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   https://doi.org/10.13001/ela.2020.5243  

   Catral, Minerva ; Ciardo, Lorenzo ; Hogben, Leslie ; Reinhart, Carolyn ( January 2020 , The Electronic Journal of Linear Algebra)

   null (Ed.)

   A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues. 

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2. Stability of the centers of group algebras of $GL_n(q)$

   https://doi.org/https://doi.org/10.1016/j.aim.2019.04.026  

   Wan, Jinkui ; Wang, Weiqiang ( April 2019 , Advances in mathematics)

   The center $Z_n(q)$ of the integral group algebra of the general linear group $GL_n(q)$ over a finite field admits a filtration with respect to the reflection length. We show that the structure constants of the associated graded algebras $\mathscr{G}_n(q)$ are independent of $n$, and this stability leads to a universal stable center with positive integer structure constants which governs the algebras $\mathscr{G}_n(q)$ for all $n$. Various structure constants of the stable center are computed and several conjectures are formulated. Analogous stability properties for symmetric groups and wreath products were established earlier by Farahat-Higman and the second author. 

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3. Analysis of signal-to-noise ratio of angle of polarization and degree of polarization

   https://doi.org/10.1364/OSAC.422541  

   Chen, Yingkai ; Zhu, Zhongmin ; Liang, Zuodong ; Iannucci, Leanne_E ; Lake, Spencer_P ; Gruev, Viktor ( April 2021 , OSA Continuum)

   Recent advancements in nanofabrication technology has led to commercialization of single-chip polarization and color-polarization imaging sensors in the visible spectrum. Novel applications have arisen with the emergence of these sensors leading to questions about noise in the reconstructed polarization images. In this paper, we provide theoretical analysis for the input and output referred noise for the angle and degree of linear polarization information. We validated our theoretical model with experimental data collected from a division of focal plane polarization sensor. Our data indicates that the noise in the angle of polarization images depends on both incident light intensity and degree of linear polarization and is independent of the incident angle of polarization. However, noise in degree of linear polarization images depends on all three parameters: incident light intensity, angle and degree of linear polarization. This theoretical model can help guide the development of imaging setups to record optimal polarization information.

    

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4. The dynamic effect of mechanical losses of transmissions on the equation of motion of legged robots

   https://doi.org/10.1109/ICRA48506.2021.9561739  

   Sim, Youngwoo ; Ramos, Joao ( January 2021 , 2021 IEEE International Conference on Robotics and Automation (ICRA))

   Industrial manipulators do not collapse under their own weight when powered off due to the friction in their joints. Although these mechanism are effective for stiff position control of pick-and-place, they are inappropriate for legged robots that must rapidly regulate compliant interactions with the environment. However, no metric exists to quantify the robot’s performance degradation due to mechanical losses in the actuators and transmissions. This paper provides a fundamental formulation that uses the mechanical efficiency of transmissions to quantify the effect of power losses in the mechanical transmissions on the dynamics of a whole robotic system. We quantitatively demonstrate the intuitive fact that the apparent inertia of the robots increase in the presence of joint friction. We also show that robots that employ high gear ratio and low efficiency transmissions can statically sustain more substantial external loads. We expect that the framework presented here will provide the fundamental tools for designing the next generation of legged robots that can effectively interact with the world. 

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5. The dynamic effect of mechanical losses of transmissions on the equation of motion of legged robots

   Sim, Youngwoo ; Ramos, Joao ( January 2021 , IEEE International Conference on Robotics and Automation)

   null (Ed.)

   Industrial manipulators do not collapse under their own weight when powered off due to the friction in their joints. Although these mechanism are effective for stiff position control of pick-and-place, they are inappropriate for legged robots that must rapidly regulate compliant interactions with the environment. However, no metric exists to quantify the robot’s performance degradation due to mechanical losses in the actuators and transmissions. This paper provides a fundamental formulation that uses the mechanical efficiency of transmissions to quantify the effect of power losses in the mechanical transmissions on the dynamics of a whole robotic system. We quantitatively demonstrate the intuitive fact that the apparent inertia of the robots increase in the presence of joint friction. We also show that robots that employ high gear ratio and low efficiency transmissions can statically sustain more substantial external loads. We expect that the framework presented here will provide the fundamental tools for designing the next generation of legged robots that can effectively interact with the world. 

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