917 research outputs found
Linear resolutions of powers and products
The goal of this paper is to present examples of families of homogeneous
ideals in the polynomial ring over a field that satisfy the following
condition: every product of ideals of the family has a linear free resolution.
As we will see, this condition is strongly correlated to good primary
decompositions of the products and good homological and arithmetical properties
of the associated multi-Rees algebras. The following families will be discussed
in detail: polymatroidal ideals, ideals generated by linear forms and Borel
fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi
deformation
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
Appropriate disclosure of a diagnosis of dementia : identifying the key behaviours of 'best practice'
Background: Despite growing evidence that many people with dementia want to know their diagnosis, there is wide variation in attitudes of professionals towards disclosure. The disclosure of the diagnosis of dementia is increasingly recognised as being a process rather than a one-off behaviour. However, the different behaviours that contribute to this process have not been comprehensively defined. No intervention studies to improve diagnostic disclosure in dementia have been reported to date. As part of a larger study to develop an intervention to promote appropriate disclosure, we sought to identify important disclosure behaviours and explore whether supplementing a literature review with other methods would result in the identification of new behaviours. Methods: To identify a comprehensive list of behaviours in disclosure we conducted a literature review, interviewed people with dementia and informal carers, and used a consensus process involving health and social care professionals. Content analysis of the full list of behaviours was carried out. Results: Interviews were conducted with four people with dementia and six informal carers. Eight health and social care professionals took part in the consensus panel. From the interviews, consensus panel and literature review 220 behaviours were elicited, with 109 behaviours over-lapping. The interviews and consensus panel elicited 27 behaviours supplementary to the review. Those from the interviews appeared to be self-evident but highlighted deficiencies in current practice and from the panel focused largely on balancing the needs of people with dementia and family members. Behaviours were grouped into eight categories: preparing for disclosure; integrating family members; exploring the patient's perspective; disclosing the diagnosis; responding to patient reactions; focusing on quality of life and well-being; planning for the future; and communicating effectively. Conclusion: This exercise has highlighted the complexity of the process of disclosing a diagnosis of dementia in an appropriate manner. It confirms that many of the behaviours identified in the literature (often based on professional opinion rather than empirical evidence) also resonate with people with dementia and informal carers. The presence of contradictory behaviours emphasises the need to tailor the process of disclosure to individual patients and carers. Our combined methods may be relevant to other efforts to identify and define complex clinical practices for further study.This project is funded by UK Medical Research Council, Grant reference number G0300999
Cluster algebras in algebraic Lie theory
We survey some recent constructions of cluster algebra structures on
coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody
groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group
Evaluation of Seasonal Water Budget Components over the Major Drainage Basins of North America Using an Ensemble-Based Land Surface Model Approach
An ensemble of land surface models and forcing data was developed to assess variability in SWE estimation over North America. In this study, the ensemble output was used to assess how SWE uncertainty impacts stream flow estimation. The analysis was conducted by major basins of North America over the 2009-2017 time period
Differential hepatic processing and biliary secretion of head-group and acyl chains of liposomal phosphatidylcholines
Holomorphic automorphisms of Danielewski surfaces II -- structure of the overshear group
We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces
and investigate their group of holomorphic automorphisms. Our main result
states that the overshear group which is known to be dense in the identity
component of the holomorphic automorphism group, is a free amalgamated product.Comment: 24 page
Hilbert Series for Moduli Spaces of Two Instantons
The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where
G is a simple gauge group, is studied in detail. For a given G, the moduli
space is a singular hyperKahler cone with a symmetry group U(2) \times G, where
U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli
space transform in irreducible representations of the symmetry group and hence
the Hilbert series admits a character expansion. For cases that G is a
classical group (of type A, B, C, or D), there is an ADHM construction which
allows us to compute the HS explicitly using a contour integral. For cases that
G is of E-type, recent index results allow for an explicit computation of the
HS. The character expansion can be expressed as an infinite sum which lives on
a Cartesian lattice that is generated by a small number of representations.
This structure persists for all G and allows for an explicit expressions of the
HS to all simple groups. For cases that G is of type G_2 or F_4, discrete
symmetries are enough to evaluate the HS exactly, even though neither ADHM
construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure
The Cohen-Macaulay property of separating invariants of finite groups
In the case of finite groups, a separating algebra is a subalgebra of the
ring of invariants which separates the orbits. Although separating algebras are
often better behaved than the ring of invariants, we show that many of the
criteria which imply that the ring of invariants is non Cohen-Macaulay actually
imply that no graded separating algebra is Cohen-Macaulay. For example, we show
that, over a field of positive characteristic p, given sufficiently many copies
of a faithful modular representation, no graded separating algebra is
Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a
Cohen-Macaulay graded separating algebra implies the group is generated by
bireflections. Furthermore, we show that, for a -group, the existence of a
Cohen-Macaulay graded separating algebra implies the group is generated by
bireflections. Additionally, we give an example which shows that Cohen-Macaulay
separating algebras can occur when the ring of invariants is not
Cohen-Macaulay.Comment: We removed the conjecture which appeared in previous versions: we
give a counter-example. We fixed the proof of Lemma 2.2 (previously Remark
2.2). 16 page
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