Extremal circular permutations with concave functions

Let {a(1), a(2), ..., a(n)} be a set of n distinct real numbers and let alpha(1), alpha(2), ..., alpha(n) an be a permutation of the numbers. We construct the permutation to maximise L-f = Sigma(i=1)(n) f(\alpha(i+1) - alpha(i)\), for any increasing concave function f, where we denote alpha(n+1) equivalent to alpha(1). The optimal permutation depends on the particular numbers {a(1), a(2), ..., a(n)} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325). (C) 2004 Elsevier Ltd. All rights reserved.

Systemic gene expression in arabidopsis during an incompatible interaction with Alternaria brassicicola

Pathogen challenge can trigger an integrated set of signal transduction pathways, which ultimately leads to a state of high alert, otherwise known as systemic or induced resistance in tissue remote to the initial infection. Although large-scale gene expression during systemic acquired resistance, which is induced by salicylic acid or necrotizing pathogens has been previously reported using a bacterial pathogen, the nature of systemic defense responses triggered by an incompatible necrotrophic fungal pathogen is not known. We examined transcriptional changes that occur during systemic defense responses in Arabidopsis plants inoculated with the incompatible fungal pathogen Alternaria brassicicola. Substantial changes (2.00-fold and statistically significant) were demonstrated in distal tissue of inoculated plants for 35 genes (25 up-regulated and 10 down-regulated), and expression of a selected subset of systemically expressed genes was confirmed using real-time quantitative polymerase chain reaction. Genes with altered expression in distal tissue included those with putative functions in cellular housekeeping, indicating that plants modify these vital processes to facilitate a coordinated response to pathogen attack. Transcriptional up-regulation of genes encoding enzymes functioning in the beta-oxidation pathway of fatty acids was particularly interesting. Transcriptional up-regulation was also observed for genes involved in cell wall synthesis and modification and genes putatively involved in signal transduction. The results of this study, therefore, confirm the notion that distal tissue of a pathogen-challenged plant has a heightened preparedness for subsequent pathogen attacks.

Recursive filtering of images with symmetric extension

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims. (c) 2005 Elsevier B.V. All rights reserved.

Protein kinases associated with the yeast phosphoproteome

Background: Protein phosphorylation is an extremely important mechanism of cellular regulation. A large-scale study of phosphoproteins in a whole-cell lysate of Saccharomyces cerevisiae has previously identified 383 phosphorylation sites in 216 peptide sequences. However, the protein kinases responsible for the phosphorylation of the identified proteins have not previously been assigned. Results: We used Predikin in combination with other bioinformatic tools, to predict which of 116 unique protein kinases in yeast phosphorylates each experimentally determined site in the phosphoproteome. The prediction was based on the match between the phosphorylated 7-residue sequence and the predicted substrate specificity of each kinase, with the highest weight applied to the residues or positions that contribute most to the substrate specificity. We estimated the reliability of the predictions by performing a parallel prediction on phosphopeptides for which the kinase has been experimentally determined. Conclusion: The results reveal that the functions of the protein kinases and their predicted phosphoprotein substrates are often correlated, for example in endocytosis, cytokinesis, transcription, replication, carbohydrate metabolism and stress response. The predictions link phosphoproteins of unknown function with protein kinases with known functions and vice versa, suggesting functions for the uncharacterized proteins. The study indicates that the phosphoproteins and the associated protein kinases represented in our dataset have housekeeping cellular roles; certain kinases are not represented because they may only be activated during specific cellular responses. Our results demonstrate the utility of our previously reported protein kinase substrate prediction approach (Predikin) as a tool for establishing links between kinases and phosphoproteins that can subsequently be tested experimentally.

Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

Exploration of the cell-cycle genes found within the RIKEN FANTOM2 data set

The cell cycle is one of the most fundamental processes within a cell. Phase-dependent expression and cell-cycle checkpoints require a high level of control. A large number of genes with varying functions and modes of action are responsible for this biology. In a targeted exploration of the FANTOM2-Variable Protein Set, a number of mouse homologs to known cell-cycle regulators as well as novel members of cell-cycle families were identified. Focusing on two prototype cell-cycle families, the cyclins and the NIMA-related kinases (NEKs), we believe we have identified all of the mouse members of these families, 24 cyclins and 10 NEKs, and mapped them to ENSEMBL transcripts. To attempt to globally identify all potential cell cycle-related genes within mouse, the MGI (Mouse Genome Database) assignments for the RIKEN Representative Set (RPS) and the results from two homology-based queries were merged. We identified 1415 genes with possible cell-cycle roles, and 1758 potential paralogs. We comment on the genes identified in this screen and evaluate the merits of each approach.

Repressor- and activator-type ethylene response factors functioning in jasmonate signaling and disease resistance identified via a genome-wide screen of Arabidopsis transcription factor gene expression

To identify transcription factors (TFs) involved in jasmonate (JA) signaling and plant defense, we screened 1,534 Arabidopsis (Arabidopsis thaliana) TFs by real-time quantitative reverse transcription-PCR for their altered transcript at 6 h following either methyl JA treatment or inoculation with the incompatible pathogen Alternaria brassicicola. We identified 134 TFs that showed a significant change in expression, including many APETALA2/ethylene response factor (AP2/ERF), MYB, WRKY, and NACTF genes with unknown functions. Twenty TF genes were induced by both the pathogen and methyl JA and these included 10 members of the AP2/ERF TF family, primarily from the B1a and B3 subclusters. Functional analysis of the B1a TF AtERF4 revealed that AtERF4 acts as a novel negative regulator of JA-responsive defense gene expression and resistance to the necrotrophic fungal pathogen Fusarium oxysporum and antagonizes JA inhibition of root elongation. In contrast, functional analysis of the B3 TF AtERF2 showed that AtERF2 is a positive regulator of JA-responsive defense genes and resistance to F. oxysporum and enhances JA inhibition of root elongation. Our results suggest that plants coordinately express multiple repressor-and activator-type AP2/ERFs during pathogen challenge to modulate defense gene expression and disease resistance.

Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models

Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling examples are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.

Objectives for multiple-species conservation planning

The first step in conservation planning is to identify objectives. Most stated objectives for conservation, such as to maximize biodiversity outcomes, are too vague to be useful within a decision-making framework. One way to clarify the issue is to define objectives in terms of the risk of extinction for multiple species. Although the assessment of extinction risk for single species is common, few researchers have formulated an objective function that combines the extinction risks of multiple species. We sought to translate the broad goal of maximizing the viability of species into explicit objectives for use in a decision-theoretic approach to conservation planning. We formulated several objective functions based on extinction risk across many species and illustrated the differences between these objectives with simple examples. Each objective function was the mathematical representation of an approach to conservation and emphasized different levels of threat Our objectives included minimizing the joint probability of one or more extinctions, minimizing the expected number of extinctions, and minimizing the increase in risk of extinction from the best-case scenario. With objective functions based on joint probabilities of extinction across species, any correlations in extinction probabilities bad to be known or the resultant decisions were potentially misleading. Additive objectives, such as the expected number of extinctions, did not produce the same anomalies. We demonstrated that the choice of objective function is central to the decision-making process because alternative objective functions can lead to a different ranking of management options. Therefore, decision makers need to think carefully in selecting and defining their conservation goals.

Salicylic acid mediates resistance to the vascular wilt pathogen Fusarium oxysporum in the model host Arabidopsis thaliana

Fusarium oxysporum is a soilborne fungal pathogen that causes major economic losses by inducing necrosis and wilting symptoms in many crop plants. In this study, the interaction between F. oxysporum and the model plant Arabidopsis thaliana has been investigated to better understand the nature of host defences that are effective against the Fusarium wilt pathogen. The expression of salicylate- and jasmonate-responsive defence genes in F. oxysporum-challenged roots of A. thaliana plants as well as in the roots of plants whose leaves were treated with salicylate or jasmonate was analysed. Unexpectedly, genes (e.g. PR1, PDF1.2, and CHIB) encoding proteins with defensive functions or transcription factors (e.g. ERF1, AtERF2, AtERF4 and AtMYC2) known to positively or negatively regulate defences against F. oxysporum were not activated in F. oxysporum-inoculated roots. In contrast, the jasmonate-responsive defence gene PDF1.2 was induced in the leaves of plants whose roots were challenged with F. oxysporum, but the salicylate- responsive PR1 gene was not induced in the leaves of inoculated plants. Exogenous salicylic acid treatment prior to inoculation, however, activated PR1 and BGL2 defence gene expression in leaves and provided increased F. oxysporum resistance as evidenced by reduced foliar necrosis and plant death. Exogenous salicylic acid treatment of the foliar tissue did not activate defence gene expression in the roots of plants. This suggests that salicylate- dependent defences may function in foliar tissue to reduce the development of pathogen-induced wilting and necrosis. Despite the induction of defence gene expression in the leaves by jasmonate, this treatment did not lead to increased resistance to F. oxysporum. Overall, the results presented here suggest that the genetic manipulation of plant defence signalling pathways is a useful strategy to provide increased Fusarium wilt resistance.

RNA interference-inducing hairpin RNAs in plants act through the viral defence pathway

RNA interference (RNAi) is widely used to silence genes in plants and animals. it operates through the degradation of target mRNA by endonuclease complexes guided by approximately 21 nucleotide (nt) short interfering RNAs (siRNAs). A similar process regulates the expression of some developmental genes through approximately 21 nt microRNAs. Plants have four types of Dicer-like (DCL) enzyme, each producing small RNAs with different functions. Here, we show that DCL2, DCL3 and DCL4 in Arabidopsis process both replicating viral RNAs and RNAi-inducing hairpin RNAs (hpRNAs) into 22-, 24- and 21 nt siRNAs, respectively, and that loss of both DCL2 and DCL4 activities is required to negate RNAi and to release the plant's repression of viral replication. We also show that hpRNAs, similar to viral infection, can engender long-distance silencing signals and that hpRNA-induced silencing is suppressed by the expression of a virus-derived suppressor protein. These findings indicate that hpRNA-mediated RNAi in plants operates through the viral defence pathway.

Production of superpositions of coherent states in traveling optical fields with inefficient photon detection

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS's) with large amplitudes out of CSS's with small amplitudes using inefficient photon detection. The small CSS's required to produce CSS's with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.