Related papers: A Reduction Algorithm for Cosmological Correlators…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order…
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…
Reduction trees are a way of encoding a substitution procedure dictated by the relations of an algebra. We use reduction trees in the subdivision algebra to construct canonical triangulations of flow polytopes which are shellable. We…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
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…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
We present an analytic model specifically designed to address the long standing issue of small scale structure on cosmic string networks. The model is derived from the microscopic string equations, together with a few motivated assumptions.…
In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We present a formulation of cosmological perturbation theory where the Boltzmann hierarchies that evolve the neutrino phase-space distributions are replaced by integrals that can be evaluated easily with fast Fourier transforms. The…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
A defining feature of many large empirical networks is their intrinsic complexity. However, many networks also contain a large degree of structural repetition. An immediate question then arises: can we characterize essential network…
Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work…
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…