1,504 research outputs found
Noether normalizations, reductions of ideals, and matroids
We show that given a finitely generated standard-graded algebra of dimension
over an infinite field, its graded Noether normalizations obey a certain
kind of `generic exchange', allowing one to pass between any two of them in at
most steps. We prove analogous generic exchange theorems for minimal
reductions of an ideal, minimal complete reductions of a set of ideals, and
minimal complete reductions of multigraded -algebras. Finally, we unify all
these results into a common axiomatic framework by introducing a new
topological-combinatorial structure we call a generic matroid, which is a
common generalization of a topological space and a matroid.Comment: 13 pages; to appear in Proceedings of the American Mathematical
Societ
Alien Registration- Epstein, Joseph (Bath, Sagadahoc County)
https://digitalmaine.com/alien_docs/9520/thumbnail.jp
Random strings and tt-degrees of Turing complete C.E. sets
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular,
sets of random strings. It is known that the set of random strings with respect
to any universal prefix-free machine is Turing complete, but that truth-table
completeness depends on the choice of universal machine. We show that for such
sets of random strings, any finite set of their truth-table degrees do not meet
to the degree~0, even within the c.e. truth-table degrees, but when taking the
meet over all such truth-table degrees, the infinite meet is indeed~0. The
latter result proves a conjecture of Allender, Friedman and Gasarch. We also
show that there are two Turing complete c.e. sets whose truth-table degrees
form a minimal pair.Comment: 25 page
Closed Quasi-Fuchsian Surfaces In Hyperbolic Knot Complements
We show that every hyperbolic knot complement contains a closed
quasi-Fuchsian surface.Comment: 69 pages, 27 figures. Made small changes suggested by refere
Statistics and compression of scl
We obtain sharp estimates on the growth rate of stable commutator length on
random (geodesic) words, and on random walks, in hyperbolic groups and groups
acting nondegenerately on hyperbolic spaces. In either case, we show that with
high probability stable commutator length of an element of length is of
order .
This establishes quantitative refinements of qualitative results of
Bestvina-Fujiwara and others on the infinite dimensionality of 2-dimensional
bounded cohomology in groups acting suitably on hyperbolic spaces, in the sense
that we can control the geometry of the unit balls in these normed vector
spaces (or rather, in random subspaces of their normed duals).
As a corollary of our methods, we show that an element obtained by random
walk of length in a mapping class group cannot be written as a product of
fewer than reducible elements, with probability going to 1 as
goes to infinity. We also show that the translation length on the complex
of free factors of a random walk of length on the outer automorphism group
of a free group grows linearly in .Comment: Minor edits arising from referee's comments; 45 page
Common and Unique Representations in pFC for Place Attractiveness
Although previous neuroimaging research has identified overlapping correlates of subjective value across different reward types in the ventromedial pFC (vmPFC), it is not clear whether this “common currency” evaluative signal extends to the aesthetic domain. To examine this issue, we scanned human participants with fMRI while they made attractiveness judgments of faces and places—two stimulus categories that are associated with different underlying rewards, have very different visual properties, and are rarely compared with each other. We found overlapping signals for face and place attractiveness in the vmPFC, consistent with the idea that this region codes a signal for value that applies across disparate reward types and across both economic and aesthetic judgments. However, we also identified a subregion of vmPFC within which activity patterns for face and place attractiveness were distinguishable, suggesting that some category-specific attractiveness information is retained in this region. Finally, we observed two separate functional regions in lateral OFC: one region that exhibited a category-unique response to face attractiveness and another region that responded strongly to faces but was insensitive to their value. Our results suggest that vmPFC supports a common mechanism for reward evaluation while also retaining a degree of category-specific information, whereas lateral OFC may be involved in basic reward processing that is specific to only some stimulus categories
Association of Pyrethroid Pesticide Exposure With Attention-Deficit/Hyperactivity Disorder in a Nationally Representative Sample of U.S. Children
Background
Pyrethroid pesticides cause abnormalities in the dopamine system and produce an ADHD phenotype in animal models, with effects accentuated in males versus females. However, data regarding behavioral effects of pyrethroid exposure in children is limited. We examined the association between pyrethroid pesticide exposure and ADHD in a nationally representative sample of US children, and tested whether this association differs by sex.
Methods
Data are from 8–15 year old participants (N = 687) in the 2001–2002 National Health and Nutrition Examination Survey. Exposure was assessed using concurrent urinary levels of the pyrethroid metabolite 3-phenoxybenzoic acid (3-PBA). ADHD was defined by either meeting Diagnostic and Statistical Manual of Mental Disorders-Fourth Edition criteria on the Diagnostic Interview Schedule for Children (DISC) or caregiver report of a prior diagnosis. ADHD symptom counts were determined via the DISC. Multivariable logistic regression examined the link between pyrethroid exposure and ADHD, and poisson regression investigated the link between exposure and ADHD symptom counts.
Results
Children with urinary 3-PBA above the limit of detection (LOD) were twice as likely to have ADHD compared with those below the LOD (adjusted odds ratio [aOR] 2.42; 95 % confidence interval [CI] 1.06, 5.57). Hyperactive-impulsive symptoms increased by 50 % for every 10-fold increase in 3-PBA levels (adjusted count ratio 1.50; 95 % CI 1.03, 2.19); effects on inattention were not significant. We observed possible sex-specific effects: pyrethroid biomarkers were associated with increased odds of an ADHD diagnosis and number of ADHD symptoms for boys but not girls.
Conclusions
We found an association between increasing pyrethroid pesticide exposure and ADHD which may be stronger for hyperactive-impulsive symptoms compared to inattention and in boys compared to girls. Given the growing use of pyrethroid pesticides, these results may be of considerable public health import
- …