Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Histone Methylation Marks on Circulating Nucleosomes as Novel Blood-Based Biomarker in Colorectal Cancer

Circulating nucleic acids (CNAs) are under investigation as a liquid biopsy in cancer as potential non-invasive biomarkers, as stable structure in circulation nucleosomes could be valuable sources for detection of cancer-specific alterations in histone modifications. Our interest is in histone methylation marks with a focus on colorectal cancer, one of the leading cancers respective the incidence and mortality. Our previous work included the analysis of trimethylations of lysine 9 on histone 3 (H3K9me3) and of lysine 20 on histone 4 (H4K20me3) by chromatin immuno- precipitation-related PCR in circulating nucleosomes. Here we asked whether global immunologic measurement of histone marks in circulation could be a suitable approach to show their potential as biomarkers. In addition to H3K9me3 and H4K20me3 we also measured H3K27me3 in plasma samples from CRC patients (n = 63) and cancer free individuals (n = 40) by ELISA-based methylation assays. Our results show that of three marks, the amounts of H3K27me3 (p = 0.04) and H4K20me3 (p < 0.001) were significantly lower in CRC patients than in healthy controls. For H3K9me3 similar amounts were measured in both groups. Areas under the curve (AUC) in receiver operating characteristic (ROC) curves indicating the power of CRC detection were 0.620 for H3K27me3, 0.715 for H4K20me3 and 0.769 for the combination of both markers. In conclusion, findings of this preliminary study reveal the potential of blood-based detection of CRC by quantification of histone methylation marks and the additive effect of the marker combination.     

Construction of Programmed Motions of Constrained Mechanical Systems Using Third-Order Polynomials

Journal of Computer and Systems Sciences International - A problem of the synthesis of programmed motions of mechanical systems based on the use of time polynomials is considered. The programmed...     

Optimization of Pathogen Capture in Flowing Fluids with Magnetic Nanoparticles

Magnetic nanoparticles have been employed to capture pathogens for many biological applications; however, optimal particle sizes have been determined empirically in specific capturing protocols. Here, a theoretical model that simulates capture of bacteria is described and used to calculate bacterial collision frequencies and magnetophoretic properties for a range of particle sizes. The model predicts that particles with a diameter of 460 nm should produce optimal separation of bacteria in buffer flowing at 1 L h⁻¹. Validating the predictive power of the model, Staphylococcus aureus is separated from buffer and blood flowing through magnetic capture devices using six different sizes of magnetic particles. Experimental magnetic separation in buffer conditions confirms that particles with a diameter closest to the predicted optimal particle size provide the most effective capture. Modeling the capturing process in plasma and blood by introducing empirical constants (c_e), which integrate the interfering effects of biological components on the binding kinetics of magnetic beads to bacteria, smaller beads with 50 nm diameters are predicted that exhibit maximum magnetic separation of bacteria from blood and experimentally validated this trend. The predictive power of the model suggests its utility for the future design of magnetic separation for diagnostic and therapeutic applications.