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We show that a group whose generalized torsion elements are torsion elements (which we call a $TR^{*}$-group) is torsion-by-$R^{*}$ group, an extension of torsion group by a group without generalized torsion elements. We also discuss a…
Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…
As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…
We present PEPSKit.jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit.jl builds on the TensorKit.jl package for tensor computations and provides…
The complete group classification of a generalization of the Heath model is carried out by connecting it to the heat equation with nonlinear source. Examples of invariant solutions are given under the terminal and the barrier option…
We propose to synthesize feasible caging grasps for a target object through computing Caging Loops, a closed curve defined in the shape embedding space of the object. Different from the traditional methods, our approach decouples caging…
We describe a simple, but effective, method for deriving families of elliptic curves, with high rank, all of whose members have the same torsion subgroup structure.
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.
In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing…
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
At present time when a new generation of TeV colliders are beginning to operate one needs to calculate cross-sections for a great number of various reactions. Such calculations are united in the framework of the collider physical program,…
We show that the mapping class group of a handlebody is a virtual duality group, in the sense of Bieri and Eckmann. In positive genus we give a description of the dualising module of any torsion-free, finite-index subgroup of the handlebody…
Grasping mechanisms must both create and subsequently hold grasps that permit safe and effective object manipulation. Existing mechanisms address the different functional requirements of grasp creation and grasp holding using a single…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…
Grasping is fundamental to robotic manipulation, and recent advances in large-scale grasping datasets have provided essential training data and evaluation benchmarks, accelerating the development of learning-based methods for robust object…
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…
To address the absence of a universal standard interface for tensor operations, we introduce the Tensor Algebra Processing Primitives (TAPP), a C-based interface designed to decouple the application layer from hardware-specific…
This paper discusses experimental techniques and considerations associated with the transition to high repetition-rate experiments in High Energy Density Physics (HEDP). We particularly highlight approaches to experimentation that become…