Related papers: Toy models for hierarchy studies
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…
Machines that can replicate human intelligence with type 2 reasoning capabilities should be able to reason at multiple levels of spatio-temporal abstractions and scales using internal world models. Devising formalisms to develop such…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model…
We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…
One way to generate an intermediate scale being consistent with gauge coupling unification is to add new Higgs scalars above the intermediate scale. We classify such scenarios according to their degree of departure from minimal…
In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself can not explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments,…
In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined,…
We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-two particles without ghosts or tachyons. In general, these Lagrangians also have a scalar mode in their spectrum. We find that, in two cases, the…
We consider scalar tensor theories of gravity assuming that the scalar field is non minimally coupled with gravity. We use this theory to study evolution of a flat homogeneous and isotropic universe. In this case the dynamical equations can…
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
We examine a dual theory of a Supersymmetric Standard Model(SSM) in terms of an $SU(3)_C$ gauge group. In this scenario, it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the…
We study the possible mixings between gauge vector fields and scalar fields through their self-energies, arising in models with two Higgs doublets. We derive the relevant set of Schwinger-Dyson equations and the Ward identities that compel…
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into…
We derive randomization-based models for experiments with a chain of randomizations. The estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the…
We propose a classically scale-invariant extension of the Georgi--Machacek model by augmenting its custodial \(SU(2)_L \times SU(2)_R\)-symmetric Higgs sector -- originally composed of a doublet and two triplets -- with a gauge-singlet…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…