Elastic properties of small-world spring networks

We construct small-world spring networks based on a one dimensional chain and study its static and quasistatic behavior with respect to external forces. Regular bonds and shortcuts are assigned linear springs of constant $k$ and $k'$, respectively. In our models, shortcuts can only stand extensions less than $\delta_c$ beyond which they are removed from the network. First we consider the simple cases of a hierarchical small-world network and a complete network. In the main part of this paper we study random small-world networks (RSWN) in which each pair of nodes is connected by a shortcut with probability $p$. We obtain a scaling relation for the effective stiffness of RSWN when $k=k'$. In this case the extension distribution of shortcuts is scale free with the exponent -2. There is a strong positive correlation between the extension of shortcuts and their betweenness. We find that the chemical end-to-end distance (CEED) could change either abruptly or continuously with respect to the external force. In the former case, the critical force is determined by the average number of shortcuts emanating from a node. In the latter case, the distribution of changes in CEED obeys power laws of the exponent $-\alpha$ with $\alpha \le 3/2$.Comment: 16 pages, 14 figures, 1 table, published versio

Three Bead Rotating Chain model shows universality in the stretching of proteins

We introduce a model of proteins in which all of the key atoms in the protein backbone are accounted for, thus extending the Freely Rotating Chain model. We use average bond lengths and average angles from the Protein Databank as input parameters, leaving the number of residues as a single variable. The model is used to study the stretching of proteins in the entropic regime. The results of our Monte Carlo simulations are found to agree well with experimental data, suggesting that the force extension plot is universal and does not depend on the side chains or primary structure of proteins

Scale-free networks with an exponent less than two

We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units -- to have different properties than those of scale free networks with $\gamma>2$: The number of links grows faster than the number of nodes and they naturally posses the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation

Towards a simplified description of thermoelectric materials: Accuracy of approximate density functional theory for phonon dispersions

We calculate the phonon-dispersion relations of several two-dimensional materials and diamond using the density-functional based tight-binding approach (DFTB). Our goal is to verify if this numerically efficient method provides sufficiently accurate phonon frequencies and group velocities to compute reliable thermoelectric properties. To this end, the results are compared to available DFT results and experimental data. To quantify the accuracy for a given band, a descriptor is introduced that summarizes contributions to the lattice conductivity that are available already in the harmonic approximation. We find that the DFTB predictions depend strongly on the employed repulsive pair-potentials, which are an important prerequisite of this method. For carbon-based materials, accurate pair-potentials are identified and lead to errors of the descriptor that are of the same order as differences between different local and semi-local DFT approaches

Major Thought Restructuring: The Roles of Different Prefrontal Cortical Regions

An important question for understanding the neural basis of problem solving is whether the regions of human prefrontal cortices play qualitatively different roles in the major cognitive restructuring required to solve difficult problems. However, investigating this question using neuroimaging faces a major dilemma: either the problems do not require major cognitive restructuring, or if they do, the restructuring typically happens once, rendering repeated measurements of the critical mental process impossible. To circumvent these problems, young adult participants were challenged with a one-dimensional Subtraction (or Nim) problem [Bouton, C. L. Nim, a game with a complete mathematical theory. The Annals of Mathematics, 3, 35-39, 1901] that can be tackled using two possible strategies. One, often used initially, is effortful, slow, and error-prone, whereas the abstract solution, once achieved, is easier, quicker, and more accurate. Behaviorally, success was strongly correlated with sex. Using voxel-based morphometry analysis controlling for sex, we found that participants who found the more abstract strategy (i.e., Solvers) had more gray matter volume in the anterior medial, ventrolateral prefrontal, and parietal cortices compared with those who never switched from the initial effortful strategy (i.e., Explorers). Removing the sex covariate showed higher gray matter volume in Solvers (vs. Explorers) in the right ventrolateral prefrontal and left parietal cortex