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This is joint with Lidman. In this talk I will discuss some applications of open book foliations to topology and contact topology. Moreover, for simple singularities, it is known that the only possible exact Lagrangians are spheres. I will explain how to construct exact Lagrangian tori in the Milnor fibres of all non-simple i.

Fefferman: Conformal Invariants

Time allowing, I will give applications to the structure of their symplectic mapping class groups. The past decade has been less than kind to this theory, as the growing knowledge of gaps in its foundations have tarnished its claim to being a well-defined contact invariant. However, recent work of Hutchings and Nelson has managed to redeem this theory in dimension 3 for dynamically convex contact manifolds.

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Abstract: Lagrangian cobordisms between two Legendrian submanifolds are known to have significant topological rigidity. For example, in the symplectization of the standard contact 3-space, the genus of an orientable Lagagrangian endocobordism for a Legendrian knot must vanish. I will describe how for non-orientable Lagrangian endocobordisms of a Legendrian knot there is some, yet restricted, topological flexibility. This is joint work with Orsola Capovilla-Searle.

Abstract: Deterministic computer simulators are based on complex mathematical models that describe the relationship of the input and output variables in a physical system. The use of deterministic simulators as experimental vehicles has become widespread in applications such as biology, physics, and engineering. One use of a computer simulator is for prediction; given a set of system inputs, the simulator is run to find the predicted output of the system.

Volume 21, 2018

However, when the mathematical model is complex, a simulator can be computationally expensive. Therefore statistical metamodels are used to make predictions of the system outputs. This talk considers settings in which both data from the simulator and data from an associated physical experiment are available.

Examples will illustrate that WIMSPE-optimal combined designs provide better prediction than standard designs for the combined traditional and simulator experiments. Abstract: When high dimensional data is given, it is often of interest to distinguish between significant non-null, Ha and non-significant null, H0 group from mixture of two by controlling type I error rate.

One popular way to control the level is the false discovery rate FDR. This talk considers a method based on the local false discovery rate. In most of the previous studies, the null group is commonly assumed to be a normal distribution. However, if the null distribution can be departure from normal, there may exist too many or too few false discoveries belongs null but rejected from the test leading to the failure of controlling the given level of FDR. We propose a novel approach which enriches a class of null distribution based on mixture distributions.

We provide real examples of gene expression data, fMRI data and protein domain data to illustrate the problems for overview.

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  • Heather Smith. Label the leaves of a star tree with the genomes in G. In this talk, I will present some complexity results for the star tree. We also explore similar computational complexity questions for mathematically motivated problems which arose from this project. Dorit S. The MRF problem involves minimizing pairwise-separation and singleton-deviation terms.

    This model is shown here to be powerful in representing classical problems of ranking, group decision making and clustering.

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    The techniques presented are stronger than continuous techniques used in image segmentation, such as total variations, denoising, level sets and some classes of Mumford-Shah functionals. This is manifested both in terms of running time and in terms of quality of solution for the prescribed optimization problem. We will sketch the first known efficient, and flow-based, algorithms for the convex MRF the non-convex is shown to be NP-hard. We then discuss the power of the MRF model and algorithms in the context of aggregate ranking.

    The aggregate ranking problem is to obtain a ranking that is fair and representative of the individual decision makers' rankings. We argue here that using cardinal pairwise comparisons provides several advantages over score-wise or ordinal models. The aggregate group ranking problem is formalized as the MRF model and is linked to the inverse equal paths problem. Sofya Raskhodnikova.

    Abstract: Many types of data can be represented as graphs, where nodes correspond to individuals and edges capture relationships between them. It turns out that the graph structure can be used to infer sensitive information about individuals, such as romantic ties. This talk will discuss the challenge of performing and releasing analyses of graph data while protecting personal information.

    It will present algorithms that satisfy a rigorous notion of privacy, called differential privacy, and compute accurate approximations to network statistics, such as subgraph counts and the degree sequence. The techniques used in these algorithms are based on combinatorial analysis, network flow, and linear and convex programming. Emilie Hogan. Abstract: With recent cyber-attacks on the front pages we realize that secure and resilient cyber systems are necessary. Using graphs as models for cyber systems is a clear choice since these systems are made up of different types of connections edges between computers vertices.

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    Our recent work has focused on developing new graph theoretical measures for labeled directed graphs and using them to discover patterns of behavior in the graphs. In this talk I will introduce our measures which generalize degree distribution in the case of labeled graphs and show how we have used them to discover events in simulated cyber data. Barna Saha. We consider this basic question, the language edit distance problem, in this talk. The language edit distance problem has several applications ranging from error-correction in databases, compiler optimization, natural language processing to computational biology etc.

    Julia Chuzhoy. The theorem states that for every fixed-size grid H, every graph whose treewidth is large enough, contains H as a minor. This theorem has found many applications in graph theory and algorithms. Let f k denote the largest value, such that every graph of treewidth k contains a grid minor of size f k. Until recently, the best known bound on f k was sub-logarithmic in k.

    In this talk we will survey new results and techniques that establish polynomial bounds on f k. We will also survey some connections between the Grid-Minor Theorem and graph routing problems, and discuss the major open problems in the area of graph routing. Partly based on joint work with Chandra Chekuri. Blair Sullivan. Abstract: As complex networks grow increasingly large and available as data, their analysis is crucial for understanding the world we live in, yet graph algorithms are only scalable when limited to relatively simplistic queries those with low-degree polynomial computational complexity.

    Publications of the Research Institute for Mathematical Sciences - Title Index

    In order to enable scientific insights, we must be able to compute solutions to more complex questions. To enable this, we turn to parameterized algorithms, which exploit non-uniform complexity to give polynomial time solutions to NP-hard problems when some parameter of the instance is bounded.

    The theoretical computer science community has been developing a suite of powerful algorithms that exploit specific forms of sparse graph structure bounded genus, bounded treewidth, etc to drastically reduce running time. On the other hand, the extensive research effort in network science to characterize the structure of real-world graphs has been primarily focused on either coarse, global properties e. We discuss recent work on bridging the gap between network science and structural graph algorithms, answering questions like: Do real-world networks exhibit structural properties that enable efficient algorithms?

    Is it observable empirically? Can sparse structure be proven for popular random graph models? How does such a framework help?