Related papers: Systematics of Aligned Axions
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
If there are a plethora of axions in nature, they may have a complicated potential and create an axion landscape. We study a possibility that one of the axions is so light that it is cosmologically stable, explaining the observed dark…
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
Theories with several hundred axion fields have enormous numbers of distinct meta-stable minima. A small fraction of these local minima have vacuum energy compatible with current measurements of dark energy. The potential also contains…
Slow-roll inflation can be studied as an effective field theory. The form of the inflaton potential consistent with the data is V(phi) = N M^4 w(phi/[sqrt{N} M_{Pl}]) where phi is the inflaton field, M is the inflation energy scale, and N ~…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We study the cosmology of complex multi-axion theories. With O(100) fields and GUT scale energies these theories contain a vast number of vacua, inflationary trajectories and a natural dark matter candidate. We demonstrate that the vacua…
Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…
We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of…
We continue our analysis of establishing the reliability of "simple" effective theories where massive fields are "frozen" rather than integrated out, in a wide class of four dimensional theories with global or local N=1 supersymmetry. We…
Composite axion scenarios offer a robust field theoretic justification for the existence of a Peccei-Quinn symmetry of high quality. We present a new class of realizations that are naturally embedded in Grand-Unified Theories, retain…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…