Hausdorff dimension of operator semistable L\'evy processes

Let $X=\{X(t)\}_{t\geq0}$ be an operator semistable L\'evy process in \rd with exponent $E$, where $E$ is an invertible linear operator on \rd and $X$ is semi-selfsimilar with respect to $E$. By refining arguments given in Meerschaert and Xiao \cite{MX} for the special case of an operator stable (selfsimilar) L\'evy process, for an arbitrary Borel set B\subseteq\rr_+ we determine the Hausdorff dimension of the partial range $X(B)$ in terms of the real parts of the eigenvalues of $E$ and the Hausdorff dimension of $B$.Comment: 23 page

The EDS1–PAD4–ADR1 node mediates Arabidopsis pattern-triggered immunity

Plants deploy cell-surface and intracellular leucine rich-repeat domain (LRR) immune receptors to detect pathogens1. LRR receptor kinases and LRR receptor proteins at the plasma membrane recognize microorganism-derived molecules to elicit pattern-triggered immunity (PTI), whereas nucleotide-binding LRR proteins detect microbial effectors inside cells to confer effector-triggered immunity (ETI). Although PTI and ETI are initiated in different host cell compartments, they rely on the transcriptional activation of similar sets of genes2, suggesting pathway convergence upstream of nuclear events. Here we report that PTI triggered by the Arabidopsis LRR receptor protein RLP23 requires signalling-competent dimers of the lipase-like proteins EDS1 and PAD4, and of ADR1 family helper nucleotide-binding LRRs, which are all components of ETI. The cell-surface LRR receptor kinase SOBIR1 links RLP23 with EDS1, PAD4 and ADR1 proteins, suggesting the formation of supramolecular complexes containing PTI receptors and transducers at the inner side of the plasma membrane. We detected similar evolutionary patterns in LRR receptor protein and nucleotide-binding LRR genes across Arabidopsis accessions; overall higher levels of variation in LRR receptor proteins than in LRR receptor kinases are consistent with distinct roles of these two receptor families in plant immunity. We propose that the EDS1–PAD4–ADR1 node is a convergence point for defence signalling cascades, activated by both surface-resident and intracellular LRR receptors, in conferring pathogen immunity

Greenville County, South Carolina historic resources survey : Greenville County, South Carolina : final report

In 2013, Brockington and Associates conducted a historical resources survey of unincorporated Greenville County for the Greenville County Recreation District and the South Carolina Department of Archives and History (SCDAH). The objective of this survey was survey was to identify a sample of 1,100 aboveground historic architectural resources in the survey universe that retain sufficient integrity to be included in the South Carolina Statewide Survey of Historic Properties (SSHP). These resources include buildings, structures, objects, districts and landscapes that have architectural or historical significance. During the course of the historic architectural survey of unincorporated Greenville County, we identified 1,100 historic architectural resources of which 20 are recommended individually eligible for listing in the [National Register of Historic Properties]. An additional six areas are recommended for future intensive survey, as they have the potential to be NRHP-eligible districts. These include Conestee Mill Village, the Piedmont Mill Village, the communities of Slater and Fork Shoals, and the communities surrounding the Union and Renfrew Bleacheries. The remaining resources of the survey universe are recommended not eligible for listing