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Implementation details for ”*VennMaster*: *Area-proportional* *Euler* *diagrams* for *functional* *GO* *analysis* of *microarrays*”

"... Intersecting convex polygons The intersection of two convex polygons can be computed in O(n + m) steps using O’Rourke’s algorithm [3]. It is assumed that the polygon borders ∂P and ∂Q with m and n points are oriented counterclockwise. After choosing two directed edges A from P and B from Q the subse ..."

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Intersecting convex polygons The intersection of two convex polygons can be computed in O(n + m) steps using O’Rourke’s algorithm [3]. It is assumed that the polygon borders ∂P and ∂Q with m and n points are oriented counterclockwise. After choosing two directed edges A from P and B from Q the subsequent steps involve counterclockwise moves of one of the two edges in order to find all crossings. The algorithm always advances the edge behind to chase the other (waiting) edge (see Figure S1). Define H(A) to be the hyperplane to the left of vector A, and A × B the crossproduct, which is greater than zero if the shortest turn of A into B is counterclockwise (see Table S1). a and b are the heads of the vectors A and B. The cases P ∩ Q = ∅, P ⊂ Q, and Q ⊂ P must be handled separately when the algorithm does not succeed in finding a polygon. For those cases it is necessary only to check whether a single point of P lies in Q and vice versa.

### Nuclear Physics B Proceedings Supplement – preprint (2014) 1–42 Nuclear Physics B Proceedings Supplement Universal Aspects of QCD-like TheoriesI

"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."

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the phase

*diagram*of two-color QCD with the*functional*renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.### Active Mask Framework for Segmentation of Fluorescence Microscope Images

"... m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of ..."

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m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of knowledge and a book in Her lotus hands. Dedicated to the Lotus Feet of the revered Sadguru. This thesis presents a new active mask (AM) framework and an algorithm for segmenta-tion of digital images, particularly those of punctate patterns from fluorescence microscopy. Fluorescence microscopy has greatly facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together with the concept of

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