CAISL: Simplification Logic for Conditional Attribute Implications

In this work, we present a sound and complete axiomatic system for conditional attribute implications (CAIs) in Triadic Concept Analysis (TCA). Our approach is strongly based on the Simplification paradigm which offers a more suitable way for automated reasoning than the one based on Armstrong’s Axioms. We also present an automated method to prove the derivability of a CAI from a set of CAI s.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Mathematical evolution in discrete networks

This paper provides a mathematical explanation for the phenomenon of \triadic closure" so often seen in social networks. It appears to be a natural consequence when network change is constrained to be continuous. The concept of chordless cycles in the network's \irreducible spine" is used in the analysis of the network's dynamic behavior. A surprising result is that as networks undergo random, but continuous, perturbations they tend to become more structured and less chaotic

BV-equivalence between triadic gravity and BF theory in three dimensions

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries

Point process modeling for directed interaction networks

Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a model is introduced for treating directed interactions as a multivariate point process: a Cox multiplicative intensity model using covariates that depend on the history of the process. Consistency and asymptotic normality are proved for the resulting partial-likelihood-based estimators under suitable regularity conditions, and an efficient fitting procedure is described. Multicast interactions--those involving a single sender but multiple receivers--are treated explicitly. The resulting inferential framework is then employed to model message sending behavior in a corporate e-mail network. The analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection.Comment: 36 pages, 13 figures; includes supplementary materia

Emotional engagements predict and enhance social cognition in young chimpanzees

Social cognition in infancy is evident in coordinated triadic engagements, that is, infants attending jointly with social partners and objects. Current evolutionary theories of primate social cognition tend to highlight species differences in cognition based on human-unique cooperative motives. We consider a developmental model in which engagement experiences produce differential outcomes. We conducted a 10-year-long study in which two groups of laboratory-raised chimpanzee infants were given quantifiably different engagement experiences. Joint attention, cooperativeness, affect, and different levels of cognition were measured in 5- to 12-month-old chimpanzees, and compared to outcomes derived from a normative human database. We found that joint attention skills significantly improved across development for all infants, but by 12 months, the humans significantly surpassed the chimpanzees. We found that cooperativeness was stable in the humans, but by 12 months, the chimpanzee group given enriched engagement experiences significantly surpassed the humans. Past engagement experiences and concurrent affect were significant unique predictors of both joint attention and cooperativeness in 5- to 12-month-old chimpanzees. When engagement experiences and concurrent affect were statistically controlled, joint attention and cooperation were not associated. We explain differential social cognition outcomes in terms of the significant influences of previous engagement experiences and affect, in addition to cognition. Our study highlights developmental processes that underpin the emergence of social cognition in support of evolutionary continuity

Beyond pairwise clustering

We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms