Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisfiability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, artificial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. In addition, each strategy has distinct advantages and disadvantages depending on problem size and available resources. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing adiabatic quantum annealing machines.Chemistry and Chemical Biolog

Virtual Ontogeny of Cortical Growth Preceding Mental Illness

Background: Morphology of the human cerebral cortex differs across psychiatric disorders, with neurobiology and developmental origins mostly undetermined. Deviations in the tangential growth of the cerebral cortex during pre/perinatal periods may be reflected in individual variations in cortical surface area later in life. Methods: Interregional profiles of group differences in surface area between cases and controls were generated using T1-weighted magnetic resonance imaging from 27,359 individuals including those with attention-deficit/hyperactivity disorder, autism spectrum disorder, bipolar disorder, major depressive disorder, schizophrenia, and high general psychopathology (through the Child Behavior Checklist). Similarity of interregional profiles of group differences in surface area and prenatal cell-specific gene expression was assessed. Results: Across the 11 cortical regions, group differences in cortical area for attention-deficit/hyperactivity disorder, schizophrenia, and Child Behavior Checklist were dominant in multimodal association cortices. The same interregional profiles were also associated with interregional profiles of (prenatal) gene expression specific to proliferative cells, namely radial glia and intermediate progenitor cells (greater expression, larger difference), as well as differentiated cells, namely excitatory neurons and endothelial and mural cells (greater expression, smaller difference). Finally, these cell types were implicated in known pre/perinatal risk factors for psychosis. Genes coexpressed with radial glia were enriched with genes implicated in congenital abnormalities, birth weight, hypoxia, and starvation. Genes coexpressed with endothelial and mural genes were enriched with genes associated with maternal hypertension and preterm birth. Conclusions: Our findings support a neurodevelopmental model of vulnerability to mental illness whereby prenatal risk factors acting through cell-specific processes lead to deviations from typical brain development during pregnancy