Andrea Procaccini

Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study

Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flocks cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.

Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law

We explore a possible connection between two aspects of loop quantum gravity which have been extensively studied in the recent literature: the black-hole area-entropy law and the energy-momentum dispersion relation. We observe that the original Bekenstein argument for the area-entropy law implicitly requires information on the energy-momentum dispersion relation and on the position-momentum uncertainty relation. Recent results show that in first approximation black-hole entropy in loop quantum gravity depends linearly on the area, with small correction terms which have logarithmic or inverse-power dependence on the area. And it has been argued that in loop quantum gravity the dispersion relation should include terms that depend linearly on the Planck length, while no evidence of modification of the position-momentum uncertainty relation has been found. We observe that this scenario with Planck-length-linear modification of the dispersion relation and unmodified position-momentum uncertainty relation is incompatible with the black-hole-entropy results, since it would give rise to a term in the entropy formula going like the square root of the area.

The STARFLAG handbook on collective animal behaviour: 2. Three-dimensional analysis

The study of collective animal behaviour must progress through a comparison between the theoretical predictions of numerical models and data coming from empirical observations. To this aim it is important to develop methods of three-dimensional (3D) analysis that are at the same time informative about the structure of the group and suitable to empirical data. In fact, empirical data are considerably noisier than numerical data, and they are subject to several constraints. We review here the tools of analysis used by the STARFLAG project to characterize the 3D structure of large flocks of starlings in the field. We show how to avoid the most common pitfalls in the quantitative analysis of 3D animal groups, with particular attention to the problem of the bias introduced by the border of the group. By means of practical examples, we demonstrate that neglecting border effects gives rise to artefacts when studying the 3D structure of a group. Moreover, we show that mathematical rigour is essential to distinguish important biological properties from trivial geometric features of animal groups.

Propagating waves in starling, Sturnus vulgaris, flocks under predation

The formation of waves is a vivid example of collective behaviour occurring in insects, birds, fish and mammals, which has been interpreted as an antipredator response. In birds a quantitative characterization of this phenomenon, involving thousands of individuals, is missing and its link with predation remains elusive. We studied waves in flocks of starlings, a highly gregarious species, by both direct observation and quantitative computer vision analysis of HD video recordings, under predation by peregrine falcons, Falco peregrinus. We found that waves originated from the position of the attacking predator and always propagated away from it. We measured their frequency and velocities, the latter often being larger than the velocity of the flock. A high positive correlation was found between the formation of waves and reduced predation success. We suggest that the tendency of a prey to escape, when initiated even by a few individuals in a cohesive group, elicits self-organized density waves. Such evident fluctuations in the local structure of the flocks are efficient in confusing predators.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code.

A GLIMPSE AT THE FLAT-SPACETIME LIMIT OF QUANTUM GRAVITY USING THE BEKENSTEIN ARGUMENT IN REVERSE

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy–momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy–momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples, we consider the energy–momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as an illustrative example for the original proposal (Preprint gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (Preprint hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity and energy–momentum conservation rules in these theories with two relativistic invariants.