Sexual dimorphism in the human brain: evidence from neuroimaging

In recent years, more and more emphasis has been placed on the investigation of sex differences in the human brain. Noninvasive neuroimaging techniques represent an essential tool in the effort to better understand the effects of sex on both brain structure and function. In this review, we provide a comprehensive summary of the findings that were collected in human neuroimaging studies in vivo thus far: we explore sexual dimorphism in the human brain at the level of (1) brain structure, in both gray and white matter, observed by voxel-based morphometry (VBM) and diffusion tensor imaging (DTI), respectively; (2) baseline neural activity, studied using resting-state functional magnetic resonance imaging (rs-fMRI) and positron emission tomography (PET); (3) neurochemistry, visualized by means of neuroreceptor ligand PET; and (4) task-related neural activation, investigated using fMRI. Functional MRI findings from the literature are complemented by our own meta-analysis of fMRI studies on sex-specific differences in human emotional processing. Specifically, we used activation likelihood estimation (ALE) to provide a quantitative approach to mapping the consistency of neural networks involved in emotional processing across studies. The presented evidence for sex-specific differences in neural structure and function highlights the importance of modeling sex as a contributing factor in the analysis of brain-related data.     

Asymptotic Growth of Associated Primes of Certain Graph Ideals

We specify a class of graphs, H _t , and characterize the irreducible decompositions of all powers of the cover ideals. This gives insight into the structure and stabilization of the corresponding associated primes; specifically, providing an answer to the question “For each integer t ≥ 0, does there exist a (hyper) graph H _t such that stabilization of associated primes occurs at n ≥ (χ(H _t ) ?1) + t?” [4 Francisco , C. A. , Hà , H. T. , Van Tuyl , A. ( 2011 ). Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals . J. Algebra 331 : 224 – 242 .[Crossref], [Web of Science ®] , [Google Scholar]]. For each t, H _t has chromatic number 3 and associated primes that stabilize at n = 2 + t.     

The Limiting Shape of the Generic Initial System of a Complete Intersection

Consider a complete intersection I of type (d ₁,…, d _r ) in a polynomial ring over a field of characteristic 0. We study the graded system of ideals {gin(I ⁿ )} _n obtained by taking the reverse lexicographic generic initial ideals of the powers of I and describe its asymptotic behavior. This behavior is nicely captured by the limiting shape which is shown to depend only on the type of the complete intersection.     

Auxiliary Variables in Multiple Imputation When Data Are Missing Not at Random

Most current implementations of multiple imputation (MI) assume that data are missing at random (MAR), but this assumption is generally untestable. We performed analyses to test the effects of auxiliary variables on MI when the data are missing not at random (MNAR) using simulated data and real data. In the analyses we varied (a) the correlation, (b) the level of missing data, (c) the pattern of missing data, and (d) sample size. Results showed that MI performed adequately without auxiliary variables but they also had a modest impact on bias in the real data and improved efficiency in both data sets. The results of this study suggest that, counter to the concern about the violation of the MAR assumption, MI appears to be quite robust to missing data that are MNAR in analytic situations such as the ones presented here. Further, results can be made even better via the use of auxiliary variables, particularly when efficiency is a primary concern.     

PRIMARY TEACHER TRAINEES’ MATHEMATICS SUBJECT KNOWLEDGE AND CLASSROOM PERFORMANCE

UK government agencies have recently set in train requirements to ‘crack down’ on primary [elementary] school teacher trainees whose own knowledge of mathematics is weak. The responsibility to identify and support (or fail) them currently rests with training providers (mainly university schools of education). We describe one approach to this process, presenting some findings concerning what trainees find difficult and how their knowledge is related to their teaching competence. We flesh out these findings with a case study of a mathematically-strong trainee whose path to qualification was less than smooth.     

Dimension Groups for Polynomial Odometers

Here we study a class of dynamical systems we call polynomial odometers. These are adic maps on regularly structured Bratteli diagrams and include the Pascal and Stirling adic maps as examples. We describe the dimension groups associated with these systems and use this to study spaces of invariant measures. For many, but not all, the space of invariant measures is affinely homeomorphic to the space of Borel probability measures on a closed interval in $\mathbb{R}$ , we call such polynomial odometers reasonable. We describe the possible isomorphisms between dimension groups for reasonable polynomial odometers, and use this to prove a version of a result of Giordano, Putnam and Skau for this situation. Namely, we show that there is an isomorphism between unital ordered groups associated with two reasonable polynomial odometers if and only if there is a special kind of orbit equivalence between the two.     

Toward a digital gene response: RNA G-quadruplexes with fewer quartets fold with higher cooperativity

Changes in RNA conformation can alter gene expression. The guanine quadruplex sequence (GQS) is an RNA motif that folds in the presence of K(+) ions. Changes in the conformation of this motif could be especially important in regulating gene expression in plants because intracellular K(+) concentrations often increase during drought stress. Little is known about the folding thermodynamics of RNA GQS. We show here that RNA GQS with tracts containing three G's [e.g., (GGGxx)(4)] have a modest dependence on the K(+) concentration, folding with no or even negative cooperativity (Hill coefficients ≤1), and are associated with populated folding intermediates. In contrast, GQS with tracts containing just two G's [e.g., (GGxx)(4)] have a steep dependence on the K(+) concentration and fold with positive cooperativity (Hill coefficients of 1.7-2.7) without significantly populating intermediate states. We postulate that in plants, the more stable G3 sequences are largely folded even under unstressed conditions, while the less stable G2 sequences fold only at the higher K(+) concentrations associated with cellular stress, wherein they respond sharply to changing K(+) concentrations. Given the binary nature of their folding, G2 sequences may find application in computation with DNA and in engineering of genetic circuits.     

Asymptotic freedom of Yang–Mills theory with gravity

We study the behaviour of Yang–Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.