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.
Holonomies match for higher local systems and principal 2-bundles.
Paper studies rigidity phenomena for elliptic systems on Riemannian manifolds.
A new method captures higher-order interactions in data clusters.
This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to sati…
We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat loc…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration amon…
New approach approximates c-space geometry of multi-loop linkages.
We describe how the dynamical system of rolling two -dimensional connected, oriented Riemannian manifolds and without twisting or slipping, can be lifted to a nonholonomic system of elements in the product of the oriented orthonormal frame bundles belonging to the manifolds. By considering the lifted pr…
These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the relevant mathematical structures underlying a local description of higher gauge …
The paper classifies electrovacuum spaces in higher dimensions, proving several key results.
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of sys…
Framework predicts nonlinear system responses using GFDT and generative models.
In this paper we derive necessary and sufficient conditions for a smooth surface in Rn+1 to admit a local 1-quasiconformal parameterization by a domain in Rn (n >= 3). We then apply these conditions to specific hypersurfaces such as cylinders, paraboloids, and ellipsoids. As a consequence, we show that the classical Li…
A framework for reducing PDEs by symmetry, preserving key structures.
Symplectic classification for a specific type of singularity in integrable systems.
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and tot…
We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge-Ampère type equations (2nd order). Next, …
The paper develops techniques to study dynamical systems with Carnot metrics.
In this paper we derive the symplectic framework for field theories defined by higher-order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher-order system of PDEs to a constrained first-order one, the symplectic structures natura…
We describe an -quasi-equivalence of dg-categories between the first authors' ---the category of category of prefect -modules with flat -connection, corresponding to the de Rham dga of a compact manifold --- and the dg-category of \emph{infinity-local syst…
Generalizes Riemann-Hilbert correspondence for curved local systems.
Let G be a split semisimple algebraic group with trivial center. Let S be a compact oriented surface, with or without boundary. We define {\it positive} representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hype…
It is shown how the well-known class of bihamiltonian structures in general position can be extended to a wider class. A generalization of the corresponding notion of a Veronese web for this wider class is presented (in the general position case Veronese webs form complete systems of local invariants for bihamiltonian …
Study derived Lie ∞-groupoids and algebroids in higher differential geometry.
We propose an extension of the differential system for constant mean curvature (CMC) surfaces in a three dimensional space form to an associated hierarchy of evolution equations by the higher-order commuting symmetries. The infinite sequence of higher-order conservation laws of CMC surfaces admit the corresponding exte…
The paper explores the geometry of holomorphic flows and orbits.
Diverse fault types, fast re-closures, and complicated transient states after a fault event make real-time fault location in power grids challenging. Existing localization techniques in this area rely on simplistic assumptions, such as static loads, or require much higher sampling rates or total measurement availabilit…
DeTurck and Yang have shown that in the neighbourhood of every point of a -dimensional Riemannian manifold, there exists a system of orthogonal coordinates (that is, whith respect to which the metric has diagonal form). We show that this property does not generalize to higher dimensions. In particular, the complex p…
Paper introduces a new operator and solves equations on higher-dimensional almost Kähler manifolds.
Let be a surface, a simply-connected classical group, and the associated adjoint form of the group. We show that the spaces of moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$, which were constructed by Fock and Goncharov (\cite{FG1}), have the structure of cluster varieties, and thus toget…
Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.
This paper provides a geometric description for Lie--Hamilton systems on with locally transitive Vessiot--Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie--Hamilton systems on the dual of a Lie algebra to even-dimensional symplectic leaves re…
New superintegrable systems derived from Frobenius structures.
A simple spin system is constructed to simulate dynamics of asset prices and studied numerically. The outcome for the distribution of prices is shown to depend both on the dimension of the system and the introduction of price into the link measure. For dimensions below 2, the associated risk is high and the price distr…
Local invertibility of higher order tensor transforms on compact manifolds.
Local Kan conditions enable differentiation of simplicial manifolds.
BO limits search to lower dimensions with LGPR, improving efficiency and accuracy.
Invariant reduction preserves Poisson structures in PDEs.
A new method for multi-criteria recommender systems using graph attention networks.
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support learning higher…
The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.
In this paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar curvature problems. The main result of the paper connects the higher index of the Dirac …
New method uses information theory to uncover causal relationships in complex systems.
Novel higher-order group synchronization for noisy local measurements on hypergraphs.
Connected sums defined for codimension two locally flat submanifolds in higher dimensions.
A general approach to formulation of supergravity in higher order anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) is given. We analyze three models of locally anisotropic supergravity.
Following the programme set out in Part I of this work, we develop a conceptual higher order differential calculus. The '' local linear algebra '' defined in Part I is generalized by '' higher order local linear algebra ''. The underlying combinatorial object of such higher algebra is the natural n-dimensional hyper-cu…
Study global geometry of dynamical systems with entire vector fields.