Related papers: Isolating clusters of zeros of analytic systems us…
Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for isolating a cluster of zeros of the given system.
We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that an operator deduced by adding $Df(x)$ and a projection of $D^2f(x)$ in a direction of the kernel of $Df(x)$ is…
An outgrowth of the idea of inflation is advanced. In the inflation regime, the singularity condition is broken. Equations which govern inflation are invariant under time reversal, so that they describe deflation as well. Those two…
We construct a toy a model which demonstrates that large field single scalar inflation can produce an arbitrarily small scalar to tensor ratio in the window of e-foldings recoverable from CMB experiments. This is done by generalizing the…
A new scenario of hybrid-like inflation is considered without using hybrid-type potential. Radiation raised continuously by a dissipating inflaton field keeps symmetry restoration in a remote sector, and the false-vacuum energy of the…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
Cosmological production of scalar, non-minimally coupled dark matter depends on the specifics of the inflationary model under consideration. We analyze both Starobinsky inflation and a quadratic potential, solve the full background…
We develop a technique to construct analytical solutions of the linear perturbations of inflation with a nonlinear dispersion relation, due to quantum effects of the early universe. Error bounds are given and studied in detail. The…
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…
In construction of an inflationary model, one usually assumes that the matter sector of the gravitational action is minimally coupled to the background. It means that the matter (inflaton) part of the action is coupled with the same metric…
Previous approaches to constructing abstractions for control systems rely on geometric conditions or, in the case of an interconnected control system, a condition on the interconnection topology. Since these conditions are not always…
We present a closest separable state to cluster states. We start by considering linear cluster chains and extend our method to cluster states that can be used as a universal resource in quantum computation. We reproduce known results for…
We set out the novel bottom up procedure to aggregate or cluster cells with small frequency counts together, in a two way classification while maintaining dependence in the table. The procedure is model free. It combines cells in a table…
Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…
Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the…
A model of inflation is proposed in which compact extra dimensions allow a graceful exit without recourse to flat potentials or super-Planckian field values. Though bubbles of true vacuum are too sparse to uniformly reheat the Universe by…
Given a set of variables and the correlations among them, we develop a method for finding clustering among the variables. The method takes advantage of information implicit in higher-order (not just pairwise) correlations. The idea is to…
In a broad class of scenarios, inflation is followed by an extended era of matter-dominated expansion during which the inflaton condensate is nonrelativistic on subhorizon scales. During this phase density perturbations grow to the point of…