The    purpose    of    Ohio    University’s    SCOPE    Lab    is    to    conduct    empirical    and    theoretical research   on   the   nature   of   concept   learning   behavior,   perception,   and   inference   in   humans and   non-human   animals.   Our   research   converges   on   a   fundamental   question:   namely,   how does   relational   cognition   (i.   e.,   the   human   capacity   to   apprehend   relationships   between entities   or   their   structure)   determines   and   influences   key   cognitive   capacities   such   as perception,   concept   learning,   memory,   and   decision   making.   Accordingly,   a   key   aspect   of our   research   involves   the   development   of   phenomenological   and   algorithmic   models   of these   cognitive   capacities   as   informed   by   relational   cognition.   Phenomenological   models are    mathematical    higher    order    descriptions    of    phenomena    in    terms    of    the    exact mathematical   relationships   between   the   variable   quantities   that   purportedly   determine   the phenomena.        These    models    are    very    much    like    the    models    encountered    in    classical Physics.   On   the   other   hand,   algorithmic   models   are   descriptions   of   the   mechanisms   that presumably    determine    phenomena.    Often,    the    mathematical    methods    and    theories necessary   to   construct   the   most   effective   and   parsimonious   phenomenological   models   are not   known.   Thus,   we   are   also   committed   to   the   development   of   mathematical   modeling frameworks   that   better   capture   the   particular   structures   in   question.   To   this   effect,   we   have proposed    a    variety    of    formal    frameworks    for    modeling    human    concept    learning    and categorization.     These     have     been     based     on     complexity,     invariance,     similarity,     and information principles (Vigo, 2006, 2009, 2011, 2013). Our   empirical   work   and   approaches   are   broad   in   scope.   Recently   we   have   been   exploring human     concept     learning     and     categorization     using     eye     tracking     technology.     More specifically,   we   use   eye   tracking   techniques   to   explore   correlations   between   saccades   and the   concept   learning   behavior   predicted   by   a   variety   of   mathematical   models,   including   the concept    invariance    model    (Vigo,    2009,    2011,    2013).    Other    research    activities    in    the SCOPE    Lab    include,    but    are    not    limited    to,    the    development    of    mathematical    and computational   models   that   predict   decision   making   behavior   as   a   function   of   similarity assessment,    dissimilarity    assessment,    and    categorization.    Also,    we    are    interested    in researching   how   humans   judge   similarity   and   dissimilarity   between   structural   or   configural stimuli   such   as   human   faces.   In   related   work,   we   have   proposed   a   mathematical   model   of similarity   that   predicts   the   empirical   similarity   ordering   of   a   key   class   of   configural   stimuli associated   with   deductive   inference   (Vigo,   2009).   Last,   but   not   least,   the   SCOPE   Lab conducts   empirical   and   theoretical   research   on   problem   solving   behavior   in   mathematical domains   such   as   geometry,   algebra,   and   physics,   and   on   the   nature   of   aesthetic   and temporal judgments.  
Ψ = kIα ψ = pe-kФ^2