Torsion pairs and rigid objects in tubes

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte

A static test-bed for the evaluation and optimization of multihop wireless network protocols, Journal of Telecommunications and Information Technology, 2008, nr 2

We investigate the performance of multicast transmissions in a simple stationary wireless multihop ad hoc network test-bed. We compare several methods for MANET multicast using implementations for the protocols MOLSR, SMOLSR and SMF with an approach that uses explicit multicast and link-layer retries for reliable multicast. Results from the test-bed are compared with simulation results. We find that implementing a combination of explicit multicast with a retry mechanism gives the most promising results in test-bed and simulation compared with other approaches

Cycle-finite module categories

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to the infinite Jacobson radical of the module category). Moreover, geometric and homological properties of these module categories are exhibited

Brauer-Thrall for totally reflexive modules over local rings of higher dimension

Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally reflexive $R/(x)$-modules are free. We show that the first and second Brauer--Thrall type theorems hold for the category of totally reflexive $R$-modules. More precisely, we prove that, for infinitely many integers $n$, there exists an indecomposable totally reflexive $R$-module of multiplicity $n$. Moreover, if the residue field of $R$ is infinite, we prove that there exist infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules of multiplicity $n$.Comment: to appear in Algebras and Representation Theor

Categorification of skew-symmetrizable cluster algebras

We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G-invariant objects of C. Using an appropriate cluster character, we can then attach to these data an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac-Moody groups, generalizing to the non simply-laced case several results of Gei\ss-Leclerc-Schr\"oer.Comment: 64 page

Post-contrast acute kidney injury. Part 2: risk stratification, role of hydration and other prophylactic measures, patients taking metformin and chronic dialysis patients: Recommendations for updated ESUR Contrast Medium Safety Committee guidelines

Objectives: The Contrast Media Safety Committee (CMSC) of the European Society of Urogenital Radiology (ESUR) has updated its 2011 guidelines on the prevention of post-contrast acute kidney injury (PC-AKI). The results of the literature review and the recommendations based on it, which were used to prepare the new guidelines, are presented in two papers. Areas covered in part 2: Topics reviewed include stratification of PC-AKI risk, the need to withdraw nephrotoxic medication, PC-AKI prophylaxis with hydration or drugs, the use of metformin in diabetic patients receiving contrast medium and the need to alter dialysis schedules in patients receiving contrast medium. Key points: \u2022 In CKD, hydration reduces the PC-AKI risk \u2022 Intravenous normal saline and intravenous sodium bicarbonate provide equally effective prophylaxis \u2022 No drugs have been consistently shown to reduce the risk of PC-AKI \u2022 Stop metformin from the time of contrast medium administration if eGFR < 30 ml/min/1.73 m2 \u2022 Dialysis schedules need not change when intravascular contrast medium is given