Intrinsically Multivariate Predictive Genes

Canalizing genes possess such broad regulatory power, and their action sweeps across a such a wide swath of processes that the full set of affected genes are not highly correlated under normal conditions. When not active, the controlling gene will not be predictable to any significant degree by its subject genes, either alone or in groups, since their behavior will be highly varied relative to the inactive controlling gene. When the controlling gene is active, its behavior is not well predicted by any one of its targets, but can be very well predicted by groups of genes under its control. To investigate this question, we introduce in this paper the concept of intrinsically multivariate predictive (IMP) genes, and present a mathematical study of IMP in the context of binary genes with respect to the coefficient of determination (CoD), which measures the predictive power of a set of genes with respect to a target gene. A set of predictor genes is said to be IMP for a target gene if all properly contained subsets of the predictor set are bad predictors of the target but the full predictor set predicts the target with great accuracy. We show that logic of prediction, predictive power, covariance between predictors, and the entropy of the joint probability distribution of the predictors jointly affect the appearance of IMP genes. In particular, we show that high-predictive power, small covariance among predictors, a large entropy of the joint probability distribution of predictors, and certain logics, such as XOR in the 2-predictor case, are factors that favor the appearance of IMP. The IMP concept is applied to characterize the behavior of the gene DUSP1, which exhibits control over a central, process-integrating signaling pathway, thereby providing preliminary evidence that IMP can be used as a criterion for discovery of canalizing genes.

Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2 + epsilon, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs. (C) 2007 Elsevier B.V. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Noncommutative Jordan superalgebras of degree n > 2

We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a ""nodal"" case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0.

On the Relative Socle for Stratifying Systems

Let A be a finite dimensional k-algebra, (, ) be a stratifying system in mod(A) and F() be the class of -filtered A-modules. In this article, we give the definition and also study some of the properties of the relative socle in F(). We approach the relative socle in three ways. Namely, we view it as (1) a -semisimple subobject of M having the largest -length, (2) a maximal -semisimple subobject of M, and (3) a minimal -essential subobject of M.

INSECT CHYMOTRYPSINS: CHLOROMETHYL KETONE INACTIVATION AND SUBSTRATE SPECIFICITY RELATIVE TO POSSIBLE COEVOLUTIONAL ADAPTATION OF INSECTS AND PLANTS

Insect digestive chymotrypsins are present in a large variety of insect orders but their substrate specificity still remains unclear. Ewer insect chymotrypsins from 3 different insect orders (Dictyoptera, Coleoptera and two Lepidoptera) were isolated using affinity chromatography. Enzymes presented molecular masses in the range of 20 to 31 kDa and pH optima in the range of 7.5 to 10.0. Kinetic characterization. using different, colorimetric and fluorescent substrates indicated that insect chymotrypsins differ from, bovine chymotrypsin in their primary specificity toward small substrates (like N-benzoyl-L-Tyr p-nitroanilide) rather than on their preference for large substrates (exemplified by Succynil-Ala-Ala-Pro-Phe P-nitroanilide). Chloromethyl ketones (TPCK, N-alpha-tosyl-L-Phe chloromethyl ketone and Z-GGF-CK, N-carbobenzoxy-Gly-Gly-phe-CK) inactivated all chymotrypsins legated. Inactivation rates follow apparent first-order kinetics with variable second order rates (TPCK, 42 to 130 M(-1)s(-1); Z-GGF-CK, 150 to 450 M(-1)s(-1) that may be remarkably low for S. frugiperda chymotrypsin (TPCK, 6 M(-1)s(-1); Z-GGF-CK, 6.1 M(-1) s(-1)). Homology modelling and sequence alignment showed that. in lepidopteran chymotrypsins, differences in the amino acid residues in the neighborhood of the catalytic His 57 may affect its pKa, value. This is Proposed as the cause of the decrease in His 57 reactivity toward chloromethyl ketones. Such amino acid replacement in the active site is proposed. to be an adaptation to the presence of dietary ketones. (C) 2009 Wiley Periodicals, Inc.

Flexural properties, microleakage, and degree of conversion of a resin polymerized with conventional light and argon laser

Objective: To evaluate the flexural strength, microleakage, and degree of conversion of a microhybrid resin polymerized with argon laser and halogen lamp. Method and Materials: For both flexural test and degree of conversion analysis, 5 bar samples of composite resin were prepared and polymerized according to ISO 4049. The halogen light-curing unit was used with 500 MW/cm(2) for 20 seconds and the argon laser with 250 mW for 10 and 20 seconds. Samples were stored in distilled water in a dark environment at 37 degrees C for 24 hours. The flexural property was quantified by a 3-point loading test. For the microleakage evaluation, 60 bovine incisors were used to prepare standardized Class 5 cavities, which were restored and polished. Specimens were stored in distilled water for 24 hours at 37 degrees C and thermocycled 500 times (6 degrees C to 60 degrees C). Specimens were then immersed in art aqueous solution of basic fuchsin for 24 hours. Longitudinal sections of each restoration were obtained and examined with a stereomicroscope for qualitative evaluation of microleakage. Fourier transform (FT)-Raman RFS 100/S spectrometer (Bruker) was used to analyze the degree of conversion. Results: ANOVA showed no statistically significant differences of flexural strength between the photoactivation types evaluated in the flexural study. Microleakage data were statistically analyzed by Mann-Whitney and Kruskal-Wallis tests. Enamel margins resulted in a statistically lower degree of leakage than dentin margins. No statistically significant difference was found among the 3 types of photocuring studied. ANOVA also showed no statistically significant difference in the degree of conversion among the studied groups. Conclusion: According to the methodology used in this research, the argon laser is a possible alternative for photocuring, providing the same quality of polymerization as the halogen lamp. None of the photocured units tested in this study completely eliminated microleakage.

Expedient, accurate methods for the determination of the degree of substitution of cellulose carboxylic esters: Application of UV-vis spectroscopy (dye solvatochromism) and FTIR

Two techniques, namely UV-vis- and FTIR spectroscopy, have been employed in order to calculate the degree of substitution (DS) of cellulose carboxylic esters, including acetates, CAs, butyrates, CBs, and hexanoates, CHs. Regarding UV-vis spectroscopy, we have employed a novel approach, based on measuring the dependence of lambda(max) of the intra-molecular charge-transfer bands of polarity probes adsorbed on DS of the ester films (solvatochromism). Additionally, we have revisited the use of FTIR for DS determination. Several methods have been used in order to plot Beer`s law graph, namely: Absorption of KBr pellets, pre-coated with CA: reflectance (DRIFTS) of CAs-KBr solid-solid mixtures with, or without the use of 1.4-dicyanobenzene as an internal reference; reflectance of KBr powder pre-coated with CA. The methods indicated are simple, fast, and accurate, requiring much less ester than the titration method. The probe method is independent of the experimental variables examined. (c) 2010 Published by Elsevier Ltd.

Probing the dependence of the properties of cellulose acetates and their films on the degree of biopolymer substitution: use of solvatochromic indicators and thermal analysis

Although cellulose acetates, CAs, are extensively employed there is scant information about the systematic dependence of their properties on their degree of substitution, DS; this is the subject of the present work. Nine CAs samples, DS from 0.83 to 3.0 were synthesized; their films were prepared. The following solvatochromic probes have been employed in order to determine the empirical polarity, E (T)(33); ""acidity, alpha""; ""basicity, beta"", and ""dipolarity/polarizability, pi*"" of the casted films: 2,6-dichloro-4-(2,4,6-triphenyl-pyridinium-1-yl) phenolate, WB; 4-nitroaniline; 4-nitroanisole; 4-nitro-N,N-dimethylaniline; 2,6-diphenyl-4-(2,4,6-triphenyl-pyridinium-1-yl)phenolate, RB. Additionally, two systems, ethanol plus ethyl acetate (EtOH-EtAc), and cellulose plus cellulose triacetate, CTA, were employed as models for CAs of different DS. Regarding the model systems, the following was observed: (i) For EtOH-EtAc, the dependence of all solvatochromic parameters on the ""equivalent-DS"" of the binary mixture was non-linear because of preferential solvation; (ii) The dependence of E (T)(33) on equivalent DS of the cellulose-CTA films is linear, but the slope is smaller than that of the corresponding plot for CAs. This is attributed to the more efficient hydrogen bonding in the model system, a conclusion corroborated by IR measurements. The dependence of solvatochromic parameters of CAs on their DS is described by the simple equations; a consequence of the substitution of the OH by the ester group. The thermal properties of bulk CAs samples were investigated by DSC and TGA; their dependence on DS is described by simple equations. The relevance of these data to the processing and applications of CAs is briefly discussed.

Tellurium in organic synthesis: a new approach to trisubstituted gamma-butyrolactones with trans-trans relative stereochemistry. Total enantioselective synthesis of (-)-Blastmycinolactol, (+)-Blastmycinone, (-)-NFX-2, and (+)-Antimycinone

The total synthesis of (-)-Blastmycinolactol, (+)-Blastmycinone, (-)-NFX-2, and (+)-Antimycinone was accomplished in few steps in high yields and ee, starting from enantiomerically enriched (S)-Z-vinylic hydroxytellurides. (C) 2010 Published by Elsevier Ltd.

FT-Raman investigation of biodegradable polymers: Poly(3-hydroxybutyrate) and poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

This work presents a FT-Raman study (lambda(0) = 1064 nm) of naturally occurring polyester poly[(R)-3-hydroxybutyrate] (PHB) and its copolymer poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyvalerate] (PHBV) with 5,8 and 12 mol % of HV (hydroxyvalerate). The FT-Raman spectra of films indicate that full width at half height of the band centered at 1725 cm(-1) and relative intensity of bands at 1443 and 1458 cm(-1) can be use to estimate the crystalline degree in film samples. The similarity between Raman spectra of molten PHB and PHBV and theirs CDCl(3) solutions suggested that molten polymers present similar conformation than polymers in solution. Raman data of these samples showed that bands at 1220, 1402, 1725, 2998 and 3009 cm(-1) are due to crystalline helical structure and the bands at 1453, 1740, 2881, 2938 and 2990 cm(-1) are originated from disordered domains. It is shown that composition of PHBV samples can be estimated by analyzing the ratio of the intensity of the bands at 2938 cm(-1) (nu C-H) and 1740 cm(-1) (nu C=O) in the spectra of solutions and of bands at 1354 (wCH(2)) and 1740 cm(-1) (nu C=O) in spectra of molten polymers. (C) 2010 Elsevier B.V. All rights reserved.