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We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…

Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…

Many resources in the grid connect to power grids via programmable grid-interfacing inverters that can provide grid services and offer greater control flexibility and faster response times compared to synchronous generators. However, the…

We propose a geometry constrained network, termed GC-Net, for weakly supervised object localization (WSOL). GC-Net consists of three modules: a detector, a generator and a classifier. The detector predicts the object location defined by a…

The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…

A convex geometry is a closure system satisfying the anti-exchange property. In this work we document all convex geometries on 4- and 5-element base sets with respect to their representation by circles on the plane. All 34 non-isomorphic…

This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

This paper presents an adaptive reference governor (RG) framework for a linear system with matched nonlinear uncertainties that can depend on both time and states, subject to both state and input constraints. The proposed framework…

Finite convex geometries are combinatorial structures. It follows from a recent result of M.\ Richter and L.G.\ Rogers that there is an infinite set $T_{rr}$ of planar convex polygons such that $T_{rr}$ with respect to geometric convex…

Equations system constructors of hierarchical circuits play a central role in device modeling, nonlinear equations solving, and circuit design automation. However, existing constructors present limitations in applications to different…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions,…

This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…

Mechanical product engineering often must comply with manufacturing or geometric constraints related to the shaping process. Mechanical design hence should rely on robust and fast tools to explore complex shapes, typically for design for…

Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based…

Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact…