Minimum Detour Index of Bicyclic Graphs

The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. A graph with n vertices and n + 1 edges is called a bicyclic graph. In this paper, we consider the detour indices of bicyclic graphs with two cycles or three cycles and determine the graphs with the first four smallest detour indices in the class of n-vertex bicyclic graphs for n ≥ 5

Integrating Passengers\u27 Routes in Periodic Timetabling: A SAT approach

The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard. Its main application is for designing periodic timetables in public transportation. To this end, the passengers\u27 paths are required as input data. This is a drawback since the final paths which are used by the passengers depend on the timetable to be designed. Including the passengers\u27 routing in the PESP hence improves the quality of the resulting timetables. However, this makes PESP even harder. Formulating the PESP as satisfiability problem and using SAT solvers for its solution has been shown to be a highly promising approach. The goal of this paper is to exploit if SAT solvers can also be used for the problem of integrated timetabling and passenger routing. In our model of the integrated problem we distribute origin-destination (OD) pairs temporally through the network by using time-slices in order to make the resulting model more realistic. We present a formulation of this integrated problem as integer program which we are able to transform to a satisfiability problem. We tested the latter formulation within numerical experiments, which are performed on Germany\u27s long-distance passenger railway network. The computation\u27s analysis in which we compare the integrated approach with the traditional one with fixed passengers\u27 weights, show promising results for future scientific investigations

Applications of Multidimensional Space of Mathematical Molecular Descriptors in Large-Scale Bioactivity and Toxicity Prediction- Applications to Prediction of Mutagenicity and Blood-Brain Barrier Entry of Chemicals

In this chapter, we review our QSAR research in the prediction of toxicities, bioactivities and properties of chemicals using computed mathematical descriptors. Robust statistical methods have been used to develop high quality predictive quantitative structure-activity relationship (QSAR) models for the prediction of mutagenicity and BBB (blood-brain barrier) entry of two large and diverse sets chemicals. This work is licensed under a Creative Commons Attribution 4.0 International License

Composite Finite Elements for Trabecular Bone Microstructures

In many medical and technical applications, numerical simulations need to be performed for objects with interfaces of geometrically complex shape. We focus on the biomechanical problem of elasticity simulations for trabecular bone microstructures. The goal of this dissertation is to develop and implement an efficient simulation tool for finite element simulations on such structures, so-called composite finite elements. We will deal with both the case of material/void interfaces (complicated domains) and the case of interfaces between different materials (discontinuous coefficients). In classical finite element simulations, geometric complexity is encoded in tetrahedral and typically unstructured meshes. Composite finite elements, in contrast, encode geometric complexity in specialized basis functions on a uniform mesh of hexahedral structure. Other than alternative approaches (such as e.g. fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes, and extended finite element methods), the composite finite elements are tailored to geometry descriptions by 3D voxel image data and use the corresponding voxel grid as computational mesh, without introducing additional degrees of freedom, and thus making use of efficient data structures for uniformly structured meshes. The composite finite element method for complicated domains goes back to Wolfgang Hackbusch and Stefan Sauter and restricts standard affine finite element basis functions on the uniformly structured tetrahedral grid (obtained by subdivision of each cube in six tetrahedra) to an approximation of the interior. This can be implemented as a composition of standard finite element basis functions on a local auxiliary and purely virtual grid by which we approximate the interface. In case of discontinuous coefficients, the same local auxiliary composition approach is used. Composition weights are obtained by solving local interpolation problems for which coupling conditions across the interface need to be determined. These depend both on the local interface geometry and on the (scalar or tensor-valued) material coefficients on both sides of the interface. We consider heat diffusion as a scalar model problem and linear elasticity as a vector-valued model problem to develop and implement the composite finite elements. Uniform cubic meshes contain a natural hierarchy of coarsened grids, which allows us to implement a multigrid solver for the case of complicated domains. Besides simulations of single loading cases, we also apply the composite finite element method to the problem of determining effective material properties, e.g. for multiscale simulations. For periodic microstructures, this is achieved by solving corrector problems on the fundamental cells using affine-periodic boundary conditions corresponding to uniaxial compression and shearing. For statistically periodic trabecular structures, representative fundamental cells can be identified but do not permit the periodic approach. Instead, macroscopic displacements are imposed using the same set as before of affine-periodic Dirichlet boundary conditions on all faces. The stress response of the material is subsequently computed only on an interior subdomain to prevent artificial stiffening near the boundary. We finally check for orthotropy of the macroscopic elasticity tensor and identify its axes.Zusammengesetzte finite Elemente für trabekuläre Mikrostrukturen in Knochen In vielen medizinischen und technischen Anwendungen werden numerische Simulationen für Objekte mit geometrisch komplizierter Form durchgeführt. Gegenstand dieser Dissertation ist die Simulation der Elastizität trabekulärer Mikrostrukturen von Knochen, einem biomechanischen Problem. Ziel ist es, ein effizientes Simulationswerkzeug für solche Strukturen zu entwickeln, die sogenannten zusammengesetzten finiten Elemente. Wir betrachten dabei sowohl den Fall von Interfaces zwischen Material und Hohlraum (komplizierte Gebiete) als auch zwischen verschiedenen Materialien (unstetige Koeffizienten). In klassischen Finite-Element-Simulationen wird geometrische Komplexität typischerweise in unstrukturierten Tetraeder-Gittern kodiert. Zusammengesetzte finite Elemente dagegen kodieren geometrische Komplexität in speziellen Basisfunktionen auf einem gleichförmigen Würfelgitter. Anders als alternative Ansätze (wie zum Beispiel fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes und extended finite element methods) sind die zusammengesetzten finiten Elemente zugeschnitten auf die Geometriebeschreibung durch dreidimensionale Bilddaten und benutzen das zugehörige Voxelgitter als Rechengitter, ohne zusätzliche Freiheitsgrade einzuführen. Somit können sie effiziente Datenstrukturen für gleichförmig strukturierte Gitter ausnutzen. Die Methode der zusammengesetzten finiten Elemente geht zurück auf Wolfgang Hackbusch und Stefan Sauter. Man schränkt dabei übliche affine Finite-Element-Basisfunktionen auf gleichförmig strukturierten Tetraedergittern (die man durch Unterteilung jedes Würfels in sechs Tetraeder erhält) auf das approximierte Innere ein. Dies kann implementiert werden durch das Zusammensetzen von Standard-Basisfunktionen auf einem lokalen und rein virtuellen Hilfsgitter, durch das das Interface approximiert wird. Im Falle unstetiger Koeffizienten wird die gleiche lokale Hilfskonstruktion verwendet. Gewichte für das Zusammensetzen erhält man hier, indem lokale Interpolationsprobleme gelöst werden, wozu zunächst Kopplungsbedingungen über das Interface hinweg bestimmt werden. Diese hängen ab sowohl von der lokalen Geometrie des Interface als auch von den (skalaren oder tensorwertigen) Material-Koeffizienten auf beiden Seiten des Interface. Wir betrachten Wärmeleitung als skalares und lineare Elastizität als vektorwertiges Modellproblem, um die zusammengesetzten finiten Elemente zu entwickeln und zu implementieren. Gleichförmige Würfelgitter enthalten eine natürliche Hierarchie vergröberter Gitter, was es uns erlaubt, im Falle komplizierter Gebiete einen Mehrgitterlöser zu implementieren. Neben Simulationen einzelner Lastfälle wenden wir die zusammengesetzten finiten Elemente auch auf das Problem an, effektive Materialeigenschaften zu bestimmen, etwa für mehrskalige Simulationen. Für periodische Mikrostrukturen wird dies erreicht, indem man Korrekturprobleme auf der Fundamentalzelle löst. Dafür nutzt man affin-periodische Randwerte, die zu uniaxialem Druck oder zu Scherung korrespondieren. In statistisch periodischen trabekulären Mikrostrukturen lassen sich ebenfalls Fundamentalzellen identifizieren, sie erlauben jedoch keinen periodischen Ansatz. Stattdessen werden makroskopische Verschiebungen zu denselben affin-periodischen Randbedingungen vorgegeben, allerdings durch Dirichlet-Randwerte auf allen Seitenflächen. Die Spannungsantwort des Materials wird anschließend nur auf einem inneren Teilbereich berechnet, um künstliche Versteifung am Rand zu verhindern. Schließlich prüfen wir den makroskopischen Elastizitätstensor auf Orthotropie und identifizieren deren Achsen

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Nenad Trinajstić – Pioneer of Chemical Graph Theory

We present a brief overview of many contributions of Nenad Trinajstić to Chemical Graph Theory, an important and fast developing branch of Theoretical Chemistry. In addition, we outline briefly the various activities of Trinajstić within the chemical community of Croatia. As can be seen, his scientific work has been very productive and has not abated despite the hostilities towards the Chemical Graph Theory in certain chemical circles over the past 30 years. On the contrary, Trinajstić continued, widened the areas of his research interest, which started with investigating the close relationship between Graph Theory and HMO, and demonstrated the importance of Chemical Graph theory for chemistry. In more than one way he has proven the opponents of Chemical Graph Theory wrong, though some continue to fail to recognize the importance of Graph Theory in Chemistry

Building Blocks for Mapping Services

Mapping services are ubiquitous on the Internet. These services enjoy a considerable user base. But it is often overlooked that providing a service on a global scale with virtually millions of users has been the playground of an oligopoly of a select few service providers are able to do so. Unfortunately, the literature on these solutions is more than scarce. This thesis adds a number of building blocks to the literature that explain how to design and implement a number of features

In silico prediction of acute chemical toxicity of biocides in marine crustaceans using machine learning

Biocides are a heterogeneous group of chemical substances intended to control the growth or kill undesired organisms. Due to their extensive use, they enter marine ecosystems via non-point sources and may pose a threat to ecologically important non-target organisms. Consequently, industries and regulatory agencies have recognized the ecotoxicological hazard potential of biocides. However, the prediction of biocide chemical toxicity on marine crustaceans has not been previously evaluated. This study aims to provide in silico models capable of classifying structurally diverse biocidal chemicals into different toxicity categories and predict acute chemical toxicity (LC50) in marine crustaceans using a set of calculated 2D molecular descriptors. The models were built following the guidelines recommended by the OECD (Organization for Economic Cooperation and Development) and validated through stringent processes (internal and external validation). Six machine learning (ML) models were built and compared (linear regression: LR; support vector machine: SVM; random forest: RF; feed-forward backpropagation-based artificial neural network: ANN; decision trees: DT and naïve Bayes: NB) for regression and classification analysis to predict toxicities. All the models displayed encouraging results with high generalisability: the feed-forward-based backpropagation method showed the best results with determination coefficient R2 values of 0.82 and 0.94, respectively, for training set (TS) and validation set (VS). For classification-based modelling, the DT model performed the best with an accuracy (ACC) of 100 % and an area under curve (AUC) value of 1 for both TS and VS. These models showed the potential to replace animal testing for the chemical hazard assessment of untested biocides if they fall within the applicability domain of the proposed models. In general, the models are highly interpretable and robust, with good predictive performance. The models also displayed a trend indicating that toxicity is largely influenced by factors such as lipophilicity, branching, non-polar bonding and saturation of molecules

Quantization of the ModMax Oscillator

We quantize the ModMax oscillator, which is the dimensional reduction of the Modified Maxwell theory to one spacetime dimension. We show that the propagator of the ModMax oscillator satisfies a differential equation related to the Laplace equation in cylindrical coordinates, and we obtain expressions for the classical and quantum partition functions of the theory. To do this, we develop general results for deformations of quantum mechanical theories by functions of conserved charges. We show that canonical quantization and path integral quantization of such deformed theories are equivalent only if one uses the phase space path integral; this gives a precise quantum analogue of the statement that classical deformations of the Lagrangian are equivalent to those of the Hamiltonian.Comment: 63 pages; LaTe

Discovery of Novel Glycogen Synthase Kinase-3beta Inhibitors: Molecular Modeling, Virtual Screening, and Biological Evaluation

Glycogen synthase kinase-3 (GSK-3) is a multifunctional serine/threonine protein kinase which is engaged in a variety of signaling pathways, regulating a wide range of cellular processes. Due to its distinct regulation mechanism and unique substrate specificity in the molecular pathogenesis of human diseases, GSK-3 is one of the most attractive therapeutic targets for the unmet treatment of pathologies, including type-II diabetes, cancers, inflammation, and neurodegenerative disease. Recent advances in drug discovery targeting GSK-3 involved extensive computational modeling techniques. Both ligand/structure-based approaches have been well explored to design ATP-competitive inhibitors. Molecular modeling plus dynamics simulations can provide insight into the protein-substrate and protein-protein interactions at substrate binding pocket and C-lobe hydrophobic groove, which will benefit the discovery of non-ATP-competitive inhibitors. To identify structurally novel and diverse compounds that effectively inhibit GSK-3â, we performed virtual screening by implementing a mixed ligand/structure-based approach, which included pharmacophore modeling, diversity analysis, and ensemble docking. The sensitivities of different docking protocols to the induced-fit effects at the ATP-competitive binding pocket of GSK-3â have been explored. An enrichment study was employed to verify the robustness of ensemble docking compared to individual docking in terms of retrieving active compounds from a decoy dataset. A total of 24 structurally diverse compounds obtained from the virtual screening experiment underwent biological validation. The bioassay results shothat 15 out of the 24 hit compounds are indeed GSK-3â inhibitors, and among them, one compound exhibiting sub-micromolar inhibitory activity is a reasonable starting point for further optimization. To further identify structurally novel GSK-3â inhibitors, we performed virtual screening by implementing another mixed ligand-based/structure-based approach, which included quantitative structure-activity relationship (QSAR) analysis and docking prediction. To integrate and analyze complex data sets from multiple experimental sources, we drafted and validated hierarchical QSAR, which adopts a multi-level structure to take data heterogeneity into account. A collection of 728 GSK-3 inhibitors with diverse structural scaffolds were obtained from published papers of 7 research groups based on different experimental protocols. Support vector machines and random forests were implemented with wrapper-based feature selection algorithms in order to construct predictive learning models. The best models for each single group of compounds were then selected, based on both internal and external validation, and used to build the final hierarchical QSAR model. The predictive performance of the hierarchical QSAR model can be demonstrated by an overall R2 of 0.752 for the 141 compounds in the test set. The compounds obtained from the virtual screening experiment underwent biological validation. The bioassay results confirmed that 2 hit compounds are indeed GSK-3â inhibitors exhibiting sub-micromolar inhibitory activity, and therefore validated hierarchical QSAR as an effective approach to be used in virtual screening experiments. We have successfully implemented a variant of supervised learning algorithm, named multiple-instance learning, in order to predict bioactive conformers of a given molecule which are responsible for the observed biological activity. The implementation requires instance-based embedding, and joint feature selection and classification. The goal of the present project is to implement multiple-instance learning in drug activity prediction, and subsequently to identify the bioactive conformers for each molecule. The proposed approach was proven not to suffer from overfitting and to be highly competitive with classical predictive models, so it is very powerful for drug activity prediction. The approach was also validated as a useful method for pursuit of bioactive conformers