相关论文: Observable Covariance and Principal Observable Ana…

For all $1\leq m\leq n-1$, we investigate the interaction of locally finite measures in $\mathbb{R}^n$ with the family of $m$-dimensional Lipschitz graphs. For instance, we characterize Radon measures $\mu$, which are carried by Lipschitz…

The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements,…

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…

The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…

Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every separable metric space admits a metric $\mathcal{M}_d$-frame.…

Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…

The classification of random objects within metric spaces without a vector structure has attracted increasing attention. However, the complexity inherent in such non-Euclidean data often restricts existing models to handle only a limited…

Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…

Advancements in modern science have led to an increased prevalence of functional data, which are usually viewed as elements of the space of square-integrable functions $L^2$. Core methods in functional data analysis, such as functional…

This paper explores visual motion-based invariants, resulting in a new instantaneous domain where: a) the stationary environment is perceived as unchanged, even as the 2D images undergo continuous changes due to camera motion, b) obstacles…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

The observing strategy of a galaxy survey influences the degree to which its resulting data can be used to accomplish any science goal. LSST is thus seeking metrics of observing strategies for multiple science cases in order to optimally…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature…

In this paper, we study the fluctuations of observables of metric measure spaces which are random discrete approximations $X_n$ of a fixed arbitrary (complete, separable) metric measure space $X=(\mathcal{X},d,\mu)$. These observables…