Invariants and separating morphisms for algebraic group actions

The first part of this paper is a refinement of Winkelmann’s work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the possibly not finitely generated ring of invariants is “almost” an algebraic variety, and that the quotient morphism π: X → X//G has a number of nice properties. One of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective. These general results are then refined for actions of the additive group Ga, where we can say much more. We get a rather explicit description of the so-called plinth variety and of the separating variety, which measures how much orbits are separated by invariants. The most complete results are obtained for representations. We also give a complete and detailed analysis of Roberts’ famous example of a an action of Ga on 7-dimensional affine space with a non-finitely generated ring of invariants

On the ideals of equivariant tree models

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.Comment: 23 pages. Greatly improved exposition, in part following suggestions by a referee--thanks! Also added exampl

Drought alters the spatial distribution, grazing patterns, and radula morphology of a fungal-farming salt marsh snail

Contains fulltext : 208086.pdf (publisher's version ) (Open Access

Colorectal cancer care and patients’ perceptions before and during COVID-19: implications for subsequent SARS-CoV-2 infection waves

BACKGROUND: Changes in colorectal cancer (CRC) care planning due to the coronavirus disease 2019 (COVID-19) pandemic and associated health-related quality of life (HRQoL) and well-being of patients with CRC are unknown. We report changes in CRC care and patient-reported outcomes (PROs) including HRQoL, distress, and loneliness during the first wave of SARS-CoV-2. METHODS: In April 2020, 4,984 patients included in the nationwide Prospective Dutch Colorectal Cancer cohort were invited to complete a COVID-19-specific questionnaire, together with the validated EORTC QLQ-C30, De Jong Gierveld, and HADS. Clinical data were obtained from the Netherlands Cancer Registry. Scores were compared with the year prior to COVID-19, and with an age- and sex-matched control population during COVID-19. RESULTS: In total, 3,247 (65.1%) patients responded between April and June 2020. Seventeen percent of patients had cancelled/postponed/changed hospital visits into a telephone- or video consult while 5.3% had adjusted/postponed/cancelled treatment. Compared to controls, patients reported worse HRQoL, but comparable distress and less social loneliness (patients = 21.2%; controls = 32.9%). Compared to pre-COVID-19, clinically meaningful deterioration of HRQoL was more prevalent in patients with changes in cancer care planning than in patients without changes. Prior to undergoing or currently undergoing treatment, and infection worries were associated with lower HRQoL. CONCLUSIONS: CRC patients reported equal anxiety and depression, but worse HRQoL than the control population. Changes in care planning were associated with deterioration of HRQoL and increased anxiety. In case of one or more risk factors, healthcare specialists should discuss (mental) health status and possible support during future SARS-CoV-2 infection waves or comparable pandemics

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

On Arnold's 14 `exceptional' N=2 superconformal gauge theories

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).Comment: 73 pages, 7 figure

Quiver Structure of Heterotic Moduli

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl

Radio Astronomy

Contains table of contents for Section 4 and reports on five research projects.National Science Foundation Grant AST 92-24191MIT Lincoln Laboratory Agreement BX-4975National Aeronautics and Space Administration/Goddard Space Flight Center Grant NAS 5-31376National Aeronautics and Space Administration/Goddard Space Flight Center Grant NAG5-10MIT Leaders for Manufacturing Progra

Predicting mental imagery based BCI performance from personality, cognitive profile and neurophysiological patterns

Mental-Imagery based Brain-Computer Interfaces (MI-BCIs) allow their users to send commands to a computer using their brain-activity alone (typically measured by ElectroEncephaloGraphy— EEG), which is processed while they perform specific mental tasks. While very promising, MI-BCIs remain barely used outside laboratories because of the difficulty encountered by users to control them. Indeed, although some users obtain good control performances after training, a substantial proportion remains unable to reliably control an MI-BCI. This huge variability in user-performance led the community to look for predictors of MI-BCI control ability. However, these predictors were only explored for motor-imagery based BCIs, and mostly for a single training session per subject. In this study, 18 participants were instructed to learn to control an EEG-based MI-BCI by performing 3 MI-tasks, 2 of which were non-motor tasks, across 6 training sessions, on 6 different days. Relationships between the participants’ BCI control performances and their personality, cognitive profile and neurophysiological markers were explored. While no relevant relationships with neurophysiological markers were found, strong correlations between MI-BCI performances and mental-rotation scores (reflecting spatial abilities) were revealed. Also, a predictive model of MI-BCI performance based on psychometric questionnaire scores was proposed. A leave-one-subject-out cross validation process revealed the stability and reliability of this model: it enabled to predict participants’ performance with a mean error of less than 3 points. This study determined how users’ profiles impact their MI-BCI control ability and thus clears the way for designing novel MI-BCI training protocols, adapted to the profile of each user