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The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper,…
For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every…
We propose a scenario where inflation is driven by non-minimally coupled massive vector fields. In an isotropic homogeneous universe these fields behave in presicely the same way as a massive minimally coupled scalar field. Therefore our…
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy…
A numerically cheap way to obtain structural information about clusters of rare gas atoms at low temperatures is developed. The semiclassical frozen Gaussian imaginary time propagator is extended such that it can account for the mean values…
We discuss a new approach to data clustering. We find that maximum likelyhood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…
We propose an inflationary scenario where the inflaton field is non-minimally coupled to spacetime curvature and inflation is driven by a vacuum energy symmetry breaking potential without specifying \emph{a priori} whether the inflaton…
We discuss a new approach to data clustering. We find that maximum likelihood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…
We construct a no-scale model of inflation with a single modulus whose real and imaginary parts are fixed by simple power-law corrections to the no-scale K{\" a}hler potential. Assuming an uplift of the minimum of the effective potential,…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
We discuss the large-scale structure of the universe in inflationary cosmology and the implications that it may have for the long-term future of civilizations. Although each civilization is doomed to perish, it may be possible to transmit…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
On compactification from higher dimensions, a single free massive scalar field gives rise to a set of effective four-dimensional scalar fields, each with a different mass. These can cooperate to drive a period of inflation known as assisted…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…
Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it…
A generic non-minimal coupling can push any higher-order terms of the scalar potential sufficiently far out in field space to yield observationally viable plateau inflation. We provide analytic and numerical evidence that this generically…
We analyze a distinctive mechanism for inflation in which particle production slows down a scalar field on a steep potential, and show how it descends from angular moduli in string compactifications. The analysis of density perturbations --…
Non-abelian discrete gauge symmetries can provide the inflaton with a flat potential even when one takes into account gravitational strength effects. The discreteness of the symmetries also provide special field values where inflation can…
We investigate the recently proposed hybrid inflation models with two stages of inflation. We show that quantum fluctuations at the time corresponding to the phase transition between the two inflationary stages can trigger the formation of…