Attaching topological spaces to a module (I): Sobriety and spatiality

In this paper we study some frames associated to an R-module M. We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of $\mathrm{Max}(M)$. We characterize the soberness of $\mathrm{Max}(M)$ in terms of the point space of that frame. Beside of this, we study the regularity of an spatial frame associated to M given by annihilator conditions.     

Characterisation of an exothermic reaction using adiabatic and isothermal calorimetry

A simple esterification reaction is used to demonstrate standard procedures for determining the thermokinetic parameters of an exothermic reaction from adiabatic calorimetric data. The influence of variations in the heat capacity of the sample due to changes in temperature and concentration is explored. Shortcomings in the simple interpretation of adiabatic data are identified and isothermal heatflow calorimetry is used to reveal autocatalytic effects which were not apparent from the adiabatic experiments. A more rigourous interpretation of the adiabatic and isothermal data is outlined and used to predict the conditions which can lead to exothermic runaway in a batch reactor. Mathematical simulation of the conditions in a jacketed reactor is used to demonstrate the importance of developing reliable kinetic expressions before assessing the safety of a batch process.

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Zusammenfassung Anhand einer einfachen Veresterungsreaktion wurden Standardverfahren zur Ermittlung thermokinetischer Parameter exothermen Reaktionen aus adiabatischen kalorimetrischen Daten demonstriert. Dabei wurde der Einfluß von Temperatur und Konzentration auf Änderungen der Wärmekapazität untersucht. Fehler bei der einfachen Interpretation adiabatischer Daten wurden identifiziert und isotherme Wärmeflußkalorimetrie wurde angewendet, um autokatalytische Effekte aufzuzeigen, die sich anhand der adiabatischen Experimente nicht ersehen lassen. Es wurde eine gründlichere Interpretation adiabatischer und isothermer Daten umrissen und verwendet, um die Bedingungen vorherzusagen, die in einem Kesselreaktor zu einem exothermen Davonlaufen der Reaktion führen. Mathematische Simulation der Bedingungen in einem Mantelkessel wurde angewendet, um zu zeigen, von welch großer Bedeutung die Entwicklung zuverlässiger kinetischer Ausdrücke ist, bevor man die Sicherheit einer Reaktion in einem Kesselreaktor beurteilt.

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Utility function estimation: The entropy approach

The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker’s preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.     

Variable neighbourhood search for bandwidth reduction

The problem of reducing the bandwidth of a matrix consists of finding a permutation of rows and columns of a given matrix which keeps the non-zero elements in a band as close as possible to the main diagonal. This NP-complete problem can also be formulated as a vertex labelling problem on a graph, where each edge represents a non-zero element of the matrix. We propose a variable neighbourhood search based heuristic for reducing the bandwidth of a matrix which successfully combines several recent ideas from the literature. Empirical results for an often used collection of 113 benchmark instances indicate that the proposed heuristic compares favourably to all previous methods. Moreover, with our approach, we improve best solutions in 50% of instances of large benchmark tests.     

Dimension and decomposition in modular upper-continuous lattices

Slim rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. They are finite semimodular lattices L such that the ordered set Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. After describing these lattices of a given length n by permutations, we determine their number, |SRectL(n)|. Besides giving recursive formulas, which are effective up to about n = 1000, we also prove that |SRectL(n)| is asymptotically (n - 2)! · \({e^{2}/2}\). Similar results for patch lattices, which are special rectangular lattices introduced by G. Czédli and E. T. Schmidt in 2013, and for slim rectangular lattice diagrams are also given.     

A modified variable neighborhood search for the discrete ordered median problem

This paper presents a modified Variable Neighborhood Search (VNS) heuristic algorithm for solving the Discrete Ordered Median Problem (DOMP). This heuristic is based on new neighborhoods’ structures that allow an efficient encoding of the solutions of the DOMP avoiding sorting in the evaluation of the objective function at each considered solution. The algorithm is based on a data structure, computed in preprocessing, that organizes the minimal necessary information to update and evaluate solutions in linear time without sorting. In order to investigate the performance, the new algorithm is compared with other heuristic algorithms previously available in the literature for solving DOMP. We report on some computational experiments based on the well-known N-median instances of the ORLIB with up to 900 nodes. The obtained results are comparable or superior to existing algorithms in the literature, both in running times and number of best solutions found.     

Cheminformatic characterization of natural products from Panama

In this work, we discuss the characterization and diversity analysis of 354 natural products (NPs) from Panama, systematically analyzed for the first time. The in-house database was compared to NPs from Brazil, compounds from Traditional Chinese Medicine, natural and semisynthetic collections used in high-throughput screening, and compounds from ChEMBL. An analysis of the “global diversity” was conducted using molecular properties of pharmaceutical interest, three molecular fingerprints of different design, molecular scaffolds, and molecular complexity. The global diversity was visualized using consensus diversity plots that revealed that the secondary metabolites in the Panamanian flora have a large scaffold diversity as compared to other composite databases and also have several unique scaffolds. The large scaffold diversity is in agreement with the broad range of biological activities that this collection of NPs from Panama has shown. This study also provided further quantitative evidence of the large structural complexity of NPs. The results obtained in this study support that NPs from Panama are promising candidates to identify selective molecules and are suitable sources of compounds for virtual screening campaigns.