Related papers: Counterexamples in Cake-Cutting
Many causal claims, such as "sugar causes hyperactivity," are disputed or outdated. Yet research on causality extraction from text has almost entirely neglected counterclaims of causation. To close this gap, we conduct a thorough literature…
We show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and equal surface areas. Similar results regarding…
We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph…
Whilst cooking is a very important human activity, there has been little consideration given to how we can formalize recipes for use in a reasoning framework. We address this need by proposing a graphical formalization that captures the…
Reprint of a 1989 paper including minor corrections of misprints. Added comments (11 pages) about later related papers in the literature concerning comparison of Gabriel-Zisman calculus of (right) fractions and the use of generalized…
Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece…
In software verification, a successful automated program proof is the ultimate triumph. The road to such success is, however, paved with many failed proof attempts. The message produced by the prover when a proof fails is often obscure,…
In this paper, we give a simple counter example to the famous Hodge conjecture.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
Counterfactual explanations can be used to interpret and debug text classifiers by producing minimally altered text inputs that change a classifier's output. In this work, we evaluate five methods for generating counterfactual explanations…
See http://www.math.msu.edu/~abbas or Wiley preprint server.
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
Counterfactual explanations provide ways of achieving a favorable model outcome with minimum input perturbation. However, counterfactual explanations can also be leveraged to reconstruct the model by strategically training a surrogate model…
There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis,…
The classic cake-cutting problem provides a model for addressing the fair and efficient allocation of a divisible, heterogeneous resource among agents with distinct preferences. Focusing on a standard formulation of cake cutting, in which…
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
This paper aims to expand on the open case $k=n$ regarding Proposition 3.6[1] and hopefully foster curiosity for its resolution.
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among $n$ players who value pieces according to…