On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Gibbs random graphs on point processes

Consider a discrete locally finite subset Gamma of R(d) and the cornplete graph (Gamma, E), with vertices Gamma and edges E. We consider Gibbs measures on the set of sub-graphs with vertices Gamma and edges E` subset of E. The Gibbs interaction acts between open edges having a vertex in common. We study percolation properties of the Gibbs distribution of the graph ensemble. The main results concern percolation properties of the open edges in two cases: (a) when Gamma is sampled from a homogeneous Poisson process; and (b) for a fixed Gamma with sufficiently sparse points. (c) 2010 American Institute of Physics. [doi:10.1063/1.3514605]

Toxicity-directed approach of polyester manufacturing industry wastewater provides useful information for conducting treatability studies

A broader characterization of industrial wastewaters, especially in respect to hazardous compounds and their potential toxicity, is often necessary in order to determine the best practical treatment (or pretreatment) technology available to reduce the discharge of harmful pollutants to the environment or publicly owned treatment works. Using a toxicity-directed approach, this paper sets the base for a rational treatability study of polyester resin manufacturing. Relevant physical and chemical characteristics were determined. Respirometry was used for toxicity reduction evaluation after physical and chemical effluent fractionation. Of all the procedures investigated, only air stripping was significantly effective in reducing wastewater toxicity. Air stripping in pH 7 reduced toxicity in 18.2%, while in pH 11 a toxicity reduction of 62.5% was observed. Results indicated that toxicants responsible for the most significant fraction of the effluent`s instantaneous toxic effect to unadapted activated sludge were organic compounds poorly or not volatilized in acid conditions. These results led to useful directions for conducting treatability studies which will be grounded on actual effluent properties rather than empirical or based on the rare specific data on this kind of industrial wastewater. (C) 2008 Elsevier B.V. All rights reserved.

Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fMRI

Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp 30:452-461, 2009. (C) 2007 Wiley-Liss, Inc.

Characterization of electrical penetration graphs of the Asian citrus psyllid, Diaphorina citri, in sweet orange seedlings

Detailed information on probing behavior of the Asian citrus psyllid, Diaphorina citri Kuwayama (Hemiptera: Psyllidae), is critical for understanding the transmission process of phloem-limited bacteria (Candidatus Liberibacter spp.) associated with citrus `huanglongbing` by this vector. In this study, we investigated stylet penetration activities of D. citri on seedlings of Citrus sinensis (L.) Osbeck cv. Pera (Rutaceae) by using the electrical penetration graph (EPG-DC system) technique. EPG waveforms were described based on amplitude, frequency, voltage level, and electrical origin of the observed traces during stylet penetration into plant tissues. The main waveforms were correlated with histological observations of salivary sheath termini in plant tissues, to determine the putative location of stylet tips. The behavioral activities were also inferred based on waveform similarities in relation to other Sternorrhyncha, particularly aphids and whiteflies. In addition, we correlated the occurrence of specific waveforms with the acquisition of the phloem-limited bacterium Ca. Liberibacter asiaticus by D. citri. The occurrence of a G-like xylem sap ingestion waveform in starved and unstarved psyllids was also compared. By analyzing 8-h EPGs of adult females, five waveforms were described: (C) salivary sheath secretion and other stylet pathway activities; (D) first contact with phloem (distinct from other waveforms reported for Sternorrhyncha); (E1) putative salivation in phloem sieve tubes; (E2) phloem sap ingestion; and (G) probably xylem sap ingestion. Diaphorina citri initiates a probe with stylet pathway through epidermis and parenchyma (C). Interestingly, no potential drops were observed during the stylet pathway phase, as are usually recorded in aphids and other Sternorrhyncha. Once in C, D. citri shows a higher propensity to return to non-probing than to start a phloem or xylem phase. Several probes are usually observed before the phloem phase; waveform D is observed upon phloem contact, always immediately followed by E1. After E1, D. citri either returns to pathway activity (C) or starts phloem sap ingestion, which was the longest activity observed.

Characterization of electrical penetration graphs of Bucephalogonia xanthophis, a vector of Xylella fastidiosa in citrus

The sharpshooter Bucephalogonia xanthophis (Berg) (Homoptera: Cicadellidae) is a vector of the xylem-limited bacterium, Xylella fastidiosa (Wells, Raju, Hung, Weisburg, Mandelco-Paul, and Brenner), which causes citrus variegated chlorosis. Despite the importance of citrus variegated chlorosis, the probing behavior of vectors on citrus and its implications for transmission of X. fastidiosa have not been studied. Here we studied electrical penetration graph (EPG-DC system) waveforms produced by B. xanthophis on Citrus sinensis (L.) Osbeck (Rutaceae), and their relationships with stylet activities and xylem ingestion. Electrical penetration graph waveforms were described based on amplitude, frequency, voltage level, and electrical origin of the observed traces during stylet penetration on plant tissues. The main waveforms were correlated with histological observations of salivary sheaths in plant tissues and excretion analysis, in order to determine stylet activities and their precise position. Six waveforms and associated activities are described: (S) secretion of salivary sheath and intracellular stylet pathway, (R) resting during stylet pathway, (Xc) contact of stylets with xylem vessels, (Xi) active xylem ingestion, (N) interruption within the xylem phase (during Xc or Xi), and (W) withdrawal of stylet from the plant. The sharpshooter spent 91.8% of its probing time with its stylet in the xylem, where the main activity was ingestion (Xi: 97.5%). During a probe, the most likely sequence of events is secretion of salivary sheath and pathway (S) through epidermal and parenchyma cells (all individuals), followed by contact with xylem (Xc) (67.6% of all individuals) and ingestion (Xi) (88.3% of those that exhibit waveform Xc). The mean time to contact the xylem (Xc) and initiate ingestion (Xi) after onset of the first probe was 27.8 and 34.2 min, respectively. However, sustained xylem ingestion (Xi > 5 min) was established after 39.8 min, on average. This information is basic for future studies on the transmission mechanisms of X. fastidiosa and in order to establish control strategies aimed at interfering with this process.

Evaluation of GFP Tag as a Screening Reporter in Directed Evolution of a Hyperthermophilic beta-Glucosidase

By applying a directed evolution methodology specific enzymatic characteristics can be enhanced, but to select mutants of interest from a large mutant bank, this approach requires high throughput screening and facile selection. To facilitate such primary screening of enhanced clones, an expression system was tested that uses a green fluorescent protein (GFP) tag from Aequorea victoria linked to the enzyme of interest. As GFP`s fluorescence is readily measured, and as there is a 1:1 molar correlation between the target protein and GFP, the concept proposed was to determine whether GFP could facilitate primary screening of error-prone PCR (EPP) clones. For this purpose a thermostable beta-glucosidase (BglA) from Fervidobacterium sp. was used as a model enzyme. A vector expressing the chimeric protein BglA-GFP-6XHis was constructed and the fusion protein purified and characterized. When compared to the native proteins, the components of the fusion displayed modified characteristics, such as enhanced GFP thermostability and a higher BglA optimum temperature. Clones carrying mutant BglA proteins obtained by EPP, were screened based on the BglA/GFP activity ratio. Purified tagged enzymes from selected clones resulted in modified substrate specificity.

Trades and Graphs

The trade spectrum of a simple graph G is defined to be the set of all t for which it is possible to assemble together t copies of G into a simple graph H, and then disassemble H into t entirely different copies of G. Trade spectra of graphs have applications to intersection problems, and defining sets, of G-designs. In this investigation, we give several constructions, both for specific families of graphs, and for graphs in general.

Packing complete multipartite graphs with 4-cycles

In this paper we completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.

The metal directed assembly of a trinuclear macrocyclic copper(II) complex

A trinuclear macrocyclic complex is reported from the metal directed condensation between melamine, formaldehyde and the Cu-II complex of a linear tetraamine.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Site-directed mutants of RTP of Bacillus subtilis and the mechanism of replication fork arrest

DNA replication fork arrest during the termination phase of chromosome replication in Bacillus subtilis is brought about by the replication terminator protein (RTP) bound to specific DNA terminator sequences (Tev sites) distributed throughout the terminus region. An attractive suggestion by others was that crucial to the functioning of the RTP-Ter complex is a specific interaction between RTP positioned on the DNA and the helicase associated with the approaching replication fork. Ln support of this was the behaviour of two site-directed mutants of RTP. They appeared to bind Ter DNA normally but were ineffective in fork arrest as ascertained by in vitro Escherichia coli DnaB helicase and replication assays. We describe here a system for assessing the fork-arrest behaviour of RTP mutants in a bona fide in vivo assay in B. subtilis. One of the previously studied mutants, RTP.Y33N, was non-functional in fork arrest in vivo, as predicted. But through extensive analyses, this RTP mutant was shown to be severely defective in binding to Ter DNA, contrary to expectation. Taken in conjunction with recent findings on the other mutant (RTP.E30K), it is concluded that there is as yet no substantive evidence from the behaviour of RTP mutants to support the Rm-helicase interaction model for fork arrest. In an extension of the present work on RTP.Y33N, we determined the dissociation rates of complexes formed by wild-type (wt) RTP and another RTP mutant with various terminator sequences. The functional wtRTP-TerI complex was quite stable (half-life of 182 minutes), reminiscent of the great stability of the E. coli Tus-Ter complex. More significant were the exceptional stabilities of complexes comprising wtRTP and an RTP double-mutant (E39K.R42Q) bound to some particular terminator sequences. From the measurement of in vivo fork-arrest activities of the various complexes, it is concluded that the stability (half-life) of the whole RTP-Ter complex is not the overriding determinant of arrest, and that the RTP-Ter complex must be actively disrupted, or RTP removed, by the action of the approaching replication fork. (C) 1999 Academic Press.

Analysis of the substrate specificity of human sulfotransferases SULT1A1 and SULT1A3: Site-directed mutagenesis and kinetic studies

Sulfonation is an important metabolic process involved in the excretion and in some cases activation of various endogenous compounds and xenobiotics. This reaction is catalyzed by a family of enzymes named sulfotransferases. The cytosolic human sulfotransferases SULT1A1 and SULT1A3 have overlapping yet distinct substrate specificities. SULT1A1 favors simple phenolic substrates such as p-nitrophenol, whereas SULT1A3 prefers monoamine substrates such as dopamine. In this study we have used a variety of phenolic substrates to functionally characterize the role of the amino acid at position 146 in SULT1A1 and SULT1A3. First, the mutation A146E in SULT1A1 yielded a SULT1A3-like protein with respect to the Michaelis constant for simple phenols. The mutation E146A in SULT1A3 resulted in a SULT1A1-like protein with respect to the Michaelis constant for both simple phenols and monoamine compounds. When comparing the specificity of SULT1A3 toward tyramine with that for p-ethylphenol (which differs from tyramine in having no amine group on the carbon side chain), we saw a 200-fold preference for tyramine. The kinetic data obtained with the E146A mutant of SULT1A3 for these two substrates clearly showed that this protein preferred substrates without an amine group attached. Second, changing the glutamic acid at position 146 of SULT1A3 to a glutamine, thereby neutralizing the negative charge at this position, resulted in a 360-fold decrease in the specificity constant for dopamine. The results provide strong evidence that residue 146 is crucial in determining the substrate specificity of both SULT1A1 and SULT1A3 and suggest that there is a direct interaction between glutamic acid 146 in SULT1A3 and monoamine substrates.