Related papers: Consistency of Relations over Monoids
For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and…
We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local…
Generalized friendship paradoxes occur when, on average, our friends have more of some attribute than us. These paradoxes are relevant to many aspects of human interaction, notably in social science and epidemiology. Here, we derive new…
We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…
Why are some neighborhoods strongly connected while others remain isolated? Although standard explanations focus on demographics, economics, and geography, movement across the city may also depend on cultural styles and amenity mix. This…
We present exact kinematic consistency relations for cosmological structures that do not vanish at equal times and can thus be measured in surveys. These rely on cross-correlations between the density and velocity, or momentum, fields.…
Dynamical systems whose linearizations along trajectories are positive in the sense that they infinitesimally contract a smooth cone field are called differentially positive. The property can be thought of as a generalization of…
A class of polynomial dynamical systems called complex-balanced are locally stable and conjectured to be globally stable. In general, complex-balancing is not a robust property, i.e., small changes in parameter values may result in the loss…
We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by Halvorson and Clifton shows that…
In this article, we prove that if a finitely generated group $G$ is not torsion then a necessary and sufficient condition for every full shift over $G$ has (continuous) cocycle superrigidity is that $G$ has one end. It is a topological…
We consider the action of a finite group $G$ by locality preserving automorphisms (quantum cellular automata) on quantum spin chains. We refer to such group actions as ``symmetries''. The natural notion of equivalence for such symmetries is…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
Kempe, Kleinberg and Tardos (KKT) proposed the following conjecture about the general threshold model in social networks: local monotonicity and submodularity imply global monotonicity and submodularity. That is, if the threshold function…
Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as "local acyclicity" which implies that cluster algebras behave reasonably. One of the earliest and…
We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove…
Using the local approach to the global structure of a symmetric space $E$ we establish a relationship between strict $K$- monotonicity, lower (resp. upper) local uniform $K$-monotonicity, order continuity and the Kadec-Klee property for…
Recent advances in data collection and technology enable a deeper understanding of complex urban commuting, yet few studies have rigorously analyzed the temporal stability and Origin-Destination (OD) heterogeneity of route choice. To…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
Kirill Mackenzie raised the following question: given a groupoid morphism $F$ which is continuous on a neighborhood of base, is it true that $F$ is continuous everywhere? This paper gives a negative answer to that question. Moreover, we…