Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page

Visual Chunking: A List Prediction Framework for Region-Based Object Detection

We consider detecting objects in an image by iteratively selecting from a set of arbitrarily shaped candidate regions. Our generic approach, which we term visual chunking, reasons about the locations of multiple object instances in an image while expressively describing object boundaries. We design an optimization criterion for measuring the performance of a list of such detections as a natural extension to a common per-instance metric. We present an efficient algorithm with provable performance for building a high-quality list of detections from any candidate set of region-based proposals. We also develop a simple class-specific algorithm to generate a candidate region instance in near-linear time in the number of low-level superpixels that outperforms other region generating methods. In order to make predictions on novel images at testing time without access to ground truth, we develop learning approaches to emulate these algorithms' behaviors. We demonstrate that our new approach outperforms sophisticated baselines on benchmark datasets.Comment: to appear at ICRA 201

Construction of Neural Network Classification Expert Systems Using Switching Theory Algorithms

A new family of neural network architectures is presented. This family of architectures solves the problem of constructing and training minimal neural network classification expert systems by using switching theory. The primary insight that leads to the use of switching theory is that the problem of minimizing the number of rules and the number of IF statements (antecedents) per rule in a neural network expert system can be recast into the problem of minimizing the number of digital gates and the number of connections between digital gates in a Very Large Scale Integrated (VLSI) circuit. The rules that the neural network generates to perform a task are readily extractable from the network's weights and topology. Analysis and simulations on the Mushroom database illustrate the system's performance

On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four