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We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a…

Algebraic Topology · Mathematics 2020-07-07 Moon Duchin , Tom Needham , Thomas Weighill

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…

Statistical Mechanics · Physics 2009-10-31 G. Caldarelli , A. Capocci

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any…

Social and Information Networks · Computer Science 2012-03-06 Animashree Anandkumar , Avinatan Hassidim , Jonathan Kelner

Machine learning techniques, such as deep learning and ensemble methods, are widely used in various domains due to their ability to handle complex real-world tasks. However, their black-box nature has raised multiple concerns about the…

In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion…

We study a network design problem motivated by the challenge of placing wildlife crossings to reconnect fragmented habitats of animal species, which is among the 17 goals towards sustainable development by the UN: Given a graph, whose…

Data Structures and Algorithms · Computer Science 2025-10-27 Christian Wallisch , Till Fluschnik , Leon Kellerhals

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

This positional paper outlines our vision of 'adaptive architecture', which involves the integration of robotic technology to physically change an architectural space in supporting the changing needs of its occupants, in response to the…

Robotics · Computer Science 2024-03-26 Binh Vinh Duc Nguyen , Andrew Vande Moere

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Computational Geometry · Computer Science 2021-03-24 Brittany Terese Fasy , Xiaozhou He , Zhihui Liu , Samuel Micka , David L. Millman , Binhai Zhu

Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…

Computer Science and Game Theory · Computer Science 2012-07-17 Haris Aziz

This study proposes two new dynamic assignment algorithms to match refugees and asylum seekers to geographic localities within a host country. The first, currently implemented in a multi-year randomized control trial in Switzerland, seeks…

Optimization and Control · Mathematics 2024-05-28 Kirk Bansak , Elisabeth Paulson

In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry -- arises from the network topology of interpersonal ties between members of the group. We follow this idea and propose…

Social and Information Networks · Computer Science 2016-12-28 Jiamou Liu , Ziheng Wei

In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…

Computer Science and Game Theory · Computer Science 2023-05-30 Siddhartha Banerjee , Matthew Eichhorn , David Kempe

Research in epidemiology often focusses on designing interventions that result in the number of infected individuals asymptotically approaching zero, without considering that this number may peak at high values during transients. Recent…

Optimization and Control · Mathematics 2020-03-24 Willem Esterhuizen , Tim Aschenbruck , Jean Lévine , Stefan Streif

The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…

Computational Complexity · Computer Science 2025-12-08 Arash Beikmohammadi , Andrei A. Bulatov

We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…

Dynamical Systems · Mathematics 2008-11-04 Sinisa Slijepcevic

An abstraction of the physical layer coding using bit pipes that are coupled through data-rates is insufficient to capture notions such as node cooperation in cooperative relay networks. Consequently, network-stability analyses based on…

Networking and Internet Architecture · Computer Science 2010-07-09 Jubin Jose , Sriram Vishwanath

The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…

Computational Complexity · Computer Science 2018-02-21 Jiehua Chen , Danny Hermelin , Manuel Sorge , Harel Yedidsion

A community needs to be partitioned into disjoint groups; each community member has an underlying preference over the groups that they would want to be a member of. We are interested in finding a stable community structure: one where no…

Computer Science and Game Theory · Computer Science 2018-11-13 Ayumi Igarashi , Jakub Sliwinski , Yair Zick
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