A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New methods improve multi-agent reinforcement learning by addressing rotational dynamics.
Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.
Classical dynamical equations describing a certain version of the nonHamiltonian interaction of two rotators (Euler tops with completely degenerate inertia tensors) are considered. The simplest case is integrated. It is shown that the dynamics is almost periodic with periods depending on the initial data.
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…
Study of rotation angles in a rotating disc model.
Investigates the rotating Kepler problem for energy values ≤ -3/2.
Study on Langevin dynamics on planar motion group, highlighting geometric mechanism.
Study uses geometric algebra to analyze credit cycles, revealing dangerous feedback loops.
The rotation angle of a rolling disc is shown to be a geometric phase related to the Hopf fibration.
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end transformation equivarian…
Study dynamic portfolio choice under rotating drivers, revealing a new geometric structure.
New tree structure for pseudo-Anosovs from interval maps.
A new algorithm computes elastic shape distances between curves efficiently.
We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian symmetric space context. Using classical symmetric space techniques we find that every such space intrinsically carries a regular Poisson structure whose symplectic leaves are para-hermitian symmetric surfaces. We also obtain a global express…
A new method for 3D surface registration using dynamic programming.
The paper studies dynamical systems with evolving geometric structure using numerical methods.
We borrow a classical construction from the study of rational billiards in dynamical systems known as the "unfolding construction" and show that it can be used to study the automorphism group of a Platonic surface. More precisely, the monodromy group, or deck group in this case, associated to the cover of a regular pol…
Develops computational methods for simulating rigid body dynamics on SO(3).
This paper proposes an improved design of the perceptron unit to mitigate the vanishing gradient problem. This nuisance appears when training deep multilayer perceptron networks with bounded activation functions. The new neuron design, named auto-rotating perceptron (ARP), has a mechanism to ensure that the node always…
Unified geometric description of Kepler flow across all energies.
Study on rotating surfaces in 4D space with matrices.
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the exp…
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric includes the existing …
A new transform links rotating calorons to solutions of a differential equation.
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
New MCMC method improves sampling efficiency across diverse structural models.
Generative model improves noise estimation in stochastic rotating shallow water models.
The paper develops algorithms and topological invariants for distinguishing dynamic systems.
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
In recent years, convolutional neural networks (CNN) have played an important role in the field of deep learning. Variants of CNN's have proven to be very successful in classification tasks across different domains. However, there are two big drawbacks to CNN's: their failure to take into account of important spatial h…
Study of timelike surfaces in Minkowski space with specific geometric properties.
The study characterizes loxodromes on specific rotational surfaces in 3D space.
We consider cocycles of isometries on spaces of nonpositive curvature . We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there…
OMD monitors stock market dynamics through matrix trajectories, revealing crisis patterns and sector rotations.
General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold encodes the dynamics up to conjugation and inversion. We also prove a generaliz…
We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to invariants of contactomorphisms which generalize the classical notion of the rotation …
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …
Rotation systems can't always be drawn in surfaces.
This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rota…
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
The rotation prediction (Rotation) is a simple pretext-task for self-supervised learning (SSL), where models learn useful representations for target vision tasks by solving pretext-tasks. Although Rotation captures information of object shapes, it hardly captures information of textures. To tackle this problem, we intr…
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases where the rotational orientation of the coordinate system does not affect the m…
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
OMD monitors stock market dynamics through matrix trajectories and reveals crisis patterns.
Minimal sets of moves for rotational Reidemeister diagrams are identified.