Algorithmic Selection of Preferred Grasp Poses using Manipulability Ellipsoid Forms

An algorithm to search for a kinematically desired robotic grasp pose with rolling contacts is presented. A manipulability measure is defined to characterise the grasp for multi-fingered robotic handling. The methodology can be used to search for the goal grasp pose with a manipulability ellipsoid close to the desired one. The proposed algorithm is modified to perform rolling based relocation under kinematic constraints of the robotic fingertips. The search for the optimal grasp pose and the improvement of the grasp pose by relocation is based on the reduction of the geodesic distance between the current and the target manipulability matrices. The algorithm also derives paths of the fingertip on the object surface in order to achieve the goal pose. An algorithmic option for the process of searching for a suitable grasp configuration is hence achieved.

Interleaving Automatic Segmentation and Expert Opinion for Retinal Conditions

Optical coherence tomography (OCT) has become the leading diagnostic tool in modern ophthalmology. We are interested here in developing a support tool for the segmentation of retina layers. The proposed method relies on graph theory and geodesic distance. As each retina layer is characterised by different features, the proposed method interleaves various gradients during detection, such as horizontal and vertical gradients or open-closed gradients. The method was tested on a dataset of 750 OCT B-Scan Spectralis provided by the Ophthalmology Department of the County Emergency Hospital Cluj-Napoca. The method has smaller signed error on layers B1, B7 and B8, with the highest value of 0.43 pixels. The average value of signed error on all layers is −1.99 ± 1.14 px. The average value for mean absolute error is 2.60 ± 0.95 px. Since the target is a support tool for the human agent, the ophthalmologist can intervene after each automatic step. Human intervention includes validation or fine tuning of the automatic segmentation. In line with design criteria advocated by explainable artificial intelligence (XAI) and human-centered AI, this approach gives more control and transparency as well as more of a global perspective on the segmentation process.

Spreading of disturbances in realistic models of transmission grids in dependence on topology, inertia and heterogeneity

The energy transition towards more renewable energy resources (RER) profoundly affects the frequency dynamics and stability of electrical power networks. Here, we investigate systematically the effect of reduced grid inertia, due to an increase in the magnitude of RER, its heterogeneous distribution and the grid topology on the propagation of disturbances in realistic power grid models. These studies are conducted with the DigSILENT PowerFactory software. By changing the power generation at one central bus in each grid at a specific time, we record the resulting frequency transients at all buses. Plotting the time of arrival (ToA) of the disturbance at each bus versus the distance from the disturbance, we analyse its propagation throughout the grid. While the ToAs are found to be distributed, we confirm a tendency that the ToA increases with geodesic distance linearly. Thereby, we can measure an average velocity of propagation by fitting the data with a ballistic equation. This velocity is found to decay with increasing inertia. Characterising each grid by its meshedness coefficient, we find that the distribution of the ToAs depends in more meshed grids less strongly on the grid inertia. In order to take into account the inhomogeneous distribution of inertia, we introduce an effective distance $$r_{\mathrm{eff}}$$ r eff , which is weighted with a factor which strongly depends on local inertia. We find that this effective distance is more strongly correlated with the ToAs, for all grids. This is confirmed quantitatively by obtaining a larger Pearson correlation coefficient between ToA and $$r_{\mathrm{eff}}$$ r eff than with r. Remarkably, a ballistic equation for the ToA with a velocity, as derived from the swing equation, provides a strict lower bound for all effective distances $$r_{\mathrm{eff}}$$ r eff in all power grids. thereby yielding a reliable estimate for the smallest time a disturbance needs to propagate that distance as function of system parameters, in particular inertia. We thereby conclude that in the analysis of contingencies of power grids it may be advisable that system designers and operators use the effective distance $$r_{\mathrm{eff}}$$ r eff , taking into account inhomogeneous distribution of inertia as introduced in Eq. (12), to locate a disturbance. Moreover, our results provide evidence for the importance of the network topology as quantified by the meshedness coefficient $$\beta$$ β .

Symmetry group of the equiangular cubed sphere

The equiangular cubed sphere is a spherical grid, widely used in computational physics. This paper deals with mathematical properties of this grid. We identify the symmetry group, i.e. the group of the orthogonal transformations that leave the cubed sphere invariant. The main result is that it coincides with the symmetry group of a cube. The proposed proof emphasizes metric properties of the cubed sphere. We study the geodesic distance on the grid, which reveals that the shortest geodesic arcs match with the vertices of a cuboctahedron. The results of this paper lay the foundation for future numerical schemes, based on rotational invariance of the cubed sphere.

Robust feature space separation for deep convolutional neural network training

This paper introduces two deep convolutional neural network training techniques that lead to more robust feature subspace separation in comparison to traditional training. Assume that dataset has M labels. The first method creates M deep convolutional neural networks called $$\{\text {DCNN}_i\}_{i=1}^{M}$$ { DCNN i } i = 1 M . Each of the networks $$\text {DCNN}_i$$ DCNN i is composed of a convolutional neural network ($$\text {CNN}_i$$ CNN i ) and a fully connected neural network ($$\text {FCNN}_i$$ FCNN i ). In training, a set of projection matrices $$\{\mathbf {P}_i\}_{i=1}^M$$ { P i } i = 1 M are created and adaptively updated as representations for feature subspaces $$\{\mathcal {S}_i\}_{i=1}^M$$ { S i } i = 1 M . A rejection value is computed for each training based on its projections on feature subspaces. Each $$\text {FCNN}_i$$ FCNN i acts as a binary classifier with a cost function whose main parameter is rejection values. A threshold value $$t_i$$ t i is determined for $$i^{th}$$ i th network $$\text {DCNN}_i$$ DCNN i . A testing strategy utilizing $$\{t_i\}_{i=1}^M$$ { t i } i = 1 M is also introduced. The second method creates a single DCNN and it computes a cost function whose parameters depend on subspace separations using the geodesic distance on the Grasmannian manifold of subspaces $$\mathcal {S}_i$$ S i and the sum of all remaining subspaces $$\{\mathcal {S}_j\}_{j=1,j\ne i}^M$$ { S j } j = 1 , j ≠ i M . The proposed methods are tested using multiple network topologies. It is shown that while the first method works better for smaller networks, the second method performs better for complex architectures.

On the asymptotic behavior of the average geodesic distance L and the compactness CB of simple connected undirected graphs whose order approaches infinity

The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval [0;1/3] and [2/3;1], respectively. Moreover, for any not necessarily rational number β ∈ [0;1/3] (α ∈ [2/3;1]) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.

Circuit complexity in U(1) gauge theory

In this paper, we study circuit complexity for a free vector field of a [Formula: see text] gauge theory in Coulomb gauge, and Gaussian states. We introduce a quantum circuit model with Gaussian states, including reference and target states. Using Nielsen’s geometric approach, the complexity then can be found as the shortest geodesic in the space of states. This geodesic is based on the notion of geodesic distance on the Lie group of Bogoliubov transformations equipped with a right-invariant metric. We use the framework of the covariance matrix to compute circuit complexity between Gaussian states. We apply this framework to the free vector field in general dimensions where we compute the circuit complexity of the ground state of the Hamiltonian.