Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

The effect of surface roughness on early in vivo plaque colonization on titanium

This study assesses in vivo the surface roughness necessary to reduce plaque colonization on titanium after 24 hours. Three groups of 16 titanium disks were assigned to 3 different polishing groups (A, B, and C). The roughness was evaluated with a laser profilometer and the morphology with a scanning electron microscope (SEM). Eight volunteers were enrolled and two stents were applied in the mandibular posterior region of each. Each stent supported 3 disks, one per group. The volunteers suspended oral hygiene for 24 hours, after which the stents were removed; one was processed for evaluation of the adherent biomass and the other for SEM study. On each specimen a global area of 100 x 125 \u3bcm was examined with SEM. The area was composed of five 20 x 25 \u3bcm randomly selected fields. For each field the density of bacteria and the morphotypes were recorded. The data quoted for the global area are cumulative of those observed in the 20 x 25 \u3bcm fields. Group A had a significantly smoother surface than groups B and C. The adherent microbial biomass determination and SEM evaluation revealed that group A contained less bacteria than the roughest group. The bacterial population was composed of cocci in group A, and of cocci and short and long rods in groups B and C. We conclude that a titanium surface with Ra 64 0.088 \u3bcm and Rz 64 1.027 \u3bcm strongly inhibits accumulation and maturation of plaque at the 24-hour time period and that such smoothness can be achieved in transgingival and healing implant components

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future states. The method consists in applying iteratively a data assimilation step, here an ensemble Kalman filter, and a neural network. Data assimilation is used to optimally combine a surrogate model with sparse noisy data. The output analysis is spatially complete and is used as a training set by the neural network to update the surrogate model. The two steps are then repeated iteratively. Numerical experiments have been carried out using the chaotic 40-variables Lorenz 96 model, proving both convergence and statistical skill of the proposed hybrid approach. The surrogate model shows short-term forecast skill up to two Lyapunov times, the retrieval of positive Lyapunov exponents as well as the more energetic frequencies of the power density spectrum. The sensitivity of the method to critical setup parameters is also presented: the forecast skill decreases smoothly with increased observational noise but drops abruptly if less than half of the model domain is observed. The successful synergy between data assimilation and machine learning, proven here with a low-dimensional system, encourages further investigation of such hybrids with more sophisticated dynamics

Recent progress in understanding and predicting Atlantic decadal climate variability

Recent Atlantic climate prediction studies are an exciting new contribution to an extensive body of research on Atlantic decadal variability and predictability that has long emphasized the unique role of the Atlantic Ocean in modulating the surface climate. We present a survey of the foundations and frontiers in our understanding of Atlantic variability mechanisms, the role of the Atlantic Meridional Overturning Circulation (AMOC), and our present capacity for putting that understanding into practice in actual climate prediction systems

Structural decomposition of decadal climate prediction errors: A Bayesian approach

Decadal climate predictions use initialized coupled model simulations that are typically affected by a drift toward a biased climatology determined by systematic model errors. Model drifts thus reflect a fundamental source of uncertainty in decadal climate predictions. However, their analysis has so far relied on ad-hoc assessments of empirical and subjective character. Here, we define the climate model drift as a dynamical process rather than a descriptive diagnostic. A unified statistical Bayesian framework is proposed where a state-space model is used to decompose systematic decadal climate prediction errors into an initial drift, seasonally varying climatological biases and additional effects of co-varying climate processes. An application to tropical and south Atlantic sea-surface temperatures illustrates how the method allows to evaluate and elucidate dynamic interdependencies between drift, biases, hindcast residuals and background climate. Our approach thus offers a methodology for objective, quantitative and explanatory error estimation in climate predictions

Electron Polarization Operators

Two types of electron polarization operators are surveyed. A three- vector operator is described that is appropriate for calculations involving plane- wave states. A four-vector operator is described that can be used for taking account of external electromagnetic fields. (T.F.H.

Consensus Report : 2nd European Workshop on Tobacco Use Prevention and Cessation for Oral Health Professionals

Tobacco use has been identified as a major risk factor for oral disorders such as cancer and periodontal disease. Tobacco use cessation (TUC) is associated with the potential for reversal of precancer, enhanced outcomes following periodontal treatment, and better periodontal status compared to patients who continue to smoke. Consequently, helping tobacco users to quit has become a part of both the responsibility of oral health professionals and the general practice of dentistry. TUC should consist of behavioural support, and if accompanied by pharmacotherapy, is more likely to be successful. It is widely accepted that appropriate compensation of TUC counselling would give oral health professionals greater incentives to provide these measures. Therefore, TUC-related compensation should be made accessible to all dental professionals and be in appropriate relation to other therapeutic interventions. International and national associations for oral health professionals are urged to act as advocates to promote population, community and individual initiatives in support of tobacco use prevention and cessation (TUPAC) counselling, including integration in undergraduate and graduate dental curricula. In order to facilitate the adoption of TUPAC strategies by oral health professionals, we propose a level of care model which includes 1) basic care: brief interventions for all patients in the dental practice to identify tobacco users, assess readiness to quit, and request permission to re-address at a subsequent visit, 2) intermediate care: interventions consisting of (brief) motivational interviewing sessions to build on readiness to quit, enlist resources to support change, and to include cessation medications, and 3) advanced care: intensive interventions to develop a detailed quit plan including the use of suitable pharmacotherapy. To ensure that the delivery of effective TUC becomes part of standard care, continuing education courses and updates should be implemented and offered to all oral health professionals on a regular basis

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions