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.
Develops a new geometric framework for non-conservative field theories.
New geometric framework for non-conservative field theories with time-dependent terms.
Develops Hamilton-Jacobi theory for non-conservative field theories in k-contact geometry.
SBMs learn manifold-like structures by mixing samples with a non-conservative field.
We study non-conservative like SODEs admitting explicit Lagrangian descriptions. Such systems are equivalent to the system of Lagrange equations of some Lagrangian , including a covariant force field which represents non-conservative forces. We find necessary and sufficient conditions for the existence of a differen…
Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
Paper introduces a PDE-free method for decomposing forces in any dimension.
New framework models non-conservative stochastic processes without energy conservation constraints.
The paper integrates dissipative and curl forces using geometric methods.
Sharp bounds on heat kernel derivatives on incomplete manifolds.
In this paper we provide generalized Helmholtz conditions, in terms of a semi-basic 1-form, which characterize when a given system of second order ordinary differential equations is equivalent to the Lagrange equations, for some given arbitrary non-conservative forces. For the particular cases of dissipative or gyrosco…
A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints -- we recall…
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of prob…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical mechanical system and arbitrary initial conditions, there exists a conservative …
New optimal transport method handles mass creation and destruction.
The paper extends a learning heuristic to high-dimensional contexts, reducing the risk of unusual actions.
New bounds for kernel regression under non-Gaussian noise.
Study on how soliton equations form singularities using L,A,B-triples.
Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal…
Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.
Diffusion models' speed-accuracy relations derived from thermodynamics.
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus appl…
A new algorithm learns from failures to optimize under constraints efficiently.
The application of machine learning to bioinformatics problems is well established. Less well understood is the application of bioinformatics techniques to machine learning and, in particular, the representation of non-biological data as biosequences. The aim of this paper is to explore the effects of giving amino acid…
Domain adaptation refers to the problem of leveraging labeled data in a source domain to learn an accurate model in a target domain where labels are scarce or unavailable. A recent approach for finding a common representation of the two domains is via domain adversarial training (Ganin & Lempitsky, 2015), which attempt…
SLdisco uses supervised learning to discover causal models from observational data.
How, and to what extent, does an interconnected financial system endogenously amplify external shocks? This paper attempts to reconcile some apparently different views emerged after the 2008 crisis regarding the nature and the relevance of contagion in financial networks. We develop a common framework encompassing seve…
New method for sampling from multivariate distributions using optimal control and quantum mechanics.
The Long-Short-Term-Memory Recurrent Neural Networks (LSTM RNNs) are a popular class of machine learning models for analyzing sequential data. Their training on modern GPUs, however, is limited by the GPU memory capacity. Our profiling results of the LSTM RNN-based Neural Machine Translation (NMT) model reveal that fea…
Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
The paper explores how fields in higher dimensions are quantized.
Paper transforms torse-forming vector fields into simpler forms.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
Conformal vector fields on LCP manifolds are orthogonal and Killing.
Paper describes holomorphic polyvector fields on toric varieties.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.
We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes…
The paper establishes a connection between force-free fields and conformally geodesic fields.
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…
Vector fields invariant under Lie group action are finitely generated by polynomial fields.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold . The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …