Weak Polynomial Identities for M1,1(E)

* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M1,1 (E)

Block-triangular matrix algebras and factorable ideals of graded polynomial identities

AbstractWe study the graded polynomial identities of block-triangular matrix algebras with respect to the grading defined by an abelian group G. In particular, we describe conditions for the TG-ideal of a such algebra to be factorable as a product of TG-ideals corresponding to the algebras defining the diagonal blocks. Moreover, for the factorable T2-ideal of a superalgebra we give a formula for computing its sequence of graded cocharacters once given the sequences of cocharacters of the T2-ideals that factorize it. We finally apply these results to a specific example of block-triangular matrix superalgebra

Groebner bases of ideals invariant under endomorphisms

We introduce the notion of Groebner S-basis of an ideal of the free associative algebra K over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Groebner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x,y,z]=0, with respect to suitable semigroups S. In the latter case, if |X|>2, the ordinary Groebner basis is infinite and our Groebner S-basis is finite. We obtain also explicit minimal Groebner bases of these ideals.Comment: 15 page

SARS-CoV-2 susceptibility and COVID-19 disease severity are associated with genetic variants affecting gene expression in a variety of tissues

Variability in SARS-CoV-2 susceptibility and COVID-19 disease severity between individuals is partly due to genetic factors. Here, we identify 4 genomic loci with suggestive associations for SARS-CoV-2 susceptibility and 19 for COVID-19 disease severity. Four of these 23 loci likely have an ethnicity-specific component. Genome-wide association study (GWAS) signals in 11 loci colocalize with expression quantitative trait loci (eQTLs) associated with the expression of 20 genes in 62 tissues/cell types (range: 1:43 tissues/gene), including lung, brain, heart, muscle, and skin as well as the digestive system and immune system. We perform genetic fine mapping to compute 99% credible SNP sets, which identify 10 GWAS loci that have eight or fewer SNPs in the credible set, including three loci with one single likely causal SNP. Our study suggests that the diverse symptoms and disease severity of COVID-19 observed between individuals is associated with variants across the genome, affecting gene expression levels in a wide variety of tissue types

Twist exome capture allows for lower average sequence coverage in clinical exome sequencing

Background Exome and genome sequencing are the predominant techniques in the diagnosis and research of genetic disorders. Sufficient, uniform and reproducible/consistent sequence coverage is a main determinant for the sensitivity to detect single-nucleotide (SNVs) and copy number variants (CNVs). Here we compared the ability to obtain comprehensive exome coverage for recent exome capture kits and genome sequencing techniques. Results We compared three different widely used enrichment kits (Agilent SureSelect Human All Exon V5, Agilent SureSelect Human All Exon V7 and Twist Bioscience) as well as short-read and long-read WGS. We show that the Twist exome capture significantly improves complete coverage and coverage uniformity across coding regions compared to other exome capture kits. Twist performance is comparable to that of both short- and long-read whole genome sequencing. Additionally, we show that even at a reduced average coverage of 70× there is only minimal loss in sensitivity for SNV and CNV detection. Conclusion We conclude that exome sequencing with Twist represents a significant improvement and could be performed at lower sequence coverage compared to other exome capture techniques

A Solve-RD ClinVar-based reanalysis of 1522 index cases from ERN-ITHACA reveals common pitfalls and misinterpretations in exome sequencing

Purpose Within the Solve-RD project (https://solve-rd.eu/), the European Reference Network for Intellectual disability, TeleHealth, Autism and Congenital Anomalies aimed to investigate whether a reanalysis of exomes from unsolved cases based on ClinVar annotations could establish additional diagnoses. We present the results of the “ClinVar low-hanging fruit” reanalysis, reasons for the failure of previous analyses, and lessons learned. Methods Data from the first 3576 exomes (1522 probands and 2054 relatives) collected from European Reference Network for Intellectual disability, TeleHealth, Autism and Congenital Anomalies was reanalyzed by the Solve-RD consortium by evaluating for the presence of single-nucleotide variant, and small insertions and deletions already reported as (likely) pathogenic in ClinVar. Variants were filtered according to frequency, genotype, and mode of inheritance and reinterpreted. Results We identified causal variants in 59 cases (3.9%), 50 of them also raised by other approaches and 9 leading to new diagnoses, highlighting interpretation challenges: variants in genes not known to be involved in human disease at the time of the first analysis, misleading genotypes, or variants undetected by local pipelines (variants in off-target regions, low quality filters, low allelic balance, or high frequency). Conclusion The “ClinVar low-hanging fruit” analysis represents an effective, fast, and easy approach to recover causal variants from exome sequencing data, herewith contributing to the reduction of the diagnostic deadlock

A first update on mapping the human genetic architecture of COVID-19

peer reviewe

Robinson-Schensted-Knuth correspondence and Weak Polynomial Identities of M1,1(E)M_{1,1}(E)

In this paper, it is proved that the ideal I_w of the weak polynomial identities of the superalgebra M_1,1(E) is generated by the proper polynomials [x_1, x_2, x_3] and [x_2, x_1 ][x_3, x_1 ][x_4, x_1]. This is proved for any infinite field F of characteristic different from 2. Precisely, if B is the subalgebra of the proper polynomials of F, we determine a basis and the dimension of any multihomogeneous component of the quotient algebra B/(B ∩ I_w ). We also compute the Hilbert series of this algebra. One of the main tools of this paper is a variant we found of the Robinson–Schensted–Knuth correspondence defined for single semistandard tableaux of double shape

Weak polynomial identities for M1,1(E)M_{1,1}(E)

We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M_1,1(E)