A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states

We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis

Diet transition to a high-fat diet for 3 weeks reduces brain omega-3-fatty acid levels, alters BDNF signaling and induces anxiety & depression-like behavior in adult rats

Background: The consumption of diets high in calories and low in nutrient value is becoming increasingly common in modern society, which can lead to metabolic disorders like diabetes and obesity, and potentially to psychiatric disorders. We have performed studies to assess how the shift from a healthy diet rich in omega-3 fatty acids to a diet rich in saturated fatty acid affects the substrates for brain plasticity and function, and anxiety and depression-like behavior. Methods: Pregnant rats were fed with omega-3 supplemented diet from their 2nd day of gestation period as well as their male pups for 12 weeks. Afterwards, the animals were randomly assigned to either a group fed on the same diet or a group fed on a high-fat diet (HFD) rich in saturated fats for 3 weeks. Anxiety and depression-like behaviors were assessed by using open field (OF) and elevated plus maze (EPM). Molecular assessments were performed in the frontal cortex and hippocampus as dysfunctions in these brain regions are main contributors towards depression, anxiety-like behavior and stress. Results: We found that the HFD increased vulnerability for anxiety and depression-like behavior, and that these modifications harmonized with changes in the anxiety-related neuropeptide Y (NPY)-1 receptor. The HFD reduced levels of brain-derived neurotrophic factor (BDNF), and the BDNF signaling receptor pTrkB, as well as the cyclic AMP response element binding protein (CREB), in these brain regions. Brain DHA contents were significantly associated with the levels of anxiety and depression-like behavior in these rats. Conclusions: These results suggest that the change in dietary lifestyle leading to alteration of dietary n3/n-6 fatty acids levels imposes a risk factor for anxiety-like behaviors. Dietary DHA might help for building cognitive reserve that can resist psychiatric disorders