arXiv research

Cyclification of orbifolds explained in cohesive higher topos theory.

We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive struct…

Unified theory of orbifolds and cohomology.

Unified classification of equivariant principal bundles using higher homotopy theory.

Higher topos theory applied to physics.

The paper defines approximate fibrations in higher topos theory.

The paper studies deformations of cohesive modules on complex manifolds.

The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.

We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products. We develop a t…

The paper bridges diffeological bundle theory with higher topos theory.

Policy-gradient method controls multiple non-cohesive targets.

Motivated by recent financial crises significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said about influence of financial news on financial markets. We propose a novel measure of collective behaviour in financial news on the Web, New…

Proof confirms preservation of projective limits in synthetic differential geometry.

It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor is really an exponentiation by the corresponding infinitesimal object is also Car…

Topo-MLP learns network representations without message passing.

The paper generalizes current constructions to cohesive modules and characteristic forms.

Study on Čech-de Rham obstruction in diffeological spaces.

Study examines how business units can benefit from group cohesion under regulatory constraints.

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a p…

Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain characteristic classes with values in Bott-Chern cohomology which refines the usual deRham…

A new method improves graph node embeddings by considering both nearby and distant node similarities.

Higher gauge theory via differential nonabelian cohomology

Let $\imath: M\to \RR^{p+2}$ be a smooth embedding from a connected, oriented, closed $p$-dimesional smooth manifold to $\RR^{p+2}$, then there is a spin structure $\imath^\sharp(ς^{p+2})$ on $M$ canonically induced from the embedding. If an orientation-preserving diffeomorphism $τ$ of $M$ extends over $\imath$ as an o…

Enhances kernel regression with network data for better predictions.

In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite the success of recent deep learning methods for diffusion, we find that they often…

Intuitive clustering algorithm balances cluster size and cohesion.

Discriminative clustering uses mutual information to cluster data.

Cohesion uses deep Koopman operators to generate long-range forecasts of chaotic dynamics.

This article constructs the moduli stack of torsionfree $G$-jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any $\infty$-topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are …

New bounds improve linkage methods for clustering, distinguishing complete-link from single-link.

Introduces a new geometric framework for non-perturbative BV-theory.

Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model …

Online PaLD extends PaLD for semi-supervised online applications.

Homotopy theory of differentiable sheaves connects manifold properties to underlying homotopy types.

This paper uses sheaf theory to model virtual knots geometrically.

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey ex…

Extends field theory foundations to infinitesimal spaces, simplifying complex concepts.

This work investigates fundamental questions related to learning features in convolutional neural networks (CNN). Empirical findings across multiple architectures such as VGG, ResNet, Inception, DenseNet and MobileNet indicate that weights near the center of a filter are larger than weights on the outside. Current regu…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of atlas. The approach is compared with the known ones that use the Grothendieck topos…

We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on thr…

This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…

Examines multiagent systems for complex learning tasks.

Extends partitioned local depth concept with probabilistic considerations.

The paper explains the importance of diffeological groupoids in modern geometry and physics.

This paper presents a simple agent-based model of an economic system, populated by agents playing different games according to their different view about social cohesion and tax payment. After a first set of simulations, correctly replicating results of existing literature, a wider analysis is presented in order to stu…

Synthetic theory defines orbifolds as microlinear types with finite identifications.

The paper explores how to fairly share longevity risk among participants of tontine schemes.

Data stream classification methods demonstrate promising performance on a single data stream by exploring the cohesion in the data stream. However, multiple data streams that involve several correlated data streams are common in many practical scenarios, which can be viewed as multi-task data streams. Instead of handli…