Time-Bounded Kolmogorov Complexity and Solovay Functions

A Solovay function is an upper bound g for prefix-free Kolmogorov complexity K that is nontrivial in the sense that g agrees with K, up to some additive constant, on infinitely many places n. We obtain natural examples of computable Solovay functions by showing that for some constant c ₀ and all computable functions t such that c ₀ n??t(n), the time-bounded version K ^t of K is a Solovay function. By unifying results of Bienvenu and Downey and of Miller, we show that a right-computable upper bound g of K is a Solovay function if and only if ?? _g =??2^?g(n) is Martin-Löf random. We obtain as a corollary that the Martin-Löf randomness of the various variants of Chaitin??s ?? extends to the time-bounded case in so far as $\Omega _{ \textnormal{K}^{t}}$ is Martin-Löf random for any t as above. As a step in the direction of a characterization of K-triviality in terms of jump-traceability, we demonstrate that a set A is K-trivial if and only if A is O(g(n)?K(n))-jump traceable for all computable Solovay functions g. Furthermore, this equivalence remains true when the universal quantification over all computable Solovay functions in the second statement is restricted either to all functions of the form K ^t for some function t as above or to a single function K ^t of this form. Finally, we investigate into the plain Kolmogorov complexity C and its time-bounded variant C ^t of initial segments of computably enumerable sets. Our main theorem here asserts that every high c.e. Turing degree contains a c.e. set B such that for any computable function t there is a constant c _t >0 such that for all m it holds that C ^t (B?m)??c _t ?m, whereas for any nonhigh c.e. set A there is a computable time bound t and a constant c such that for infinitely many m it holds that C ^t (A?m)??logm+c. By similar methods it can be shown that any high degree contains a set B such that C ^t (B?m)??⁺ m/4. The constructed sets B have low unbounded but high time-bounded Kolmogorov complexity, and accordingly we obtain an alternative proof of the result due to Juedes et al. (Theor. Comput. Sci. 132(1?C2):37?C70, 1994) that every high degree contains a strongly deep set.     

Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin)

A general subresultant method is introduced to compute elements of a given ideal with few terms and bounded coefficients. This subresultant method is applied to solve over-determined polynomial systems by either finding a triangular representation of the solution set or by reducing the problem to eigenvalue computation. One of the ingredients of the subresultant method is the computation of a matrix that satisfies certain requirements, called the subresultant properties  . Our general framework allows us to use matrices of significantly smaller size than previous methods. We prove that certain previously known matrix constructions, in particular, Macaulay’s, Chardin’s and Jouanolou’s resultant and subresultant matrices possess the subresultant properties. However, these results rely on some assumptions about the regularity of the over-determined system to be solved. The appendix, written by Marc Chardin, contains relevant results on the regularity of n$n$ homogeneous forms in n$n$ variables.     

Evaluation of Root Exudates of Seven Sorghum Accessions

Seven sorghum accessions were evaluated quantitatively and qualitatively for the composition of their root exudates. Utilizing a unique capillary mat growing system, root exudates were collected from all sorghum accessions. Exudates were subjected to TLC and HPLC analysis to evaluate their chemical composition. Within each sorghum accession, variation existed in the amount of exudate produced and the chemical constituents of each exudate. Sorgoleone was the predominant constituent identified in each accession's exudate. Other closely related compounds, including 5-ethoxysorgoleone, 2,5-dimethoxysorgoleone, three other minor components (MW = 364, 388, and 402), and one unidentified component comprised the minor constituents of the root exudate. Our past work has shown that several of these compounds have potent phytotoxic activity as photosystem II inhibitors, thereby lending further support to the concept that Sorghum spp. are allelopathic and weed suppressive.     

Inhibition of human recombinant cytochromes P450 CYP1A1 and CYP1B1 by trans-resveratrol methyl ethers

CYP1A1 and CYP1B1 are the inducible forms of cytochrome P450 expressed in extrahepatic tissues, which are responsible for the biotransformation of polycyclic aromatic hydrocarbons, heterocyclic amines and estradiol to the carcinogenic intermediates. The aim of our research was to determine and compare the inhibitory effect of naturally occurring analogues of trans-resveratrol on the catalytic activities of human recombinant CYP1A1 and CYP1B1. Pinostilbene (3,4'-dihydroxy-5-methoxystilbene), desoxyrhapontigenin (3,5-dihydroxy-4'-methoxystilbene), and pterostilbene (3,5-dimethoxy-4'-hydroxystilbene) appeared to be very potent inhibitors of CYP1A1 catalytic activity with Ki values of 0.13, 0.16 and 0.57 microM, respectively. Results from this study indicate that trans-resveratrol analogues in which the hydroxy groups are substituted by methoxy groups exhibit a remarkably stronger inhibitory effect towards CYP1A1 in comparison to the parent compound. On the contrary, the potency of pinostilbene, desoxyrhapontigenin and pterostilbene towards CYP1B1 with Ki values of 0.90, 2.06 and 0.91 microM, respectively, was comparable to that of resveratrol. It appears that between these analogues, inhibition of CYP1A1 and CYP1B1 catalytic activities does not vary much regardless of the number and position of methylether substitution. The results suggest that the trans-resveratrol analogues: pinostilbene, desoxyrhapontigenin and pterostilbene, which occur in some food plants, might be considered as promising chemopreventive agents.     

Implicit measures: A normative analysis and review.

Implicit measures can be defined as outcomes of measurement procedures that are caused in an automatic manner by psychological attributes. To establish that a measurement outcome is an implicit measure, one should examine (a) whether the outcome is causally produced by the psychological attribute it was designed to measure, (b) the nature of the processes by which the attribute causes the outcome, and (c) whether these processes operate automatically. This normative analysis provides a heuristic framework for organizing past and future research on implicit measures. The authors illustrate the heuristic function of their framework by using it to review past research on the 2 implicit measures that are currently most popular: effects in implicit association tests and affective priming tasks. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Correlation of physicochemical and nutritional properties of dry matter and starch in potatoes grown in different locations

The physicochemical and nutritional properties of dry matter and starches were studied from 13 potato varieties grown in different locations in Canada. Pearson correlation and principal component analysis were employed to examine relationships amongst variables. Phosphorus content in starch was negatively correlated to rapidly and slowly digestible starch content, while positively correlated to resistant starch content (RS) in raw dry matter and raw starch (p < 0.001). RS content of cooked starch was positively correlated to phosphorus content (0.48, p < 0.01), enthalpy of retrograded starch (0.48, p < 0.01), peak viscosity (0.52, p < 0.001) and breakdown of starch (0.43, p < 0.01). The principal component analysis grouped the 13 potato varieties by growing location, where phosphorus content in starch was the major difference. The results would imply that phosphorus content of starch was a key factor affecting physicochemical and nutritional properties of dry matter and starch in potatoes.     

Tocopheryl polyethylene glycol succinate as a safe, antioxidant surfactant for processing carbon nanotubes and fullerenes

This work investigates the physical interactions between carbon nanomaterials and tocopheryl polyethylene glycol succinate (TPGS). TPGS is a synthetic amphiphile that undergoes enzymatic cleavage to deliver the lipophilic antioxidant, α-tocopherol (vitamin E) to cell membranes, and is FDA approved as a water-soluble vitamin E nutritional supplement and drug delivery vehicle. Here we show that TPGS 1000 is capable of dispersing multi-wall and single-wall carbon nanotubes in aqueous media, and for multi-wall tubes is more effective than the commonly used non-ionic surfactant Triton X-100. TPGS is also capable of solubilizing C₆₀ in aqueous phases by dissolving fullerene in the core of its spherical micelles. Drying of these solutions leads to fullerene/TPGS phase separation and the self-assembly of highly ordered asymmetric nanoparticles, with fullerene nanocrystals attached to the hydrophobic end of crystalline TPGS nanobrushes. The article discusses surface charge, colloidal stability, and the potential applications of TPGS as a safe surfactant for “green” processing of carbon nanomaterials.     

Analysis of countercurrent membrane vapor extraction of a dilute aqueous biosolute

Removal of dilute bioproducts from fermenter broths is a major challenge both to avoid microbe inhibition and to recover solutes economically without water loss. We analyze a proposed new process, membrane vapor extraction (MVE), where semi‐volatile dilute aqueous solutes vaporize at the upstream side of an omniphobic, microporous membrane and dissolve into a nonpolar solvent highly favorable to the solutes but not to water. A new membrane‐process analysis is outlined and applied to the countercurrent recovery of 2 wt % aqueous butanol by a prototype solvent (dodecane) at 40°C. Thermodynamic phase equilibria, pioneered by the Prausnitz school, are crucial to MVE process design. Over 90% of the feed butanol is recovered with essentially no water loss giving a separation factor of over 1000. Energy requirements in MVE are low. Our design calculations demonstrate that MVE is a viable separation process to remove and recover dilute aqueous biosolutes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2795–2809, 2015     

An Evaluation of Different 3D Cultivation Models on Expression Profiles of Human Periodontal Ligament Fibroblasts with Compressive Strain

The effects of compressive strain during orthodontic treatment on gene expression profiles of periodontal ligament fibroblasts (PDLFs) have mostly been studied in 2D cell culture. However, cells behave differently in many aspects in 3D culture. Therefore, the effect of pressure application on PDLFs in different 3D structures was investigated. PDLFs were either conventionally seeded or embedded into different 3D structures (spheroids, Mebiol^® gel, 3D scaffolds) and exposed to compressive force or incubated without pressure. For one 3D scaffold (POR), we also tested the effect of different compressive forces and application times. Expression of an angiogenic gene (VEGF), a gene involved in extracellular matrix synthesis (COL1A2), inflammatory genes (IL6, PTGS2), and genes involved in bone remodelling (OPG, RANKL) were investigated by RT–qPCR. Depending on the used 3D cell culture model, we detected different effects of compressive strain on expression profiles of PDLFs. COL1A2 was downregulated in all investigated 3D culture models. Angiogenetic and proinflammatory genes were regulated differentially between models. In 3D scaffolds, regulation of bone-remodelling genes upon compressive force was contrary to that observed in 3D gels. 3D cell culture models provide better approximations to in vivo physiology, compared with conventional 2D models. However, it is crucial which 3D structures are used, as these showed diverse effects on the expression profiles of PDLFs during mechanical strain.     

Efficacy of gamma radiation and aqueous chlorine on Escherichia coli O157:H7 in hydroponically grown lettuce plants

Interaction of Escherichia coli O157:H7/pGFP with hydroponically grown lettuce plants was evaluated in this study. Lettuce seedlings were planted in contaminated Hoagland's nutrient solution and thereafter subjected to gamma radiation at 0.25, 0.5, and 0.75 kGy, and aqueous chlorine at 200 ppm. There was no trace of E. coli O157:H7/pGFP in lettuce leaves harvested from noncontaminated nutrient solution (control); however, for plants grown in contaminated nutrient solution, the pathogen was recovered from the leaves disinfected with 80% ethanol and 0.1% mercuric chloride. Most of the lettuce seedlings grown in contaminated nutrient solution tested negative for E. coli O157:H7/pGFP under controlled conditions. Gamma radiation at 0.25 and 0.5 kGy, and aqueous chlorine at 200 ppm failed to eliminate E. coli O157:H7/pGFP in lettuce tissue completely; however, the bacteria were not detected in 0.75-kGy treated plants. The presence of E. coli O157:H7/pGFP in lettuce leaves is an indication that the pathogen migrated from the contaminated hydroponic system through the roots to the internal locations of lettuce tissue. Due to inaccessibility and limited penetrating power, aqueous chlorine could not eliminate the bacteria localized in the internal tissue. Findings from this study suggest that gamma irradiation was more efficacious than was aqueous chlorine to control internal contamination in hydroponically grown lettuce. Gamma irradiation is a process that processors can use to inactivate E. coli O157:H7 and therefore, consumers benefit from a safer food product [corrected]