Nearest neighbor search in general metric spaces using a tree data structure with a simple heuristic

We present a new algorithm for nearest neighbor search in general metric spaces. The algorithm organizes the database into recursively partitioned Voronoi regions and represents these partitions in a tree. The separations between the Voronoi regions as well as the radius of each region are used with triangular inequality to derive the minimum possible distance between any point in a region and the query and to discard the region from further search if a smaller distance has already been found. The algorithm also orders the search sequence of the tree branches using the estimate of the minimum possible distance. This simple heuristic proves to considerably enhance the pruning of the search tree. The efficiency of the algorithm is demonstrated on several artificial data sets and real problems in computational chemistry.     

K-means clustering analysis,ADME/pharmacokinetic prediction,MEP, and molecular docking studies of potential cytotoxic agents

Structural Chemistry - In this paper, a combined approach based on a k-means algorithm and statistical analysis has been applied successfully to classify 500 cytotoxic agents using 21 molecular...     

K-means Find Density Peaks in Molecular Conformation Clustering

Performing cluster analysis on molecular conformation is an important way to find the representative conformation in the molecular dynamics trajectories. Usually, it is a critical step for interpreting complex conformational changes or interaction mechanisms. As one of the density-based clustering algorithms, find density peaks (FDP) is an accurate and reasonable candidate for the molecular conformation clustering. However, facing the rapidly increasing simulation length due to the increase in computing power, the low computing efficiency of FDP limits its application potential. Here we propose a marginal extension to FDP named K-means find density peaks (KFDP) to solve the mass source consuming problem. In KFDP, the points are initially clustered by a high efficiency clustering algorithm, such as K-means. Cluster centers are defined as typical points with a weight which represents the cluster size. Then, the weighted typical points are clustered again by FDP, and then are refined as core, boundary, and redefined halo points. In this way, KFDP has comparable accuracy as FDP but its computational complexity is reduced from O\begin{document}$(n^2)$\end{document} to O\begin{document}$(n)$\end{document}. We apply and test our KFDP method to the trajectory data of multiple small proteins in terms of torsion angle, secondary structure or contact map. The comparing results with K-means and density-based spatial clustering of applications with noise show the validation of the proposed KFDP.     

Some comments on the properties of unitary transformations on linear spaces having an indefinite metric and the connection with the theory of spin

After a brief review of the history of the discovery of the spin, some fundamental properties of linear spaces having an indefinite metric are being discussed. The study starts with an elementary survey of the theory of matrices and their stability problem. It is emphasized that—by a similarity transformation—all matrices may be brought to classical canonical form characterized by the diagonal elements called eigenvalues, their multiplicities, their Jordan blocks, and their Segré characteristics. In connection with the reduced Cayley-Hamilton equation, the existence of the product projection operators and their main properties is briefly discussed. Particular attention is paid to the concept of a basis for the linear space and the associated metric matrix, which is self-adjoint and may be brought to diagonal form with the eigenvalues ± 1 by a unitary transformation, which reveals the indices of inertia, p and q. The Minkowski space having p = 3 and q = 1 is used as an example. After this introduction, some properties of linear operators defined on an indefinite space are discussed, and it is pointed out that self-adjoint operators and unitary operators may now have a rather peculiar and unexpected behavior, and the special Lorentz transformations are used as an example. It is then shown that these features are of essential importance in studying rotations as special cases of unitary transformations defined on an indefinite space. The rotations are here defined by means of their reduced Cayley-Hamilton equation, and their properties are studied by means of the associated product projection operators, which are idempotent, mutually exclusive, and form a resolution of the identity. In a previous article, it was shown that, in a positive definite space, there is a close connection between the requirement that all rotations around an external axis form a group and the existence of an anticommutator algebra leading to the concept of spinors. The rotations are expressed in the exponential form U=exp(iO), where O is a self-adjoint operator which is independent of any choice basis, coordinate system, etc., and which is, hence, a true invariant. It is shown that this approach may now be extended also to indefinite spaces and may lead to operators O which are both rotationally and relativistically invariant. In this connection, the full Lorentz transformations are given a particularly simple form. The article may be considered as a simple exercise in linear algebra, in which the mathematical connection between the concept of rotations and the existence of spinors is strongly emphasized. © John Wiley & Sons, Inc.     

On the optimal partitioning of data with K-means,growing K-means,neural gas,and growing neural gas

In this paper, the performance of new clustering methods such as Neural Gas (NG) and Growing Neural Gas (GNG) is compared with the K-means method for real and simulated data sets. Moreover, a new algorithm called growing K-means, GK, is introduced as the alternative to Neural Gas and Growing Neural Gas. It has small input requirements and is conceptually very simple. The GK leads to nearly optimal values of the cost function, and, contrary to K-means, it is independent of the initial data set partition. The incremental property of GK additionally helps to estimate the number of "natural" clusters in data, i.e., the well-separated groups of objects in the data space.     

Accelerated 18O-labeling in urinary proteomics

Proteolytic (18)O-labeling of peptides has been studied and optimized in order to improve the labeling efficiency and to accelerate the process without increasing the degree of incomplete labeling. Using peptides generated from tryptic digested bovine serum albumin (BSA) and cytochrome c as model proteins, it was shown that complete labeling was achieved after 2 h at pH 6. To increase the sample throughput in a bottom-up proteomic setup, tryptic digestion of proteins in-solution was replaced with tryptic digestion using immobilized trypsin. As a result, an integrated approach was made possible, where both digestion (pH 8) and (18)O/(16)O-labeling of the resulting peptides (pH 6) were done using immobilized trypsin beads. This simplified the sample handling and reduced the overall reaction time significantly: the setup enabled tryptic digestion and (18)O/(16)O-labeling without sample transfer steps within 3.5 h with average (18)O/(16)O-ratios of 0.96±0.13 in aqueous buffer. The initial results were confirmed with a more complex matrix, by spiking urine with the model proteins, yielding results comparable with the ratios obtained in buffer. Satisfying ratios were also achieved regarding urinary proteins identified in a full scale bottom-up experiment. Average (18)O/(16)O-peptide ratios of 0.83±0.13 and 0.91±0.27 indicated good performance in a highly relevant matrix for biomarker discovery.     

Anchimerically Accelerated Bond Homolyses

Radical reactions of the type R¹? a? b? R²→^?a? b? R¹ + ^?R² are feasible if the new bond formed between b and R¹ is considerably stronger than the old bond between a and R¹. Furthermore, both the radical fragments formed must be resonance stabilized. An example of this reaction type is the thermolysis of benzyl trimethylsilylmethyl ethers, in which the trimethylsilyl group (with empty orbitals) migrates to the oxygen atom (with lone pairs). Assumption of a cyclic reactive intermediate with pentacoordinated silicon explains the observed intramolecular nature and the negative entropy of activation of such homolyses.     

Accelerated approach to self-consistency in molecular-orbital methods

Interpolation between two successive approximations for the bond-order matrix is used in a method of deducing corrections to the matrix; a matrix equation for the corrections is derived and solved. It is shown by reference to pyridine that the correction greatly accelerates the approach to self-consistency.Read at the Symposium on Quantum Chemistry, Palanga, June 1965.     

Accelerated reactions in field desorption mass spectrometry

Field desorption mass spectrometry under ambient conditions is used to study solution‐phase organic reactions in micro‐volumes. Reagent solution is transferred onto the microdendrites of the field emitter, and reaction products are examined online by mass spectrometry. Three reactions, hydrazone formation by phenyl hydrazine and indoline‐2,3‐dione, the Katritzky reaction between a pyrylium salt and anisidine, and the Hantzsch synthesis of 1,4‐dihydropyridine, were investigated, and reaction acceleration was observed to different extents. The increase in rate relative to the corresponding bulk reactions is attributed to solvent evaporation (simple concentration effect) and to the increase of surface‐to‐volume ratio (enhanced interfacial reactions). A distinguishing feature of this method of reaction acceleration, relative to that based on nano electrospray ionization, is the observation of radical cations and the formation of radical cation products. The study also breaks new ground in using field emitters at atmospheric pressure.     

Quasi-equilibria in reduced Liouville spaces

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.     

Diffusion in complementary pore spaces

The rate of mass transfer is among the key numbers determining the efficiency of nanoporous materials in their use for matter upgrading by heterogeneous catalysis or mass separation. Transport enhancement by pore space optimization is, correspondingly, among the main strategies of efficiency promotion. Any such activity involves probing and testing of the appropriate routes of material synthesis and post-synthesis modification just as the exploration of the transport characteristics of the generated material. Modelling and molecular simulation is known to serve as a most helpful tool for correlating these two types of activities and their results. The present paper reports about a concerted research activity comprising these three types of activities. Recent progress in producing pore space replicas enabled focusing, in these studies, on “complementary” pore spaces, i.e. on pairs of material, where the pore space of one sample did just coincide with the solid space of the other. We report about the correlations in mass transfer as observable, in this type of material, by pulsed field gradient NMR diffusion studies, with reference to the prediction as resulting from a quite general, theoretical treatment of mass transfer in complementary pore spaces.     

Molecular quantum similarity measures in Minkowski metric vector semispaces

Minkowski metric vector semispaces can be chosen as the natural mathematical framework, where quantum similarity measures are described and evaluated. The obtained results in this study show that the Minkowski metric option is easily feasible, providing a new set of computationally simpler expressions, computationally faster when compared with Euclidian based quantum similarity measures.     

Accelerated Characterization of Electrode-Electrolyte Equilibration

Operational durability is poorly characterized by traditional (photo)electrocatalyst discovery workflows, creating a barrier to scale-up and deployment. Corrosion is a prominent degradation mechanism whose thermodynamics depend on the concentration of corrosion products in electrolyte. We present an automated system for characterizing the equilibration of (photo)electrodes with dissolved metals in electrolyte for a given electrode, pH, and electrochemical potential. Automation of electrode selection, electrolyte preparation, and electrolyte aliquoting enables rapid identification of self-passivating electrodes and estimation of the equilibrium dissolved metals concentrations. The technique is demonstrated for metal oxide photoanodes in alkaline electrolyte, where BiVO₄ is found to continually corrode, in agreement the literature. An amorphous Ni−Sb−O photoanode is found to passivate with a Ni-rich coating on the order of 1 monolayer with less than 1 μM total dissolved metals in electrolyte, demonstrating its suitability for durable photoelectrochemical operation. The automation and throughput of the instrument are designed for incorporation in accelerated electrocatalyst discovery workflows so that durability can be considered on equal footing with activity.     

Accelerated polymorphic transformations of alumina

In binary systems MeO/Al₂O₃ (Me=Mg, Zn, Cu), the accelerated polymorphic transformation of alumina to α-Al₂O₃ was observed in the presence of Cu²⁺. The phenomenon is explained as catalytic, considering the Cu²⁺ electron configuration and Jahn-Teller effect.     

Accelerated glycosylation under frozen conditions

O-Glycosylations using thiomethyl glycosides as donors were compared under both frozen and unfrozen conditions. In the presence of MeOTf as a promoter, enormous rate acceleration was observed when the glycosylation was conducted in p-xylene below its freezing point.     

Accelerated Bergman cyclization of porphyrinic-enediynes

The Bergman cyclization of simple diethynylporphyrinic-enediynes exhibits a double activation barrier to the formation of Bergman cyclized product. Addition of H-atom acceptor accelerates the formation of the picenoporphyrin, indicating that the second barrier is rate limiting.