Thermodynamic quantum critical behavior of the Kondo necklace model

We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\geq 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^{\psi}$ where the shift exponent $\psi=1/(d-1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\Delta\approx \sqrt{|g|}$ for $d \ge 3$ consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for $k_BT\gg\Delta$ and along the non-Fermi liquid trajectory. For $k_BT \ll\Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.Comment: Submitted to PR

Prediction of protein-protein interactions using one-class classification methods and integrating diverse data

This research addresses the problem of prediction of protein-protein interactions (PPI) when integrating diverse kinds of biological information. This task has been commonly viewed as a binary classification problem (whether any two proteins do or do not interact) and several different machine learning techniques have been employed to solve this task. However the nature of the data creates two major problems which can affect results. These are firstly imbalanced class problems due to the number of positive examples (pairs of proteins which really interact) being much smaller than the number of negative ones. Secondly the selection of negative examples can be based on some unreliable assumptions which could introduce some bias in the classification results. Here we propose the use of one-class classification (OCC) methods to deal with the task of prediction of PPI. OCC methods utilise examples of just one class to generate a predictive model which consequently is independent of the kind of negative examples selected; additionally these approaches are known to cope with imbalanced class problems. We have designed and carried out a performance evaluation study of several OCC methods for this task, and have found that the Parzen density estimation approach outperforms the rest. We also undertook a comparative performance evaluation between the Parzen OCC method and several conventional learning techniques, considering different scenarios, for example varying the number of negative examples used for training purposes. We found that the Parzen OCC method in general performs competitively with traditional approaches and in many situations outperforms them. Finally we evaluated the ability of the Parzen OCC approach to predict new potential PPI targets, and validated these results by searching for biological evidence in the literature