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.
DOODL learns shared spectral dynamics across related dynamical systems.
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…
Study shows increased VRE penetration reduces electricity prices and volatility.
Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condi…
Invariant reduction preserves Poisson structures in PDEs.
Dynamic Structural Causal Models handle time-dependent systems with cycles and latent confounding.
The Darboux-Egoroff system of PDEs with any number of independent variables plays an essential role in the problems of describing -dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operator and its inverse for symmetries of the Darboux-Egoroff system and des…
New integrable systems constructed for non-diagonal Killing tensors.
This study provides a new mathematical structure for Koopman eigenfunctions.
Study introduces new Bernstein inequalities for dependent data in Hilbert spaces.
The independence of Central Banks is shown to be a myth.
Distributed machine learning (ML) is a modern computation paradigm that divides its workload into independent tasks that can be simultaneously achieved by multiple machines (i.e., agents) for better scalability. However, a typical distributed system is usually implemented with a central server that collects data statis…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. However, non-tri…
Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.
Paper introduces a Gaussian Process for operator learning in computational mechanics.
Human computer interaction facilitates intelligent communication between humans and computers, in which gesture recognition plays a prominent role. This paper proposes a machine learning system to identify dynamic gestures using tri-axial acceleration data acquired from two public datasets. These datasets, uWave and So…
Redundancy in AI perception systems doesn't guarantee independent error occurrences.
VANO uses neural operators for unsupervised learning of functional data.
A Carter like constant for the geodesic motion in the Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geode…
New EiV models correct bias in operator learning with noisy data.
An efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and l*-covering. The latter serves the role of the cotangent bundle in the category of nonlinear evolution PDEs. We first consider two illustrative examples …
We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent …
Derives PDEs from data using manifold learning and neural networks.
In this article, we define an independence system for a classical knot diagram and prove that the independence system is a knot invariant for alternating knots. We also discuss the exchange property for minimal unknotting sets. Finally, we show that there are knot diagrams where the independence system is a matroid and…
Bayesian method optimizes rescheduling for multipurpose batch processes with incomplete look-ahead information.
The failure of a complex and safety critical industrial asset can have extremely high consequences. Close monitoring for early detection of abnormal system conditions is therefore required. Data-driven solutions to this problem have been limited for two reasons: First, safety critical assets are designed and maintained…
The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.
The study describes Nijenhuis operators with specific properties.
RI-DeepONet learns neural operators from arbitrary sensor data.
Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems. The limited ability of humans to process such complex information hinders physicians to readily recognize and act on early signs of patient deterioration. We used machine learnin…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to …
Classifies 3D non-degenerate left-symmetric algebras.
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other…
We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough () coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered through a decision/game theory formulation of the problems of (1) identifying restri…
Modern society heavily relies on strongly connected, socio-technical systems. As a result, distinct risks threatening the operation of individual systems can no longer be treated in isolation. Consequently, risk experts are actively seeking for ways to relax the risk independence assumption that undermines typical risk…
Efficiently solves high-dimensional ODEs with probabilistic methods.
Two-stage recommender systems show better performance when components interact rather than operate independently.
Revisits orbital minimization for neural operator decomposition.
As the Industrial Internet of Things (IIoT) grows, systems are increasingly being monitored by arrays of sensors returning time-series data at ever-increasing 'volume, velocity and variety' (i.e. Industrial Big Data). An obvious use for these data is real-time systems condition monitoring and prognostic time to failure…
We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA reduces the overall complexity from 8N down to 5N serial arithmetic operations, a…
This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict tactical solutions to a given operational problem. In this context, the tactical solution is less detailed than the operational one but it has to be comput…
The paper studies the local structure of a moduli space for a specific string theory system.
Koopman operator theory simplifies complex systems analysis.
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with in…
Recently, large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of the self-organized criticality (SOC). Recent empirical work has suggested that some extreme events systematically deviate from the SOC paradigm, requiring a diffe…
Method discovers local independence in systems with continuous variables.
The paper solves the Cauchy problem for Friedrichs systems on specific spacetime manifolds.
Study shows neural operators can efficiently solve complex reaction-diffusion systems.