Glauber Dynamics for Ising Model on Convergent Dense Graph Sequences

We study the Glauber dynamics for Ising model on (sequences of) dense graphs. We view the dense graphs through the lens of graphons. For the ferromagnetic Ising model with inverse temperature beta on a convergent sequence of graphs G_n with limit graphon W we show fast mixing of the Glauber dynamics if beta * lambda_1(W) 1 (where lambda_1(W)is the largest eigenvalue of the graphon). We also show that in the case beta * lambda_1(W) = 1 there is insufficient information to determine the mixing time (it can be either fast or slow)

Synthesis, X-ray structure and in vitro cytotoxicity studies of Cu(I/II) complexes of thiosemicarbazone: special emphasis on their interactions with DNA

4-(p-X-phenyl)thiosemicarbazone of napthaldehyde {where X = Cl (HL¹) and X = Br (HL²)}, thiosemicarbazone of quinoline-2-carbaldehyde (HL³) and 4-(p-fluorophenyl)thiosemicarbazone of salicylaldehyde (H₂L⁴) and their copper(I) {[Cu(HL¹)(PPh₃)₂Br]·CH₃CN (1) and [Cu(HL²)(PPh₃)₂Cl]·DMSO (2)} and copper(II) {[(Cu₂L³₂Cl)₂(μ-Cl)₂]·2H₂O (3) and [Cu(L⁴)(Py)] (4)} complexes are reported herein. The synthesized ligands and their copper complexes were successfully characterized by elemental analysis, cyclic voltammetry, NMR, ESI-MS, IR and UV-Vis spectroscopy. Molecular structures of all the Cu(I) and Cu(II) complexes have been determined by X-ray crystallography. All the complexes (1–4) were tested for their ability to exhibit DNA-binding and -cleavage activity. The complexes effectively interact with CT-DNA possibly by groove binding mode, with binding constants ranging from 10⁴ to 10⁵ M⁻¹. Among the complexes, 3 shows the highest chemical (60%) as well as photo-induced (80%) DNA cleavage activity against pUC19 DNA. Finally, the in vitro antiproliferative activity of all the complexes was assayed against the HeLa cell line. Some of the complexes have proved to be as active as the clinical referred drugs, and the greater potency of 3 may be correlated with its aqueous solubility and the presence of the quinonoidal group in the thiosemicarbazone ligand coordinated to the metal

FairyTED: A Fair Rating Predictor for TED Talk Data

With the recent trend of applying machine learning in every aspect of human life, it is important to incorporate fairness into the core of the predictive algorithms. We address the problem of predicting the quality of public speeches while being fair with respect to sensitive attributes of the speakers, e.g. gender and race. We use the TED talks as an input repository of public speeches because it consists of speakers from a diverse community and has a wide outreach. Utilizing the theories of Causal Models, Counterfactual Fairness and state-of-the-art neural language models, we propose a mathematical framework for fair prediction of the public speaking quality. We employ grounded assumptions to construct a causal model capturing how different attributes affect public speaking quality. This causal model contributes in generating counterfactual data to train a fair predictive model. Our framework is general enough to utilize any assumption within the causal model. Experimental results show that while prediction accuracy is comparable to recent work on this dataset, our predictions are counterfactually fair with respect to a novel metric when compared to true data labels. The FairyTED setup not only allows organizers to make informed and diverse selection of speakers from the unobserved counterfactual possibilities but it also ensures that viewers and new users are not influenced by unfair and unbalanced ratings from arbitrary visitors to the ted.com website when deciding to view a talk

Synthesis, Structural Studies and Catalytic Activity of a Series of Dioxidomolybdenum(VI)-Thiosemicarbazone Complexes

Reaction of the thiosemicarbazone ligands, [4-(p-bromophenyl)thiosemicarbazone of salicylaldehyde (H2L1), 4-(p-X-phenyl)thiosemicarbazone of o-vanillin {X = F (H2L2), X = Cl (H2L3) and X = OMe (H2L4)}, 4-(p-bromophenyl)thiosemicarbazone of 5-bromosalicylaldehyde (H2L5), and 4-(p-chlorophenyl)thiosemicarbazone of o-hydroxynaphthaldehyde (H2L6)] with [MoO2(acac)2] afforded a series of new oxidomolybdenum(VI) complexes [Mo(VI)O2L1–6(solv)] (1–6) {where solv (solvent) = DMSO (1, 3, 5 & 6) and H2O (2 & 4)}. The molecular structures of 2 and 3 were determined by X-ray crystallography, demonstrating the dibasic tridentate behavior of ligands. The cyclic voltammogram pattern is similar for 1–6, which includes two irreversible reduction processes within the potential window −0.71 to −0.66 V and −0.92 to −0.85 V corresponding to the metal centered reduction from Mo(VI)/Mo(V) and Mo(V)/Mo(IV) respectively. Catalytic potential of 1–6 was tested for the oxidation of styrene and cyclohexene. The effect of various parameters such as the amount of catalyst, oxidant, NaHCO3, and solvent was checked to optimize the conditions for the best performance of the catalyst. 100% product selectivity for the formation of cyclohexene oxide from cyclohexene and ∼98–99% product selectivity for the oxidation of styrene to styrene oxide was observed

Mixed-ligand Nickel(II) Thiosemicarbazone Complexes: Synthesis, Characterization and Biological Evaluation

The syntheses and characterization of some new mixed-ligand nickel(II) complexes [Ni(L1)(PPh3)] (1), [Ni(L1)(Py)] (2), [Ni(L2)(PPh3)]·DMSO (3), [Ni(L 2)(Imz)] (4), [Ni(L3)(4-pic)] (5) and [Ni(L 3)2(μ-4,4′-byp)]·2DMSO (6) of three selected thiosemicarbazones the 4-(p-X-phenyl)thiosemicarbazones of salicylaldehyde (H2L1-3) (A, Scheme 1) are described in the present study, differing in the inductive effect of the substituent X (X = F, Br and OCH3), in order to observe its influence, if any, on the redox potentials and biological activity of the complexes. All the synthesized ligands and the metal complexes were successfully characterized by elemental analysis, IR, UV-Vis, NMR spectroscopy and cyclic voltammetry. The molecular structures of four mononuclear (1-3 and 5) and one dinuclear (6) Ni(II) complex have been determined by X-ray crystallography. The complexes have been screened for their antibacterial activity against Escherichia coli and Bacillus. The minimum inhibitory concentrations of these complexes and their antibacterial activities indicate that compound 4 is the potential lead molecule for drug designing. © 2012 Elsevier Ltd. All rights reserved

Chemistry of oxidomolybdenum(IV) and -(VI) complexes with ONS donor ligands: synthesis, computational evaluation and oxo-transfer reactions

A series of dioxidomolybdenum(VI) complexes, [MoVIO2L1–6] (1–6) and [MoVIO2L1–6(solv)] (1a–6a) {where solv (solvent) = DMSO (1a, 3a, 5a and 6a) and H2O (2a and 4a)} have been synthesized using thiosemicarbazone ligands, H2L1–6. Furthermore, six monooxidomolybdenum(IV) complexes [MoIVOL1–6(N-N)] (7–12) {where co-ligand (N-N) = 2,2′-bipyridine (bipy) (7, 10 and 11) and 1,10-phenanthroline (phen) (8, 9 and 12)} have also been synthesized from the corresponding Mo(VI) precursors, [MoVIO2L1–6] (1–6) by oxygen atom transfer (OAT) reaction. Complexes have been characterized by conventional methods, including X-ray crystallography, and DFT (density functional theory) calculations. OAT reactivity of Mo(VI) and Mo(IV) complexes have been successfully established through the formation of OPPh3 and Me2S. These OAT products have been characterized by 31P NMR (OPPh3), UV–Vis spectroscopy and GC–MS (Me2S) and DFT simulations supported this finding through the prediction of ΔGtotsol for the reaction of oxygen atom transfer. DFT methods suggested that the oxygen atom transfer from [MoVIO2L] species to PPh3 to give [MoIVOL(bipy)] and from DMSO to [MoIVOL(bipy)] to yield [MoVIO2L] is strongly favored, whereas the formation of μ-oxido dimer [MoV2O3L2], is much less probable