Cyclic automorphic graph decompositions

Chapter 1 introduces the tools and mechanics necessary for this report. Basic definitions and topics of graph theory which pertain to the report and discussion of automorphic decompositions will be covered in brief detail. An automorphic decomposition D of a graph H by a graph G is a G-decomposition of H such that the intersection of graph (D) @H. H is called the automorhpic host, and G is the automorphic divisor. We seek to find classes of graphs that are automorphic divisors, specifically ones generated cyclically. Chapter 2 discusses the previous work done mainly by Beeler. It also discusses and gives in more detail examples of automorphic decompositions of graphs. Chapter 2 also discusses labelings and their direct relation to cyclic automorphic decompositions. We show basic classes of graphs, such as cycles, that are known to have certain labelings, and show that they also are automorphic divisors. In Chapter 3, we are concerned with 2-regular graphs, in particular rCm, r copies of the m-cycle. We seek to show that rCm has a ρ-labeling, and thus is an automorphic divisor for all r and m. we discuss methods including Skolem type difference sets to create cycle systems and their correlation to automorphic decompositions. In the Appendix, we give classes of graphs known to be graceful and our java code to generate ρ-labelings on rCm.

Comparison between two caller groups of a medical call centre in Switzerland

OBJECTIVES: The incidence distribution of triage advice in the medical call centre Medi24 and the pattern of service utilisation were analysed with respect to two groups of callers with different insurance schemes. Individuals having contracted insurance of the Medi24 model could use the telephone consultation service of the medical call centre Medi24 (mainly part of the mandatory basic health insurance) voluntarily and free of charge whereas individuals holding an insurance policy of the Telmed model (special contract within the mandatory basic health insurance with a premium discount ranging from 8% to 12%) were obliged to have a telephone consultation before arranging an appointment with a medical doctor. METHODS: A cross-sectional study was carried out in the medical call centre Medi24 based on all triage datasets of the Medi24 and Telmed groups collected during the one year period from July 1st 2005 to June 30th 2006. The distribution of the six different urgency levels within the two groups and their respective pattern of service utilisation was determined. In a multivariable logistic regression model the Odds Ratio for every enquiry originating from the Telmed group versus those originating from the Medi24 group was calculated. RESULTS: During a one-year period 48 388 triage requests reached the medical call centre Medi24, 56% derived from the Telmed group and 44% from the Medi24 group. Within the Medi24 group more than 25% of the individuals received self-care advice, within the Telmed group, on the other hand, only about 18% received such advice. In contrast, 27% of the Telmed triage requests but only 18% of the Medi24 triage requests resulted in the advice to make a routine appointment with a medical doctor. The probability that an individual of the Telmed group obtained the advice to go to the accident and emergency department was lower than for an individual of the Medi24 group (OR 0.77, 95% CI 0.60-0.99). Likewise, the probability of self-care advice was decreased in regard to the Medi24 group (OR 0.80, 95% CI 0.75-0.85). However, regarding the advice to make a routine appointment with a medical doctor, the Telmed group was represented more frequently than the Medi24 group (OR 1.36, 95% CI 1.28-1.44). CONCLUSION: In respect of the triage advice, the Telmed group differed significantly from the Medi24 group within all urgency levels. The differences between the two groups in respect of the advice given were still less pronounced than expected against the background of their different contract conditions and the disparate temporal pattern of utilisation. We interprete this finding with the fact that appraising the urgency of health problems appropriately seems to be very difficult for the majority of people seeking advice.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Call for a reference model of chronic hind limb ischemia to investigate therapeutic angiogenesis

A large number of studies utilize animal models to investigate therapeutic angiogenesis. However, the lack of a standardized experimental model leaves the comparison of different studies problematic. To establish a reference model of prolonged moderate tissue ischemia, we created unilateral hind limb ischemia in athymic rnu-rats by surgical excision of the femoral vessels. Blood flow of the limb was monitored for 60 days by laser Doppler imaging. Following a short postoperative period of substantially depressed perfusion, the animals showed a status of moderate hind limb ischemia from day 14 onwards. Thereafter, the perfusion remained at a constant level (55.5% of normal value) until the end of the observation period. Histopathological assessment of the ischemic musculature on postoperative days 28 and 60 showed essentially no inflammatory cell infiltrate or fibrosis. However, the mitochondrial activity and capillary-to-fiber ratio of the muscular tissue was reduced to 52.7% of normal, presenting with a significant weakness of the ischemic limb evidenced by a progressive decline in performance. Intramuscular injection of culture-expanded human endothelial progenitor cells (EPC) resulted in a significant increase in blood flow (82.0+/-3.5% of normal), capillary density (1.60+/-0.08/muscle fiber) and smooth muscle covered arterioles (8.0+/-0.6/high power field) in the ischemic hind limb as compared to controls (55.0+/-3.1%; 0.99+/-0.03; 5.0+/-0.2). In conclusion, chronic, moderate hind limb ischemia with consistently reduced perfusion levels persisting over a prolonged period can be established reliably in rnu athymic nude rats and is responsive to pro-angiogenic treatments such as EPC transplantation. This study provides a detailed protocol of a highly reproducible reference model to test novel therapeutic options for limb ischemia.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.