"In this paper we define what we call an affinity system, which is a set of individuals, each with a vector characterizing its preference for all other individuals in the set. The preference of a member can be given either by a ranking of all members or by a weighted vector that defines the degrees of its affinity to others. Affinity systems are useful for modeling social systems as well as general data sets, as social interactions are often determined by affinities among the members. We also define a natural notion of (potentially overlapping) communities in an affinity system, in which the members of a given community collectively prefer each other to anyone else outside the community. Thus these communities are "self-determined" or "self-certified" by the affinity system. We provide a tight polynomial bound on the number of self-determined communities as a function of the robustness of the community. Moreover, we present a polynomial-time algorithm for enumerating these communities, as well as a local algorithm with a strong stochastic performance guarantee that can find a community in time nearly linear in the of size the community.…"

"The self assembly of core-corona discs interacting via anisotropic potentials is investigated using Monte Carlo computer simulations. A minimal interaction potential that incorporates anisotropy in a simple way is introduced. It consists in a core-corona architecture in which the center of the core is shifted with respect to the center of the corona. Anisotropy can thus be tuned by progressively shifting the position of the core. Despite its simplicity, the system self organize in a rich variety of structures including stripes, triangular and rectangular lattices, and unusual plastic crystals. Our results indicate that the amount of anisotropy does not alter the lattice spacing and only influences the type of clustering (stripes, micells, etc.) of the individual particles."

"… We examine here how the algorithm of phyllotaxis could contribute to the analysis of the structure of collagen fibrils. Such an algorithm indeed leads to organizations giving to each element of the assembly the most homogeneous and isotropic dense environment in a situation of cylindrical symmetry. The scattered intensity expected from a phyllotactic distribution of triple helices in collagen fibrils well agrees with the major features observed along the equatorial direction of their X ray patterns. Following this approach, the aggregation of triple helices in fibrils should be considered within the frame of soft condensed matter studies rather than that of molecular crystal studies."

"We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the self-assembly process. The relationship between the model's rule set and its resulting self-assembled structure can be viewed as a genotype-phenotype map and incorporated into a genetic algorithm."

"We use computer simulation to study crystal-forming model proteins equipped with interactions that are both orientationally specific and nonspecific. Distinct dynamical pathways of crystal formation can be selected by tuning the strengths of these interactions. When the nonspecific interaction is strong, liquidlike clustering can precede crystallization; when it is weak, growth can proceed via ordered nuclei. Crystal yields are in certain parameter regimes enhanced by the nonspecific interaction, even though it promotes association without local crystalline order. Our results suggest that equipping nanoscale components with weak nonspecific interactions (such as depletion attractions) can alter both their dynamical pathway of assembly and optimize the yield of the resulting material."

"Laboratory investigations have shown that a formal theory of fault-tolerance will be essential to harness nanoscale self-assembly as a medium of computation. Several researchers have voiced an intuition that self-assembly phenomena are related to the field of distributed computing. This paper formalizes some of that intuition. We construct tile assembly systems that are able to simulate the solution of the wait-free consensus problem in some distributed systems. (For potential future work, this may allow binding errors in tile assembly to be analyzed, and managed, with positive results in distributed computing, as a "blockage" in our tile assembly model is analogous to a crash failure in a distributed computing model.) …We show that solution of this strengthened consensus problem can be simulated by a two-dimensional tile assembly model only for two processes, whereas a three-dimensional tile assembly model can simulate its solution in a distributed system with any number of processes

"This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic (CTL), a temporal logic often used in model checking. We then consider the class of "rectilinear" tile assembly systems. This class includes most aTAM systems studied in the theoretical literature, and all (algorithmic) DNA tile self-assembling systems that have been realized in laboratories to date. We present a polynomial-time algorithm that, given a tile assembly system T as input, either provides a counterexample to T's rectilinearity or verifies whether T has a unique terminal assembly. …"

"We study the phase behavior of bowl-shaped particles using computer simulations. These particles were found experimentally to form a meta-stable worm-like fluid phase in which the bowl-shaped particles have a strong tendency to stack on top of each other [M.Marechal et al, Nano Letters 10, 1907 (2010)]. In this work, we show that the transition from the low-density fluid to the worm-like phase has an interesting effect on the equation of state. The simulation results also show that the worm-like fluid phase transforms spontaneously into a columnar phase for bowls that are sufficiently deep. Furthermore, we describe the phase behavior as obtained from free energy calculations employing Monte Carlo simulations. The columnar phase is stable for bowl shapes ranging from infinitely thin bowls to surprisingly shallow bowls. … the phase diagram features four novel crystal phases and a region where the stable fluid contains worm-like stacks."

"A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms. The fact that different viruses adopt similar structural forms is an indication of a common underlying design, motivating the use of simplified, low-resolution models in exploring the assembly process. Several versions of a molecular dynamics approach are described. Polyhedral shells of different sizes are involved, the assembly pathways are either irreversible or reversible, and an explicit solvent is optionally included. …Among the key observations are that efficient growth proceeds by means of a cascade of highly reversible stages, and that while there are a large variety of possible partial assemblies, only a relatively small number of strongly bonded configurations are actually encountered."

"…The conclusion is that nondeterminism confers extra power to assemble a shape from a small tile system, but unless the polynomial hierarchy collapses, it is computationally more difficult to exploit this power by finding the size of the smallest tile system, compared to finding the size of the smallest deterministic tile system."