Related papers: Path of pathology
We address some phenomena about the interaction between lower semicontinuous submeasures on $\mathbb{N}$ and $F_{\sigma}$ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $F_\sigma$…
When we study the paradoxes of set theory we find out that there are mainly 2 types: the pathologies and the antinomies. These 2 notions are made precise and compared with the somehow inductively definable concept "abnormal". (See my paper…
We construct examples of Lipschitz continuous functions, with pathological subgradient dynamics both in continuous and discrete time. In both settings, the iterates generate bounded trajectories, and yet fail to detect any (generalized)…
In this note, we shall overview some results related to ultraparacompactness and ultranormality in the general topological and point-free contexts. This note contains some standard results and counterexamples along with some results which…
We record a general asymptotic formula for colon of ideals and proceed to give some applications regarding $m$-full, weakly $m$-full, and full ideals.
Patient subtyping based on temporal observations can lead to significantly nuanced subtyping that acknowledges the dynamic characteristics of diseases. Existing methods for subtyping trajectories treat the evolution of clinical observations…
There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…
Several counterexamples in analysis show the existence of some special object with some sort of pathological behavior. We present three different examples where the pathological behavior is not an isolated exception, but it is the "typical"…
We determine the asymptotic behaviour of certain incomplete Betafunctions.
We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on $\omega$ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by…
Consideration of certain properties of group rings and their ideals search
We consider a potential pathology in the derivation of plate theories as Gamma-limits of 3-dimensional nonlinear elasticity by Friesecke James and Muller (Comm. Pure Appl. Math., 55:1461-1506 and Arch. Ration. Mech. Anal., 180:183-236),…
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.
Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such…
We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions.
This paper shows that some of the limit-like quantities currently used in statistical mechanics are ill-defined in the mathematical sense. Along the line, it is shown that significant progresses in non-equilibrium gas dynamics can be made…
This article investigates pathological behavior at the first limit stage in the sequence of inner mantles, obtained by iterating the definition of the mantle to get smaller and smaller inner models. I show: (A) it is possible that the…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur…