arXiv research

The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…

Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.

Topology on commensurability classes of hyperbolic 3-manifolds studied.

Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (…

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…

Generalizes Milnor's axiomatic homology theorems to Polish spaces.

Axiomatizes the bid-ask market maker's quoting rule

Paper introduces a new time separation function for $C^0$ spacetimes.

A new axiom for Finsler geometry leads to constant flag curvature.

Unified framework connects two market-making models, revealing their underlying equivalence.

The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of $r$-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …

The aim of this paper is to develop a new axiomatization of planar geometry by reinterpreting the original axioms of Euclid. The basic concept is still that of a line segment but its equivalent notion of betweenness is viewed as a topological, not a metric concept. That leads quickly to the notion of connectedness with…

Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.

Universal Bayes consistency proved in metric spaces.

A Morse complex for Axiom A flows on smooth manifolds.

As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Cha…

Study Vassiliev invariants and periodic orbits of Axiom A flows.

The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.

Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.

This research proposes a new distance metric using Isolation Forests.

It is known, that if a 2m-dimensional Kahler manifold satisfies the axiom of holomorphic 2n-spheres (1<n<m) or the axiom of antiholomorphic n-spheres (2<n), it is of constant holomorphic sectional curvature. In this paper the same result is obtained under weaker assumptions.

The notion of Courant algebroid was introduced by Liu, Weinstein and Xu in 1997. Its definition consists of five axioms and an assumption for a derivation. It is shown that two of the axioms and the assumption for the derivation follow from the rest of the axioms.

We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic $(2n+1)$-spheres. We proved that a nearly Kählerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifold $M$ of dimension $2m\geq…

New axioms justify ES without NRC, linking it to mean-ES portfolio selection.

The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to Kähler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds ($r$-planes) and extrinsic spheres ($r$-spheres) by a wider class of specia…

Solves clustering contradictions by high-dimensional embedding with wide gaps.

Shapley values criticized for feature selection, leading to new insights.

It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

Study examines how machine learning attribution methods reflect risk in finance.

The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes …

Caratheodory's axiom limits arbitrage in resource-limited systems.

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…

Paper solves a max-min game for complex performance benchmarks.

The paper establishes axioms for AMMs to ensure fair pricing and fee structures.

We provide the proof that the space of time series data is a Kolmogorov space with $T_{0}$-separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.

The paper develops axioms for uniquely decomposing functions with real arguments.

Defines Alexandrov spaces via axioms, focusing on curvature bounds.

New axioms for singquandles simplify applications and reveal algebraic aspects.

Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.

We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category $\mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subcategory. Objects of $\mathfrak F_0$ may have non-Hausdorff topology u…

This study redefines probability for finite outcomes using axioms and examples.

Recently V. Arnold introduced Strangeness and $J^{\pm}$ invariants of generic immersions of an oriented circle to $\R^2$. Here these invariants are generalized to the case of generic immersions of an oriented circle to an arbitrary surface $F$. We explicitly describe all the invariants satisfying axioms, which naturall…

We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, and Roseman moves. Our homology has a degenerate subcomplex. T…

We consider the pair of degenerate compatible antibrackets satisfying a generalization of the axioms imposed in the triplectic quantization of gauge theories. We show that this actually encodes a Lie group structure, with the antibrackets being related to the left- and right- invariant vector fields on the group. The s…

In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…

The paper compares LOCO and Shapley values for feature importance, highlighting their limitations and suggesting improvements.