相关论文: Topological methods for studying contextuality: $N…

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…

Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under…

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…

We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

This research creates a general class of "perturbation models" which are described by an underlying "null" model that accounts for most of the structure in data and a perturbation that accounts for possible small localized departures. The…

Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of…

The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to…

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…

The variety of complex algorithmic approaches for tackling time-series classification problems has grown considerably over the past decades, including the development of sophisticated but challenging-to-interpret deep-learning-based…

We consider the detection of multivariate spatial clusters in the Bernoulli model with $N$ locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to…

The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…

In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…

Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the…

Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…