arXiv research

Defines relations between Dirac structures and spinors using Courant algebroid relations.

It is known that holomorphic Poisson structures are closely related to theories of generalized Kähler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely related to generalized Kähler structures /bi-Hermitian structures. By resulting nonco…

We study a bordism relation for stable 3-forms on a 6-manifold, which is a binary relation on the set of closed $SL(3;\mathbb{C})$-structures on a 6-manifold via closed $G_2$-structures. Under $SO(3)$-symmetry and a co-associative condition the relation is reduced to a relation for geometric structures on a 3-manifold.…

Relational Structural Causal Models enable causal reasoning about unseen object combinations.

This paper characterizes projective models in statistical relational learning.

The development of fair machine learning models that effectively avert bias and discrimination is an important problem that has garnered attention in recent years. The necessity of encoding complex relational dependencies among the features and variables for competent predictions require the development of fair, yet ex…

Study the pullbacks and blowups of Lie algebroids and related structures.

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…

Language helps RL agents learn complex relational and causal structures.

We analyze oversquashing in topological message-passing using relational structures.

Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of the same schema. The need for existing datasets can be avoided by using a univer…

Survey on hyperplane arrangements and their topology.

Study relates Finsler structures to Clifford bundles for flat metrics.

Algorithm learns causal structures from time-series data, reducing tests for temporal vs. contemporaneous relations.

With the expeditious advancement of information technologies, health-related data presented unprecedented potentials for medical and health discoveries but at the same time significant challenges for machine learning techniques both in terms of size and complexity. Those challenges include: the structured data with var…

The paper studies properties of group relations induced by compatible coarse structures.

We consider equivalence relations among smooth map germs with respect to geometry of G-structures on the target space germ. These equivalence relations are natural generalization of right-left equivalence (i.e., A-equivalence) in the sense of Thom-Mather depending on geometric structures on the target space germ. Unfor…

Study groups with polynomial growth, finding structure and applications.

We show that the algebra of functions on the Grassmann supergroup Gr$_q(1| 1)$ has a (graded) Hopf algebra structure related to GL$_q(1| 1)$.

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…

Study of pseudo-Riemannian metrics related to Monge-Ampère structures.

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tow…

Develops TCD maps to relate discrete differential geometry and cluster algebras.

We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain related manifolds. These structures occur in bouquets and exhaust the Sasaki cones in all except one case in which there are no extremal metrics.

New scoring rule predicts causal relations from data with selection bias.

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…

Proposes a new Bayesian score for learning network structure from related datasets.

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres c…

Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between entities, embeddings are typically compared in the latent space following a relation-spe…

We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary bialgebras are provided. We also describe ternary distributive algebraic structures com…

This paper extends geometric structure theory to infinite type structures.

We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure on its ideal boundary (absolute). Such relation encompasses, for instance, the us…

Paper improves Bayesian network learning from related data sets.

We review results about $G_2$-structures in relation to the existence of special metrics, such as Einstein metrics and Ricci solitons, and the evolution under the Laplacian flow on non-compact homogeneous spaces. We also discuss some examples in detail.

A new algorithm tackles delayed combinatorial semi-bandit with causal relations.

Study super cluster algebras from super Plücker and Ptolemy relations.

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to represent different "views" to or aspects of the same entities, one may be more inte…

Effectively modelling hidden structures in a network is very practical but theoretically challenging. Existing relational models only involve very limited information, namely the binary directional link data, embedded in a network to learn hidden networking structures. There is other rich and meaningful information (e.…

New test determines appropriate number of biclusters in relational data.

Monograph explores algebraic structures related to Yang-Baxter equation.

While current deep learning systems excel at tasks such as object classification, language processing, and gameplay, few can construct or modify a complex system such as a tower of blocks. We hypothesize that what these systems lack is a "relational inductive bias": a capacity for reasoning about inter-object relations…

We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between th…

We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kähler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence of Vaisman structures and we establish some relations with other geometric notions, such as Sa…

We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action of TG on TP. The symplectic structures corresponding to connections on P(M,G) a…

This paper proves that one-relator groups have a weak Z-structure.

We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.

Introduces a new geometric structure for statistical manifolds with degenerate metrics.

Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…