On the Weak Lefschetz Property for Artinian Gorenstein algebras of codimension three

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1,3,6,6,3,1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from $\mathbb P^2$ to $\mathbb P^3$, and Hesse configurations in $\mathbb P^2$.Comment: A few changes with respect to the previous version. 17 pages. To appear in the J. of Algebr

The minimal resolution conjecture on a general quartic surface in P3

Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in P3 this conjecture has been proven for points on quadric surfaces and on general cubic surfaces. In the latter case, Gorenstein liaison was the main tool. Here we prove the conjecture for general quartic surfaces. Gorenstein liaison continues to be a central tool, but to prove the existence of our links we make use of certain dimension computations. We also discuss the higher degree case, but now the dimension count does not force the existence of our links

On the Weak Lefcchetz property for artinian Gorenstein algebras

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function , we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from to , and Hesse configurations in

Significant increase in natural disturbance impacts on European forests since 1950

Over the last decades, the natural disturbance is increasingly putting pressure on European forests. Shifts in disturbance regimes may compromise forest functioning and the continuous provisioning of ecosystem services to society, including their climate change mitigation potential. Although forests are central to many European policies, we lack the long-term empirical data needed for thoroughly understanding disturbance dynamics, modeling them, and developing adaptive management strategies. Here, we present a unique database of >170,000 records of ground-based natural disturbance observations in European forests from 1950 to 2019. Reported data confirm a significant increase in forest disturbance in 34 European countries, causing on an average of 43.8 million m3 of disturbed timber volume per year over the 70-year study period. This value is likely a conservative estimate due to under-reporting, especially of small-scale disturbances. We used machine learning techniques for assessing the magnitude of unreported disturbances, which are estimated to be between 8.6 and 18.3 million m3/year. In the last 20 years, disturbances on average accounted for 16% of the mean annual harvest in Europe. Wind was the most important disturbance agent over the study period (46% of total damage), followed by fire (24%) and bark beetles (17%). Bark beetle disturbance doubled its share of the total damage in the last 20 years. Forest disturbances can profoundly impact ecosystem services (e.g., climate change mitigation), affect regional forest resource provisioning and consequently disrupt long-term management planning objectives and timber markets. We conclude that adaptation to changing disturbance regimes must be placed at the core of the European forest management and policy debate. Furthermore, a coherent and homogeneous monitoring system of natural disturbances is urgently needed in Europe, to better observe and respond to the ongoing changes in forest disturbance regimes

Genome-wide association meta-analysis in 269,867 individuals identifies new genetic and functional links to intelligence

Intelligence is highly heritable(1) and a major determinant of human health and well-being(2). Recent genome-wide meta-analyses have identified 24 genomic loci linked to variation in intelligence3-7, but much about its genetic underpinnings remains to be discovered. Here, we present a large-scale genetic association study of intelligence (n = 269,867), identifying 205 associated genomic loci (190 new) and 1,016 genes (939 new) via positional mapping, expression quantitative trait locus (eQTL) mapping, chromatin interaction mapping, and gene-based association analysis. We find enrichment of genetic effects in conserved and coding regions and associations with 146 nonsynonymous exonic variants. Associated genes are strongly expressed in the brain, specifically in striatal medium spiny neurons and hippocampal pyramidal neurons. Gene set analyses implicate pathways related to nervous system development and synaptic structure. We confirm previous strong genetic correlations with multiple health-related outcomes, and Mendelian randomization analysis results suggest protective effects of intelligence for Alzheimer's disease and ADHD and bidirectional causation with pleiotropic effects for schizophrenia. These results are a major step forward in understanding the neurobiology of cognitive function as well as genetically related neurological and psychiatric disorders.Peer reviewe

On the shape of a pure O-sequence

A monomial order ideal is a finite collection $X$ of (monic) monomials such that, whenever $M\in X$ and $N$ divides $M$, then $N\in X$. Hence $X$ is a poset, where the partial order is given by divisibility. If all, say $t$, maximal monomials of $X$ have the same degree, then $X$ is pure (of type $t$). A pure $O$-sequence is the vector, $\underline {h}=(h_0=1,h_1,...,h_e)$, counting the monomials of $X$ in each degree. Equivalently, pure $O$-sequences can be characterized as the $f$-vectors of pure multicomplexes, or, in the language of commutative algebra, as the $h$-vectors of monomial Artinian level algebras. Pure $O$-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their $f$-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure $O$-sequences. Our work, which makes an extensive use of both algebraic and combinatorial techniques, in particular includes: (i) A characterization of the first half of a pure $O$-sequence, which yields the exact converse to a $g$-theorem of Hausel; (ii) A study of (the failing of) the unimodality property; (iii) The problem of enumerating pure $O$-sequences, including a proof that almost all $O$-sequences are pure, a natural bijection between integer partitions and type 1 pure $O$-sequences, and the asymptotic enumeration of socle degree 3 pure $O$-sequences of type $t$; (iv) A study of the Interval Conjecture for Pure $O$-sequences (ICP), which represents perhaps the strongest possible structural result short of an (impossible?) full characterization; (v) A pithy connection of the ICP with Stanley's conjecture on the $h$-vectors of matroid complexes; (vi) A more specific study of pure $O$-sequences of type 2, including a proof of the Weak Lefschetz Property in codimension 3 over a field of characteristic zero. As an immediate corollary, pure $O$-sequences of codimension 3 and type 2 are unimodal (over an arbitrary field). (vii) An analysis, from a commutative algebra viewpoint, of the extent to which the Weak and Strong Lefschetz Properties can fail for monomial algebras. (viii) Some observations about pure $f$-vectors, an important special case of pure $O$-sequences

Item-level analyses reveal genetic heterogeneity in neuroticism

Genome-wide association studies (GWAS) of psychological traits are generally conducted on (dichotomized) sums of items or symptoms (e.g., case-control status), and not on the individual items or symptoms themselves. We conduct large-scale GWAS on 12 neuroticism items and observe notable and replicable variation in genetic signal between items. Within samples, genetic correlations among the items range between 0.38 and 0.91 (mean r g =.63), indicating genetic heterogeneity in the full item set. Meta-analyzing the two samples, we identify 255 genome-wide significant independent genomic regions, of which 138 are item-specific. Genetic analyses and genetic correlations with 33 external traits support genetic differences between the items. Hierarchical clustering analysis identifies two genetically homogeneous item clusters denoted depressed affect and worry. We conclude that the items used to measure neuroticism are genetically heterogeneous, and that biological understanding can be gained by studying them in genetically more homogeneous clusters

On the shape of a pure O-sequence

A monomial order ideal is a finite collection $X$ of (monic) monomials such that, whenever $M\in X$ and $N$ divides $M$, then $N\in X$. Hence $X$ is a poset, where the partial order is given by divisibility. If all, say $t$, maximal monomials of $X$ have the same degree, then $X$ is pure (of type $t$). A pure $O$-sequence is the vector, $\underline {h}=(h_0=1,h_1,...,h_e)$, counting the monomials of $X$ in each degree. Equivalently, pure $O$-sequences can be characterized as the $f$-vectors of pure multicomplexes, or, in the language of commutative algebra, as the $h$-vectors of monomial Artinian level algebras. Pure $O$-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their $f$-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure $O$-sequences. Our work, which makes an extensive use of both algebraic and combinatorial techniques, in particular includes: (i) A characterization of the first half of a pure $O$-sequence, which yields the exact converse to a $g$-theorem of Hausel; (ii) A study of (the failing of) the unimodality property; (iii) The problem of enumerating pure $O$-sequences, including a proof that almost all $O$-sequences are pure, a natural bijection between integer partitions and type 1 pure $O$-sequences, and the asymptotic enumeration of socle degree 3 pure $O$-sequences of type $t$; (iv) A study of the Interval Conjecture for Pure $O$-sequences (ICP), which represents perhaps the strongest possible structural result short of an (impossible?) full characterization; (v) A pithy connection of the ICP with Stanley's conjecture on the $h$-vectors of matroid complexes; (vi) A more specific study of pure $O$-sequences of type 2, including a proof of the Weak Lefschetz Property in codimension 3 over a field of characteristic zero. As an immediate corollary, pure $O$-sequences of codimension 3 and type 2 are unimodal (over an arbitrary field). (vii) An analysis, from a commutative algebra viewpoint, of the extent to which the Weak and Strong Lefschetz Properties can fail for monomial algebras. (viii) Some observations about pure $f$-vectors, an important special case of pure $O$-sequences

Genome-wide analysis of insomnia in 1,331,010 individuals identifies new risk loci and functional pathways

Insomnia is the second most prevalent mental disorder, with no sufficient treatment available. Despite substantial heritability, insight into the associated genes and neurobiological pathways remains limited. Here, we use a large genetic association sample (n = 1,331,010) to detect novel loci and gain insight into the pathways, tissue and cell types involved in insomnia complaints. We identify 202 loci implicating 956 genes through positional, expression quantitative trait loci, and chromatin mapping. The meta-analysis explained 2.6% of the variance. We show gene set enrichments for the axonal part of neurons, cortical and subcortical tissues, and specific cell types, including striatal, hypothalamic, and claustrum neurons. We found considerable genetic correlations with psychiatric traits and sleep duration, and modest correlations with other sleep-related traits. Mendelian randomization identified the causal effects of insomnia on depression, diabetes, and cardiovascular disease, and the protective effects of educational attainment and intracranial volume. Our findings highlight key brain areas and cell types implicated in insomnia, and provide new treatment targets