The directed Physarum dynamics is known to solve positive linear programs: minimize @math subject to @math and @math for a positive cost vector @math . The directed Physarum dynamics evolves a positive vector @math according to the dynamics @math . Here @math is the solution to @math that minimizes the "energy" @math . In this paper, we study the non-uniform directed dynamics @math , where @math is a positive diagonal matrix. The non-uniform dynamics is more complex than the uniform dynamics (with @math being the identity matrix), as it allows each component of @math to react with different speed to the differences between @math and @math . Our contribution is to show that the non-uniform directed dynamics solves positive linear programs.
Nakagaki et.-al. @cite_3 pointed out that different edge may react with different speed to the differences between flow and capacity. For example, Physarum prefers darkness over bright light and hence edges in a bright environment react differently than edges in darkness. This let to the non-uniform dynamics where @math is an indicator for the reactivity of an edge.
@cite_3
2031275178
Our goal is to turn an intensity image into its perceived luminance without parsing it into depths, surfaces, or scene illuminations. We start with jarring intensity differences at two scales mixed according to edges, identified by a pixel-centric edge detector. We propose angular embedding as a more robust, efficient, and versatile alternative to LS, LLE, and NCUTS for obtaining a global brightness ordering from local differences. Our model explains a variety of brightness illusions with a single algorithm. Brightness of a pixel can be understood locally as its intensity deviating in the gradient direction and globally as finding its rank relative to others, particularly the lightest and darkest ones. This paper proposes an edge-based robust RGB-D visual odometry (VO)using 2-D edge divergence minimization. Our approach focuses on enabling the VO to operate in more general environments subject to low texture and changing brightness, by employing image edge regions and their image gradient vectors within the iterative closest points (ICP)framework. For more robust and stable ICP-based optimization, we propose a robust edge matching criterion with image gradient vectors. In addition, to reduce a bad effect of outlier residuals, we propose an improved edge registration problem of 2-D edge divergence minimization in the manner of an iterative reweight least squares (IRLS)motion estimation. To accelerate the proposed approach, a pixel sub-sampling method is employed. We evaluate estimation performance of our method in changing brightness conditions and low-textured scenes. Our approach shows more robust motion estimation than state-of-the-art methods while maintaining comparable accuracy in challenging image sequences at real-time (25 Hz)operation. Let H d (n,p) signify a random d -uniform hypergraph with n vertices in which each of the @math possible edges is present with probability p = p(n) independently, and let H d (n,m) denote a uniformly distributed d -uniform hypergraph with n vertices and m edges. We derive local limit theorems for the joint distribution of the number of vertices and the number of edges in the largest component of H d (n,p) and H d (n,m) in the regime @math , resp. d(d−1)m n >1+ϵ, where ϵ>0 is arbitrarily small but fixed as n → ∞. The proofs are based on a purely probabilistic approach. Summary Many animals rely on visual motion detection for survival. Motion information is extracted from spatiotemporal intensity patterns on the retina, a paradigmatic neural computation. A phenomenological model, the Hassenstein-Reichardt correlator (HRC), relates visual inputs to neural activity and behavioral responses to motion, but the circuits that implement this computation remain unknown. By using cell-type specific genetic silencing, minimal motion stimuli, and in vivo calcium imaging, we examine two critical HRC inputs. These two pathways respond preferentially to light and dark moving edges. We demonstrate that these pathways perform overlapping but complementary subsets of the computations underlying the HRC. A numerical model implementing differential weighting of these operations displays the observed edge preferences. Intriguingly, these pathways are distinguished by their sensitivities to a stimulus correlation that corresponds to an illusory percept, "reverse phi," that affects many species. Thus, this computational architecture may be widely used to achieve edge selectivity in motion detection.