Related papers: Completeness and Transitivity of Preferences on Mi…
Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…
We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our results are based on a novel method for controlling $\chi^2$…
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…
In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appropriate measure of complexity. We show that the measure is…
We prove that any strongly mixing action of a countable abelian group on a probability space has higher order mixing properties. This is achieved via introducing and utilizing $\mathcal R$-limits, a notion of convergence which is based on…
We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…
The stable set associated to a given set S of nonerasing endomorphisms or substitutions is the set of all right infinite words that can be indefinitely desubstituted over S. This notion generalizes the notion of sets of fixed points of…
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and…
We study the manipulability of social choice correspondences in situations where individuals have incomplete information about others' preferences. We propose a general concept of manipulability that depends on the extension rule used to…
New insights into the combinatorial structure of the Mandelbrot set are given by `Correspondence' and `Translation' Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles…
We revisit, in the framework of Mach-Zehnder interferometry, the connection between the complementarity and uncertainty principles of quantum mechanics. Specifically, we show that, for a pair of suitably chosen observables, the trade-off…
We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special case of ordinary schemes, are reasonably…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on a fine investigation of the…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple…
We give a combinatorial characterization of conjugacy in the sylvester monoid (the monoid of binary search trees), showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous…
In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…
We present several combinatorial properties of semiselective ideals on the set of natural numbers. The continuum hypothesis implies that the complement of every selective ideal contains a selective ultrafilter, however for semiselective…