Response Curves and Preimage Sequences of Two-Dimensional Cellular Automata

We consider the problem of finding response curves for a class of binary two-dimensional cellular automata with $L$-shaped neighbourhood. We show that the dependence of the density of ones after an arbitrary number of iterations, on the initial density of ones, can be calculated for a fairly large number of rules by considering preimage sets. We provide several examples and a summary of all known results. We consider a special case of initial density equal to 0.5 for other rules and compute explicitly the density of ones after $n$ iterations of the rule. This analysis includes surjective rules, which in the case of $L$-shaped neighbourhood are all found to be permutive. We conclude with the observation that all rules for which preimage curves can be computed explicitly are either finite or asymptotic emulators of identity or shift.Comment: 7 pages, 3 figure

Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules

Silver(I), gold(I) and palladium(II) complexes of a NHC-pincer ligand with an aminotriazine core: a comparison with pyridyl analogues

Dinuclear silver, di- and tetra-nuclear gold, and mononuclear palladium complexes with chelating C,N,C diethylaminotriazinyl-bridged bis(NHC) pincer ligands were prepared and characterised. The silver and gold complexes exist in a twisted, helical conformation in both the solution- and the solid state. In contrast, an analogous dinuclear gold complex with pyridyl-bridged NHCs exists in a linear conformation. Computational studies have been performed to rationalise the formation of twisted/helical vs. linear forms

Long non-coding RNA ROCR contributes to SOX9 expression and chondrogenic differentiation of human mesenchymal stem cells

Long non-coding RNAs (lncRNAs) are expressed in a highly tissue-specific manner where they function in various aspects of cell biology, often as key regulators of gene expression. In this study we established a role for lncRNAs in chondrocyte differentiation. Using RNA sequencing we identified a human articular chondrocyte repertoire of lncRNAs from normal hip cartilage donated by neck of femur fracture patients. Of particular interest are lncRNAs upstream of the master chondrocyte transcription factor SOX9 locus. SOX9 is an HMG-box transcription factor which is essential for chondrocyte development by directing the expression of chondrocyte specific genes. Two of these lncRNAs are upregulated during chondrogenic differentiation of MSCs. Depletion of one of these lncRNA, LOC102723505, which we termed ROCR (regulator of chondrogenesis RNA), by RNAi disrupted MSC chondrogenesis, concomitant with reduced cartilage-specific gene expression and incomplete matrix component production, indicating an important role in chondrocyte biology. Specifically, SOX9 induction was significantly ablated in the absence of ROCR, and overexpression of SOX9 rescued the differentiation of MSCs into chondrocytes. Our work sheds further light on chondrocyte specific SOX9 expression and highlights a novel method of chondrocyte gene regulation involving a lncRNA