Related papers: Topological Connectedness and Behavioral Assumptio…
Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the…
We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the…
The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…
What makes two computational systems equivalent? Topos theory answers with classifying toposes: a system's semantic content is encoded in the geometric theory it classifies, and two presentations are equivalent when their classifying…
Social network extensions of Heider's balance theory have not always been consistent. Structural balance theory primarily focuses on graph partitioning, thereby assuming, homogeneity in balance-driven behavior of nodes. We present a general…
Whether two boundary conditions of a two-dimensional topological order can be continuously connected without a phase transition in between remains a challenging question. We tackle this challenge by constructing an effective Hamiltonian,…
Roughly speaking, a recurrence relation is nested if it contains a subexpression of the form ... A(...A(...)...). Many nested recurrence relations occur in the literature, and determining their behavior seems to be quite difficult and…
This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…
We generalise the main theorems from the paper "The Borel cardinality of Lascar strong types" by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence relations. We apply them to describe relationships between…
Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of…
Networks such as organizational network of a global company play an important role in a variety of knowledge management and information diffusion tasks. The nodes in these networks correspond to individuals who are self-interested. The…
Two-stage bipartite matching is a fundamental problem of optimization under uncertainty introduced by Feng, Niazadeh, and Saberi (2021), who study it under the stochastic and adversarial paradigms of uncertainty. We propose a method to…
Hyperproperties, like observational determinism or symmetry, cannot be expressed as properties of individual computation traces, because they describe a relation between multiple computation traces. HyperLTL is a temporal logic that…
Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…
Structural balance theory describes stable configurations of topologies of signed interpersonal appraisal networks. Existing models explaining the convergence of appraisal networks to structural balance either diverge in finite time, or…
A rational map $f:\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ on the Riemann sphere $\widehat{\mathbb{C}}$ is called critically fixed if each critical point of $f$ is fixed under $f$. In this article, we study the properties of a…
We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…