Strong spatial mixing of list coloring of graphs

The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise known to be #P hard. In the context of coloring, strong spatial mixing has been established for Kelly trees in (Ge and Stefankovic, arXiv:1102.2886v3 (2011)) when where q the number of colors, Δ is the degree and .. is the unique solution to . It has also been established in (Goldberg et al., SICOMP 35 (2005) 486–517) for bounded degree lattice graphs whenever for some constant β, where Δ is the maximum vertex degree of the graph. We establish strong spatial mixing for a more general problem, namely list coloring, for arbitrary bounded degree triangle‐free graphs. Our results hold for any whenever the size of the list of each vertex v is at least where is the degree of vertex v and β is a constant that only depends on α. The result is obtained by proving the decay of correlations of marginal probabilities associated with graph nodes measured using a suitably chosen error function. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,599–613, 2015     

Self-regeneration of Pd-LaFeO3 catalysts: new insight from atomic-resolution electron microscopy

Aberration-corrected transmission electron microscopy was used to study atomic-scale processes in Pd-LaFeO(3) catalysts. Clear evidence for diffusion of Pd into LaFeO(3) and out of LaFe(0.95)Pd(0.05)O(3-δ) under high-temperature oxidizing and reducing conditions, respectively, was found, but the extent to which these processes occurred was quite limited. These observations cast doubt that such phenomena play a significant role in a postulated mechanism of self-regeneration of this system as an automotive exhaust-gas catalyst.     

Distance measures for dynamic citation networks

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent an important type of acyclic digraph. For example, the study of such networks includes the spread of ideas through academic citations, the spread of innovation through patent citations, and the development of precedent in common law systems. The specific dynamics that produce such acyclic digraphs not only differentiate them from other classes of graphs, but also provide guidance for the development of meaningful distance measures. In this article, we develop and apply our sink distance measure together with the single-linkage hierarchical clustering algorithm to both a two-dimensional directed preferential attachment model as well as empirical data drawn from the first quarter-century of decisions of the United States Supreme Court. Despite applying the simplest combination of distance measure and clustering algorithm, analysis reveals that more accurate and more interpretable clusterings are produced by this scheme.     

Probabilistic Inference with Polymerizing Biochemical Circuits

Probabilistic inference—the process of estimating the values of unobserved variables in probabilistic models—has been used to describe various cognitive phenomena related to learning and memory. While the study of biological realizations of inference has focused on animal nervous systems, single-celled organisms also show complex and potentially “predictive” behaviors in changing environments. Yet, it is unclear how the biochemical machinery found in cells might perform inference. Here, we show how inference in a simple Markov model can be approximately realized, in real-time, using polymerizing biochemical circuits. Our approach relies on assembling linear polymers that record the history of environmental changes, where the polymerization process produces molecular complexes that reflect posterior probabilities. We discuss the implications of realizing inference using biochemistry, and the potential of polymerization as a form of biological information-processing.     

Blended Conjugated Host and Unconjugated Dopant Polymers Towards N-type All-Polymer Conductors and High-ZT Thermoelectrics

N-Type thermoelectrics typically consist of small molecule dopant+polymer host. Only a few polymer dopant+polymer host systems have been reported, and these have lower thermoelectric parameters. N-type polymers with high crystallinity and order are generally used for high-conductivity ( ) organic conductors. Few n-type polymers with only short-range lamellar stacking for high-conductivity materials have been reported. Here, we describe an n-type short-range lamellar-stacked all-polymer thermoelectric system with highest of 78 S⁻¹, power factor (PF) of 163 μW m⁻¹ K⁻², and maximum Figure of merit (ZT) of 0.53 at room temperature with a dopant/host ratio of 75 wt%. The minor effect of polymer dopant on the molecular arrangement of conjugated polymer PDPIN at high ratios, high doping capability, high Seebeck coefficient (S) absolute values relative to , and atypical decreased thermal conductivity ( ) with increased doping ratio contribute to the promising performance.     

The effect of torsional vibrations superimposed on a creep loaded adhesive joint on its final tensile properties

Aluminum - epoxy single lap joints were subjected at different temperatures to torsional vibrations at constant amplitude superimposed on a creep load. This combination of dynamic and static stresses was chosen in order to simulate to a certain extent the real service conditions of an ordinary bonded joint. The shear strength of these joints was checked in tension at room temperature after their removal from the special device in which the superimposed stresses were applied. It was found that the shear strength of the joint is very dependent on its thermo-mechanical history. DSC analyses and SEM micrographs of the failure surface were used in an attempt to find some correlation between the mechanical properties and the microstructure of the adhesive.