Related papers: Stable Independance and Complexity of Representati…
In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Using the language of twisted skew-commutative algebras, we define \emph{secondary representation stability}, a stability pattern in the {\it unstable} homology of spaces that are representation stable in the sense of Church, Ellenberg, and…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…
An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We seek a general description of state collapse spanning…
Let C_n(M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H_i(C_n(M); Q) are representation stable in the sense of [Church-Farb].…
A model to describe the spontaneous formation of military and economic coalitions among a group of countries is proposed using spin glass theory. Between each couple of countries, there exists a bond exchange coupling which is either zero,…
We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing…
We provide several crucial technical extensions of the theory of stable independence notions in accessible categories. In particular, we describe circumstances under which a stable independence notion can be transferred from a subcategory…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…
Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur's Galois deformation theory for representations with that property. We introduce an axiomatic definition of…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference…
Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These…