Region graph partition function expansion and approximate free energy landscapes: Theory and some numerical results

Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theoretical approaches for treating the complicated short-loop-induced local correlations. For graphical models represented by non-redundant or redundant region graphs, approximate free energy landscapes are constructed in this paper through the mathematical framework of region graph partition function expansion. Several free energy functionals are obtained, each of which use a set of probability distribution functions or functionals as order parameters. These probability distribution function/functionals are required to satisfy the region graph belief-propagation equation or the region graph survey-propagation equation to ensure vanishing correction contributions of region subgraphs with dangling edges. As a simple application of the general theory, we perform region graph belief-propagation simulations on the square-lattice ferromagnetic Ising model and the Edwards-Anderson model. Considerable improvements over the conventional Bethe-Peierls approximation are achieved. Collective domains of different sizes in the disordered and frustrated square lattice are identified by the message-passing procedure. Such collective domains and the frustrations among them are responsible for the low-temperature glass-like dynamical behaviors of the system.Comment: 30 pages, 11 figures. More discussion on redundant region graphs. To be published by Journal of Statistical Physic

Non-motor symptom burden in patients with Parkinson's disease with impulse control disorders and compulsive behaviours : results from the COPPADIS cohort

The study was aimed at analysing the frequency of impulse control disorders (ICDs) and compulsive behaviours (CBs) in patients with Parkinson's disease (PD) and in control subjects (CS) as well as the relationship between ICDs/CBs and motor, nonmotor features and dopaminergic treatment in PD patients. Data came from COPPADIS-2015, an observational, descriptive, nationwide (Spain) study. We used the validated Questionnaire for Impulsive-Compulsive Disorders in Parkinson's Disease-Rating Scale (QUIP-RS) for ICD/CB screening. The association between demographic data and ICDs/CBs was analyzed in both groups. In PD, this relationship was evaluated using clinical features and treatment-related data. As result, 613 PD patients (mean age 62.47 ± 9.09 years, 59.87% men) and 179 CS (mean age 60.84 ± 8.33 years, 47.48% men) were included. ICDs and CBs were more frequent in PD (ICDs 12.7% vs. 1.6%, p < 0.001; CBs 7.18% vs. 1.67%, p = 0.01). PD patients had more frequent previous ICDs history, premorbid impulsive personality and antidepressant treatment (p < 0.05) compared with CS. In PD, patients with ICDs/CBs presented younger age at disease onset, more frequent history of previous ICDs and premorbid personality (p < 0.05), as well as higher comorbidity with nonmotor symptoms, including depression and poor quality of life. Treatment with dopamine agonists increased the risk of ICDs/CBs, being dose dependent (p < 0.05). As conclusions, ICDs and CBs were more frequent in patients with PD than in CS. More nonmotor symptoms were present in patients with PD who had ICDs/CBs compared with those without. Dopamine agonists have a prominent effect on ICDs/CBs, which could be influenced by dose

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele