相关论文: Incompatibility boundaries for properties of commu…

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated…

This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation…

Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically…

The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…

Pairwise comparisons between alternatives are a well-established tool to decompose decision problems into smaller and more easily tractable sub-problems. However, due to our limited rationality, the subjective preferences expressed by…

In a typical two-slits experiments we face the question whether it is possible or not to attain knowledge about properties incompatible with Which-Slit property together with the measurement of the final impact point. A wide family of…

We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not…

The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of…

The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem…

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…

To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their…

Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks…

Community detection is one of the most studied problems on complex networks. Although hundreds of methods have been proposed so far, there is still no universally accepted formal definition of what is a good community. As a consequence, the…

The main result of the paper is the Fibonacci-like property of the partition function. The partition function $p(n)$ has a property: $p(n) \leq p(n-1) + p(n-2)$. Our result shows that if we impose certain restrictions on the partition, then…

Most community detection algorithms from the literature work as optimization tools that minimize a given \textit{fitness function}, while assuming that each node belongs to a single community. Since there is no hard concept of what a…

The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While…

Dense sub-graphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Most existing community detection algorithms produce a hierarchical structure of community and seek…

This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…

We study partition properties for uncountable regular cardinals that arise by restricting partition properties defining large cardinal notions to classes of simply definable colourings. We show that both large cardinal assumptions and…

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…