Anomalous heat-kernel decay for random walk among bounded random conductances

We consider the nearest-neighbor simple random walk on $\Z^d$, $d\ge2$, driven by a field of bounded random conductances $\omega_{xy}\in[0,1]$. The conductance law is i.i.d. subject to the condition that the probability of $\omega_{xy}>0$ exceeds the threshold for bond percolation on $\Z^d$. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the $2n$-step return probability $P_\omega^{2n}(0,0)$. We prove that $P_\omega^{2n}(0,0)$ is bounded by a random constant times $n^{-d/2}$ in $d=2,3$, while it is $o(n^{-2})$ in $d\ge5$ and $O(n^{-2}\log n)$ in $d=4$. By producing examples with anomalous heat-kernel decay approaching $1/n^2$ we prove that the $o(n^{-2})$ bound in $d\ge5$ is the best possible. We also construct natural $n$-dependent environments that exhibit the extra $\log n$ factor in $d=4$. See also math.PR/0701248.Comment: 22 pages. Includes a self-contained proof of isoperimetric inequality for supercritical percolation clusters. Version to appear in AIHP + additional correction

Modeling of SAR signatures of shallow water ocean topography

A hydrodynamic/electromagnetic model was developed to explain and quantify the relationship between the SEASAT synthetic aperture radar (SAR) observed signatures and the bottom topography of the ocean in the English Channel region of the North Sea. The model uses environmental data and radar system parameters as inputs and predicts SAR-observed backscatter changes over topographic changes in the ocean floor. The model results compare favorably with the actual SEASAT SAR observed backscatter values. The developed model is valid for only relatively shallow water areas (i.e., less than 50 meters in depth) and suggests that for bottom features to be visible on SAR imagery, a moderate to high velocity current and a moderate wind must be present

Studies on the inheritance of resistance to crown gall disease of grapevine

Nearly 1800 seedlings of 27 hybrid families were screened for resistance to A. tumefaciens strain AT-1 belonging to biotype 3. The tested families included 12 crosses of sensitive and of resistant phenotypes, and 15 self-pollinated families both of sensitive and of resistant parents. Resistance originated from V. amurensis. The segregation ratio corresponded to 1 : 1 among the crosses and was 3 : 1 (resistant to sensitive) among the selfings of resistant parents. All seedlings from selved susceptible parents formed tumors. According to our results, a Mendelian dominant inheritance can be proposed for resistance to A. tumefaciens strain AT-1.Untersuchungen zur Vererbung der Mauke-Resistenz bei der RebeAnnähernd 1800 Genotypen aus 27 Kreuzungsfamilien wurden auf ihre Anfälligkeit gegen den Stamm AT-1 des Biotyps 3 von Agrobacterium tumefaciens geprüft. Die untersuchten Kreuzungsfamilien umfaßten 12 Kreuzungskombinationen resistenter und anfälliger Phänotypen und 15 Selbstungen resistenter und anfälliger Eltern. Die Quelle der Mauke-Resistenz ist Vitis amurensis. Das Aufspaltungsverhältnis zwischen resistenten und anfälligen Sämlingen beträgt bei Fremdbefruchtung 1 : 1 und bei Selbstung der resistenten Eltern 3 : 1; bei Selbstung der anfälligen Eltern bildete jeder Sämling Tumoren aus. Aufgrund der Ergebnisse kann eine dominante Vererbung der Resistenz gegen A. tumefaciens AT-1 angenommen werden

TMFoldWeb: a web server for predicting transmembrane protein fold class.

BACKGROUND: Here we present TMFoldWeb, the web server implementation of TMFoldRec, a transmembrane protein fold recognition algorithm. TMFoldRec uses statistical potentials and utilizes topology filtering and a gapless threading algorithm. It ranks template structures and selects the most likely candidates and estimates the reliability of the obtained lowest energy model. The statistical potential was developed in a maximum likelihood framework on a representative set of the PDBTM database. According to the benchmark test the performance of TMFoldRec is about 77 % in correctly predicting fold class for a given transmembrane protein sequence. RESULTS: An intuitive web interface has been developed for the recently published TMFoldRec algorithm. The query sequence goes through a pipeline of topology prediction and a systematic sequence to structure alignment (threading). Resulting templates are ordered by energy and reliability values and are colored according to their significance level. Besides the graphical interface, a programmatic access is available as well, via a direct interface for developers or for submitting genome-wide data sets. CONCLUSIONS: The TMFoldWeb web server is unique and currently the only web server that is able to predict the fold class of transmembrane proteins while assigning reliability scores for the prediction. This method is prepared for genome-wide analysis with its easy-to-use interface, informative result page and programmatic access. Considering the info-communication evolution in the last few years, the developed web server, as well as the molecule viewer, is responsive and fully compatible with the prevalent tablets and mobile devices. REVIEWERS: This article was reviewed by Dr. Michael Gromiha, Dr. Sandor Pongor and Dr. Frank Eisenhaber with Wing-Cheong Wong

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure