Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

Synthesis and crystal structure of the dinuclear cyclopalladated compounds of methyl (E)-4-(benzylideneamino)benzoate with acetato and chlorido bridge ligands: Study of their splitting reactions with pyridine

Reaction of methyl (E)-4-(benzylideneamino)benzoate C6H5CH=N(C6H4-4-CO2Me) with Pd(OAc)(2) produced the dinuclear acetato bridge ortho-cyclopalladated compound [Pd{C6H4CH=N(C6H4-4-CO2Me)-kappa C-ortho,kappa(N)}](2)(mu-OAc)(2) (1). Compounds [Pd{C6H4CH=N(C6H4-4-CO2Me)-kappa C-ortho,kappa(N)}](2)(mu-Cl)(2) (2) and [Pd {C6H4CH] N(C6H4-4-CO2Me)-kappa C-ortho,kappa(N)}(py)(X)] [3 (X = OAc); 4 (X = Cl)] were also prepared and isolated in good yields by substitution reactions. H-1 and C-13{H-1} NMR in CDCl3 solution of compounds 3 and 4 revealed that they consisted of a mixture of trans-and cis-N,N isomers. Addition of pyridine-d(5) to solutions of 1 and 2 in CDCl3 in a molar ratio pyridine-d(5)/1 or 2 approximate to 50-55 gave solutions A and B, respectively, which contained compounds 5 and 6 analogous to 3 and 4, but with pyridine-d(5) rather than pyridine in their structural formula. In these solutions, the trans-and cis-N,N geometrical isomers of compounds 5 and 6 were interconverting between them in a dynamic equilibrium. In addition, an exchange between free and coordinated pyridine-d(5) was also taking place in solutions A and B. The NMR data for solution A showed that the dynamic equilibrium between the cis-and trans-N,N isomers of compound 5 was shifted to the trans-N,N isomer. However, the NMR data for solution B suggested that in this solution the equilibrium between the cis- and trans-N,N isomers of compound 6 was shifted to the cis-N,N isomer. Interconversion between the trans- and cis-N,N isomers of compounds 5 and 6 in solutions A and B plausibly proceeded through the intermediate ionic complexes [Pd{C6H4CH] N(C6H4-4CO(2)Me)-kappa C-ortho,kappa(N)}(py-d(5))(2)]X [7 (X = OAc), 8 (X = Cl)]. Ionic complexes 7 and 8 were not observed in CDCl3 solution but were the major species in D2O solutions containing compounds 1 and 2 and pyridine-d(5) in a molar ratio pyridine-d(5)/1 or 2 approximate to 50-55. The crystal structure of the adduct 1.2(CH3COOH) and that of compound 2 were determined by single crystal X-ray diffraction. A theoretical study on the difference in free Gibbs energy in CHCl3 solution between the cis-and trans-N,N isomers of compounds 3 and 4 is also included in this work

A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra

A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, a new relativistic theory with two observer-independent scales (or DSR theory). Deformed momentum representation, finite boost transformations, range of rapidity, energy and momentum, as well as position and velocity operators are explicitly studied and compared with those of previous DSR theories based on kappa-Poincare algebra. The main novelties of the DSR theory here presented are the new features of momentum saturation and a new type of deformed position operators.Comment: 13 pages, LaTeX; some references and figures added, and terminology is more precis

Cyclopalladated and cycloplatinated benzophenone imines: antitumor, antibacterial and antioxidant activities, DNA interaction and cathepsin B inhibition

The antitumor, antibacterial and antioxidant activity, DNA interaction and cathepsin B inhibition of cyclo-orthopalladated and -platinated compounds [Pd(C,N)]2(μ-X)2 [X = OAc (1), X = Cl (2)] and trans-N,P-[M(C,N)X(PPh3)] [M = Pd, X = OAc (3), M = Pd, X = Cl (4), M = Pt, X = Cl (5)] are discussed [(C,N)= cyclo-orthometallated benzophenone imine]. The cytotoxicity of compound 5 has been evaluated towards human breast (MDA-MB-231 and MCF-7) and colon (HCT-116) cancer cell lines and that of compounds 1-4 towards the HCT-116 human colon cancer cell line. These cytotoxicities have been compared with those previously reported for compounds 1-4 towards MDA-MB-231 and MCF-7 cancer cell lines. Compound 3 and 4 were approximately four times more active than cisplatin against the MDA-MB-231 andMCF-7 cancer cell lines, and compound 5, was approximately four times more potent than cisplatin against the HCT-116 cancer cell line. The antibacterial activity of compounds 1-5 was in between the ranges of activity of the commercial antibiotic compounds cefixime and roxithromycin. Complexes 1-2 and 4-5 presented also antioxidant activity. Compounds 1-5 alter the DNA tertiary structure in a similar way to cisplatin, but at higher concentration, and do not present a high efficiency as cathepsin B inhibitors. Compound 5 has not been previously described, and its preparation, characterization, and X-ray crystal structure are reported

A New Family of Doubly Cyclopalladated Diimines. A Remarkable Effect of the Linker between the Metalated Units on Their Cytotoxicity

The cyclopalladation of a series of symmetric diimines with the formula (RC6H4CHNZ)2, where Z = CH2 or (CH2)2OCH2 and R = p-Cl, p-OMe, p-NO2, and o-Cl, is described. Optimal conditions to obtain the dimetalated compounds were found to be palladium(II) acetate, in toluene, at 60 °C and with a reaction time of 2−4 h. The reactivity of the dimetalated compounds with monodentate, bidentate, and bis(monodentate) Lewis bases was also studied. The cytotoxic activity of some selected compounds was evaluated against a panel of adenocarcinoma cell lines (colon HCT116 and breast MCF7 and MDA-MB231). Compounds containing the fragment NCH2CH2OCH2CH2OCH2CH2N exhibited a remarkable cytotoxic activity in the three cancer cells assayed, but complexes containing the NCH2CH2N fragment showed no activity. It seems that the length and flexibility of the central saturated chain in the imine molecule, as well as its lipophilicity and hydrophilicity, explain the different cytotoxicity of the two series of coordination compounds here reported

Corrigendum to 'Cyclopalladated and cycloplatinated benzophenone imines: Antitumor, antibacterial and antioxidant activities, DNA interaction and cathepsin B inhibition' [J. Inorg. Biochem. 140 (2014) 80-88]

The magnitudes of MIC for the antibacterial activity and of the IC50 for the antioxidant activity reported in μM are really mM. Thus, in page 84: 0.18-0.34 μM is 0.18-0.34 mM; in Tables 2 and 3: μM is mM; in page 85: 0.12 and 0.14 μM is 0.12 and 0.14 mM; and in page 87: 0.12-0.14 μM is 0.12-0.14 mM. The authors apologize for any inconvenience caused

Associating Genes and Protein Complexes with Disease via Network Propagation

A fundamental challenge in human health is the identification of disease-causing genes. Recently, several studies have tackled this challenge via a network-based approach, motivated by the observation that genes causing the same or similar diseases tend to lie close to one another in a network of protein-protein or functional interactions. However, most of these approaches use only local network information in the inference process and are restricted to inferring single gene associations. Here, we provide a global, network-based method for prioritizing disease genes and inferring protein complex associations, which we call PRINCE. The method is based on formulating constraints on the prioritization function that relate to its smoothness over the network and usage of prior information. We exploit this function to predict not only genes but also protein complex associations with a disease of interest. We test our method on gene-disease association data, evaluating both the prioritization achieved and the protein complexes inferred. We show that our method outperforms extant approaches in both tasks. Using data on 1,369 diseases from the OMIM knowledgebase, our method is able (in a cross validation setting) to rank the true causal gene first for 34% of the diseases, and infer 139 disease-related complexes that are highly coherent in terms of the function, expression and conservation of their member proteins. Importantly, we apply our method to study three multi-factorial diseases for which some causal genes have been found already: prostate cancer, alzheimer and type 2 diabetes mellitus. PRINCE's predictions for these diseases highly match the known literature, suggesting several novel causal genes and protein complexes for further investigation

Development and Validation of Predictive Model for a Diagnosis of First Episode Psychosis Using the Multinational EU-GEI Case–control Study and Modern Statistical Learning Methods

Background and Hypothesis: It is argued that availability of diagnostic models will facilitate a more rapid identification of individuals who are at a higher risk of first episode psychosis (FEP). Therefore, we developed, evaluated, and validated a diagnostic risk estimation model to classify individual with FEP and controls across six countries. / Study Design: We used data from a large multi-center study encompassing 2627 phenotypically well-defined participants (aged 18-64 years) recruited from six countries spanning 17 research sites, as part of the European Network of National Schizophrenia Networks Studying Gene-Environment Interactions study. To build the diagnostic model and identify which of important factors for estimating an individual risk of FEP, we applied a binary logistic model with regularization by the least absolute shrinkage and selection operator. The model was validated employing the internal-external cross-validation approach. The model performance was assessed with the area under the receiver operating characteristic curve (AUROC), calibration, sensitivity, and specificity. / Study Results: Having included preselected 22 predictor variables, the model was able to discriminate adults with FEP and controls with high accuracy across all six countries (rangesAUROC=0.84-0.86). Specificity (range=73.9-78.0%) and sensitivity (range=75.6-79.3%) were equally good, cumulatively indicating an excellent model accuracy; though, calibration slope for the diagnostic model showed a presence of some overfitting when applied specifically to participants from France, the UK, and The Netherlands. / Conclusions: The new FEP model achieved a good discrimination and good calibration across six countries with different ethnic contributions supporting its robustness and good generalizability