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 Cowen-Douglas operators from analytic function spaces.
There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are described. A special attention is paid to the Rarita-Schwinger operator the second…
Paper introduces new fractional Dirac operator and Q-curvature.
Paper proposes operator deep Q-learning for quick reward adaptation.
Extends Calabi operator to Riemannian locally symmetric spaces.
We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial quandles coincide, we give a simple description of this closure operator, and analy…
The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator. Surprisingly, despite these concerns, and independent of its effect on explorati…
ICON learns differential equation operators from prompts, reducing retraining and improving few-shot learning.
CR Killing operator derived from tractor calculus for CR structures.
Paper generalizes paracomposition and change of variables for paradifferential operators.
Study estimates eigenvalues for concave Hessian operators on convex domains.
Mathai, Melrose, and Singer introduced the notion of projective elliptic operators on manifolds equipped with an Azumaya bundle. In this note we compute the equivariant index of transversally elliptic operators that are the pullback of projective elliptic operators on the trivialization of the Azumaya bundle. It encomp…
We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.
We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural operations to the study of polynomial maps between (vector) spaces of jets which are equi…
The paper provides formulas for Hadamard coefficients using Green's operators.
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We…
Study differential operators over maps and their applications in supermanifolds.
Quantum connections replace metrics with operator inner products.
The article studies eigenvalues and spectrum of magnetic Dirac operators.
This paper introduces a neural operator for probabilistic conditioning.
We prove some Fredholm conditions for many algebras of differential operators on particular classes of open manifolds, which include asymptotically Euclidean or asymptotically hyperbolic manifolds. Our typical result is that an operator is Fredholm if, and only if, it is elliptic and some limit operators $(P_α)_{α\…
In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a possible candidate for such an operator but unfortunately it proves out to be badly di…
Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. It deals with results for the Jacobi operator, the higher order Jacobi opera…
Study uses SGD to learn operators in Hilbert spaces with convergence analysis.
Given a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when composed with Berezin-Toeplitz quantization map and its adjoint up to an error w…
Paper introduces magnetic Steklov operator on differential forms and its properties.
The paper classifies real hypersurfaces with a specific Jacobi operator in complex Grassmannians.
Bayesian approach calibrates DNN confidence for field use.
We establish a rigorous link between infinite-dimensional regular Frölicher Lie groups built out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We introduce a version of the Kadomtsev-Petviashvili hierarchy on a regular Frölicher Lie group of series of non-formal odd-class pseudodi…
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…
Identifies Lorentzian locally symmetric spaces where Calabi operator suffices to determine Killing operator range.
ICON learns differential equation operators from examples, revealing probabilistic inference.
Paper introduces a Gaussian Process for operator learning in computational mechanics.
The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…
New operators generalize Michelsohn's on almost Hermitian manifolds.
The study shows conditions for Kähler manifolds to have rational cohomology of complex projective space.
Develops a new approach to spectral asymmetry using microlocal analysis.
CR Paneitz operator on non-embeddable tori has infinitely many negative eigenvalues
The paper bounds eigenvalues of specific operators on certain manifolds.
We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac operator on Einstein manifolds and spectral analysis of the Dirac operator on the as…
A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one's weight behind a sing…
The paper broadens the class of manifolds where Dirac operator spectra are maximal.
The study confirms essential self-adjointness for certain differential operators on manifolds.
Classifies and constructs intertwining differential operators between vector bundles over real projective space.
Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.
Kernel method approximates dynamical operators from data.
Completes the proof of curvature tensor existence for Jacobi operators.
We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator…