On C*-algebras associated to right LCM semigroups

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroups or semigroups that satisfy Clifford's condition. Our main findings are results about uniqueness of the full semigroup C*-algebra. We build our analysis upon a rich interaction between the group of units of the semigroup and the family of constructible right ideals. As an application we identify algebraic conditions on S under which C*(S) is purely infinite and simple.Comment: 31 page

C*-Algebras of algebraic dynamical systems and right LCM semigroups

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As part of our analysis of these C*-algebras we prove results for right LCM semigroups. More precisely we discuss functoriality of the full semigroup C*-algebra and compute its K-theory for a large class of semigroups. We introduce the notion of a Nica-Toeplitz algebra of a product system over a right LCM semigroup, and show that it provides a useful alternative to study algebraic dynamical systems.Comment: 28 pages, to appear in Indiana Univ. Math.

Equilibrium states on right LCM semigroup C*-algebras

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on $\mathbb{N} \rtimes \mathbb{N}^\times$, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for large classes of right LCM semigroups, including those associated to algebraic dynamical systems.Comment: 43 pages, to appear in Int. Math. Res. No

Feasibility of rapid and automated importation of 3D echocardiographic left ventricular (LV) geometry into a finite element (FEM) analysis model

BACKGROUND: Finite element method (FEM) analysis for intraoperative modeling of the left ventricle (LV) is presently not possible. Since 3D structural data of the LV is now obtainable using standard transesophageal echocardiography (TEE) devices intraoperatively, the present study describes a method to transfer this data into a commercially available FEM analysis system: ABAQUS(©). METHODS: In this prospective study TomTec LV Analysis TEE(© )Software was used for semi-automatic endocardial border detection, reconstruction, and volume-rendering of the clinical 3D echocardiographic data. A newly developed software program MVCP FemCoGen(©), written in Delphi, reformats the TomTec file structures in five patients for use in ABAQUS and allows visualization of regional deformation of the LV. RESULTS: This study demonstrates that a fully automated importation of 3D TEE data into FEM modeling is feasible and can be efficiently accomplished in the operating room. CONCLUSION: For complete intraoperative 3D LV finite element analysis, three input elements are necessary: 1. time-gaited, reality-based structural information, 2. continuous LV pressure and 3. instantaneous tissue elastance. The first of these elements is now available using the methods presented herein

Plant Litter Type Dictates Microbial Communities Responsible for Greenhouse Gas Production in Amended Lake Sediments

The microbial communities of lake sediments play key roles in carbon cycling, linking lakes to their surrounding landscapes and to the global climate system as incubators of terrestrial organic matter and emitters of greenhouse gasses, respectively. Here, we amended lake sediments with three different plant leaf litters: a coniferous forest mix, deciduous forest mix, cattails (Typha latifolia) and then examined the bacterial, fungal and methanogen community profiles and abundances. Polyphenols were found to correlate with changes in the bacterial, methanogen, and fungal communities; most notably dominance of fungi over bacteria as polyphenol levels increased with higher abundance of the white rot fungi Phlebia spp. Additionally, we saw a shift in the dominant orders of fermentative bacteria with increasing polyphenol levels, and differences in the dominant methanogen groups, with high CH4 production being more strongly associated with generalist groups of methanogens found at lower polyphenol levels. Our present study provides insights into and basis for future study on how shifting upland and wetland plant communities may influence anaerobic microbial communities and processes in lake sediments, and may alter the fate of terrestrial carbon entering inland waters

Utilizing FEM-Software to quantify pre- and post-interventional cardiac reconstruction data based on modelling data sets from surgical ventricular repair therapy (SVRT) and cardiac resynchronisation therapy (CRT)

BACKGROUND: Left ventricle (LV) 3D structural data can be easily obtained using standard transesophageal echocardiography (TEE) devices but quantitative pre- and intraoperative volumetry and geometry analysis of the LV is presently not feasible in the cardiac operation room (OR). Finite element method (FEM) modelling is necessary to carry out precise and individual volume analysis and in the future will form the basis for simulation of cardiac interventions. METHOD: A Philips/HP Sonos 5500 ultrasound device stores volume data as time-resolved 4D volume data sets. In this prospective study TomTec LV Analysis TEE(© )Software was used for semi-automatic endocardial border detection, reconstruction, and volume-rendering of the clinical 3D echocardiographic data. With the software FemCoGen(© )a quantification of partial volumes and surface directions of the LV was carried out for two patients data sets. One patient underwent surgical ventricular repair therapy (SVR) and the other a cardiac resynchronisation therapy (CRT). RESULTS: For both patients a detailed volume and surface direction analysis is provided. Partial volumes as well as normal directions to the LV surface are pre- and post-interventionally compared. CONCLUSION: The operation results for both patients are quantified. The quantification shows treatment details for both interventions (e.g. the elimination of the discontinuities for CRT intervention and the segments treated for SVR intervention). The LV quantification is feasible in the cardiac OR and it gives a detailed and immediate quantitative feedback of the quality of the intervention to the medical

Finite-element-method (FEM) model generation of time-resolved 3D echocardiographic geometry data for mitral-valve volumetry

INTRODUCTION: Mitral Valve (MV) 3D structural data can be easily obtained using standard transesophageal echocardiography (TEE) devices but quantitative pre- and intraoperative volume analysis of the MV is presently not feasible in the cardiac operation room (OR). Finite element method (FEM) modelling is necessary to carry out precise and individual volume analysis and in the future will form the basis for simulation of cardiac interventions. METHOD: With the present retrospective pilot study we describe a method to transfer MV geometric data to 3D Slicer 2 software, an open-source medical visualization and analysis software package. A newly developed software program (ROIExtract) allowed selection of a region-of-interest (ROI) from the TEE data and data transformation for use in 3D Slicer. FEM models for quantitative volumetric studies were generated. RESULTS: ROI selection permitted the visualization and calculations required to create a sequence of volume rendered models of the MV allowing time-based visualization of regional deformation. Quantitation of tissue volume, especially important in myxomatous degeneration can be carried out. Rendered volumes are shown in 3D as well as in time-resolved 4D animations. CONCLUSION: The visualization of the segmented MV may significantly enhance clinical interpretation. This method provides an infrastructure for the study of image guided assessment of clinical findings and surgical planning. For complete pre- and intraoperative 3D MV FEM analysis, three input elements are necessary: 1. time-gated, reality-based structural information, 2. continuous MV pressure and 3. instantaneous tissue elastance. The present process makes the first of these elements available. Volume defect analysis is essential to fully understand functional and geometrical dysfunction of but not limited to the valve. 3D Slicer was used for semi-automatic valve border detection and volume-rendering of clinical 3D echocardiographic data. FEM based models were also calculated. METHOD: A Philips/HP Sonos 5500 ultrasound device stores volume data as time-resolved 4D volume data sets. Data sets for three subjects were used. Since 3D Slicer does not process time-resolved data sets, we employed a standard movie maker to animate the individual time-based models and visualizations. Calculation time and model size were minimized. Pressures were also easily available. We speculate that calculation of instantaneous elastance may be possible using instantaneous pressure values and tissue deformation data derived from the animated FEM