Comparison of tumor surface marking by experienced neurosurgeon versus neuronavigation guidance

Introduction: Accurate flap marking has always been a challenge for neurosurgeons during tumor surgery. The use of neuronavigation has somewhat overcome this problem by allowing the navigation of intraoperative 3D neuroanatomy of the lesion. In this study, we aim to evaluate the percentage discrepancy of tumor surface marking by experienced neurosurgeon versus neuronavigation guidance. Methods: This is a prospective analytical study. Initial surface marking of the tumor was done by experienced neurosurgeon on the basis of sagittal, coronal and axial Magnetic Resonance Imaging films; and later was re-marked using neuronavigation. Photographs of surface markings were taken then comparison was done by plotting marking on the standard graph paper and percentage discrepancies were calculated for every case. Results: Percentage discrepancy ranged from 15 % to 81 % and the mean discrepancy score was 44%. Conclusion: Even in experienced neurosurgeon's hand, flap marking is not always accurate and neuronavigation definitely seems to be an effective tool.

An MBO Scheme for Minimizing the Graph Ohta–Kawasaki Functional

We study a graph-based version of the Ohta–Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph-based problems inspired by partial differential equations (PDEs) and variational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph-based problems to pattern-forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman–Bence–Osher (MBO) scheme for minimizing the graph Ohta–Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme $$\Gamma $$ Γ -converge to the Ohta–Kawasaki functional (which includes the standard graph-based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta–Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta–Kawasaki functional with a mass constraint.

Dominating Sequences in Grid-Like and Toroidal Graphs

A longest sequence $S$ of distinct vertices of a graph $G$ such that each vertex of $S$ dominates some vertex that is not dominated by its preceding vertices, is called a Grundy dominating sequence; the length of $S$ is the Grundy domination number of $G$. In this paper we study the Grundy domination number in the four standard graph products: the Cartesian, the lexicographic, the direct, and the strong product. For each of the products we present a lower bound for the Grundy domination number which turns out to be exact for the lexicographic product and is conjectured to be exact for the strong product. In most of the cases exact Grundy domination numbers are determined for products of paths and/or cycles.

Multi-amalgamation of rules with application conditions in -adhesive categories

Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions.For this reason, in the current paper we present the theory of amalgamation for$\mathcal{M}$-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation.

Graph Based Path Planning

Graphs are keenly studied by people of numerous domains as most of the applications we encounter in our daily lives can be easily given a graph-based representation. All the problems may then be easily studied as grap-based problems. In this chapter, the authors study the problem of robot motion planning as a graph search problem. The key steps involve the representation of the problem as a graph and solving the problem as a standard graph search problem. A number of graph search algorithms exist, each having its own advantages and disadvantages. In this chapter, the authors explain the concept, working methodology, and issues associated with some of these algorithms. The key algorithms under discussion include Breadth First Search, Depth First Search, A* Algorithm, Multi Neuron Heuristic Search, Dijkstra’s Algorithm, D* Algorithm, etc. Experimental results of some of these algorithms are also discussed. The chapter further presents the advantages and disadvantages of graph-based motion planning.

Speaking Stata: Turning over a New Leaf

Stem-and-leaf displays have been widely taught since John W. Tukey publicized them energetically in the 1970s. They remain useful for many distributions of small or modest size, especially for showing fine structure such as digit preference. Stata's implementation stem produces typed text displays and has some inevitable limitations, especially for comparison of two or more displays. One can re-create stem-and-leaf displays with a few basic Stata commands as scatterplots of stem variable versus position on line with leaves shown as marker labels. Comparison of displays then becomes easy and natural using scatter, by(). Back-to-back presentation of paired displays is also possible. I discuss variants on standard stem-and-leaf displays in which each distinct value is a stem, each distinct value is its own leaf, or axes are swapped. The problem shows how one can, with a few lines of Stata, often produce standard graph forms from first principles, allowing in turn new variants. I also present a new program, stemplot, as a convenience tool.

Graph rewriting for the π-calculus

We propose a graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph. Our implementation is sound and complete with respect to the structural congruence for the calculus: two processes are equivalent if and only if they are mapped into graphs with the same normal form. Most importantly, the encoding allows the use of standard graph rewriting mechanisms for modelling the reduction semantics of the calculus.