Diffusive persistence on disordered lattices and random networks.

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or, in general, that the node remained active or inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P(t,L)∼t^{-θ} with an exponent θ≃0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ≃0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power law P(t,L)∼L^{-zθ} with z≃2.86 instead of the value of z=2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdos-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.

A continuous-time MaxSAT solver with high analog performance.

Many real-life optimization problems can be formulated in Boolean logic as MaxSAT, a class of problems where the task is finding Boolean assignments to variables satisfying the maximum number of logical constraints. Since MaxSAT is NP-hard, no algorithm is known to efficiently solve these problems. Here we present a continuous-time analog solver for MaxSAT and show that the scaling of the escape rate, an invariant of the solver's dynamics, can predict the maximum number of satisfiable constraints, often well before finding the optimal assignment. Simulating the solver, we illustrate its performance on MaxSAT competition problems, then apply it to two-color Ramsey number R(m, m) problems. Although it finds colorings without monochromatic 5-cliques of complete graphs on N ≤ 42 vertices, the best coloring for N = 43 has two monochromatic 5-cliques, supporting the conjecture that R(5, 5) = 43. This approach shows the potential of continuous-time analog dynamical systems as algorithms for discrete optimization.

A multiscale cerebral neurochemical connectome of the rat brain.

Understanding the rat neurochemical connectome is fundamental for exploring neuronal information processing. By using advanced data mining, supervised machine learning, and network analysis, this study integrates over 5 decades of neuroanatomical investigations into a multiscale, multilayer neurochemical connectome of the rat brain. This neurochemical connectivity database (ChemNetDB) is supported by comprehensive systematically-determined receptor distribution maps. The rat connectome has an onion-type structural organization and shares a number of structural features with mesoscale connectomes of mouse and macaque. Furthermore, we demonstrate that extremal values of graph theoretical measures (e.g., degree and betweenness) are associated with evolutionary-conserved deep brain structures such as amygdala, bed nucleus of the stria terminalis, dorsal raphe, and lateral hypothalamus, which regulate primitive, yet fundamental functions, such as circadian rhythms, reward, aggression, anxiety, and fear. The ChemNetDB is a freely available resource for systems analysis of motor, sensory, emotional, and cognitive information processing.

Biocompatibility study of three distinct carbon pastes for application as electrode material in neural stimulations and recordings.

Neural interfaces hold great promise for research and treatment of a wide variety of neurological diseases. Medical electrodes are designed to interface with the nervous system and provide control signals for neural prostheses. We fabricated previously a hook-up neural electrode. Here we investigate the in vitro cytotoxicity of three commercial carbon pastes used for printing the conductor tracks of this electrode. At first, the carbon pastes were characterized with respect to their microstructure and chemical composition. SEM images showed a grainy texture that is associated to the carbon/graphite microparticles dispersed by the polymeric binder. All the three pastes contained in major proportions carbon and in different proportions other elements. The surface roughness analysis evidenced differences in the smoothness of the carbon paste surfaces. Sterilization procedures did not alter the microstructure or surface morphology of the pastes. Finally, cell viability based on -(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) test and fluorescence staining experiments proved non-cytotoxicity and suitability of the studied carbon pastes as electrode material for measuring neural activity during surgeries (up to a certain time period).

Truncation Derivatives of the S-Layer Protein of Sporosarcina ureae ATCC 13881 (SslA): Towards Elucidation of the Protein Domain Responsible for Self-Assembly.

The cell surface of Sporosarcina ureae ATCC 13881 is covered by an S-layer (SslA) consisting of identical protein subunits that assemble into lattices exhibiting square symmetry. In this work the self-assembly properties of the recombinant SslA were characterised with an emphasis on the identification of protein regions responsible for self-assembly. To this end, recombinant mature SslA (aa 31-1097) and three SslA truncation derivatives (one N-terminal, one C-terminal and one CN-terminal) were produced in a heterologous expression system, isolated, purified and their properties analysed by in vitro recrystallisation experiments on a functionalised silicon wafer. As a result, recombinant mature SslA self-assembled into crystalline monolayers with lattices resembling the one of the wild-type SslA. The study identifies the central protein domain consisting of amino acids 341-925 self-sufficient for self-assembly. Neither the first 341 amino acids nor the last 172 amino acids of the protein sequence are required to self-assemble into lattices.

Order-to-chaos transition in the hardness of random Boolean satisfiability problems.

Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k-SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ, an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N, the hardness of formulas in random k-SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α, hardness appears through a second-order phase transition at α_{χ} in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ∼N^{B|α-α_{χ}|^{1-γ}} with 0<γ<1. We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.

Targeting at the Nanoscale: A Novel S-Layer Fusion Protein Enabling Controlled Immobilization of Biotinylated Molecules.

With the aim of constructing an S-layer fusion protein that combines both excellent self-assembly and specific ligand i.e., biotin binding ability, streptavidin (aa 16-133) was fused to the S-layer protein of Sporosarcina ureae ATCC 13881 (SslA) devoid of its N-terminal 341 and C-terminal 172 amino acids. The genetically engineered chimeric protein could be successfully produced in E. coli, isolated, and purified via Ni affinity chromatography. In vitro recrystallisation experiments performed with the purified chimeric protein in solution and on a silicon wafer have demonstrated that fusion of the streptavidin domain does not interfere with the self-assembling properties of the S-layer part. The chimeric protein self-assembled into multilayers. More importantly, the streptavidin domain retained its full biotin-binding ability, a fact evidenced by experiments in which biotinylated quantum dots were coupled to the fusion protein monomers and adsorbed onto the in vitro recrystallised fusion protein template. In this way, this S-layer fusion protein can serve as a functional template for the controlled immobilization of biotinylated and biologically active molecules.

Multilevel animal societies can emerge from cultural transmission.

Multilevel societies, containing hierarchically nested social levels, are remarkable social structures whose origins are unclear. The social relationships of sperm whales are organized in a multilevel society with an upper level composed of clans of individuals communicating using similar patterns of clicks (codas). Using agent-based models informed by an 18-year empirical study, we show that clans are unlikely products of stochastic processes (genetic or cultural drift) but likely originate from cultural transmission via biased social learning of codas. Distinct clusters of individuals with similar acoustic repertoires, mirroring the empirical clans, emerge when whales learn preferentially the most common codas (conformism) from behaviourally similar individuals (homophily). Cultural transmission seems key in the partitioning of sperm whales into sympatric clans. These findings suggest that processes similar to those that generate complex human cultures could not only be at play in non-human societies but also create multilevel social structures in the wild.

Ordering in spatial evolutionary games for pairwise collective strategy updates.

Evolutionary 2×2 games are studied with players located on a square lattice. During the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood. In the case of the anticoordination game this system behaves like an antiferromagnetic kinetic Ising model. Within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker's payoff. The comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation.