Related papers: Notes on the stable regularity lemma
We discuss the close relationship between structural theorems in generalized stability theory and graph regularity theorems.
The topic of stable matchings (marriages) in a bipartite graph has become widely popular, starting with the appearance of the classical work by Gale and Shapley. We give a detailed survey on selected known results in this field that…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and…
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. Tokumaru, who, in a series of papers,…
We consider several graphs classes defined in terms of conditions on cliques and stable sets, including CIS, split, equistable, and other related classes. We pursue a systematic study of the relations between them. As part of this study, we…
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence…
In this paper we obtain the stability theorem for the independence number of $G(n, r, 1)$ graphs. This result was previously stated in the paper of M. Pyaderkin but the proof there was incorrect. We introduce the correct proof of the key…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal…
This paper clarifies the main research methods and ideas of the thesis [1,2,4]. The special calculation process is also realized by corresponding computer algorithm. Finally, we introduce zero rows sum case and give the corresponding…
A pair of graphs $(\Gamma,\Sigma)$ is said to be stable if the full automorphism group of $\Gamma\times\Sigma$ is isomorphic to the product of the full automorphism groups of $\Gamma$ and $\Sigma$ and unstable otherwise, where…
The purpose of this simple note is to provide elementary model-theoretic proofs to some existing results on sumset phenomena and IP sets, motivated by Hrushovski's work on the stabilizer theorem.
This survey article is a much extended version of a lecture given at a Clay Institute workshop in October 2006. It describes all known results on the existence of stable coherent systems on algebraic curves.
We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-modules currently in the…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…