Related papers: Good Frames With A Weak Stability

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random…

Let K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,\Gamma)$ for the number of solutions…

We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper we explore stability results in this context. We…

A class K of structures is controlled if for all cardinals lambda, the relation of L_{infty,lambda}-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that no pseudo-elementary class with the…

Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods…

We consider odd symmetric (1+1)-scalar field models with one internal mode. Under natural and robust assumptions, including the Fermi golden rule, we prove the asymptotic stability of the kink by odd perturbations in the energy space. For…

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $F$-regularity to mixed characteristic and identify certain stable…

L. Soukup formulated an abstract framework in his introductory paper for proving theorems about uncountable graphs by subdividing them by an increasing continuous chain of elementary submodels. The applicability of this method relies on the…

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

Although deep learning has achieved appealing results on several machine learning tasks, most of the models are deterministic at inference, limiting their application to single-modal settings. We propose a novel general-purpose framework…

We like to develop model theory for $T$, a complete theory in $\mathbb{L}_{\theta,\theta}(\tau)$ when $\theta$ is a compact cardinal. By [Sh:300a] we have bare bones stability and it seemed we can go no further. Dealing with ultrapowers…

Examples are constructed of sparse subsequences of the integers for which the associated maximal averages operator is of weak type (1,1). A consequence, by transference, is that an almost everywhere L^1 -- type ergodic theorem holds for…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

Let $\{ A_k\}_{k=1}^\infty$ be a sequence of finite subsets of $\mathbb{R}^d$ satisfying that $\# A_k \ge 2$ for all integers $k \ge 1$. In this paper, we first give a sufficient and necessary condition for the existence of the infinite…

Let K be a compact Lie group and W a finite-dimensional real K-module. Let X be a K-stable real algebraic subset of W. Let I(X) denote the ideal of X in R[W] and let I_K(X) be the ideal generated by I(X)^K. We find necessary conditions and…

In this paper, we first prove a theorem by a little modification on the Lax-Milgram theorem. Then, using $K$-frames, we obtain lower and upper bounds for the results obtained from this theorem. Also, we present some methods for the…

We show that if M is a stable unsuperstable homogeneous structure, then for most kappa < |M|, the number of elementary submodels of M of power kappa is 2^kappa .