The state space of a quantum system is defined; kets and bras are introduced, and their inner and outer products are defined; adjoint, hermitian , and unitary operators are introduced; representations of states and operators on discrete and/or continuous bases are discussed; the properties of commuting hermitian operators are examined; tensor products are defined.

Generative phonologists share the goal of modeling the internalized grammars that allow members of a linguistic community to produce and understand utterances they have not previously encountered. But while most generativists assume that the internalized grammar maps lexical to surface representations, they may disagree on the nature of that mapping, the makeup of the mental representations of phonological structure, and the role of universal well-formedness constraints in grammar. This chapter surveys analyses of data from multilinguals, foreign language learners, and loanword adapters within different generative models, exploring both strengths and limitations of competing approaches. Issues addressed include the role of phonological vs. phonetic structure, the relationship between the production grammar and the perception grammar, and the role of putative innate learning biases vs. factors such as input frequency and perceptual salience.

Uncle Tom’s Cabin, Harriet Beecher Stowe’s antislavery novel, was a tremendous success and the source of intense polemic when it first appeared in 1852. Since then, the novel has never entirely disappeared from the scene and has remained the locus of heated discussion on the representation of race and on race relations in the United States. This chapter will attempt to trace the role Uncle Tom’s Cabin – Stowe’s novel, but also its rewritings, tie-ins, and adaptations – has played in discussions of race in the United States since the 1850s. The first part will investigate the inception of the novel, its strategies, publishing circumstances, and immediate reception. The second part will focus on the afterlife of Uncle Tom’s Cabin, both in terms of scholarly commentary and popular appropriations.

Symbolic tools represent, organize, and transform our knowledge of objects and events. The acquisition and internalization of symbolic tools change the way we think about the world. Different cultural subgroups use different symbolic tools and as a result, they shape their cognitive processes, even those as basic as spatial memory, differently. Moreover, some of the psychological functions that at the first glance should progress developmentally irrespective of the person’s experience actually depend on the acquisition and mastery of specific tools, for example, the graphic representation of objects. Even in societies with formal educational systems, the teaching of symbolic tools as tools is often neglected. Tables, graphs, and formulae appear as a part of the content material instead of being learned as specific tools. Many of the problem-solving mistakes made by students, for example in international exams such as PISA and TIMMS, reflect their poor mastery of symbolic tools rather than a lack of curricular knowledge. Educational interventions aimed at teaching students how to identify and apply the instrumental properties of symbolic tools lead to improved problem-solving in subjects ranging from mathematics to foreign language learning.

This chapter explores literary and cinematic works that capture the emergence of technogenic life-forms in war zones through the artificial vision of the drone: that terror-inducing aerial surveillance apparatus and killing machine that is planetary in its reach and catastrophic in its impact. By technogenic life-forms, I mean machinic abstractions of the organic human form that are available for manipulation, expulsion, and annihilation. These life-forms are the product of a scalar transformation of ordinary human vision through the composite digital infrastructure of the drone. The aesthetic repertoire of the chapter ranges from novels such as Richard Clark’s The Sting of the Drone (2014) and Namwali Serpell’s The Old Drift (2019), films such as Madiha Tahir’s Wounds of Waziristan (2013) and Atef Abu Saif’s war diary The Drone Eats with Me (2016).

Working memory and language are tightly intertwined cognitive systems. Working memory enables language acquisition and vocabulary expansion; it supports both language comprehension and language production. Language, on the other hand, provides key representations that support efficient and robust encoding and maintenance of information in working memory, as well as the ability to compress information and the redundancy to reconstruct it in case of partial information loss. The close relationship can also be observed in the overlap and integration of brain systems and networks supporting working memory and language processing. This chapter examines the brain substrate of working memory and language processes, focusing on their interdependence, synergy, and the mechanisms underlying their close integration. It integrates key theoretical models and empirical evidence from behavioural and neuroimaging studies, computational modelling, and insights based on patterns of working memory and language dysfunctions due to brain injury and disease.

Chapter 10 focuses on representatations and warranties made by parties in IP agreements, as well as liability-allocation mechanisms such as indemnification. The chapter begins by discussing warranties of title (Loew’s v. Wolff) and general “corporate” warranties, then addresses warranties relating to performance (including malicious computer code) and remedial procedures. Disclaimers, exclusions from liabilty for consequential and indirect damages, and limitations of liability are also addressed. the chapter next discusses IP indemnification clauses, including a detailed analysis of the drafting and negotiation of such clauses (So. Cal. Gas v. Syntellect). It concludes with a discussion of insurance requirements and clauses.

In France, Cécile Goï questions the notion of cultural otherness while mocking the times when she played with the Gypsies in her small village as a child. This experience was the seed of her first "gesture of indignation" in response to ostracism related to cultural and linguistic diversity.  Making sense of such experiences produced to a profound reflection on social cohesion, equal opportunities, and educational success, in particular for newly arrived students.

This chapter argues that the discursive construction of the herders as terrorists exacerbates suspicion and fear in herder–farmer relations and further destroys the prospect of peace in Nigeria. Applying a corpus-assisted critical discourse analysis to analyze the representations of the main actors in the conflict, 175 news headlines of seven popular Nigerian broadsheet newspapers were studied. The study reveals that the herdsmen are consistently constructed as terrorists, as violent actions such as unprovoked attacks and killings are attributed to them. However, the farmers are constructed as non-violent and as the victims. Hence, the press explicitly constructs the herder–farmer conflict in terms of the “killer-herdsmen” script with which the herders are generally evaluated.

We give a mini-review of representations of the Poincaré group, emphasizing the role of irreducible unitary representations in identifying ‘elementary particles’. Young tableaux are used to identify irreducible representations of the little group and thus the particle content of the excitation spectrum of a string.

This chapter analyses the move of historians away from text and towards the interpretation of visuals. Starting with art history’s turn to the social and the cultural, it traces the interest of historians for an ever wider group of images, including popular images. It also highlights the emergence of perspectivalism and transdisciplinarity in the field of visual history. The main bulk of the chapter is taken up with presenting a range of examples showing how the visual turn in historical writing has contributed to deconstructing national identites, class identities and racial/ethnic identities. Ranging widely across different parts of the globe it also discusses the deconstruction of religious and gender identities through visual histories that have in total contributed much towards a much higher self-reflexivity among historians when it comes to the construction of collective identities through historical writing.

The social life of animals poses specific adaptive challenges that may be cognitively different to challenges from ecological adaptations to their physical environment.Social cognitive adaptations for dealing with other agents are evolutionarily remarkable in that they automatically become an adaptive challenge that may trigger counter- or co-adaptations. This chapter discusses three main problems in social cognition: first, the issue of mentalism or theory of mind, or whether social cognitive adaptations in animals are based on mentalistic attribution skills that may involve representing the intentions and knowledge of others; second, the cognitive underpinnings of animal communication, with a focus on referential and intentional communication; and third, the problem of how animals know and represent the social relations structuring their groups. There is widespread debate about how the social knowledge and reasoning demonstrated in animal social behavior are exactly implemented. The traditional debate in comparative psychology between reductionist behavioristic explanations and complex cognitive explanations has become especially pronounced in social cognition. A widespread proposal is that the type of knowledge demonstrated by animals is ‘implicit,’ distinct both from the verbally expressible knowledge evolved by humans, and from low-level, reflex-like associative behaviours and habits. However, the key notion of implicit knowledge remains elusive and ill-defined.

The introductory chapter introduces the main questions that animate the book as a whole. It has a section on methods and a discussion of the theoretical and methodological traditions the book draws on. It elaborates on the stakes in construing Afghanistan as an ‘interve+G6nable object’. It uses an image of a textbook used in Afghanistan in the 1980s to show how knowledge about Afghanitan is produced and packaged and how it circulates around the world.

Turner and colleagues (this volume) have written a thoughtful and comprehensive overview of theory and research across a vast literature: environmental and sociocultural influences on the development of personality disorders (PDs). They review behavioral genetics studies and studies on the prevalence of PDs in different countries and from different socioeconomic backgrounds. They describe a wide variety of theories of how PDs develop and review environmental risk factors from early childhood adversity to the quality of communities. This commentary, focusing on borderline PD (for which there is the most research), extends this work in two ways. First, the authors propose an overarching theory of environmental and sociocultural influences on the development of PDs. Second, they add empirical support for two of the theories that Turner and colleagues present: attachment and biosocial theories. In this way, the authors aim to identify processes underlying the development of PDs that may be the focus of interventions. An appropriate intervention at the level of the individual would include Young’s Schema Therapy (Young, 1994), and at the level of the family system the Family Connections Program (Hoffman et al., 2005).

The bridging concept between the abstract and geometric is the theory of realizations. This chapter concentrates on symmetric sets, namely, finite sets on which a group of permutations acts transitively. After a discussion of their basic properties, the concept of their realizations is introduced, with operations on them (such as blending) showing that the family of their congruences classes has the structure of a convex cone. A key idea is that of the inner product and cosine vectors of realizations, which define them up to congruence. The theory up to this point is then illustrated by some examples. It is next shown that, corresponding to the tensor product of representations, there is a product of realizations. Another fundamental notion is that of orthogonality relations for cosine vectors. The different realizations derived from an irreducible representation of the abstract group may form a subcone of the realization cone that is more than 1-dimensional. These are looked at more closely, leading to a definition of cosine matrices for the general realization domain. There follows a discussion of cuts and their relationship with duality. Cosine vectors may have entries in some subfield of the real numbers, with implications for the corresponding realizations. The chapter ends with a brief account of how representations of groups are related to realizations.