Phytoconstituents of Methanolic Extract of Fenugreek Seeds as a Green Corrosion Inhibitor of Metals (Fe, Al and Cu)

DFT calculations were carried out on significant Fenugreek seed compounds (1-Methylpyridinium-3-carboxylate MPC, Apigenin-8-C-glucose ACG, and 2-Isobutyl-3-methoxypyrazine IBMP) as a green source of ecologically friendly Fe, Al, and Cu metal corrosion inhibitors. Complete geometry optimizations were performed by DFT-B3LYP/6-31G* to determine any relationship between the chemical structure and corrosion inhibition, mostly on metals' surfaces. Global computational parameters of the inhibitors and thermodynamic Gibbs process of adsorption of metals were calculated and used to evaluate each corrosion inhibitor's performance. Our findings showed that MPC has the maximum anti-corrosion efficiency across all molecules with a physical adsorption mechanism. It exhibited significant inhibition efficiency with Cu when compared with Fe and Al, based on the highest electrophilicity index (ω) values compared to other inhibitors and its impact on metals in the following manner: Cu>Fe>Al. In regards, the range of inhibitors increased by the following order: IBMP>ACG>MPC. Remarkable corrosion inhibition of MPC is demonstrated by its unique high electrophilicity, softness (σ), and lowest ∆Egap on the metal surface. These outcomes are close to the experimental

Gibbs Process Determines Survival and Reveals Contact-Inhibition Genes in Glioblastoma Multiforme

Tumor growth is a spatiotemporal birth-and-death process with loss of heterotypic contact-inhibition of locomotion (CIL) of tumor cells promoting invasion and metastasis. Therefore, representing tumor cells as two-dimensional points, we can expect the tumor tissues in histology slides to reflect realizations of spatial birth-and-death process which can be mathematically modeled to reveal molecular mechanisms of CIL, provided the mathematics models the inhibitory interactions. Gibbs process as an inhibitory point process is a natural choice since it is an equilibrium process of the spatial birth-and-death process. That is if the tumor cells maintain homotypic contact inhibition, the spatial distributions of tumor cells will result in Gibbs hard core process over long time scales. In order to verify if this is the case, we applied the Gibbs process to 411 TCGA Glioblastoma multiforme patient images. Our imaging dataset included all cases for which diagnostic slide images were available.The model revealed two clusters, one of which - the “Gibbs cluster,” showed the convergence of the Gibbs process with significant survival difference. Further smoothing the discretized (and noisy) inhibition metric, for both increasing and randomized survival time, we found a significant association of the patients in the Gibbs cluster with increasing survival time. The mean inhibition metric also revealed the point at which the homotypic CIL establishes in tumor cells. Besides, RNAseq analysis between patients with loss of heterotypic CIL and intact homotypic CIL in the Gibbs cluster unveiled cell movement gene signatures and differences in Actin cytoskeleton and RhoA signaling pathways as key molecular alterations. These genes and pathways have established roles in CIL. Taken together, our integrated analysis of patient images and RNAseq data provides for the first time a mathematical basis for CIL in tumors, explains survival as well as uncovers the underlying molecular landscape for this key tumor invasion and metastatic phenomenon.

FACADE INTERPRETATION USING A MARKED POINT PROCESS

Our objective is the interpretation of facade images in a top-down manner, using a Markov marked point process formulated as a Gibbs process. Given single rectified facade images, we aim at the accurate detection of relevant facade objects as windows and entrances, using prior knowledge about their possible configurations within facade images. We represent facade objects by a simplified rectangular object model and present an energy model, which evaluates the agreement of a proposed configuration with the given image and the statistics about typical configurations, which we learned from training data. We show promising results on different datasets and provide a qualitative evaluation, which demonstrates the capability of complete and accurate detection of facade objects.

FACADE INTERPRETATION USING A MARKED POINT PROCESS

Our objective is the interpretation of facade images in a top-down manner, using a Markov marked point process formulated as a Gibbs process. Given single rectified facade images, we aim at the accurate detection of relevant facade objects as windows and entrances, using prior knowledge about their possible configurations within facade images. We represent facade objects by a simplified rectangular object model and present an energy model, which evaluates the agreement of a proposed configuration with the given image and the statistics about typical configurations, which we learned from training data. We show promising results on different datasets and provide a qualitative evaluation, which demonstrates the capability of complete and accurate detection of facade objects.

The distribution of interparticle distance and its application in finite-element modelling of composite materials

The distribution of interparticle distance, based on a Voronoi tessellation, is found approximately for a hard-core Gibbs process. The moments of this distribution are then used as input for finite-element analysis of the region surrounding a single filler sphere within a composite material. Statistical analysis provides close bounds for overall elastic properties of the material. Results from finite-element analysis can therefore be applied to real composite materials; reasonable agreement is found with a particular set of experimental data.