EPR studies of phase transitions in cadmium calcium acetate hexahydrate as a function of different paramagnetic impurity-ion concentrations

The phase tt':lnsition in cadmium calcium acetate hexahydrate (CCDAH) has been studied in detail with electron paramagnetic resonance (J;PR) as a function of two different paramagnetic ion concentrations. namely. Cu:• and Mn:• ions. The change in transition temperature (1:!2-143 Kl with Cuz• ion concentrations is explained in terms of mean-field theory and a soft vibrational mode of the -Ca-Cd1 _ ,Cu,-Ca- chain along the c axis of the crystal. While the same theory can also explain our observed transition temperature ( 118-128 K) as a function of the Mn2• ion concentration in this crystal. it does not explain why the limiting value of the transition temperature (i.e .• 145 K) of CaCd1 -.,CuzCCH3C00)4 ·6H~O as x tends to zero, is strikingly different from the limiting value of ( -128..+ K) of CaCd1_.,Mn,(CH3C00)4·6H:O as x tends to zero. The same theory also successfully c:xplains the absence of any phase transition in isomorphous CaCu(CH 3C00)~·6H 20. The value of -dT~Id.t is significantly higher with Mn:• than with Cu!• in CCDAH. [50163-1829(97)01329-5

Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.Comment: Preliminary version appeared in ECML201