Exploration of Shared Genetic Architecture Between Subcortical Brain Volumes and Anorexia Nervosa

In MRI scans of patients with anorexia nervosa (AN), reductions in brain volume are often apparent. However, it is unknown whether such brain abnormalities are influenced by genetic determinants that partially overlap with those underlying AN. Here, we used a battery of methods (LD score regression, genetic risk scores, sign test, SNP effect concordance analysis, and Mendelian randomization) to investigate the genetic covariation between subcortical brain volumes and risk for AN based on summary measures retrieved from genome-wide association studies of regional brain volumes (ENIGMA consortium, n = 13,170) and genetic risk for AN (PGC-ED consortium, n = 14,477). Genetic correlations ranged from − 0.10 to 0.23 (all p > 0.05). There were some signs of an inverse concordance between greater thalamus volume and risk for AN (permuted p = 0.009, 95% CI: [0.005, 0.017]). A genetic variant in the vicinity of ZW10, a gene involved in cell division, and neurotransmitter and immune system relevant genes, in particular DRD2, was significantly associated with AN only after conditioning on its association with caudate volume (pFDR = 0.025). Another genetic variant linked to LRRC4C, important in axonal and synaptic development, reached significance after conditioning on hippocampal volume (pFDR = 0.021). In this comprehensive set of analyses and based on the largest available sample sizes to date, there was weak evidence for associations between risk for AN and risk for abnormal subcortical brain volumes at a global level (that is, common variant genetic architecture), but suggestive evidence for effects of single genetic markers. Highly powered multimodal brain- and disorder-related genome-wide studies are needed to further dissect the shared genetic influences on brain structure and risk for AN

Codes for Write-Once Memories

A write-once memory (WOM) is a storage device that consists of cells that can take on q values, with the added constraint that rewrites can only increase a cell's value. A length-n, t-write WOM-code is a coding scheme that allows t messages to be stored in n cells. If on the ith write we write one of M_i messages, then the rate of this write is the ratio of the number of written bits to the total number of cells, i.e., log_2 M_i/n. The sum-rate of the WOM-code is the sum of all individual rates on all writes. A WOM-code is called a fixed-rate WOM-code if the rates on all writes are the same, and otherwise, it is called a variable-rate WOM-code. We address two different problems when analyzing the sum-rate of WOM-codes. In the first one, called the fixed-rate WOM-code problem, the sum-rate is analyzed over all fixed-rate WOM-codes, and in the second problem, called the unrestricted-rate WOM-code problem, the sum-rate is analyzed over all fixed-rate and variable-rate WOM-codes. In this paper, we first present a family of two-write WOM-codes. The construction is inspired by the coset coding scheme, which was used to construct multiple-write WOM-codes by Cohen and recently by Wu, in order to construct from each linear code a two-write WOM-code. This construction improves the best known sum-rates for the fixed- and unrestricted-rate WOM-code problems. We also show how to take advantage of two-write WOM-codes in order to construct codes for the Blackwell channel. The two-write construction is generalized for two-write WOM-codes with q levels per cell, which is used with ternary cells to construct three- and four-write binary WOM-codes. This construction is used recursively in order to generate a family of t-write WOM-codes for all t. A further generalization of these t-write WOM-codes yields additional families of efficient WOM-codes. Finally, we show a recursive method that uses the previously constructed WOM-codes in order to construct fixed-rate WOM-codes. We conclude and show that the WOM-codes constructed here outperform all previously known WOM-codes for 2 ≤ t ≤ 10 for both the fixed- and unrestricted-rate WOM-code problems