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.
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
In this paper, we give precisely the geometric constraint conditions of canonical symplectic form and regular reduced symplectic forms for the dynamical vector fields of a regular controlled Hamiltonian (RCH) system and its regular reduced systems, which are called the Type I and Type II of Hamilton-Jacobi equations. A…
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly, we derive precisely the geometric constraint conditions of the induced distribu…
Constructs coordinate systems from spectral curve sheaves.
A framework for reducing PDEs by symmetry, preserving key structures.
Deep neural networks with memory learn reduced equations from partial data.
Let denote the -punctured disk in the complex plane, where the punctures are on the real axis. An -braid is said to be \emph{reducible} if there exists an essential curve system $\C$ in , called a \emph{reduction system} of , such that $α*\C=\C$ where $α*\C$ denotes the action of the braid o…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in one-to-one correspondence with the moduli space of regular solutions of the prolong…
WSINDy identifies reduced Hamiltonian systems from particle interactions.
Reduced models derived from agent-based systems using Koopman theory.
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group. Next, as an application of the theoretical results, we consider the underwater …
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the reduction process is a discrete dynamical system that we call the discrete reduce…
The paper discusses reducing Hamiltonian systems by scaling and standard symmetries, leading to Kirillov Hamiltonian systems.
Reduces symplectic Hamiltonian systems to contact systems, realizing Poincaré's dream.
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The presymplectic approach leads to a reduced system whose iteration map is symplectic with r…
SpeakerStew verifies 46 languages with reduced training and inference costs.
The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link component. However, for four or more components, this invariant does not yield a complete link-homotopy invariant. This paper provides two characte…
Recommendation systems have been integrated into the majority of large online systems. They tailor those systems to individual users by filtering and ranking information according to user profiles. This adaptation process influences the way users interact with the system and, as a consequence, increases the difficulty …
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only proper, the reduced nonlinear control system need not be smooth. Using the smooth …
Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.
Recommendation systems have been integrated into the majority of large online systems to filter and rank information according to user profiles. It thus influences the way users interact with the system and, as a consequence, bias the evaluation of the performance of a recommendation algorithm computed using historical…
We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are rational curves the construction procedure reduces to solving systems of linear equatio…
Paper reduces nonholonomic systems with symmetries.
We consider gradient Ricci solitons conformal to a -dimensional pseudo-Euclidean space and we completely describe the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations. As a consequence, the gradient Ricci solitons that arise from t…
Reduces multisymplectic Lie systems through symmetry analysis.
BayPOD-AL learns reduced-order models from high-fidelity data efficiently.
CG-BGs combine flow-based models with PMFs to sample large systems efficiently.
A new method reduces Volterra kernel complexity and uncertainty quantification.
In this paper we consider an alternative approach to "un-reduction". This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential …
We study very small trees from the point of view of reducing systems of free factors, which are analogues of reducing systems of curves for a surface lamination; a non-trivial, proper free factor $F \leq \FN$ reduces if and only if acts on some subtree of with dense orbits. We characterize those trees, call…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to constraints, optimal control theory and so on. This generalized variational calculu…
This research creates efficient models for cyclo-stationary systems using generative methods.
In this paper, from the viewpoint of completeness of Marsden-Weinstein reduction, we illustrate how to give the definitions of a controlled Hamiltonian (CH) system and a reducible controlled Hamiltonian system with symmetry; and how to describe the dynamics of a CH system and the controlled Hamiltonian equivalence; as …
Generalizes energy-momentum method for non-autonomous Hamiltonian systems.
Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is availabl…
Constructing solutions to the heterotic G system on specific types of manifolds.
Method learns latent dynamics of complex systems from noisy data.
A new method predicts non-Markovian closure terms for complex systems.
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…
Machine learning models learn what we teach them to learn. Machine learning is at the heart of recommender systems. If a machine learning model is trained on biased data, the resulting recommender system may reflect the biases in its recommendations. Biases arise at different stages in a recommender system, from existi…
Because deep neural networks (DNNs) rely on a large number of parameters and computations, their implementation in energy-constrained systems is challenging. In this paper, we investigate the solution of reducing the supply voltage of the memories used in the system, which results in bit-cell faults. We explore the rob…
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
SDA method reduces memory and time for assimilating noisy geophysical data.
In addition to constraining bilateral exposures of financial institutions, there are essentially two options for future financial regulation of systemic risk (SR): First, financial regulation could attempt to reduce the financial fragility of global or domestic systemically important financial institutions (G-SIBs or D…
This paper deals with a general method for the reduction of quantum systems with symmetry. For a Riemannian manifold M admitting a compact Lie group G as an isometry group, the quotient space Q = M/G is not a smooth manifold in general but stratified into a collection of smooth manifolds of various dimensions. If the a…
The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity of any compact invariant set of the Hamiltonian flow restricted to a prescribed…