Related papers: Good and bad points in scales
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
I describe and analyze the various energy scales that emerge from studying the structure of the Standard Models of particle physics and cosmology. Remarkably, save for the scale of the cosmological vacuum energy, all the scales below the…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…
We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b species of complex bosons and N_f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a…
Chi-squared tests for lack of fit are traditionally employed to find evidence against a hypothesized model, with the model accepted if the Karl Pearson statistic comparing observed and expected numbers of observations falling within cells…
A fine tuned hierarchy between a strongly coupled high energy compositeness scale and a much lower chiral symmetry breaking scale is a requisite ingredient in many models of dynamical electroweak symmetry breaking. Using a nonperturbative…
Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal $\delta$ of countable cofinality and every regular uncountable $\mu<\delta$ there are stationarily many non-approachable…
In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model whit cosmological constant, containing a stiff fluid and a classical Dirac field. The proposed cosmological scenario describes the evolution of…
Critical two-point correlation functions in the continuous and lattice phi^4 models with scalar order parameter phi are considered. We show by different non-perturbative methods that the critical correlation functions <phi^n(0) phi^m(x)>…
Goodness-of-fit tests based on the Euclidean distance often outperform chi-square and other classical tests (including the standard exact tests) by at least an order of magnitude when the model being tested for goodness-of-fit is a discrete…
In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of $6$-division points on the Fermat cubic $F$ and various conics naturally attached to them. Most facts presented here were derived by…
The Standard Model has some intrinsic beauty in the sector of fermions and gauge bosons. Its scalar sector, though minimal, is however haunted by the hierarchy problem. The fermionic spectrum also have two major problems, the flavor problem…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
Positive configurations of points in the affine building were introduced in \cite{Le} as the basic object needed to define higher laminations. We start by giving a self-contained, elementary definition of positive configurations of points…
We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for…
A strictly linear evolution of the scale factor is a characteristic feature in several classes of alternative gravity theories. In this article we investigate the overall viability of an open linear coasting cosmological model. We report…
The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological…
We consider the application of the Multiple Point Criticality Principle to the Standard Model and its extension to the anti-grand gauge group $SMG^3 \otimes U(1)_f$ at the Planck scale. In particular we discuss the predictions for the fine…
If a discrete probability distribution in a model being tested for goodness-of-fit is not close to uniform, then forming the Pearson chi-square statistic can involve division by nearly zero. This often leads to serious trouble in practice…