Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

A Direct Construction of Nontransitive Dice Sets

In this paper, we give a direct construction for a set of dice realizing any given tournament T. The construction for a tournament with n vertices requires dice with n sides if n is odd, sides if n is divisible by 4, and sides if mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory.     

Divergent and Overlapping Roles for Selected Phytochemicals in the Regulation of Pathological Cardiac Hypertrophy

Plant-based foods, like fruits, vegetables, whole grains, legumes, nuts, seeds and other foodstuffs, have been deemed as heart healthy. The chemicals within these plant-based foods, i.e., phytochemicals, are credited with protecting the heart. However, the mechanistic actions of phytochemicals, which prevent clinical endpoints, such as pathological cardiac hypertrophy, are still being elucidated. We sought to characterize the overlapping and divergent mechanisms by which 18 selected phytochemicals prevent phenylephrine- and phorbol 12-myristate 13-acetate-mediated cardiomyocyte enlargement. Of the tested 18 compounds, six attenuated PE- and PMA-mediated enlargement of neonatal rat ventricular myocytes. Cell viability assays showed that apigenin, baicalein, berberine hydrochloride, emodin, luteolin and quercetin dihydrate did not reduce cell size through cytotoxicity. Four of the six phytochemicals, apigenin, baicalein, berberine hydrochloride and emodin, robustly inhibited stress-induced hypertrophy and were analyzed further against intracellular signaling and genome-wide changes in mRNA expression. The four phytochemicals differentially regulated mitogen-activated protein kinases and protein kinase D. RNA-sequencing further showed divergence in gene regulation, while pathway analysis demonstrated overlap in the regulation of inflammatory pathways. Combined, this study provided a comprehensive analysis of cardioprotective phytochemicals. These data highlight two defining observations: (1) that these compounds predominantly target divergent gene pathways within cardiac myocytes and (2) that regulation of overlapping signaling and gene pathways may be of particular importance for the anti-hypertrophic actions of these phytochemicals. Despite these new findings, future works investigating rodent models of heart failure are still needed to understand the roles for these compounds in the heart.     

Thermal,morphological, and mechanical properties of ethyl vanillin immobilized in polyvinyl alcohol by electrospinning process

In this study, polyvinyl alcohol (PVA) nanofibers with ethyl vanillin as an active compound were prepared using electrospinning technique. The final products of electrospinning process were in the form of nanofibers films. PVA/ethyl vanillin nanofibers, having fibers diameters in the range 100–1700 nm, were successfully electrospun from ethanol/water mixture of PVA and ethyl vanillin. The effects of immobilization process on ethyl vanillin thermal properties were investigated by differential scanning calorimetry (DSC). The results of DSC showed significant influence of immobilization process on thermal properties of ethyl vanillin. It was noticed that melting point of immobilized ethyl vanillin was lower (~55 °C) compared to free flavor (~77 °C). Our results showed that films based on PVA/ethyl vanillin nanofibers are mechanically stable.     

Is it True That the Normal Valence‐Length Correlation Is Irrelevant for Metal–Metal Bonds?

The most intriguing feature of metal–metal bonds in inorganic compounds is an apparent lack of correlation between the bond order and the bond length. In this study, we combine a variety of literature data obtained by quantum chemistry and our results based on the empirical bond valence model (BVM), to confirm for the first time the existence of a normal exponential correlation between the effective bond order (EBO) and the length of the metal–metal bonds. The difference between the EBO and the formal bond order is attributed to steric conflict between the (TM)_n cluster (TM=transition metal) and its environment. This conflict, affected mainly by structural type, should cause high lattice strains, but electron redistribution around TM atoms, evident from the BVM calculations, results in a full or partial strain relaxation.     

Effect of oxidized silicon (SiOx) surfaces functionalization on real‐time PCR by Lab‐on‐a‐chip microdevices

There is a great need to improve the biocompatibility of silicon‐based lab‐on‐chip substrate materials for reliable quantitative analysis of biological solutions. These advanced microdevice surfaces need not only be biocompatible but also have surfaces of defined wettability characteristics. The inhibition of biomolecular activity due to microdevice surface interaction is common and can result in inaccurate results or decreased reaction yields. In this work we investigate different techniques for the chemical functionalization of oxidized silicon (SiO_x) surfaces in order to: (i) obtain defined hydrophobic/hydrophilic surfaces; and (ii) increase the efficiency of performing Real‐Time Polymerase Chain Reaction (PCR) on a silicon‐based lab‐on‐chip. Silicon oxide surfaces are functionalized by grafting alkylic chain silanes and poly(ethylene glycol) (PEG) chains to the surfaces, rendering them hydrophobic or hydrophilic. Functionalized surfaces are characterized through contact angle and atomic force microscopy (AFM) measurements, showing stable hydrophobic surfaces with contact angles of 69–78° and layer thicknesses of 11–15 Å and hydrophilic surfaces displaying contact angles of 5–6° and thicknesses of 22–52 Å. PCR experiments carried out directly on bare silicon oxide lab‐on‐chip surfaces show low yields of DNA amplification. Hydrophobic surfaces decrease the inhibition of PCR. Hydrophilic surfaces are a major improvement on the bare silicon oxide exhibiting the same maximum reaction yield as obtained with a standard thermocycler. We have found that the best results are associated with PEG modified surfaces, which prove very suitable for the fabrication of reliable PCR silicon lab‐on‐chips. Copyright © 2011 John Wiley & Sons, Ltd.     

Chemical Antibody Mimics Inhibit Cadherin-Mediated Cell–Cell Adhesion: A Promising Strategy for Cancer Therapy

One of the most promising strategies to treat cancer is the use of therapeutic antibodies that disrupt cell–cell adhesion mediated by dysregulated cadherins. The principal site where cell–cell adhesion occurs encompasses Trp2 found at the N-terminal region of the protein. Herein, we employed the naturally exposed highly conserved peptide Asp1-Trp2-Val3-Ile4-Pro5-Pro6-Ile7, as epitope to prepare molecularly imprinted polymer nanoparticles (MIP-NPs) to recognize cadherins. Since MIP-NPs target the site responsible for adhesion, they were more potent than commercially available therapeutic antibodies for inhibiting cell–cell adhesion in cell aggregation assays, and for completely disrupting three-dimensional tumor spheroids as well as inhibiting invasion of HeLa cells. These biocompatible supramolecular anti-adhesives may potentially be used as immunotherapeutic or sensitizing agents to enhance antitumor effects of chemotherapy.