Related papers: A class of dissimilarity semimetrics for preferenc…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full…
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…
Motivated by classification, up to order isomorphism, of some dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on…
The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…
Motivated by Williams' problem of measuring novel differences between shift equivalence (SE) and strong shift equivalence (SSE), we introduce three equivalence relations that provide new ways to obstruct SSE while merely assuming SE. Our…
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…
The notion of preferences plays an important role in many disciplines including service robotics which is concerned with scenarios in which robots interact with humans. These interactions can be favored by robots taking human preferences…
We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point…
We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by a problem posed by Kelly in 1991 and remained unsolved, we investigate the problem of recognizing which permutation…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
Schelling's model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this…
We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are…
A preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan (resp. $d$-Euclidean) if both the alternatives and the voters can be placed into the $d$-dimensional space such that between each pair of alternatives, every voter…
We define a distance analogous to the Gromov-Hausdorff distance that enables the comparison of arbitrary quasi-isometric spaces. We also investigate properties preserved under limits with respect to this distance, as well as properties of…
Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…
We prove a representation theorem for the Choquet integral model. The preference relation is defined on a two-dimensional heterogeneous product set $X = X_1 \times X_2$ where elements of $X_1$ and $X_2$ are not necessarily comparable with…
We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…