The Bernstein-Sato b-Function of the Space of Cyclic Pairs

We compute the Bernstein-Sato polynomial of $f$, a function which given a pair $(M,v)$ in $X = M_n(\mathbf{C}) \times \mathbf{C}^n$ tests whether $v$ is a cyclic vector for $M$. The proof includes a description of shift operators corresponding to the Calogero-Moser operator $L_k$ in the rational case.Comment: 14 pages, Referee suggested changes made, to appear in Publ. RIM

The QR decomposition for radial neural networks

We provide a theoretical framework for neural networks in terms of the representation theory of quivers, thus revealing symmetries of the parameter space of neural networks. An exploitation of these symmetries leads to a model compression algorithm for radial neural networks based on an analogue of the QR decomposition. A projected version of backpropogation on the original model matches usual backpropogation on the compressed model.Comment: 30 page

On the Finkelberg-Ginzburg Mirabolic Monodromy Conjecture

We compute the monodromy of the mirabolic Harish-Chandra D-module for all but an explicit codimension two set of values of the parameters (theta,c). In particular, we show that the Finkelberg-Ginzburg conjecture, which is known to hold for generic values of the parameters, fails at special values even in rank 1. Our main tools are Opdam's shift operators and normalised intertwiners for the extended affine Weyl group, which allow for the resolution of resonances outside the codimension two set.Comment: 33 pages, 7 figures. Comments welcom

Blessed Peacemakers: 365 Extraordinary People Who Changed the World

All of us yearn for a peaceable and just world, but some roll up their sleeves and set to work to make the dream real. Blessed Peacemakers celebrates 365 of them, one for each day of the year.Their stories are richly diverse. They share a commitment to peace and justice, but the various contexts in which they work make each of their stories uniquely instructive. The peacemakers include women, men, and children from across the globe, spanning some twenty-five hundred years. Many are persons of faith, but some are totally secular. Some are well known, while others will be excitingly new. They are human rights and antiwar activists, scientists and artists, educators and scholars, songwriters and poets, film directors and authors, diplomats and economists, environmentalists and mystics, prophets and policymakers. Some are unlettered, but all are wise. A few died in the service of the dream. All sacrificed for it.The world is a better place for the presence of blessed peacemakers. Their inspiring stories embolden readers to join them in nonviolent resistance to injustice and the creative pursuit of peace. [From the publisher]https://cupola.gettysburg.edu/books/1045/thumbnail.jp

Meta-Learning Dynamics Forecasting Using Task Inference

Current deep learning models for dynamics forecasting struggle with generalization. They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder which infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on both turbulent flow and real-world ocean data forecasting tasks

Equivariant Transporter Network

Transporter Net is a recently proposed framework for pick and place that is able to learn good manipulation policies from a very few expert demonstrations. A key reason why Transporter Net is so sample efficient is that the model incorporates rotational equivariance into the pick module, i.e. the model immediately generalizes learned pick knowledge to objects presented in different orientations. This paper proposes a novel version of Transporter Net that is equivariant to both pick and place orientation. As a result, our model immediately generalizes place knowledge to different place orientations in addition to generalizing pick knowledge as before. Ultimately, our new model is more sample efficient and achieves better pick and place success rates than the baseline Transporter Net model.Comment: Project Website: https://haojhuang.github.io/etp_page