arXiv research

Investigate AR-Finsler metrics for local dual flatness and projective flatness.

This article announces the completion of the classification of rank 4 locally projective polytopes and their quotients. There are seventeen universal locally projective polytopes (nine nondegenerate). Amongst their 441 quotients are a further four (nonuniversal) regular polytopes, and 152 nonregular but section regular…

This paper solves the inversion problem for jump processes using Markovian projections.

Study identifies subvarieties of projective varieties mapping to models.

Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant tensors algebraically constructed from the projective Weyl curvature. We show, by examples, that …

A method to visualize multidimensional local subspaces using implicit differentiation.

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller informatio…

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(α,β)$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fiel…

The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions …

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental proje…

This paper generalizes monodromy maps for projective structures with poles.

The paper studies projections of asset prices under equivalent martingale measures.

Stable planes are locally isomorphic to classical projective planes.

Projects Markovian processes from Itô semimartingales with jumps.

We define a partition of the space of projectively flat metrics in three classes according to the sign of the Chern scalar curvature; we prove that the class of negative projectively flat metrics is empty, and that the class of positive projectively flat metrics consists precisely of locally conformally flat-Kähler met…

Generalizing the notion of local $φ$-symmetry of Takahashi, in the present paper, we introduce the notion of local $φ$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $φ$-semisymmetry of a Sasakian manifold …

Study shows zero Pontrjagin classes for sprays.

Link projections with the same circle arrangement can be transformed by specific moves.

Classifies flat projective structures with specific symmetries.

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational cost of orthogonal projections would be prohibitive. However, they do not enjoy …

The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2) tensor under projective coordinate transformations, so long as u transforms as a section of a certain line bundle. On a locally projectively flat manifold M, the section u can be regarded as a metric potential analogous to the local potential …

We introduce a method, KL-LIME, for explaining predictions of Bayesian predictive models by projecting the information in the predictive distribution locally to a simpler, interpretable explanation model. The proposed approach combines the recent Local Interpretable Model-agnostic Explanations (LIME) method with ideas …

Study on null-projectability of Levi-Civita connections in neutral metrics.

New projection operators for multipatch spaces with stable properties.

A vector field on a Kähler manifold is called c-projective if its flow preserves the J-planar curves. We give a complete local classification of Kähler real 4-dimensional manifolds that admit an essential c-projective vector field. An important technical step is a local description of 4-dimensional c-projectively equiv…

Let $S$ be a closed oriented surface of genus at least two. Gallo, Kapovich, and Marden asked if 2π-graftings produce all projective structures on $S$ with arbitrarily fixed holonomy (Grafting Conjecture). In this paper, we show that the conjecture holds true "locally" in the space $GL$ of geodesic laminations on $S$ v…

3D projective structures can be metrized with conformal structures.

The paper extends a formula linking surface curvature to projection invariants.

The study proves properties of 4D projective manifolds and builds non-hyperbolic examples.

The non-convexity of a smooth and compact connected component of a real algebraic plane curve can be measured by a combinatorial object called the Poincare-Reeb tree associated to the curve and to a direction of projection. In this paper we show that if the chosen projection avoids the bitangents and the inflectional t…

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(α,β)$-metrics which are locally projectively flat with constant flag curvature in dimension $n= 2$ and $n \ge 3$ respectively. Further, we determine t…

This paper explores how local behavior of meromorphic connections on the projective line determines the global connection.

Resolves conjectures on non-abelian Hodge loci for quasi-projective varieties.

New insights into continual learning for deep models, showing convergence issues but local linear solutions.

Generalizes Riemann-Hilbert correspondence for curved local systems.

The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave…

We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification of Monge forms and bifurcations of parabolic curves and flecnodal curves.

Efficiently checks local robustness in neural networks using geometric projections.

We are interested in the local extrinsic geometry of smooth surfaces in 4-space, and classify jets of Monge forms by projective transformations according to $\mathcal{A}^3$-types of their central projections.

FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence.

Derives variance kernel for reaction boundary in financial models.

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of singular Finsler metrics defined by a Riemann metric $α$ and 1-form $β$ and characterize those which are respectively Douglasian and locally projectively flat in di…

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.

Projective manifolds with specific bundles are isomorphic to simpler spaces.

Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…

PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.