Related papers: Measures for a Transdimensional Multiverse
The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann-Robertson-Walker cosmology. We explore…
The actual existence of collections of universes -- multiverses -- is strongly suggested by leading approaches to quantum cosmology, and has been proposed earlier as an attractive way to explain the apparent fine-tuned character of our…
We propose that the existence of the string landscape suggests the universe can be in a quantum glass state, where an extremely large viscosity is generated, and long distance dynamics slows down. At the same time, the short distance…
We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a…
This paper discusses the origin of the small parameters with the aim of explaining the Hierarchy problem. The flexible extra dimensions are an essential tool in the process by which physical parameters are formed. The evolution of a…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
There is a deep cosmological mystery: although dependent on very different underlying physics, the timescales of structure formation, of galaxy cooling (both radiatively and against the CMB), and of vacuum domination do not differ by many…
The quantum gravity conjectures that aim to separate the landscape from the swampland among the low energy theories were originally formulated in the context of scalar field spaces spanned by moduli. Because these conjectures have…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
Galaxy velocities in clusters, rotation curves of galaxies, and "vertical" oscillations in the Milky Way currently show too high velocities with respect to the masses thought to be involved. While these velocity excesses are currently…
We consider the problem of estimating the counterfactual joint distribution of multiple quantities of interests (e.g., outcomes) in a multivariate causal model extended from the classical difference-in-difference design. Existing methods…
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…
It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…
Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult…
It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.