相关论文: Carnival of Samplings: Nets, Approximations, Relat…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…

Open problems from the 15th Annual ACM Symposium on Computational Geometry.

Comment on ``Gibbs Sampling, Exponential Families and Orthogonal Polynomials'' [arXiv:0808.3852]

Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…

We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…

Comment on ``Gibbs Sampling, Exponential Families, and Orthogonal Polynomials'' [arXiv:0808.3852]

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.

From social networks to P2P systems, network sampling arises in many settings. We present a detailed study on the nature of biases in network sampling strategies to shed light on how best to sample from networks. We investigate connections…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…

The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.