CCI Reprographics (United States)

Summary We revive an old lateral-thinking puzzle by Michael Rabin, involving poisons with strange properties. We show that the puzzle admits several unintended solutions that are just as interesting as the intended solution. Analyzing these alternative solutions using game theory yields surprisingly subtle results and several unanswered questions.

Abstract On a projective variety defined over a global field, any Brauer–Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show that this subgroup can require arbitrarily many generators.

Let ϝ ( n ) \digamma (n) denote a multiplicative function with range { − 1 , 0 , 1 } \{-1,0,1\} , and let F ( x ) = ∑ n = 1 ⌊ x ⌋ ϝ ( n ) F(x) = \sum _{n=1}^{\left \lfloor x\right \rfloor } \digamma (n) . Then F ( x ) / x = a x + b + E ( x ) F(x)/\sqrt {x} = a\sqrt {x} + b + E(x) , where a a and b b are constants and E ( x ) E(x) is an error term that either tends to 0 0 in the limit or is expected to oscillate about 0 0 in a roughly balanced manner. We say F ( x ) F(x) has persistent bias b b (at the scale of x \sqrt {x} ) in the first case, and apparent bias b b in the latter. For example, if ϝ ( n ) = μ ( n ) \digamma (n)=\mu (n) , the Möbius function, then F ( x ) = ∑ n = 1 ⌊ x ⌋ μ ( n ) F(x) = \sum _{n=1}^{\left \lfloor x\right \rfloor } \mu (n) has apparent bias 0 0 , while if ϝ ( n ) = λ ( n ) \digamma (n)=\lambda (n) , the Liouville function, then F ( x ) = ∑ n = 1 ⌊ x ⌋ λ ( n ) F(x) = \sum _{n=1}^{\left \lfloor x\right \rfloor } \lambda (n) has apparent bias 1 / ζ ( 1 / 2 ) 1/\zeta (1/2) . We study the bias when ϝ ( p k ) \digamma (p^k) is independent of the prime p p , and call such functions fake μ ′ s \mu ’s . We investigate the conditions required for such a function to exhibit a persistent or apparent bias, determine the functions in this family with maximal and minimal bias of each type, and characterize the functions with no bias. For such a function F ( x ) F(x) with apparent bias b b , we also show that F ( x ) / x − a x − b F(x)/\sqrt {x}-a\sqrt {x}-b changes sign infinitely often.

Este artigo observa o tema da visualidade sob um ponto de vista filosófico crítico acerca do formalismo presente em teorias de percepção visual de autores contemporâneos do Design Gráfico, em específico no livro Gramática Visual (2015), de Christian Leborg. A abordagem crítica empreendida na análise foi a pós-estruturalista, que busca revisar discursos explicitando seus pressupostos universais, naturais e atemporais. Para tanto, contextualizamos o que pode ser considerado nos sistemas formalistas; descrevemos o método pelo qual a análise foi feita; apresentamos uma síntese das características identificadas e sua ligação com uma das tradições formalistas apresentadas por Michael Foucault no livro As palavras e as coisas (2000). O artigo se alinha ao eixo temático Design: história e teoria do P&D 2022, e busca contribuir com uma reflexão informada aos elementos constituintes do campo em sua dimensão epistemológica.

The digitization of museum collections has led to millions of digital representations of objects to be experienced, shared and discussed by online visitors.In most cases, these digital copies live a life of their own, disconnected from the real objects they represent.'Hybrid museum experiences' seek to bring together the original object and digital technology to facilitate visitor experiences that are meaningful, personal and inclusive.Combining the emotional and intellectual force of objects in museum spaces with the participatory, narrative and immersive potential of digital, hybrid experiences aim at reconfiguring the relationship between the visitor, the exhibit and the museum that surrounds them.This book is an ideal reading for anyone interested in museums who is open to an ambitious yet deeper and more nuanced approach to digital technology.Although it is mostly written by academic researchers, it has been informed by work with a variety of museum practitioners, including the authors of this preface.We met as part of the action research strand of the GIFT project, which brought together museum professionals from f ive different countries.Although we represented a variety of museums differing greatly in scope and size, we recognized several shared challenges.How do we get more of our colleagues working with digital technologies?How do we create genuinely audience-focused experiences?How do we embed experimental practice into our organizations?These are thorny questions which resist simple solutions and require a good deal of honesty and self-awareness to try and answer.The workshops supported by GIFT created a safe space for reflection, discussion and using design thinking tools to work collectively toward common goals.Moreover, by establishing a dialogue between different museum sectors, country borders and various disciplines (design, academia, cultural heritage, visual arts, computer science) it equipped those discussions with a rich conceptual vocabulary that helped all the participants to rethink what a museum can mean to its visitors.PrEfacE 13