58 research outputs found

    Ante Graovac – Life and Works

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    Ivan Gutman, Biserka Pokrić, Damir Vukičević (Eds.) Ante Graovac – Life and Works Mathematical Chemistry Monographs, Vol. 16 Faculty of Science, University of Kragujevac, Kragujevac (Serbia), 2014 306 + IV pages ◦ ISBN 978-86-6009-021-0 This work is licensed under a Creative Commons Attribution 4.0 International License

    The topology of fullerenes

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    Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website

    Characterization of topological phases in models of interacting fermions

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    The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions. In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z_N charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z_N symmetry, we find a non-Abelian group structure under the addition of phases. In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i)~the Hall conductivity, (ii)~the spectral flow and level counting in the ES, (iii)~the topological entanglement entropy, and (iv)~the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order. In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI) induced by next-nearest neighbor interactions has been predicted by mean field theory. However, various subsequent studies challenged this picture and it was still unclear whether the CI would survive quantum fluctuations. We therefore map out the phase diagram of the model as a function of the interactions on an infinite cylinder with DMRG and find evidence for the absence of the CI phase. However, we report the detection of two novel charge-ordered phases and corroborate the existence of the remaining phases that had been predicted in mean field theory. Furthermore, we characterize the transitions between the various phases by studying the behavior of correlation length and entanglement entropy at the phase boundaries. Finally, we develop an improvement to the DMRG algorithm for fermionic lattice models on cylinders. By using a real space representation in the direction along the cylinder and a real space representation in the perpendicular direction, we are able to use the momentum around the cylinder as conserved quantity to reduce computational costs. We benchmark the method by studying the interacting Hofstadter model and report a considerable speedup in computation time and a severely reduced memory usage

    Maximum cardinality resonant sets and maximal alternating sets of hexagonal systems

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    AbstractIt is shown that the Clar number can be arbitrarily larger than the cardinality of a maximal alternating set. In particular, a maximal alternating set of a hexagonal system need not contain a maximum cardinality resonant set, thus disproving a previously stated conjecture. It is known that maximum cardinality resonant sets and maximal alternating sets are canonical, but the proofs of these two theorems are analogous and lengthy. A new conjecture is proposed and it is shown that the validity of the conjecture allows short proofs of the aforementioned two results. The conjecture holds for catacondensed hexagonal systems and for all normal hexagonal systems up to ten hexagons. Also, it is shown that the Fries number can be arbitrarily larger than the Clar number

    The Chemistry Development Kit (CDK) v2.0: atom typing, depiction, molecular formulas, and substructure searching

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    open access articleBackground: The Chemistry Development Kit (CDK) is a widely used open source cheminformatics toolkit, providing data structures to represent chemical concepts along with methods to manipulate such structures and perform computations on them. The library implements a wide variety of cheminformatics algorithms ranging from chemical structure canonicalization to molecular descriptor calculations and pharmacophore perception. It is used in drug discovery, metabolomics, and toxicology. Over the last 10 years, the code base has grown significantly, however, resulting in many complex interdependencies among components and poor performance of many algorithms. Results: We report improvements to the CDK v2.0 since the v1.2 release series, specifically addressing the increased functional complexity and poor performance. We first summarize the addition of new functionality, such atom typing and molecular formula handling, and improvement to existing functionality that has led to significantly better performance for substructure searching, molecular fingerprints, and rendering of molecules. Second, we outline how the CDK has evolved with respect to quality control and the approaches we have adopted to ensure stability, including a code review mechanism. Conclusions: This paper highlights our continued efforts to provide a community driven, open source cheminformatics library, and shows that such collaborative projects can thrive over extended periods of time, resulting in a high-quality and performant library. By taking advantage of community support and contributions, we show that an open source cheminformatics project can act as a peer reviewed publishing platform for scientific computing software

    Development of Integrated Machine Learning and Data Science Approaches for the Prediction of Cancer Mutation and Autonomous Drug Discovery of Anti-Cancer Therapeutic Agents

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    Few technological ideas have captivated the minds of biochemical researchers to the degree that machine learning (ML) and artificial intelligence (AI) have. Over the last few years, advances in the ML field have driven the design of new computational systems that improve with experience and are able to model increasingly complex chemical and biological phenomena. In this dissertation, we capitalize on these achievements and use machine learning to study drug receptor sites and design drugs to target these sites. First, we analyze the significance of various single nucleotide variations and assess their rate of contribution to cancer. Following that, we used a portfolio of machine learning and data science approaches to design new drugs to target protein kinase inhibitors. We show that these techniques exhibit strong promise in aiding cancer research and drug discovery
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