Variational approach to self-adjointness and some applications to biomathematics

AbstractIn this paper using variational approach, we obtain necessary and sufficient conditions for a nonlinear boundary value problem to be self-adjoint. Analytic representations of Lagrangian and Hamiltonian are given. Several interesting applications to biological models are also discussed

Approximate Pattern Matching using Hierarchical Graph Construction and Sparse Distributed Representation

With recent developments in deep networks, there have been significant advances in visual object detection and recognition. However, some of these networks are still easily fooled/hacked and have shown “bag of features” failures. Some of this is due to the fact that even deep networks make only marginal use of the complex structure that exists in real-world images, even after training on huge numbers of images. Biology appears to take advantage of such a structure, but how? In our research, we are studying approaches for robust pattern matching using still, 2D Blocks World images based on graphical representations of the various components of an image. Such higher order information represents the “structure” of the visual object. Here we discuss how the structural information of an image can be captured in a Sparse Distributed Representation (SDR) loosely based on cortical circuits. We apply probabilistic graph isomorphism and subgraph isomorphism to our 2D Blocks World images and achieve O (1) and O (nk ) complexity for an approximate match. The optimal match is an NP-Hard problem. The image labeled graph is created using OpenCV to find the object contours and objects\u27 labels and a fixed radius nearest neighbor algorithm to build the edges between the objects. Pattern matching is done using the properties of SDRs. Our research shows the promise of applying graph-based neuromorphic techniques for pattern matching of images based on such structur