Linear and Nonlinear Trees: Multiplicity Lists of Symmetric Matrices

Let A be a real symmetric matrix whose graph is a tree, T. If T is a linear tree (meaning all vertices with degree 3 or larger lie on the same induced path), then we can use a ”Linear Superposition Principle” to determine all possible multiplicities of eigenvalues of A. If T is a nonlinear tree, we must use other ad hoc methods. I utilize these methods to compute all possible multiplicity lists of trees on 12 vertices, and augment an existing multiplicities database. This database allows us to examine of the effects that the structure of tree can have on a multiplicity list. Then, I investigate the enumeration of linear and nonlinear trees, and examine the ratio of nonlinear trees to total trees

Surficial Materials Mapping using Remote Sensing and Classification Methods: A Geological Knowledge and Statistical Approach

Mapping the geology of Northern regions in Canada is an essential step in providing key knowledge for resource development and economic prosperity of northern communities. However, mapping this large remote region presents a major challenge both in terms of financial resources and the time required to cover such a large area. With convenient access to remotely sensed imagery, new automatic and remote approaches are emerging that support the surficial geological mapping of vast northern regions at scales appropriate for mineral exploration and related land-use management. An approach using LANDSAT 7 TM imagery, field-based data and a maximum likelihood classification algorithm is employed to produce remote predictive maps of the surficial materials in the Repulse Bay area, Nunavut (NTS 46M-SW, 46L-W and S and 46K-SW). Two approaches in the remote predictive mapping (RPM) process are used to determine the optimal class combination and resultant maps. The first approach employs general and field knowledge from Quaternary geologists to the map evaluation. This approach allows training areas to be grouped and merged based on Quaternary geology principles. The second approach uses statistical techniques to produce classified maps based on training areas along with measures of classification accuracy. These qualitative (geological knowledge-based) and quantitative (statistical-based) methods are used and compared to determine optimal class combinations. Four classification maps that offer the highest overall classification accuracies - through analysis of a confusion matrix and associated variability maps - were produced (two for each approach). Exposed marine sediments, carbonate-rich tills, organics and boulder terrains are the most accurately (>75%) classified of the surficial materials classes; confusion occurs between remaining till, sand and gravel, and bedrock units. Variability maps were produced using these optimal class combinations and corresponding classifications, through which it is found that the geological knowledge-based approach is more suitable for remotely mapping surficial materials in this study area. A comparison to surficial materials maps derived from surficial geology maps was conducted with results of classification outputs using the most optimal class combinations with LANDSAT and SPOT 4/5 imagery. This visual and GIS analysis comparison allowed for evaluation of the classification products, while an overlay analysis compared a pixel-to-pixel correspondence between the maps. Although it is found that both imageries are useful for mapping marine and alluvial sediments, it has limitations in mapping organic materials, till and bedrock. It is apparent that LANDSAT imagery is more appropriate for general mapping while SPOT is better suited for mapping marine sediments

Infectious endocarditis complicated by an ischemic stroke and revealing Marfan syndrome

Marfan syndrome is a systematic genetic disease of the connective tissue. The cardiac affection would predict the prognosis and ischemic stroke might complicate it. The purpose of this work is to discuss the mechanisms of the ischemic stroke in Marfan syndrome which have to be considered in all young patients of ischemic strokes. We report the case of a 17-year-old male patient who presented with right hemiparesis with brachio-facial dominance, hemihypoesthesia and Broca's aphasia; these symptoms were followed by partial right somato-motor epileptic seizure. The cerebral computed tomographic (CT) scan demonstrated early signs of ischemic stroke in the left Sylvian artery. Cardiovascular examination revealed a systolic murmur in the mitral site. Marfan syndrome with infectious endocarditis complicated by ischemic stroke was diagnosed. However, the family pathological history was negative. The Marfan syndrome diagnosis was approved considering the following criteria: Ligamentous hyperlaxity, crystalline ectopia and mitral valve prolapsus with mitral insufficiency. The patient benefited of antibiotherapy for 4 weeks. The patient underwent sessions of motor physical therapy and orthophonic rehabilitation. Then, cardiac surgery was carried out and valvuloplasty was performed. The surgical treatment confirmed the presence of mitral insufficiency and prolapsus of the big mitral valve and multiple friable anterior-posterior vegetations with broken cordage of the small mitral valve. Replacement of the mitral valve was achieved, and the post-surgery follow-ups were simple. The diagnosis of Marfan syndrome was based on well-defined criteria. The evolution of the patient was marked by a complete improvement of the cardiac and motor deficits, and disappearance of the Broca's aphasia. A fibroelastic disease such Marfan syndrome has to be considered in unexplained ischemic stroke in all young patients. Hence, the diagnosis of Marfan syndrome involves an anticipation of the neurovascular complications by early cardiovascular care

N-(4-Methyl­piperazin-4-ium-1-yl)dithio­carbamate sesquihydrate

In the crystal structure of the title compound, C6H13N3S2·1.5H2O, weak N—H⋯S inter­actions between the zwitterionic mol­ecules are observed, leading to an extensively folded layered arrangement parallel to (100). There are three crystallographically independent water mol­ecules in the asymmetric unit, which are disordered and only half occupied