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We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
The abundance of peaks in weak gravitational lensing maps is a potentially powerful cosmological tool, complementary to measurements of the shear power spectrum. We study peaks detected directly in shear maps, rather than convergence maps,…
The topology of the observable Universe is not yet known. The most significant observational sign of a non-trivial topology would be multiple images (``ghosts'') of a single object at (in general) different sky positions and redshifts. It…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
Despite compelling theoretical arguments, the use of clusters as cosmological probes is, in practice, frequently questioned because of the many uncertainties impinging on cluster mass estimates. Our aim is to develop a fully self-consistent…
Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift ($z \geq 4$) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in…
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ on the microwave background sky. Previous efforts to search for this topology have focused on…
Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make…
Given a collection of Boolean spatial feature types, their instances, a neighborhood relation (e.g., proximity), and a hierarchical taxonomy of the feature types, the goal is to find the subsets of feature types or their parents whose…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
Hot big bang cosmology says nothing about the topology of the Universe. A topology-independent algorithm is presented which is complementary to that of Lehoucq et al. 1996 and which searches for evidence of multi-connectedness using…
Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One…
Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the…