Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barab\'asi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks

Riding the Right Wavelet:Quantifying Scale Transitions in Fractured Rocks

Peer reviewedPublisher PD

Analysis of bistable behavior and early warning signals of extinction in a class of predator-prey models

In this paper, we develop a method of detecting an early warning signal of catastrophic population collapse in a class of predator-prey models with two species of predators competing for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near {\em{singular Hopf bifurcation}} of a coexistence equilibrium point, we assume that the class of models exhibits bistability between a periodic attractor and a boundary equilibrium point, where the invariant manifolds of the coexistence equilibrium play central roles in organizing the dynamics. To determine whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the point attractor, we reduce the equations to a suitable normal form, which is valid near the singular Hopf bifurcation, and study its geometric structure. A key component of our study includes an analysis of the transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. As a result of our analysis, we could devise a method for identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator-prey model considered in [\emph{Discrete and Continuous Dynamical Systems - B} 2021, 26(10), pp. 5251-5279] and we find that our theory is in good agreement with the numerical simulations carried out for this model

Event Horizon Telescope Observations as Probes for Quantum Structure of Astrophysical Black Holes

The need for a consistent quantum evolution for black holes has led to proposals that their semiclassical description is modified not just near the singularity, but at horizon or larger scales. If such modifications extend beyond the horizon, they influence regions accessible to distant observeration. Natural candidates for these modifications behave like metric fluctuations, with characteristic length and time scales set by the horizon radius. We investigate the possibility of using the Event Horizon Telescope to observe these effects, if they have a strength sufficient to make quantum evolution consistent with unitarity. We find that such quantum fluctuations can introduce a strong time dependence for the shape and size of the shadow that a black hole casts on its surrounding emission. For the black hole in the center of the Milky Way, detecting the rapid time variability of its shadow will require non-imaging timing techniques. However, for the much larger black hole in the center of the M87 galaxy, a variable black-hole shadow, if present with these parameters, would be readily observable in the individual snapshots that will be obtained by the Event Horizon Telescope.Comment: To appear in Phys. Rev. D. For animations, see http://xtreme.as.arizona.edu/~dpsaltis/?page_id=275

A Comparison Study on Control Moment Gyroscope Arrays and Steering Laws

Current reaction wheels and magnetorquers for microsatellite are limited by low slew rate and heavily depends on orbital parameters for coverage area. Control moment gyroscope (CMG) clusters offer an alternative solution for high slew rates and rapid retargeting. Though CMGs are often used in large space missions, their use in microsatellites is limited due to the stringent mass budget. Most literature reports only on pyramid configuration, and there are no definite cross-comparison studies between various CMG clusters and steering laws. In this research, a generic tool in Matlab and Simulink is developed to further understand CMG configurations and steering laws for a microsat mission. Various steering laws necessary for mitigating singularities in CMG clusters are compared in two distinct missions. The simulation results were evaluated based on the pointing accuracy, platform jitter, and pointing stability achieved by the spacecraft for each combination of CMG clusters, and steering laws and trajectories. The simulation results demonstrate that the pyramid cluster is marginally better than the rooftop cluster in pointing accuracy. The comparison of steering laws shows that, counterintuitively, Singularity Robust steering law, which passes through singularities, outperforms both Moore-Penrose and Local Gradient methods for almost all evaluation criteria for the two missions it was tested on. The simulation results would aid systems engineers in designing low-cost actuation systems and corresponding control software, which can increase the data acquisition rate of remote sensing missions

On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining

We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.Juan de la Cierva - Formation [grant number FJC2019-039804-I] Ram\ón y Cajal fellowship RYC-2017-22649