Related papers: No Efficient Disjunction or Conjunction of Switch-…
We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass…
The largest component (``the leader'') in evolving random structures often exhibits universal statistical properties. This phenomenon is demonstrated analytically for two ubiquitous structures: random trees and random graphs. In both cases,…
In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…
If the inflaton is a pseudo-scalar axion, the axion shift symmetry can protect the flatness of its potential from too large radiative corrections. This possibility, known as natural inflation, requires an axion scale which is greater than…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
It is shown that non-supersymmetric spacetime varying string vacua can lead to an exponential hierarchy between the electroweak and the gravitational scales. The hierarchy is naturally generated by a string coupling of O(1).
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…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are Simpson's reversal and the disjunction effect where the…
We comment of the widespread belief among some undergraduate students that the amplitude of any harmonic oscillator in the presence of any type of friction, decays exponentially in time. To dispel that notion, we compare the amplitude decay…
We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation…
We calculate high-energy massive string scattering amplitudes of compactified open string. We derive infinite linear relations, or stringy symmetries, among soft high-energy string scattering amplitudes of different string states in the…
In this note we give a short proof that graphs having no linearly small F{\o}lner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for graphs admitting linearly small maximal F{\o}lner sets and…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show…
The paper is concerned with the existence and blow-up behavior of the minimizers for the 2D attractive Gross-Pitaevskii functional when the interaction strength increases to a critical value. Our results hold for all bounded external…
We study the natural extended-variable formulation for the disjunction of $n+1$ polytopes in $\mathbb{R}^d$. We demonstrate that the convex hull $D$ in the natural extended-variable space $\mathbb{R}^{d+n}$ is given by full optimal big-M…
We explore the possibility of putting constraints on quintessence models with large-scale structure observations. In particular we compute the linear and second order growth rate of the fluctuations in different flavors of quintessence…
The interpretation of the apparent unification of gauge couplings within supersymmetric theories depends on uncertainties induced through heavy particle thresholds. While in standard grand unified theories these effects can be estimated…