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Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…
We study applications of 3D printing to the broad goal of understanding how mathematical objects vary continuously in families. To do so, we model the varying parameter as the vertical axis of a 3D print, introducing the notion of a static…
A linearly constrained framework in $\mathbb{R}^d$ is a bar-joint framework where, in addition, vertices with loops are constrained to lie in given affine subspaces. In the generic case, when each vertex is incident to sufficiently many…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
We present a formalism for simulating quantum dynamics of lattice spin-one systems by first introducing local hidden variables and then doing semiclassical (truncated Wigner) approximation in the extended phase space. In this way we exactly…
In recent years, a plethora of diverse methods have been proposed for 3D pose estimation. Among these, self-attention mechanisms and graph convolutions have both been proven to be effective and practical methods. Recognizing the strengths…
Graphical techniques provide a very useful practical device for calculations involving the so-called spin network states, which encode the quantum degrees of freedom of spatial geometry in loop quantum gravity. Graphical calculus of SU(2),…
This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…
Due to the complexity of the human body and its neuromuscular stabilization, it has been challenging to efficiently and accurately predict human motion and capture posture while being driven. Existing simple models of the seated human body…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
Tensegrities synergistically combine tensile (cable) and rigid (link) elements to achieve structural integrity, making them lightweight, packable, and impact resistant. Consequently, they have high potential for locomotion in unstructured…
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports,…
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain…
A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data…
We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the…
This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion…
Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…
This paper primarily focuses on evaluating and benchmarking the robustness of visual representations in the context of object assembly tasks. Specifically, it investigates the alignment and insertion of objects with geometrical extrusions…
The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure…
The gonihedric spin model was first introduced as the action for a discretized tensionless string in a discretized embeding space. Afterwards was found that there are interesting features on the dynamical behavior of this model in 3…