Related papers: Majority is Stablest : Discrete and SoS
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this…
Maximum likelihood estimation furnishes powerful insights into voting theory, and the design of voting rules. However the MLE can usually be badly corrupted by a single outlying sample. This means that a single voter or a group of colluding…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
Subgroup stability is a strong notion of quasiconvexity that generalizes convex cocompactness in a variety of settings. In this paper, we characterize stability of a subgroup by properties of its limit set on the Morse boundary. Given…
For nonautonomous linear difference equations in Banach spaces we show that a very general type of dichotomic behavior persists under small enough additive linear perturbations. By using a new approach, we obtain two general robustness…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…
Recent analysis of the divergence constraint in the incompressible Stokes/Navier--Stokes problem has stressed the importance of equivalence classes of forces and how it plays a fundamental role for an accurate space discretization. Two…
It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice.…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
This paper proposes normative criteria for voting rules under uncertainty about individual preferences. The criteria emphasize the importance of responsiveness, i.e., the probability that the social outcome coincides with the realized…
Let $E \subset \mathbb R^d$, $d \ge 2$, be compact, and let $\phi(x,y)$ be a smooth function satisfying the Phong--Stein rotational curvature condition on $\{\phi(x,y)=1\}$. We prove that if $\dim_{\mathcal H}(E)>1$, then $$…
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the existence…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…
We describe a web of connections between the following topics: the mathematical theory of voting and social choice; the computational complexity of the Maximum Cut problem; the Gaussian Isoperimetric Inequality and Borell's generalization…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…