Graph partitioning induced phase transitions

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree k. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if nonoptimal) that partitions the graph into essentially equal sized connected components (clusters), the system undergoes a percolation phase transition at f = fc = 1-2/k where f is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find S approximately N 0.4 where S is the size of the clusters and l approximately N 0.25 where l is their diameter. Also, we find that S undergoes multiple nonpercolation transitions for f相似文献   

Solvation free energy of amino acids and side-chain analogues

The solvation free energies of amino acids and their side-chain analogues in water and cyclohexane are calculated by using Monte Carlo simulation. The molecular interactions are described by the OPLS-AA force field for the amino acids and the TIP4P model for water, and the free energies are determined by using the Bennett acceptance method. Results for the side-chain analogues in cyclohexane and in water are used to evaluate the performance of the force field for the van der Waals and the electrostatic interactions, respectively. Comparison of the calculated hydration free energies for the amino acid analogues and the full amino acids allows assessment of the additivity of the side chain contributions on the number of hydrating water molecules. The hydration free energies of neutral amino acids can be reasonably approximated by adding the contributions of their side chains to that of the hydration of glycine. However, significant nonadditivity in the free energy is found for the zwitterionic form of amino acids with polar side chains. In serine and threonine, intramolecular hydrogen bonds are formed between the polar side chains and backbone groups, leading to weaker solvation than for glycine. In contrast, such nonadditivity is not observed in tyrosine, in which the hydroxyl group is farther separated from, and therefore cannot form an intramolecular hydrogen bond with, the backbone. For histidine we find that a water molecule can form a bridge when the intramolecular hydrogen bond between the polar group and the backbone is broken.     

Thermodynamic characterization of separations on alkaline-stable silica-based C18 columns: why basic solutes may have better capacity and peak performance at higher pH

A systematic study was made to explain the large improvements in separation performance and capacity of basic compounds at alkaline conditions. The adsorption of three probe components was investigated on four alkaline-stable silica-based C18 columns at three different pH-levels: 3, 7 and 11. The probes were 3-phenyl-1-propanol (neutral), 2-phenylbutyric acid (acidic) and metoprolol (basic). Adsorption isotherms were acquired over a broad concentration range, in order to detect both high and low energy sites. Before the choice of the proper adsorption isotherm model, the adsorption energy distribution (AED) was calculated yielding the number of different kinds of interaction sites between the solute and the stationary phase. The neutral probe was entirely unaffected by pH and its AED was unimodal (one site) indicating homogenous adsorption. For the acidic probe the interactions were unimodal at pH 3 where the probe is uncharged and at least bimodal (two sites) at pH 7 and 11 where the probe is charged. For the basic probe, the interactions were heterogeneous at both pH 3 and 11. The equilibrium constants of the high and low energy sites were different by a factor of 55-100 at pH 3 and only 6-7 at pH 11. The difference in saturation capacities between the two sites was much smaller at pH 11 where 20% of the total capacity is from the high energy site, as compared to pH 3 where the high energy site was only 2-5% of the total capacity. This explains why peaks of amines (basic solutes) tail at low pH while their peaks are symmetrical at alkaline pH. The Langmuir model fit the unimodal data and the bi-Langmuir model fit the bimodal AED data. The calculated band profiles based on these parameters agreed excellently with the experimental data. The electrostatic-modified Langmuir, on the other hand, did not describe this adsorption process well.     

Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.     

Elevation of charring level of polyamide-6,6 films via ionic introduction of phosphoric acid and boric acid esters

Phosphorus and boron containing materials have the feature of increasing char formation, which can be effectively used as flame retardants especially in textiles. This paper discusses the ionic addition of phosphorus and boron esters to polyamide-6,6 (PA66), and its effect on the charring level. A mixture of phosphoric acid–boric acid ester at different degrees of esterification (ED) was prepared and two theoretical mechanisms for the esterification reaction were suggested. Ionically grafted polymer films were prepared by introducing the ester of highest ED to PA66–formic acid solution via three different processes: open air (cold) grafting, ultraviolet irradiation grafting, and hot vacuum oven grafting. Thermogravimetry was conducted for all synthesized esters and films, and the formation of new bonds between the ester and PA66 was verified using Fourier transform infrared spectroscopy.     

Regularity of Intermittent Bursts in BriggsRauscher Oscillating Systems with Phenol

The intermittency or intermittent bursting as the type of dynamic state when two qualitatively different behaviors replace one another randomly during the course of the reaction, although all the control parameters remain constant, is found in the Briggs? Rauscher oscillating system moderated by a very small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude is diminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts of oscillations. For the concentrations used here, the range of phenol concentrations where intermittent bursting oscillations occur in a closed reactor is ca. 1.8×10^?5 to 3.6×10^?5 M . Bursting also occurs in an open reactor and can be sustained indefinitely at 5.53×10^?5 M concentration. The intermittent bursting behavior is robust, and can be achieved at a variety of conditions.     

Total Synthesis of Ascospiroketal A Through a AgI‐Promoted Cyclization Cascade

The total synthesis of four candidate stereostructures for the marine octaketide ascospiroketal A have been achieved. These concise and highly stereocontrolled syntheses feature a unique Ag^I‐promoted cyclization cascade involving an oxetanyl ketochlorohydrin to access the entire tricyclic core of the natural product in one step. These syntheses also establish the full stereochemistry for the ascospiroketal natural products.     

Catalytic,Stereoselective Dihalogenation of Alkenes: Challenges and Opportunities

Although recent years have witnessed significant advances in the development of catalytic, enantioselective halofunctionalizations of alkenes, the related dihalogenation of olefins to afford enantioenriched vicinal dihalide products remains comparatively underdeveloped. However, the growing number of complex natural products bearing halogen atoms at stereogenic centers has underscored this critical gap in the synthetic chemist’s arsenal. This Review highlights the selectivity challenges inherent in the design of enantioselective dihalogenation processes, and formulates a mechanism‐based classification of alkene dihalogenations, including those that may circumvent the “classical” haliranium (or alkene‐dihalogen π‐complex) intermediates. A variety of metal and main group halide reagents that have been used for the dichlorination or dibromination of alkenes are discussed, and the proposed mechanisms of these transformations are critically evaluated.     

Atmospheric pressure deposition of fluorine‐doped SnO2 thin films from organotin fluorocarboxylate precursors

Nine organotin fluorocarboxylates R_nSnO₂CR_f (n = 3, R = Bu, R_f = CF₃, C₂F₅, C₃F₇, C₇F₁₅; R = Et, R_f = CF₃, C₂F₅; R = Me, R_f = C₂F₅; n = 2, R = Me, R_f = CF₃) have been synthesized; key examples have been used to deposit fluorine‐doped SnO₂ thin films by atmospheric pressure chemical vapour deposition. Et₃SnO₂CC₂F₅, in particular, gives high‐quality films with fast deposition rates despite adopting a polymeric, carboxylate‐bridged structure in the solid state, as determined by X‐ray crystallography. Gas‐phase electron diffraction on the model compound Me₃SnO₂CC₂F₅ shows that accessible conformations do not allow contact between tin and fluorine, and that direct transfer is therefore unlikely to be part of the mechanism for fluorine incorporation in SnO₂ films. The structure of Me₂Sn(O₂CCF₃)₂(H₂O) has also been determined and adopts a trans‐Me₂SnO₃ coordination sphere about tin in which each carboxylate group is monodentate. Copyright © 2005 John Wiley & Sons, Ltd.