A Generalization Of Reifenberg’s Theorem In {\mathbb{R}}^3

In 1960 Reifenberg proved the topological disc property. He showed that a subset of which is well approximated by m-dimensional affine spaces at each point and at each (small) scale is locally a bi-H?lder image of the unit ball in . In this paper we prove that a subset of which is well approximated in the Hausdorff distance sense by one of the three standard area-minimizing cones at each point and at each (small) scale is locally a bi-H?lder deformation of a minimal cone. We also prove an analogous result for more general cones in . Received: July 2006, Revised: August 2007, Accepted: January 2008     

Clustering versus percolation in the assembly of colloids coated with long DNA

We report an experimental study in which we compare the self-assembly of 1 mum colloids bridged through hybridization of complementary single-stranded DNA (ssDNA) strands (12 bp) attached to variable-length double-stranded DNA spacers that are grafted to the colloids. We considered three different spacer lengths: long spacers (48 500 bp), intermediate length spacers (7500 bp), and no spacers (in which case the ssDNA strands were directly grafted to the colloids). In all three cases, the same ssDNA pairs were used. However, confocal microscopy revealed that the aggregation behavior is very different. Upon cooling, the colloids coated with short and intermediate length DNAs undergo a phase transition to a dense amorphous phase that undergoes structural arrest shortly after percolation. In contrast, the colloids coated with the longest DNA systematically form finite-sized clusters. We speculate that the difference is due to the fact that very long DNA can easily be stretched by the amount needed to make only intracluster bonds, and in contrast, colloids coated with shorter DNA always contain free binding sites on the outside of a cluster. The grafting density of the DNA decreases strongly with increasing spacer length. This is reflected in a difference in the temperature dependence of the aggregates: for the two systems coated with long DNA, the resulting aggregates were stable against heating, whereas the colloids coated with ssDNA alone would dissociate upon heating.     

Hydrogen adsorption in a highly stable porous rare-earth metal-organic framework: sorption properties and neutron diffraction studies

A highly stable porous lanthanide metal-organic framework, Y(BTC)(H2O).4.3H2O (BTC = 1,3,5-benzenetricarboxylate), with pore size of 5.8 A has been constructed and investigated for hydrogen storage. Gas sorption measurements show that this porous MOF exhibits highly selective sorption behaviors of hydrogen over nitrogen gas molecules and can take up hydrogen of about 2.1 wt % at 77 K and 10 bar. Difference Fourier analysis of neutron powder diffraction data revealed four distinct D2 sites that are progressively filled within the nanoporous framework. Interestingly, the strongest adsorption sites identified are associated with the aromatic organic linkers rather than the open metal sites, as occurred in previously reported MOFs. Our results provide for the first time direct structural evidence demonstrating that optimal pore size (around 6 A, twice the kinetic diameter of hydrogen) strengthens the interactions between H2 molecules and pore walls and increases the heat of adsorption, which thus allows for enhancing hydrogen adsorption from the interaction between hydrogen molecules with the pore walls rather than with the normally stronger adsorption sites (the open metal sites) within the framework. At high concentration H2 loadings (5.5 H2 molecules (3.7 wt %) per Y(BTC) formula), H2 molecules form highly symmetric novel nanoclusters with relatively short H2-H2 distances compared to solid H2. These observations are important and hold the key to optimizing this new class of rare metal-organic framework (RMOF) materials for practical hydrogen storage applications.     

The Scalar-photon Coupling with Mie Invariant Within the Scope of Bianchi Type-I Cosmological Model

We investigate the Bianchi type-I cosmological model with the scalar and electromagnetic fields possessing non-minimal couplings. They contain the Mie invariant that leads to the flat Friedman’s cosmological model. We found the lagrangian for interaction, which the isotropization process of the expansion takes place. Two cases are considered, when the Mie invariant is constat or time-dependent. We study the canonical scalar field and the phantom one.     

Bioelectronic Interface Connecting Reversible Logic Gates Based on Enzyme and DNA Reactions

It is believed that connecting biomolecular computation elements in complex networks of communicating molecules may eventually lead to a biocomputer that can be used for diagnostics and/or the cure of physiological and genetic disorders. Here, a bioelectronic interface based on biomolecule‐modified electrodes has been designed to bridge reversible enzymatic logic gates with reversible DNA‐based logic gates. The enzyme‐based Fredkin gate with three input and three output signals was connected to the DNA‐based Feynman gate with two input and two output signals—both representing logically reversible computing elements. In the reversible Fredkin gate, the routing of two data signals between two output channels was controlled by the control signal (third channel). The two data output signals generated by the Fredkin gate were directed toward two electrochemical flow cells, responding to the output signals by releasing DNA molecules that serve as the input signals for the next Feynman logic gate based on the DNA reacting cascade, producing, in turn, two final output signals. The Feynman gate operated as the controlled NOT gate (CNOT), where one of the input channels controlled a NOT operation on another channel. Both logic gates represented a highly sophisticated combination of input‐controlled signal‐routing logic operations, resulting in redirecting chemical signals in different channels and performing orchestrated computing processes. The biomolecular reaction cascade responsible for the signal processing was realized by moving the solution from one reacting cell to another, including the reacting flow cells and electrochemical flow cells, which were organized in a specific network mimicking electronic computing circuitries. The designed system represents the first example of high complexity biocomputing processes integrating enzyme and DNA reactions and performing logically reversible signal processing.     

Heart rate variability analysis by chaotic global techniques in children with attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is characterized by decreased attention span, impulsiveness, and hyperactivity. Autonomic nervous system imbalance was previously described in this population. We aim to compare the autonomic function of children with ADHD and controls by analyzing heart rate variability (HRV). Children with ADHD (22 boys, mean age 9.964 years) and 28 controls (15 boys, mean age 9.857 years) rested in supine position with spontaneous breathing for 20 min. Heart rate was recorded beat by beat. HRV analysis was performed by use of chaotic global techniques. ADHD promoted an increase in the chaotic forward parameter. The algorithm which applied all three chaotic global parameters was only the second optimum statistically measured by Kruskal–Wallis (P < 0.0001) and low standard deviations. It was also highly influential by principal component analysis with almost all variation covered by the first two components. The third algorithm which lacked the (high spectral Detrended Fluctuation Analysis) parameter performed best statistically. However, we chose the algorithm which applied all three chaotic globals due to previous studies mentioned in the text—forward and inverse problems. Comparison of the autonomic function by analyzing HRV with chaotic global techniques suggests an increase in chaotic activity in children with ADHD in relation to the control group. © 2015 Wiley Periodicals, Inc. Complexity 21: 412–419, 2016     

Gelatin Nanoparticles with Enhanced Affinity for Calcium Phosphate

Gelatin nanoparticles can be tuned with respect to their drug loading efficiency, degradation rate, and release kinetics, which renders these drug carriers highly suitable for a wide variety of biomedical applications. The ease of functionalization has rendered gelatin an interesting candidate material to introduce specific motifs for selective targeting to specific organs, but gelatin nanoparticles have not yet been modified to increase their affinity to mineralized tissue. By means of conjugating bone‐targeting alendronate to biocompatible gelatin nanoparticles, a simple method is developed for the preparation of gelatin nanoparticles which exhibit strong affinity to mineralized surfaces. It has been shown that the degree of alendronate functionalization can be tuned by controlling the glutaraldehyde crosslinking density, the molar ratio between alendronate and glutaraldehyde, as well as the pH of the conjugation reaction. Moreover, it has been shown that the affinity of gelatin nanoparticles to calcium phosphate increases considerably upon functionalization with alendronate. In summary, gelatin nanoparticles have been developed, which exhibit great potential for use in bone‐specific drug delivery and regenerative medicine.

     

Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances.     

On the role of higher-order correlation effects on the induction interactions between closed-shell molecules

High-order correlation contributions to the second-order induction energy were studied for various representative van der Waals complexes. It was found that the induction energy obtained by the truncation of the relaxed M?ller-Plesset expansion in the second or third order is in most cases quite close to the induction energy computed with the coupled-cluster method (restricted to single and double excitations). Also, the effect of triples excitations on this perturbation term is usually small. However, given an oscillatory behaviour of the M?ller-Plesset induction corrections, the coupled-cluster method seems to be better suited to a reliable calculation of the induction energy. The sources of the remaining differences between the interaction energies computed by symmetry-adapted perturbation theory and those computed by the supermolecule coupled-cluster method (restricted to single, double, and noniterative triple excitations) are examined. It has been found that they can be attributed to the higher-order correlation terms in the second-order dispersion and exchange-induction corrections.