On bases of some simple modules of symmetric groups and Hecke algebras

We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules Dλ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra RΛ0nRnΛ0 over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde,p(λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of Dλ. In particular, we prove that the q-character of Dλ can be described in terms of DStde,p(λ). We show that a certain natural approach to constructing a basis of an arbitrary Dλ does not work in general, giving a counterexample to a conjecture of Mathas

Products of Borel fixed ideals of maximal minors

We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolutions. The main tools are an extension of straightening law and a very surprising primary decomposition formula. We study also the homological properties of associated multi-Rees algebra which are shown to be Cohen-Macaulay, Koszul and defined by a Gr\"obner basis of quadrics

Matrices commuting with a given normal tropical matrix

Consider the space $M_n^{nor}$ of square normal matrices $X=(x_{ij})$ over $\mathbb{R}\cup\{-\infty\}$, i.e., $-\infty\le x_{ij}\le0$ and $x_{ii}=0$. Endow $M_n^{nor}$ with the tropical sum $\oplus$ and multiplication $\odot$. Fix a real matrix $A\in M_n^{nor}$ and consider the set $\Omega(A)$ of matrices in $M_n^{nor}$ which commute with $A$. We prove that $\Omega(A)$ is a finite union of alcoved polytopes; in particular, $\Omega(A)$ is a finite union of convex sets. The set $\Omega^A(A)$ of $X$ such that $A\odot X=X\odot A=A$ is also a finite union of alcoved polytopes. The same is true for the set $\Omega'(A)$ of $X$ such that $A\odot X=X\odot A=X$. A topology is given to $M_n^{nor}$. Then, the set $\Omega^{A}(A)$ is a neighborhood of the identity matrix $I$. If $A$ is strictly normal, then $\Omega'(A)$ is a neighborhood of the zero matrix. In one case, $\Omega(A)$ is a neighborhood of $A$. We give an upper bound for the dimension of $\Omega'(A)$. We explore the relationship between the polyhedral complexes $span A$, $span X$ and $span (AX)$, when $A$ and $X$ commute. Two matrices, denoted $\underline{A}$ and $\bar{A}$, arise from $A$, in connection with $\Omega(A)$. The geometric meaning of them is given in detail, for one example. We produce examples of matrices which commute, in any dimension.Comment: Journal versio

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde

European Society for Swallowing Disorders: European Union Geriatric Medicine Society white paper: oropharyngeal dysphagia as a geriatric syndrome

This position document has been developed by the Dysphagia Working Group, a committee of members from the European Society for Swallowing Disorders and the European Union Geriatric Medicine Society, and invited experts. It consists of 12 sections that cover all aspects of clinical management of oropharyngeal dysphagia (OD) related to geriatric medicine and discusses prevalence, quality of life, and legal and ethical issues, as well as health economics and social burden. OD constitutes impaired or uncomfortable transit of food or liquids from the oral cavity to the esophagus, and it is included in the World Health Organization’s classification of diseases. It can cause severe complications such as malnutrition, dehydration, respiratory infections, aspiration pneumonia, and increased readmissions, institutionalization, and morbimortality. OD is a prevalent and serious problem among all phenotypes of older patients as oropharyngeal swallow response is impaired in older people and can cause aspiration. Despite its prevalence and severity, OD is still underdiagnosed and untreated in many medical centers. There are several validated clinical and instrumental methods (videofluoroscopy and fiberoptic endoscopic evaluation of swallowing) to diagnose OD, and treatment is mainly based on compensatory measures, although new treatments to stimulate the oropharyngeal swallow response are under research. OD matches the definition of a geriatric syndrome as it is highly prevalent among older people, is caused by multiple factors, is associated with several comorbidities and poor prognosis, and needs a multidimensional approach to be treated. OD should be given more importance and attention and thus be included in all standard screening protocols, treated, and regularly monitored to prevent its main complications. More research is needed to develop and standardize new treatments and management protocols for older patients with OD, which is a challenging mission for our societies

The Toric Geometry of Triangulated Polygons in Euclidean Space

Speyer and Sturmfels [SpSt] associated Gr\"obner toric degenerations \mathrm{Gr}_2(\C^n)^{\tree} of \mathrm{Gr}_2(\C^n) to each trivalent tree \tree with $n$ leaves. These degenerations induce toric degenerations M_{\br}^{\tree} of M_{\br}, the space of $n$ ordered, weighted (by \br) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers as stratified symplectic spaces and describe the action of the compact part of the torus as "bendings of polygons." We prove the conjecture of Foth and Hu [FH] that the toric fibers are homeomorphic to the spaces defined by Kamiyama and Yoshida [KY].Comment: 41 pages, 10 figure

Cycling Through Cancer: Exploring Childhood Cancer Survivors’ Experiences of Well- and Ill-Being

The benefits of informal physical activity during recovery from childhood cancer have rarely been investigated. This study adopted a multiple case study approach to explore the impact of recreational cycling on childhood cancer survivors’ experiences of well- and ill-being. Three semistructured interviews were conducted over a 3-month period with four survivors to explore their experiences of physical, psychological, and social well- and ill-being. Within-case analysis followed by cross-case analysis identified three themes that captured their well- and ill-being experiences with recreational cycling and cancer: (a) cultivating feelings and emotions, (b) experiencing physical changes, and (c) encountering positive and negative social interactions. The results from this study show that recreational cycling may be a useful adjunct to conventional treatments for the self-management of multiple domains of well- and ill-being during recovery from childhood cancer

The effects of neuromuscular electrical stimulation for dysphagia in opercular syndrome: a case study

A 76-year-old man with opercular syndrome characterized by complete bilateral loss of voluntary control of facial, lingual, pharyngeal and masticatory muscles is presented with focus on the severe dysphagia. Three years earlier the patient had experienced two strokes resulting in opercular syndrome with severe dysphagia. Despite initial logopedic dysphagia treatment, swallowing did not improve. A new treatment for dysphagia, consisting of neuromuscular electrical stimulation was applied on the patient. He returned to oral feeding. Clinical and treatment observations are reported

Baseline autoantibody profile in rheumatoid arthritis is associated with early treatment response but not long-term outcomes

Transplantation and autoimmunit