Combinatorial methods in Dehn surgery

This is an expository paper, in which we give a summary of some of the joint work of John Luecke and the author on Dehn surgery. We consider the situation where we have two Dehn fillings $M(\alpha)$ and $M(\beta)$ on a given 3-manifold $M$, each containing a surface that is either essential or a Heegaard surface. We show how a combinatorial analysis of the graphs of intersection of the two corresponding punctured surfaces in $M$ enables one to find faces of these graphs which give useful topological information about $M(\alpha)$ and $M(\beta)$, and hence, in certain cases, good upper bounds on the intersection number $\Delta(\alpha, \beta)$ of the two filling slopes

Regularization and Kernelization of the Maximin Correlation Approach

Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor classification, the maximin correlation approach (MCA) provides the worst-case optimal solution by minimizing the maximum misclassification risk through an iterative procedure. Despite the optimality, the original MCA has drawbacks that have limited its wide applicability in practice. That is, the MCA tends to be sensitive to outliers, cannot effectively handle nonlinearities in datasets, and suffers from having high computational complexity. To address these limitations, we propose an improved solution, named regularized maximin correlation approach (R-MCA). We first reformulate MCA as a quadratically constrained linear programming (QCLP) problem, incorporate regularization by introducing slack variables in the primal problem of the QCLP, and derive the corresponding Lagrangian dual. The dual formulation enables us to apply the kernel trick to R-MCA so that it can better handle nonlinearities. Our experimental results demonstrate that the regularization and kernelization make the proposed R-MCA more robust and accurate for various classification tasks than the original MCA. Furthermore, when the data size or dimensionality grows, R-MCA runs substantially faster by solving either the primal or dual (whichever has a smaller variable dimension) of the QCLP.Comment: Submitted to IEEE Acces

Organic farming and multicriteria decisions: An economic survey

Organic food production is a sphere where decision making is multi-facetted and complex. This applies to producers, political decision makers and consumers alike. This paper provides an overview of the economic methods that can aid such multi criteria decision making. We first provide an outline of the many different Multi-Criteria Analysis (MCA) techniques available and their relative advantages and disadvantages. In addition, theoretical and practical problems related to the use of Cost-Benefit Analysis (CBA) and MCA respectively are briefly discussed. We then review the MCA literature on case studies on organic farming. Based on this review we provide directional markers for future research where MCA may possibly be applied and adapted in order to provide useful knowledge and support for decision makers in the context of organic farming

Magnetocrystalline anisotropy of Fe and Co slabs and clusters on SrTiO_3\_3 by first-principles

In this work, we present a detailed theoretical investigation of the electronic and magnetic properties of ferromagnetic slabs and clusters deposited on SrTiO$\_3$ via first-principles, with a particular emphasis on the magneto-crystalline anisotropy (MCA). We found that in the case of Fe films deposited on SrTiO$\_3$ the effect of the interface is to quench the MCA whereas for Cobalt we observe a change of sign of the MCA from in-plane to out-of-plane as compared to the free surface. We also find a strong enhancement of MCA for small clusters upon deposition on a SrTiO$\_3$ substrate. The hybridization between the substrate and the $d$-orbitals of the cluster extending in-plane for Fe and out-of-plane for Co is at the origin of this enhancement of MCA. As a consequence, we predict that the Fe nanocrystals (even rather small) should be magnetically stable and are thus good potential candidates for magnetic storage devices.Comment: Physical ReviewB, 201

An Alloy Verification Model for Consensus-Based Auction Protocols

Max Consensus-based Auction (MCA) protocols are an elegant approach to establish conflict-free distributed allocations in a wide range of network utility maximization problems. A set of agents independently bid on a set of items, and exchange their bids with their first hop-neighbors for a distributed (max-consensus) winner determination. The use of MCA protocols was proposed, $e.g.$, to solve the task allocation problem for a fleet of unmanned aerial vehicles, in smart grids, or in distributed virtual network management applications. Misconfigured or malicious agents participating in a MCA, or an incorrect instantiation of policies can lead to oscillations of the protocol, causing, $e.g.$, Service Level Agreement (SLA) violations. In this paper, we propose a formal, machine-readable, Max-Consensus Auction model, encoded in the Alloy lightweight modeling language. The model consists of a network of agents applying the MCA mechanisms, instantiated with potentially different policies, and a set of predicates to analyze its convergence properties. We were able to verify that MCA is not resilient against rebidding attacks, and that the protocol fails (to achieve a conflict-free resource allocation) for some specific combinations of policies. Our model can be used to verify, with a "push-button" analysis, the convergence of the MCA mechanism to a conflict-free allocation of a wide range of policy instantiations