Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Self-organized criticality and synchronization in a coupled map lattice model of integrate-and-fire oscillators

We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Self-similar community structure in a network of human interactions

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

Noise and dynamics of self-organized critical phenomena

Different microscopic models exhibiting self-organized criticality are studied numerically and analytically. Numerical simulations are performed to compute critical exponents, mainly the dynamical exponent, and to check universality classes. We find that various models lead to the same exponent, but this universality class is sensitive to disorder. From the dynamic microscopic rules we obtain continuum equations with different sources of noise, which we call internal and external. Different correlations of the noise give rise to different critical behavior. A model for external noise is proposed that makes the upper critical dimensionality equal to 4 and leads to the possible existence of a phase transition above d=4. Limitations of the approach of these models by a simple nonlinear equation are discussed.

Toward synthetic combinatorial peptide libraries in positional scanning format (PS-SCL)-based identification of CD8+ Tumor-reactive T-Cell Ligands: a comparative analysis of PS-SCL recognition by a single tumor-reactive CD8+ cytolytic T-lymphocyte clone.

The use of synthetic combinatorial peptide libraries in positional scanning format (PS-SCL) has emerged recently as an alternative approach for the identification of peptides recognized by T lymphocytes. The choice of both the PS-SCL used for screening experiments and the method used for data analysis are crucial for implementing this approach. With this aim, we tested the recognition of different PS-SCL by a tyrosinase 368-376-specific CTL clone and analyzed the data obtained with a recently developed biometric data analysis based on a model of independent and additive contribution of individual amino acids to peptide antigen recognition. Mixtures defined with amino acids present at the corresponding positions in the native sequence were among the most active for all of the libraries. Somewhat surprisingly, a higher number of native amino acids were identifiable by using amidated COOH-terminal rather than free COOH-terminal PS-SCL. Also, our data clearly indicate that when using PS-SCL longer than optimal, frame shifts occur frequently and should be taken into account. Biometric analysis of the data obtained with the amidated COOH-terminal nonapeptide library allowed the identification of the native ligand as the sequence with the highest score in a public human protein database. However, the adequacy of the PS-SCL data for the identification for the peptide ligand varied depending on the PS-SCL used. Altogether these results provide insight into the potential of PS-SCL for the identification of CTL-defined tumor-derived antigenic sequences and may significantly implement our ability to interpret the results of these analyses.

Self-organized evolution in a socio-economic environment

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

T cell affinity regulates asymmetric division, effector cell differentiation, and tissue pathology.

The strength of interactions between T cell receptors and the peptide-major histocompatibility complex (pMHC) directly modulates T cell fitness, clonal expansion, and acquisition of effector properties. Here we show that asymmetric T cell division is an important mechanistic link between increased signal strength, effector differentiation, and the ability to induce tissue pathology. Recognition of pMHC above a threshold affinity drove responding T cells into asymmetric cell division. The ensuing proximal daughters underwent extensive division and differentiated into short-lived effector cells expressing the integrin VLA-4, allowing the activated T cell to infiltrate and mediate destruction of peripheral target tissues. In contrast, T cells activated by below-threshold antigens underwent symmetric division, leading to abortive clonal expansion and failure to fully differentiate into tissue-infiltrating effector cells. Antigen affinity and asymmetric division are important factors that regulate fate specification in CD8(+) T cells and predict the potential of a self-reactive T cell to mediate tissue pathology.