arXiv research

The paper develops a new approach to conditional risk measures using modular convex analysis.

New conditional risk measures called conditional generalized quantiles defined and characterized.

A new algorithm for robust causal discovery in small sample sizes.

We study some equivalent properties of the curvature-dimension conditions $CD(n,K)$ inequality on infinite, but locally finite graph. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. And we also obtain one equivalent property of gradient estimate for a new notion o…

Timelike curvature and Brunn-Minkowski inequality linked in non-smooth spacetimes.

Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Delta-equivalent) to a trivial link. We study link-homotopy and self Delta-equivalence on a certain componen…

Study confirms equivalence in Heisenberg groups between curvature-dimension conditions and strong Brunn-Minkowski inequalities.

We show that 4-dimensional Riemannian manifolds which satisfy the Rakić duality principle are Osserman (i.e. the eigenvalues of the Jacobi operator are constant), thus both conditions are equivalent.

The paper classifies pretzel links with 2 components and gives conditions for those with 3 or more.

An analysis is made of reality conditions within the context of noncommutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule is equivalent to the reality condition. We show also that the matrix which determines the reality condition must satisfy the Yang-…

This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence pro…

Paper proves Brunn-Minkowski inequality and curvature dimension condition are equivalent in weighted Riemannian manifolds.

We prove the equivalence of two conditions on the primitive elements in an $SL(2,\mathbb C)$ representation of the free group $F_2$ on two generators, which may hold even when the image of $F_2$ is not discrete. One is Minsky's condition of primitive stability and the other is the $BQ$-condition introduced by Bowditch …

Paper solves equivalence problems for fifth-order differential operators using Cartan's method.

In this paper, two sufficient conditions are provided for given two K-equivalent map-germs to be bi-Lipschitz A-equivalent. These are Lipschitz analogues of the known results on C^r-A-equivalence $(0 \leq r \leq \infty)$ for given two K-equivalent map-germs. As a corollary of one of our results, a Lipschitz version of …

Equivalence of norms on manifolds with curvature bounds established.

Paper defines topology automaton for Barański carpets and proves Hölder equivalence conditions.

The Cartan's method of equivalence and moving coframe method has been applied to solve the local equivalence problem for KDV-type equations under the action of a pseudo-group of contact transformations. The structure equations, the sets of differential invariants for symmetry groups and equivalent conditions of these e…

The paper studies Finsler spaces with semi-concurrent vector fields and their equivalence to Riemannian spaces.

New R-equivalence classes found for torus knot diagrams.

In present paper, the equivalence problem for fourth order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are considered. First, the direct equivalence problem and second equivalence problem i…

The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditi…

We give a solution to the equivalence and the embedding problems for smooth CR-submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all CR-equivalences or CR-embeddings respectively (local and global). For the equivalence p…

The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein distance contraction properties at different times.…

The paper classifies Finsler surfaces satisfying the T-condition or σT-condition.

Study absolute equivalence for Pfaffian systems, applying to control systems.

Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.

In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclas…

New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.

A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twisted link. Twisted links are in one-to-one correspondence with stable equivalence classes of links in oriented thickenings of (possibly non-…

Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.

Improve exposition and explain metric bundle equivalence.

We discuss theoretical aspects of the product rule for classification problems in supervised machine learning for the case of combining classifiers. We show that (1) the product rule arises from the MAP classifier supposing equivalent priors and conditional independence given a class; (2) under some conditions, the pro…

Study 3D manifolds with specific curvature conditions.

Study bi-Lipschitz equivalence of mixed polynomials under specific conditions.

By means of color chord diagrams we establish a necessary and sufficient condition for $O$-topological equivalence of functions with one essentially critical point on oriented surfaces with edge. We also calculate the number of $O$-topologically non-equivalent functions with one essentially critical point on oriented s…

Establishes Morita equivalence for Nijenhuis structures and proves invariance of modular class.

In the present paper we establish the necessary and sufficient conditions for two generalized Abel differential equations to be locally equivalent under the action of the pseudogroup of linear transformations of the form $\{x\mapsto f(x),~ y\mapsto g(x)\cdot y + h(x)\}$. These conditions are formulated in terms of diff…

Simplified proof of equivalence between stability and Bowditch conditions.

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …

Unified framework for fairness, robustness, and distribution shifts.

In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the pseudogroup of contact transformations. These conditions are formulated in terms of integrals of some one-dimensional d…

We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equivalence class under certain conditions.

Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Lioville property and the Khas'minski…

Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.

Paper shows equivalence between NA and ACLMM in diffusion models.

We study differential invariants of the third order linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles on two dimensional manifolds with respect to groups of authomorphisms.

Authors classify 3D locally standard T-pseudomanifolds under weaker conditions.