The Influence of Mucosa Thickness and Quality on Single Implant Tissue Stability: A Prospective Controlled Clinical Trial.

This prospective controlled clinical trial investigated the possible correlation among mucosa thickness, mucosa height, and width of keratinized mucosa on the contour changes of the peri-implant soft tissue collar over a period of 12 months. Forty patients were selected to undergo implant placement. Impressions were taken with polyether impression material at delivery of the final restorations (baseline) and at 1, 3, 6, and 12 months. Master casts were fabricated and scanned using an indirect digitalization. Baseline and corresponding follow-up scans were then virtually superimposed and matched. At 1 year, 20 patients who received the buccal pedicle flap showed an average thickness increase of 1.49 mm (ρs = 0.95; range: 0.01 to 2.56 mm), whereas the 5 patients who received a connective tissue graft at second-stage surgery reported an average thickness increase of 0.33 mm (ρs = 0.70; range: -0.62 to 1.23 mm). Finally, the remaining 15 patients who did not receive any soft tissue grafting nor any type of plastic surgery showed an average mucosa thickness increase of 0.51 mm (ρs = 0.28; range: -2.33 to 2.52 mm).

Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems.

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In condensed matter systems, order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable and spontaneously change their global state on relatively short time scales. Here we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state on finite time scales and off-equilibrium behavior: the nonsymmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. Our results might explain what is observed in several living systems and are consistent with recent experimental data on bird flocks and other animal groups.

Local equilibrium in bird flocks.

The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. The effect of this off-equilibrium element is well studied theoretically, but its impact on actual biological groups deserves more experimental attention. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accodomates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment happens on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws.

Information transfer is an essential factor in determining the robustness of biological systems with distributed control. The most direct way to study the mechanisms ruling information transfer is to experimentally observe the propagation across the system of a signal triggered by some perturbation. However, this method may be inefficient for experiments in the field, as the possibilities to perturb the system are limited and empirical observations must rely on natural events. An alternative approach is to use spatio-temporal correlations to probe the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. Here we test this method on models of collective behaviour in their deeply ordered phase by using ground truth data provided by numerical simulations in three dimensions. We compare two models characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an underdamped inertial dynamics. By using dynamic finite-size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.

GReTA-A Novel Global and Recursive Tracking Algorithm in Three Dimensions.

Tracking multiple moving targets allows quantitative measure of the dynamic behavior in systems as diverse as animal groups in biology, turbulence in fluid dynamics and crowd and traffic control. In three dimensions, tracking several targets becomes increasingly hard since optical occlusions are very likely, i.e., two featureless targets frequently overlap for several frames. Occlusions are particularly frequent in biological groups such as bird flocks, fish schools, and insect swarms, a fact that has severely limited collective animal behavior field studies in the past. This paper presents a 3D tracking method that is robust in the case of severe occlusions. To ensure robustness, we adopt a global optimization approach that works on all objects and frames at once. To achieve practicality and scalability, we employ a divide and conquer formulation, thanks to which the computational complexity of the problem is reduced by orders of magnitude. We tested our algorithm with synthetic data, with experimental data of bird flocks and insect swarms and with public benchmark datasets, and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap. The results obtained on very heterogeneous data show the potential applicability of our method to the most diverse experimental situations.

Emergence of collective changes in travel direction of starling flocks from individual birds' fluctuations.

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external alarm cue, directional switching can also emerge from the intrinsic fluctuations in individual behaviour. However, the cause and the mechanism by which such collective changes of direction occur are not fully understood yet. Here, we present an experimental study of spontaneous collective turns in natural flocks of starlings. We employ a recently developed tracking algorithm to reconstruct three-dimensional trajectories of each individual bird in the flock for the whole duration of a turning event. Our approach enables us to analyse changes in the individual behaviour of every group member and reveal the emergent dynamics of turning. We show that spontaneous turns start from individuals located at the elongated tips of the flocks, and then propagate through the group. We find that birds on the tips deviate from the mean direction of motion much more frequently than other individuals, indicating that persistent localized fluctuations are the crucial ingredient for triggering a collective directional change. Finally, we quantitatively verify that birds follow equal-radius paths during turning, the effects of which are a change of the flock's orientation and a redistribution of individual locations in the group.

Short-range interactions versus long-range correlations in bird flocks.

Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.

Silent flocks: constraints on signal propagation across biological groups.

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces the Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations, and second-sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap in momentum space sharply separates first- from second-sound modes. This gap implies the existence of silent flocks, namely, of medium-sized systems across which information cannot propagate in a linear and underdamped way, either under the form of orientational fluctuations or under that of density fluctuations, making it hard for the group to achieve coordination.

Finite-size scaling as a way to probe near-criticality in natural swarms.

Collective behavior in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behavior of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes.

Information transfer and behavioural inertia in starling flocks.

Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition fast and robust transfer of information is essential to prevent cohesion loss. The mechanism by which natural groups achieve such robustness, though, is not clear. Here we present an experimental study of starling flocks performing collective turns. We find that information about direction changes propagates across the flock with a linear dispersion law and negligible attenuation, hence minimizing group decoherence. These results contrast starkly with current models of collective motion, which predict diffusive transport of information. Building on spontaneous symmetry breaking and conservation laws arguments, we formulate a new theory that correctly reproduces linear and undamped propagation. Essential to the new framework is the inclusion of the birds' behavioural inertia. The new theory not only explains the data, but also predicts that information transfer must be faster the stronger the group's orientational order, a prediction accurately verified by the data. Our results suggest that swift decision-making may be the adaptive drive for the strong behavioural polarization observed in many living groups.

Collective behaviour without collective order in wild swarms of midges.

Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of non-interacting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

Social interactions dominate speed control in poising natural flocks near criticality.

Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameters--completely determined by the data--are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.

Statistical mechanics for natural flocks of birds.

Flocking is a typical example of emergent collective behavior, where interactions between individuals produce collective patterns on the large scale. Here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data. We construct the minimally structured (maximum entropy) model consistent with experimental correlations in large flocks of starlings. The maximum entropy model shows that local, pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings, with no free parameters. We also find that the number of interacting neighbors is independent of flock density, confirming that interactions are ruled by topological rather than metric distance. Finally, by comparing flocks of different sizes, the model correctly accounts for the observed scale invariance of long-range correlations among the fluctuations in flight direction.

Scale-free correlations in starling flocks.

From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations.