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4.
  • Aas, Erik, et al. (författare)
  • Limiting directions for random walks in classical affine Weyl groups
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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5.
  • Aas, Erik, 1990- (författare)
  • Stationary probability of the identity for the TASEP on a Ring
  • 2012
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • Consider the following Markov chain on permutations of length n. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise nothing happens, corresponding to a loop in the Markov chain. This is the circular TASEP. We compute the average proportion of time the chain spends at the identity permutation (and, in greater generality, at sorted words). This answers a conjecture by Thomas Lam.
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6.
  • Aas, Erik (författare)
  • TASEP in any Weyl group
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • We investigate a Markov chain dened by Thomas Lam [6], whichgeneralizes the multi-type TASEP on a ring to any Weyl group. For groups of typeC we dene an analogue of the multiline queues of Ferrari and Martin (which com-pute the stationary distribution for the classical TASEP). While our constructiondoes not suce for nding the stationary distribution, the construction gives thestationary distribution of a certain projection of Lam's chain. Also, our approach isincremental, in the sense that the construction appears to t into a pattern of 'con-jugation matrices', which remains to be fully worked out. We conjecture an explicitformula for the partition function of the model. Finally, we prove a theorem for theclassical TASEP which ts into the picture of viewing TASEP in a permutation-freeway.
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10.
  • Abdul Khader, Shahbaz, et al. (författare)
  • Learning Deep Neural Policies with Stability Guarantees
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • Deep reinforcement learning (DRL) has been successfully used to solve various robotic manipulation tasks. However, most of the existing works do not address the issue of control stability. This is in sharp contrast to the control theory community where the well-established norm is to prove stability whenever a control law is synthesized. What makes traditional stability analysis difficult for DRL are the uninterpretable nature of the neural network policies and unknown system dynamics. In this work, unconditional stability is obtained by deriving an interpretable deep policy structure based on the energy shaping control of Lagrangian systems. Then, stability during physical interaction with an unknown environment is established based on passivity. The result is a stability guaranteeing DRL in a model-free framework that is general enough for contact-rich manipulation tasks. With an experiment on a peg-in-hole task, we demonstrate, to the best of our knowledge, the first DRL with stability guarantee on a real robotic manipulator.
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