Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model

In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability . We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal which refer to that for one- two- and three-dimensions they have same value independent of spatial dimensionality in contrast to static (equilibrium) critical exponents.Comment: 9 page

Solvable Kinetic Gaussian Model in External Field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.Comment: 11 page

Cycle-based Cluster Variational Method for Direct and Inverse Inference

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We end up with a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. The inverse problem of finding the couplings of a Markov random field from empirical covariances can be addressed region wise. It turns out that this can be done efficiently in particular in the Ising context, where fixed point equations can be derived along with a one-parameter log likelihood function to minimize. Numerical experiments confirm the effectiveness of these considerations both for the direct and inverse MRF inference.Comment: 47 pages, 16 figure

Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model

We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of these equations to obtain the phase diagrams of the model on the square and triangular lattices. In both cases the spin-glass transition temperatures and the tricritical point estimations improve largely over the Bethe predictions. Moreover, we show that this phase diagram is consistent with the behavior of inference algorithms on single instances of the problem. Finally, we present a method to consistently find approximate solutions to the equations in the glassy phase. The method is applied to the triangular lattice down to T=0, also in the presence of an external field.Comment: 22 pages, 11 figure

Loss of estrogen receptor beta expression correlates with shorter overall survival and lack of clinical response to chemotherapy in ovarian cancer patients

Background: Estrogen receptor beta (ERβ) belongs to a large family of nuclear receptors. Recent studies have suggested that ERβ in contrast to ERα might act as a tumour suppressor in ovarian cancer (OVCA). Materials and Methods: Expression of ERβ was detected by immunocytochemistry in 11 OVCA cell lines and by immunohistochemistry in 43 (41 FIGO stage III) OVCA specimens prepared before chemotherapy and 30 specimens from the same group after chemotherapy. Cisplatin sensitivity in the 11 cell lines was also analysed. Results: No significant correlations between cisplatin-sensitivity and expression of ERβ was found in the cell lines. In the cases which responded well to chemotherapy (complete response) ERβ expression at preliminary laparotomy (PL) was significantly higher (p=0.0004) than in those with progressive disease. Kaplan-Meier analysis revealed that the patients with higher ERβ expression (>30% of cells) at PL had an increased overall survival time and progression-free time (p=0.00161 and p=0.03255, respectively) than the patients with lower ERβ espression. Significantly shorter overall survival time characterized the cases with lower immunoreactivity score of ERβ expression at secondary cytoreduction (SCR) (p=0.00346). Conclusion: The loss of ERβ expression in ovarian tumours may be a feature of malignant transformation

Cymantrene–Triazole "Click" Products: Structural Characterization and Electrochemical Properties

We report the first known examples of triazole-derivatized cymantrene complexes (η5-[4-substituted triazol-1-yl]cyclopentadienyl)tricarbonylmanganese(I), obtained via a “click” chemical synthesis, bearing a phenyl, 3-aminophenyl, or 4-aminophenyl moiety at the 4-position of the triazole ring. Structural characterization data using multinuclear NMR, UV–vis, ATR-IR, and mass spectrometric methods are provided, as well as crystallographic data for (η5-[4-phenyltriazol-1-yl]cyclopentadienyl)tricarbonylmanganese(I) and (η5-[4-(3-aminophenyl)triazol-1-yl]cyclopentadienyl)tricarbonylmanganese(I). Cyclic voltammetric characterization of the redox behavior of each of the three cymantrene–triazole complexes is presented together with digital simulations, in situ infrared spectroelectrochemistry, and DFT calculations to extract the associated kinetic and thermodynamic parameters. The trypanocidal activity of each cymantrene–triazole complex is also examined, and these complexes are found to be more active than cymantrene alone