Globally optimal clusterwise regression by mixed logical-quadratic programming

Exact global optimization of the clusterwise regression problem is challenging and there are currently no published feasible methods for performing this clustering optimally, even though it has been over thirty years since its original proposal. This work explores global optimization of the clusterwise regression problem using mathematical programming and related issues. A mixed logical-quadratic programming formulation with implication of constraints is presented and contrasted against a quadratic formulation based on the traditional big-M, which cannot guarantee optimality because the regression line coefficients, and thus errors, may be arbitrarily large. Clusterwise regression optimization times and solution optimality for two clusters are empirically tested on twenty real datasets and three series of synthetic datasets ranging from twenty to one hundred observations and from two to ten independent variables. Additionally, a few small real datasets are clustered into three lines.     

Possibility distributions: A unified representation of usual direct-probability-based parameter estimation methods

The paper presents a possibility theory based formulation of one-parameter estimation that unifies some usual direct probability formulations. Point and confidence interval estimation are expressed in a single theoretical formulation and incorporated into estimators of a generic form: a possibility distribution. New relationships between continuous possibility distribution and probability concepts are established. The notion of specificity ordering of a possibility distribution, corresponding to fuzzy subsets inclusion, is then used for comparing the efficiency of different estimators for the case of data points coming from a symmetric probability distribution. The usefulness of the approach is illustrated on common mean and median estimators from identical independent data sample of different size and of different common symmetric continuous probability distributions.     

Valid inequalities and branch-and-cut for the clique pricing problem

Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. We formulate the problem as a linear mixed integer program and propose strong valid inequalities, some of which define facets of the two-commodity polyhedron. The numerical efficiency of these inequalities is assessed by embedding them within a branch-and-cut framework.     

The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.     

Synthesis, Characterization and Electrochemical Behavior of CoII, NiII and CdII Complexes with N2O2 Donor Ligands Derived from 4,4′-Diaminobiphenyl and?2-Hydroxybenzaldehyde or?2,4-Dihydroxybenzaldehyde

The condensation of 2-hydroxybenzaldehyde or 2,4-dihydroxybenzaldehyde with 4,4′-diaminobiphenyl in absolute EtOH in a molar ratio 2:1 gave, respectively, the Schiff base ligands H₂L1 or H₂L2. The bases served as tetradentate ligands to coordinate Co^II, Ni^II and Cd^II chlorides, leading to complexes where the metal:ligand ratio is 2:1. All of the compounds were characterized by elemental analysis, infrared, electronic and mass spectroscopy, ¹H-n.m.r. and d.s.c. The cyclic voltammograms of the ligands and their complexes in DMF are discussed.     

A New Highly Versatile Handle for Chemistry on a Solid Support: The Pipecolic Linker

The design, synthesis, and potential application of the pipecolic linker is presented. This new versatile handle can immobilize primary, secondary, and aromatic amines, as well as alcohols, phenols, and hydrazides, on a solid support. Compared with other linkers, the anchoring step is easy and efficient. The release of final products from the resin proceeds upon acidic treatment with high purities. The pipecolic linker offers the promise of being using in peptide chemistry to produce peptides modified at the N and C terminus, peptidomimetics, as well as small organic molecules.     

Zwitterionic pyrrolidine‐2,2‐diylbis(phosphonic acid) at 100, 150 and 293 K

The title compound, C₄H₁₁NO₆P₂, reveals a two‐dimensional network of P—O—H?O=P and N—H?O=P hydrogen‐bond interactions, forming molecular slabs parallel with the (010) plane. One O—H?O interaction is distinct within these sets: whilst forming the shortest intermolecular hydrogen bond, it possesses a short P—O(H) bond of 1.5291 (10) Å. Weak C—H?O contacts link individual stacks to produce a three‐dimensional array. The compound is zwitterionic: one H atom from a P—O—H group has transferred to the pyrrolidine ring N atom.     

Interaction Modes and Absolute Affinities of α‐Amino Acids for Mn2+: A Comprehensive Picture

Manganese is involved as a cofactor in the activation of numerous enzymes as well as the oxygen‐evolving complex of photosystem II. Full understanding of the role played by the Mn²⁺ ion requires detailed knowledge of the interaction modes and energies of manganese with its various environments, a knowledge that is far from complete. To bring detailed insight into the local interactions of Mn in metallopeptides and proteins, theoretical studies employing first‐principles quantum mechanical calculations are carried out on [Mn‐amino acid]²⁺ complexes involving all 20 natural α‐amino acids (AAs). Detailed investigation of [Mn‐serine]²⁺_, [Mn‐cysteine]²⁺, [Mn‐phenylalanine]²⁺, [Mn‐tyrosine]²⁺, and [Mn‐tryptophan]²⁺ indicates that with an electron‐rich side chain, the most stable species involves interaction of Mn²⁺ with carbonyl oxygen, amino nitrogen, and an electron‐rich section of the side chain of the AA in its canonical form. This is in sharp contrast with aliphatic side chains for which a salt bridge is formed. For aromatic AAs, complexation to manganese leads to partial oxidation as well as aromaticity reduction. Despite multisite binding, AAs do not generate strong enough ligand fields to switch the metal to a low‐ or even intermediate‐spin ground state. The affinities of Mn²⁺ for all AAs are reported at the B3LYP and CCSD(T) levels of theory, thereby providing the first complete series of affinities for a divalent metal ion. The trends are compared with those of other cations for which affinities of all AAs have been previously obtained.     

Applicability domains for classification problems: Benchmarking of distance to models for Ames mutagenicity set

The estimation of accuracy and applicability of QSAR and QSPR models for biological and physicochemical properties represents a critical problem. The developed parameter of "distance to model" (DM) is defined as a metric of similarity between the training and test set compounds that have been subjected to QSAR/QSPR modeling. In our previous work, we demonstrated the utility and optimal performance of DM metrics that have been based on the standard deviation within an ensemble of QSAR models. The current study applies such analysis to 30 QSAR models for the Ames mutagenicity data set that were previously reported within the 2009 QSAR challenge. We demonstrate that the DMs based on an ensemble (consensus) model provide systematically better performance than other DMs. The presented approach identifies 30-60% of compounds having an accuracy of prediction similar to the interlaboratory accuracy of the Ames test, which is estimated to be 90%. Thus, the in silico predictions can be used to halve the cost of experimental measurements by providing a similar prediction accuracy. The developed model has been made publicly available at http://ochem.eu/models/1 .     

Mixed metallic Ba(Co,Fe)X(0.2)O(3-δ) (X = F, Cl) hexagonal perovskites: drastic effect of Fe-incorporation on structural and electronic features

Starting from the parent 10H-Ba(5)Co(5)X(1-x)O(13-δ) (trimeric strings of face-sharing CoO(6) octahedra with terminal CoO(4) tetrahedra, stacking sequence (chhch')(2)) and 6H-Ba(6)Co(6)X(1-x)O(16-δ) (similar with tetrameric strings, stacking sequence chhhch') hexagonal perovskites forms (X = F, Cl; c, h = [BaO(3)] layers ; h' = [BaOX(1-y)] layers), we show here that the Fe incorporation leads to large domains of solid solutions for both X = F and Cl but exclusively stabilizes the 10H-form independently of the synthesis method. In this form, the lowest concentration of h-layers is stabilized by a sensitive metal reduction with increasing the Fe ratio. In a more general context of competition between several hexagonal perovskite polymorphs available for most of the transition metals, this redox change is most probably the key factor driving 1D (face-sharing chains) to 3D (corner-sharing) connectivities. Strikingly, ND data evidence the location of oxygen deficiencies in the tetrahedral (Co/Fe) coordination. This effect is exaggerated at high temperature, while (Co/Fe)O(4-δ) coordinations are completed by the displacement of X(-) anions toward the (Co/Fe) sphere of coordination following a "push-and-pull" mechanism within h'-[BaOX(1-y)] layers. The Fe-incorporation is also accompanied by increasing conduction gaps with predominant 1D variable range hopping. The full series show antiferromagnetic behavior with increasing T(N) as [Fe] increases. For Fe-rich compounds T(N) is estimated about 600 K, as rarely observed for hexagonal perovskite compounds. Finally, magnetic structures of all iron-doped compounds show a site-to-site AFM ordering, different of the magnetic structure of Co-only parent compounds. Here, DFT calculations predict low-spin octahedral Co configurations, but high-spin Fe species in the same sites.