Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Origin of the Scaling Law in Human Mobility: Hierarchical Organization of Traffic Systems

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which a random walker will generate a power-law travel displacement distribution with exponent -2. When considering the inhomogeneities of cities' locations and attractions, this model reproduces a power-law displacement distribution with an exponential cutoff, as well as a scaling behavior in the probability density of having traveled a certain distance at a certain time. Our results agree very well with the empirical observations reported in [D. Brockmann et al., Nature 439, 462 (2006)].Comment: 6 figures, 4 page

Electronic, dynamical, and thermal properties of ultra-incompressible superhard rhenium diboride: A combined first-principles and neutron scattering study

Rhenium diboride is a recently recognized ultra-incompressible superhard material. Here we report the electronic (e), phonon (p), e-p coupling and thermal properties of ReB$_2$ from first-principles density-functional theory (DFT) calculations and neutron scattering measurements. Our calculated elastic constants ($c_{11}$ = 641 GPa, $c_{12}$ = 159 GPa, $c_{13}$ = 128 GPa, $c_{33}$ = 1037 GPa, and $c_{44}$ = 271 GPa), bulk modulus ($B$ $\approx$ 350 GPa) and hardness ($H$ $\approx$ 46 GPa) are in good agreement with the reported experimental data. The calculated phonon density of states (DOS) agrees very well with our neutron vibrational spectroscopy result. Electronic and phonon analysis indicates that the strong covalent B-B and Re-B bonding is the main reason for the super incompressibility and hardness of ReB$_2$. The thermal expansion coefficients, calculated within the quasi-harmonic approximation and measured by neutron powder diffraction, are found to be nearly isotropic in $a$ and $c$ directions and only slightly larger than that of diamond in terms of magnitude. The excellent agreement found between calculations and experimental measurements indicate that first-principles calculations capture the main interactions in this class of superhard materials, and thus can be used to search, predict, and design new materials with desired properties.Comment: submitted to pr

Manipulating Memory Associations Changes Decision-making Preferences in a Preconditioning Task

Memories of past experiences can guide our decisions. Thus, if memories are undermined or distorted, decision making should be affected. Nevertheless, little empirical research has been done to examine the role of memory in reinforcement decision-making . We hypothesized that if memories guide choices in a conditioning decision-making task, then manipulating these memories would result in a change of decision preferences to gain reward. We manipulated participants’ memories by providing false feedback that their memory associations were wrong before they made decisions that could lead them to win money . Participants’ memory ratings decreased significantly after receiving false feedback. More importantly, we found that false feedback led participants’ decision bias to disappear after their memory associations were undermined . Our results suggest that reinforcement decision-making can be altered by fasle feedback on memories . The results are discussed using memory mechanisms such as spreading activation theories

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations

The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. A heterogeneity transition is predicted to occur in the solution space as the constraint density alpha reaches a critical value alpha_cm. This transition marks the emergency of exponentially many solution communities in the solution space. After the heterogeneity transition the solution space is still ergodic until alpha reaches a larger threshold value alpha_d, at which the solution communities disconnect from each other to become different solution clusters (ergodicity-breaking). The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local search algorithm SEQSAT, which performs a random walk of single-spin flips, is investigated. The relevance of this work to glassy dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of Physics: Conference Series (Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan