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.
Study curvature and torsion in Gaussian distribution's dual coordinate system.
Dual representations for systemic risk measures using acceptance sets.
Inferring a person's goal from their behavior is an important problem in applications of AI (e.g. automated assistants, recommender systems). The workhorse model for this task is the rational actor model - this amounts to assuming that people have stable reward functions, discount the future exponentially, and construc…
Proves partial-dual genus polynomial is a knot invariant weight system.
The paper explores reductions of self-dual conformal structure equations.
New connections share geodesics with superintegrable systems.
A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …
Study dual representations for quasiconvex systemic risk measures.
Researchers found a geometric duality for systems of conservation laws.
New algorithm learns optimal resource allocation in wireless systems without models.
Study systemic risk measures adjusted to financial markets.
The paper analyzes the observability of relative pose estimation using dual quaternions.
Construct dual F-manifolds for regular F-manifolds.
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deform…
The paper explores Guichard nets and their dual properties.
Method identifies dual cognitive system interactions using eye-tracking data.
New -dual solutions found for -Strominger system.
We simplify Hitchin's description of SU(2)-invariant self-dual Einstein metrics, making use of the tau-function of related four-pole Schlesinger system.
Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first decompose the field into self-dual and anti-self-dual components, by implementing the…
The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as `master dispersionless systems' in four and three dimensions respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note we present, in specially adapted coordinate systems…
Extended dual Coxeter and Artin groups theory to rank-three systems.
Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.
Optimizes power allocation for WDM in RoFSO systems.
We construct new examples of solutions of the Hull-Strominger system on non-Kähler torus bundles over K3 surfaces, with the property that the connection on the tangent bundle is Hermite-Yang-Mills. With this ansatz for the connection , we show that the existence of solutions reduces to known results ab…
We consider an embedding of a -dimensional CW complex into the -sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the -dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system of linear equa…
We show that any hyperbolic Inoue surface (or Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result also holds for any of its small deformations as far as its anti-canonical system is non-empty. Similar results are obtained for parabolic Inoue surfaces. Our method also yie…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual banks before aggregation of their risks. In the present paper, we prove the dual re…
Following Simpson we consider the integrable system structure on the moduli spaces of Higgs bundles on a compact Kähler manifold . We propose a description of the corresponding spectral cover of as the fiberwise projective dual to a hypersurface in the projectivization $\mathbb{P}(\mathcal{T}_{X} \oplus \mathcal…
Paper tackles BA in dual-band systems using ML.
Visible Lagrangians in Hitchin systems are studied for pillowcase covers.
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as this is often practised in cont…
The closed string model in the background gravity field is considered as a bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets(PB), depending of the background fields and of their derivatives, are obtained. The in…
We study the anti-self-dual equation for non-diagonal SU(2)-invariant metrics and give an equivalent ninth-order system. This system reduce to a sixth-order system if the metric is in the conformal class of scalar-flat-Kaehler metric.
The paper explores how AI systems use information geometry to encode semantic structure.
Paper presents a deep learning approach to AC Optimal Power Flow.
The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable Hamiltonian systems this means that the dual space $\goth g^*$ endowed with the standard …
Stochastic dual coordinate ascent (SDCA) is an effective technique for solving regularized loss minimization problems in machine learning. This paper considers an extension of SDCA under the mini-batch setting that is often used in practice. Our main contribution is to introduce an accelerated mini-batch version of SDC…
This paper considers the design of optimal resource allocation policies in wireless communication systems which are generically modeled as a functional optimization problem with stochastic constraints. These optimization problems have the structure of a learning problem in which the statistical loss appears as a constr…
Study rigidifies geometry of electrostatic systems with specific tensor properties.
In recent years, there has been a surge of interest in developing deep learning methods for non-Euclidean structured data such as graphs. In this paper, we propose Dual-Primal Graph CNN, a graph convolutional architecture that alternates convolution-like operations on the graph and its dual. Our approach allows to lear…
In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture …
This paper improves robot grasping by integrating meta-control and latent-space imagination.
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can…
Two geometric tests for forward-flatness are shown to be dual.
Paper tackles class-incremental time series classification with dual-stream feature extraction.
A machine learning model for PMD compensation in dual-polarization systems.
The paper proves conditions for the isomorphism between standard and dual Artin groups.
A new dual test for forward-flatness simplifies computations.