Related papers: No Where to Go But High: A Perspective on High Dim…
A four-dimensional effective theory that arises as the low-energy limit of some extra-dimensional model is constrained by the higher dimensional Einstein equations. Steinhardt & Wesley use this to show that accelerated expansion in our four…
Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find…
Astronomy is the study of the Universe and all the objects that it comprises. Our attention is therefore usually focused beyond Earth, home to the only form of life known today. However, how can we continue to explore the secrets of the…
In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes, yields for every dimension, an infinite family of…
We describe new no-go theorems for producing four-dimensional accelerating universes from warped dimensional reduction. The new theorems improve upon previous results by including dynamical extra dimensions and by treating four-dimensional…
While it remains the staple of virtually all cosmological teaching, the concept of expanding space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the…
Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived…
Intuitively, the totality of physical reality -- the Cosmos -- has a beginning only if (i) all parts of the Cosmos agree on the direction of time (the Direction Condition) and (ii) there is a boundary to the past of all non-initial…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
In cosmology the number of scientists using the framework of an expanding universe is very high. This model, the big-bang, is now overwhelmingly present in almost all aspects of society. It is the main stream cosmology of today. A small…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
Query expansion is a technique widely used in image search consisting in combining highly ranked images from an original query into an expanded query that is then reissued, generally leading to increased recall and precision. An important…
The answer to the question in the title is: in search of new physics beyond the Standard Model, for which there are many motivations, including the likely instability of the electroweak vacuum, dark matter, the origin of matter, the masses…
In recent years, high dimensional expanders have been found to have a variety of applications in theoretical computer science, such as efficient CSPs approximations, improved sampling and list-decoding algorithms, and more. Within that, an…
The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general…
What if physics is just the way we perceive geometry? That is, what if geometry and physics will one day become one and the same discipline? I believe that will mean we will at last really understand physics, without postulates other than…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
The meaning of the expansion of the universe, or the `expansion of space,' is explored using two phenomena: the motion of a test particle against a homogeneous background and the cosmological redshift. Contrary to some expectations, a…