13 pages, no figures. Submitted to the Proceedings of the American Mathematical Societ

Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A dyadic model on a tree

We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case

Smooth solutions for the dyadic model

We consider the dyadic model, which is a toy model to test issues of well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier-Stokes. Likewise we prove well-posedness for the inviscid problem (in a suitable regularity class) when the parameter corresponds to the strongest transport effect of the non-linearity

Positive and non-positive solutions for an inviscid dyadic model. Well-posedness and regularity

We improve regolarity and uniqueness results from the literature for the inviscid dyadic model. We show that positive dyadic is globally well-posed for every rate of growth $\beta$ of the scaling coefficients k_n = 2^{bn}. Some regularity results are proved for positive solutions, namely \sup_n n^{-a} k_n^{1/3} X_n(t) < \infty for a.e. t and \sup_n k_n^{1/3-1/(3b)} X_n(t) \leq C t^{-1/3}$for all$t$. Moreover it is shown that under very general hypothesis, solutions become positive after a finite time

Reproducibility and speed of landmarking process in cephalometric analysis using two input devices: mouse-driven cursor versus pen

To define if the new portable appliances, like smartphone, iPad, small laptop and tablet can be used in cephalometric tracing without dropping out the validity of any measurement. METHODS:We investigated and compared the reproducibility and the speed of landmarks identification process on lateral X-rays in two input devices: a mouse-driven cursor and a pen used as input means in mobile devices. One expert located 22 landmarks on 15 lateral X-rays in a repeated measure design two times, at time T1 and T2, after at least one month. The Intraclass Correlation coefficient was used to evaluate the reproducibility for each landmark tracing and the agreement between the value derived from both input devices. Also, the mean errors in measurements, the standard deviation and the Friedman Test significans (P < 0.05) between both input were statistically evaluated. RESULTS:All landmarks had a high agreement and the Friedman Test indicated statistically significant differences (P<0.05) for the identification of Na, Po, Pt, PNS, Ba, Pg, Gn, UIE, UIA, APOcc and PPOcc landmarks. CONCLUSIONS:Even if the mouse input give higher agreement for landmark tracing the differences are really minimal and they can be ignored in private practice. We suggest the adequacy of pen input in clinical setting

DepthFormer: Multimodal Positional Encodings and Cross-Input Attention for Transformer-Based Segmentation Networks

Most approaches for semantic segmentation use only information from color cameras to parse the scenes, yet recent advancements show that using depth data allows to further improve performances. In this work, we focus on transformer-based deep learning architectures, that have achieved state-of-the-art performances on the segmentation task, and we propose to employ depth information by embedding it in the positional encoding. Effectively, we extend the network to multimodal data without adding any parameters and in a natural way that makes use of the strength of transformers' self-attention modules. We also investigate the idea of performing cross-modality operations inside the attention module, swapping the key inputs between the depth and color branches. Our approach consistently improves performances on the Cityscapes benchmark

Oral hygiene management in patients with visual sensory disabilities

Aim: Oral hygiene maintenance is one of the most difficult tasks for visually impaired people. The aim of study was to investigate about knowledge on oral hygiene practices among patients with visual sensory disabilities by proposing an effective management in order to achieve and maintain oral health status of these patients. Methods:It was administered a questionnaire about oral health management to the patients with visual disabilities accessing to dental unit of “Mons. Di Liegro” Hospital of Gaeta. Results: The survey covered a sample of 49 patients, aged between 14 and 95 years. More than half (66%) was blind ( 65% of cases with primary blindness and the remain ing 35% with secondary blindness). Only 32.65% brushed their teeth 3 times a day; 68% of the surveyed patients limited home oral hygiene procedures to toothbrush and toothpaste; 79% used manual toothbrush; 49% of respondents report ed odontophobia (it was basically generated by pain) often due to bad experience during childhood. More than half declared a dental office attendance as needed. Conclusions: This study showed as, although starting from a compromised oral health and inadequate knowledge of oral hygiene practices, visual impaired/ blind patients were able to achieve and maintain a good level of oral hygiene, using the most appropriate techniques and instrument