Related papers: Simplifying the Kohlberg Criterion on the Nucleolu…
The nucleolus offers a desirable payoff-sharing solution in cooperative games thanks to its attractive properties - it always exists and lies in the core (if the core is non-empty), and is unique. Although computing the nucleolus is very…
Nguyen and Thomas (2016) claimed that they have found a method to compute the nucleoli of games with more than $50$ players using nested linear programs (LP). Unfortunately, this claim is false. They incorrectly applied the indirect proof…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In…
This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
Clustering algorithms rely on complex optimisation processes that may be difficult to comprehend, especially for individuals who lack technical expertise. While many explainable artificial intelligence techniques exist for supervised…
Frequently, a set of objects has to be evaluated by a panel of assessors, but not every object is assessed by every assessor. A problem facing such panels is how to take into account different standards amongst panel members and varying…
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
A substantial portion of the literature on fairness in algorithms proposes, analyzes, and operationalizes simple formulaic criteria for assessing fairness. Two of these criteria, Equalized Odds and Calibration by Group, have gained…
An algorithm for $n-1$-strong-equillibrium for distributed consensus in a ring with rational agents was proposed by Afek et al. (2014). A proof of impossibility of $n-1$-strong-equillibrium for distributed consensus in every topology with…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the…
Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental…
Classical nucleation theory (CNT) is built upon the capillarity approximation, i.e., the assumption that the nucleation properties can be inferred from the bulk properties of the melt and the crystal. Although CNT's simplicity and…
In this paper, I argue that counterfactual fairness does not constitute a necessary condition for an algorithm to be fair, and subsequently suggest how the constraint can be modified in order to remedy this shortcoming. To this end, I…
The purpose of this article is to show that the introduction of hidden variables to describe individual events is fully consistent with the statistical predictions of quantum theory. We illustrate the validity of this assertion by…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
This short technical note points out an erroneous claim about a new rule of combination of basic belief assignments presented recently by Kenn et al. in 2023, referred as Kenn's rule of combination (or just as KRC for short). We prove…