Dual Categories Research Articles

The Elusive Progress of Prosodical Study: Essays in Honor of Thomas Cable

The Elusive Progress of Prosodical Study: Essays in Honor of Thomas Cable

Entanglement duality in spin-spin interactions

We examine entanglement of thermal states for spin-1/2 dimers in external magnetic fields. Entanglement transition in the temperature-magnetic-field plane demonstrates a duality in spin-spin interactions. This identifies a pair of dual categories of symmetric and antisymmetric dimers with each category classified into toric entanglement classes. The entanglement transition line is preserved from each toric entanglement class to its dual toric class. The toric classification is an indication of the topological signature of the entanglement, which bring about topological stability that could be relevant for quantum information processing.

The Distinction between “<i>shi</i>” 師and “<i>kujie</i>” 苦節 in Baochang’s <i>Mingseng zhuan</i>

By utilizing previous studies that have identified the biographies of the monks included in the now-lost Mingseng zhuan 名僧伝 from the Gaoseng zhuan 高僧伝, this paper analyzes the uneven distribution of social traits among the monks who were categorized as “shi” 師 and “kujie” 苦節 in the Mingseng zhuan, and proposes the possibility that Baochang’s use of the dual categories of “shi” and “kujie” in the Mingseng zhuan reflected the dualistic class structure of the early medieval Chinese saṃgha.

Categorical joins

We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. Our main theorem says that the homological projective dual category of the categorical join is naturally equivalent to the categorical join of the homological projective dual categories. This categorifies the classical version of this assertion and has many applications, including a nonlinear version of the main theorem of homological projective duality.

Möbius Polar Coordinate System Based on Entangled Pull Back of Contradictory Oneself and Its Topos

In this paper, the emergence of the contradiction oneself of object u is not only attributed to a mechanism that opposite transmission between the function x(t) that carrying the location information of u and its returned back x−1 (t−1) and is meeting at a contradiction point, but also is conversed into the questions: “How long time will be taken for the function x(t) transports from own position to v with the velocity , and return back?” It is shown that not only a pair of dual categories and their presheaft and topos can be induced by x(t) and x−1 (t−1), but also a Möbius Entangled Polar Coordinate System can be established by an entangled pull back and a dual of mirror manifolds. In this way, a framework that runs through Philosophy, Information, Mathematics, Physic, Logic to Neural Network can be constructed too.

Math Education in Intercultural Contexts: a logical-mathematical interpretation for duality Kaingang Kamé-Kairu

Abstract: The aim of this paper is to present the results of research carried out in a Mathematics and Science training program for indigenous teachers of the Kaingang ethnic group by the Unochapecó in the municipality of Chapecó, Santa Catarina, Brazil. Based on the paradigm of ethno mathematics, one of the objectives of the program is to look for relations between traditional indigenous thinking and classical mathematics. We propose an analogy between logical-mathematical binary calculation systems and the Kaingang thought system expressed in its social organization and supported by two opposite and complementary dual categories: Kamé-Kairu. Our hypothesis postulates a certain similarity between the binary logic used for example, in logical circuits, and the binary system with which the traditional Kaingang culture encodes its social, natural, and even supernatural world. The binary pair Kaingang, Kamé-Kairu serves to codify relations of kinship, exchange, and alliances of the tribe, as well as the natural world that surrounds them. The analogy formulated provides interesting information for mathematical and scientific education in intercultural contexts.

ПРОБЛЕМА СУЩЕСТВОВАНИЯ И ПРИНЦИП ДОПОЛНИТЕЛЬНОСТИ ФИЛОСОФСКИХ КАТЕГОРИЙ

The paper introduces a new principle called the principle of duality of philosophical categories by example of the four pairs of concepts: perception/accepting, recognition/support, believing/supposition, thing/would. This principle consists in the following: certain philosophical categories cannot be correctly considered with-out a parallel study of dual categories. We also consider the problem of the relation between the notions of being and existence and the connection between categories related to existence and three dimensions of time.

Unpacking distinction within mobility: Social prestige and international students

AbstractThis paper investigates the complex ways in which young people engage in social distinction within international mobility. The study offers novel conceptual and empirical insights by examining how distinction and social advantage is reproduced through short‐term student mobility from the Global North to the Global South. In doing so, it elucidates the iterative process of distinction‐making within mobility and argues that young mobile people negotiate a tension between different forms of distinction. Specifically, it unpacks and conceptualises distinction into dual categories—collective and individual—and suggests that students alternate and waver between these categories in order to both validate and elevate their position within a mobility hierarchy. The paper also considers how particular places are viewed as more distinctive and affording greater gains in cultural and symbolic capital. It concludes with future interrogations and ways forward for research on international mobility and distinction.

New-from-old full dualities via axiomatisation

We study different full dualities based on the same finite algebra. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too. We use this theorem to obtain a better understanding of several important examples from the theory of natural dualities. We also clarify what it means for two full dualities based on the same finite algebra to be different. Throughout the paper, a fundamental role is played by the universal Horn theory of the dual categories.

‘Oh Joy, Oh Rapture’: The Oily Chart Opera Company reflects the enduring charm of Gilbert and Sullivan in South Africa

ABSTRACTFor over four decades ‘The Oily Chart Opera Company’ have annually produced and performed a Gilbert and Sullivan Savoy opera in Pretoria, South Africa. In this strictly amateur group, designed to allow busy people to participate over six to seven weeks, members undertake all the roles on stage as well as making costumes and stage sets. Unique to the group is a single music ‘coach and accompanist’ having served for 45 years and many of the current members having performed in all of the Gilbert and Sullivan operas more than once. Data was gathered in a survey forming part of a research project Spirituality and Well-being: Music in the community. Interpretative Phenomenological Analysis was used to code the data into four broad themes: Joining, Learning and Leadership, Benefits of Community Music, Connections to Well-being and Spiritual Connections. The findings show the typical benefits experienced by those who perform regularly in groups, although this group draws special joy from their strict focus on Gilbert and Sullivan's operas. They also understand the spiritual connection to their music in the familiar dual categories of religious and secular spirituality. This particular group of performers is keeping Savoy operas alive in modern-day sub-Saharan Africa.

The World's Oldest Church: Bible, Art, and Ritual at Dura-Europos, Syria by Michael Peppard

Reviewed by: The World's Oldest Church: Bible, Art, and Ritual at Dura-Europos, Syria by Michael Peppard Joan Branham Michael Peppard The World's Oldest Church: Bible, Art, and Ritual at Dura-Europos, Syria New Haven: Yale University Press, 2016 Pp. xi + 320. $50.00. Dura-Europos—arguably the most important archaeological discovery in the twentieth century for the history of art in early Judaism and Christianity—forever changed scholarly views on how these two communities formulated their identities in the third century. The spectacular preservation of the site on the outskirts of the Roman empire presented scholars with exciting "firsts." The synagogue displays the first known Biblical narrative cycle within a sophisticated visual [End Page 340] system, forcing scholars to rewrite the history of Jewish art, its influences, and its relationship to aniconic traditions. The baptistery, the oldest securely datable church, offers a tantalizing glimpse into the ritual space of pre-Constantinian Christianity and some of the first New Testament artistic representations. Now, nearly a century after its unearthing, Michael Peppard boldly compels us to reexamine long-established interpretations of texts and images and view the baptistery with fresh eyes. Peppard draws methodologically on a number of scholars, including Jas; Elsner, Robert Nelson, Robin Jensen, and Dominic Serra, stating his goal is "to provide new possibilities for visual exegesis by opening up the treasury of textual resources from early Christianity and attending to ritual contexts" (34). The book—well written, like a thriller in pursuit of decoding visual symbols—sets out to 1) examine non-canonical texts, recently attributed patristic texts, and neglected artistic comparanda in relation to the site, 2) shift the focus of Syrian baptism from water to oil—both real and represented—as a ritual substance of anointing, sealing, stamping, marking, and messianic light, and 3) privilege ritual action as the primary context for interpreting the baptistery's artistic program, thereby reconstructing the experiential perspective of the participant in the space. For example, we follow in the footsteps of the neophyte Isseos—attested to in an inscription—as he makes his way through actual thresholds, processions, and spaces accompanied by represented thresholds, processions, and spaces. Peppard's insistence on the embeddedness of the baptistery's paintings in their ritual setting leads him to employ the dual categories of optic and haptic, proposed by Annabel Wharton, as ways of experiencing images. Peppard argues that the upper register of images—healing of the paralytic, walking on water—function optically, as a single visual sign of a text or historical moment. But the lower portion functions haptically, the meaning derived in the inherent physicality of the images. Indeed, the lower figures in procession are noticeably near life size, placed directly at the viewer's level, and move toward the baptismal font in the same direction as the participant. The figures mirror, echo, and reinforce the actions of the initiates. Peppard points out that a woman named Hera even carved her name in the wall beside the head of one of the processing women, perhaps identifying haptically with the figure. While helpful, the optic/haptic approach raises questions, such as the role of gender in the relationship of painted figures to participants. Peppard argues that the soldiers and military population of this town would have resonated with the armed David and Goliath scene as they entered the baptistery. How then does the same military population or our neophyte Isseos relate to the painted procession of women? Likewise, how does Hera relate to the military scene of David? Peppard addresses gender questions by turning to the important work of Elizabeth Clark and others for analyses of early Christian texts that describe initiates, both male and female, in non sex-specific terms, both as married to Christ (139). Such literary figurations are key to what Peppard calls the "heart of the book"—unlocking the meaning of the enigmatic procession of veiled women. Usually interpreted as women at Jesus's empty tomb, Peppard identifies the wall painting as an altogether different subject: the Parable of the Wise and Foolish [End Page 341] Virgins/Brides of Christ. Although there are no other contemporary images of this parable, Peppard writes that it was "a...

State Policies toward Islam in Twenty Countries in Western Europe: The Accommodation of Islam Index

AbstractThis study creates an index that reveals the extent to which Western European countries accommodate Islamic traditions and practices. The index covers six realms in which Muslim communities seek accommodation: (1) education, (2) chaplaincy services, (3) mosques, (4) cemeteries, (5) Islamic attire, and (6) halal food. The study examines and quantifies the state policies in twenty Western European countries on both national and municipal levels with a particular focus on actual implementation. Results indicate that Western European countries vary widely in terms of their accommodation of Islam. There are also notable within-country differences, due in part to regional governments, as they also make and/or implement policy decisions. Both between- and within-country variations in the accommodation of Islam reveal a variety of nuances, and blur dual categories, such as ethnic-civic and assimilationist-integrationist.

Continuous cohomology and homology of profinite groups

We develop cohomological and homological theories for a profinite group G with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite G -modules, respectively. The standard results of group (co)homology hold for this theory: we prove versions of the Universal Coefficient Theorem, the Lyndon–Hochschild–Serre spectral sequence and Shapiro's Lemma.

A COMPARISON OF THE INTERACTION OF PRONOMINALS AND WORD ORDER IN NARO AND GǁANA

ABSTRACTThis article compares PGN markers, the pronoun system and word order in declaratives in Naro ǁGana. These languages are similar in that (a) nouns are marked for person, gender and number; (b) both have complex pronoun systems; (c) the plural and dual categories distinguish inclusive from exclusive pronouns; (d) main lexical items in both languages can be focused through fronting. They differ in that ǁGana NPs are marked for nominative and oblique case through the PGN marker, while in Naro this is not so. In Naro if constituents are re- ordered, the PGN marker of the fronted constituent hosts the PGN marker of the subject NP, thus identifying the subject. The use of pronouns in a sentence impacts word order at sentential level in Naro but not in ǁGana. PGN markers are obligatory for subjects only in ǁGana.

The Question of Alterity and the Problem of Encounters, Communication, and Dialogue

L'anaiyse de la perception d'autrui rencontre la difficulte de Principe que souleve le monde culture!, puisqu'elle doit resoudre !e paradoxe q'une conscience vue par !e dehors, d'une pensee qui reside dans!' exterieur, et qui donc au regard de !a mienne, est deja sans sujet et anonyme --Merleau-Ponty Nous naissonsgrace a autrui, nous vivons avec autrui, nous devrns mourir un jour avec ou sans autrui.Comment concevoir I'existence humain et meme I'humanite de I'homme sans !a relation a autrui sans qu'elle soit assume? --Dominique Janicaud Alterity was the essential discovery of great voyages undertaken in 15th and 16th centuries. The exploration of new continents confronted Europeans with people different from them, whom they did not even imagine their existence. Before savages, these primitive people who seemed to live near nature, Europeans adopted diverse perspectives. For some respect, curiosity, interest; for others assimilation and predation. Europe, from 16th century to 19th century, whether in the African, or Asian continent, intended to subject the Other, to exploit, to convert it to a culture, to European civilization, the conveyor of progress. For the Other is difference, and difference is dreadful, appalling, also, it must be driven underground. Faced with encounters, what has been the attitude of writers, philosophers, etc., across the centuries? Some denounced injustices, seeing themselves as defenders of the oppressed and awakeners of consciences. Others, on the contrary, where the mouth pieces of the dominant discourse, the apostles of the colonial order, considering that civilization and progress justify all the violence done against people considered as inferior. In the 21st century the problem of alterity yet exists and it still goes unanswered. Also, in the United States it is a constant subject of debate in philosophy, especially in continental philosophy. Philosophy, specifically Western philosophy, has a horror of the notion of the other; it prefers Being that has no alterity. Philosophy as such is essentially structured around Being, immanence, and autonomy. The primary behavior of the world at large, is positioning. Further to me, is the unknown; the inaccessible, and practically everyone. Then there is an approach which can be one of resentment, reciprocity without recognition, contract (which implies exchange, competition, and defiance) and the gift. Into the bargain, the fundamental problem in contemporary philosophy, especially contemporary continental philosophy, is the importance it accords to relation, which is primarily difference, the difference between A and B. These two people can hardly understand themselves inasmuch as they are different, therefore, they are doomed to mutual misunderstanding thanks to their differences. By laying too much emphasis on difference, there is a tendency to show the abyss that separates people. Now, all communication supposes something that is common. If I had nothing in common with the other, I could not communicate with him. It is necessary that sameness prevails over the other for communication to become possible. If I am incapable of seeing in front of me a human being, if I see only what I think by representing a Jew, a Moslem, or an American, black etc., it is clear that the image of the other contributes to reinforcing separation and to render impossible all communication. Post-war currents of thought have insisted overmuch on alterity to the disadvantage of unity. Contemporary thinkers as such, seem to have misread the Greeks. In existence, Plato emphasizes, things participate in the Sameness and Other. Nature surmounts in advance our dual categories. Nature as such promotes difference, but it promotes difference only within the identical. There is in reality a reciprocal inclusion of alterity and identity. Difference never completely differs; resemblance never resembles completely. …

Topological duality and lattice expansions, I: A topological construction of canonical extensions

The two main objectives of this paper are (a) to prove purely topological duality theorems for semilattices and bounded lattices, and (b) to show that the topological duality from (a) provides a construction of canonical extensions of bounded lattices. In previously known dualities for semilattices and bounded lattices, the dual spaces are compact 0-dimensional spaces with additional algebraic structure. For example, semilattices are dual to 0-dimensional compact semilattices. Here we establish dual categories in which the spaces are characterized purely in topological terms, with no additional algebraic structure. Thus the results can be seen as generalizing Stone’s duality for distributive lattices rather than Priestley’s. The paper is the first of two parts. The main objective of the sequel is to establish a characterization of lattice expansions, i.e., lattices with additional operations, in the topological setting built in this paper.

The IgE repertoire in patients with food allergy resolved at component level

Background Currently, more than 1200 purified allergens with defined structures are available. Some of them are used for food allergy diagnostics. We aimed to assess individual patientssensitizationtization profiles of food allergens by means of component resolved diagnosis. Methods Serum samples were analysed by microarray Immuno CAP ISAC (Phadia), which allows to detect specific IgE against more than 100 of molecular components. We have retrospectively analyzed 153 patients with proven food allergy, 96 of them being children under 18 years. We recorded occurence of early reactions including OAS and anaphylaxis and also delayed reactions (atopic eczema and eosinophilic gastrointestinal diseases). IgE antibodies against individual food alergens were divided to groups based on their origin and affiliation to any of panalergen families. With this approach, antibodies against ten groups of alergens were analyzed in indivi- dual age categories and diagnostic groups: cow' sm ilk allergens, hen's egg allergens, parvalbumins, lipid trans- fer proteins, flour allergens including gluten, vicilins, conglutins, cupin family allergens, 2S albumins and PR- 10 family proteins. Results As expected, in patients below age of 3 years, allergens to mild and egg occured most frequently. Suprisingly, however, we detected more than 40% of patients being sensitization against seed storage proteins (2 s albumins) and almost 30 % of patients have been sensitized by alergens of PR-10 group. In children allergic to peanut sensitization to proanafylactis alergens (Arah h 1, 2, 3) prevailed. In contrary, in older patients over 18 years we have found mainly sensitization to Ara h 8 from Bet v 1 family homologous proteins. Patients with eosinophilic gastrointestinal diseases, mainly eosinophilic esophagitis, demonstrated sensitization to Bet v 1 homologous pro- teins in more than 50% and almost 30% sensitization to allergens from seed storage protein families. Approxi- mately 20% of our patients had detectable antibodies against one or more of lipid transfer proteins. Conclusion CRD using microarray technics enables to detect IgE sen- sitisation profile not only in one patient, but also in a group of patients with defined age and diagnosis. This fact could contribute to optimalisation of diet according to possible cross-reactivity. Sensitization to proanaphylactic alergens, like LTPs and seed storage proteins, enables to detect individual risk of food induced anaphylaxis.

Module categories over graded fusion categories

Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,α) of C. We also describe functor categories over C (and in particular the dual categories of C). We use this in order to classify module categories over the Tambara Yamagami fusion categories, and their duals.

Natural dualities for three classes of relational structures

Motivated by the work of Hofmann [14] and Davey [7] on dualities for structures, we will construct natural dualities for the classes of quasi-ordered sets, equivalence-relationed sets, and reflexive (undirected) graphs. We describe the dual structures by giving finite sets of quasi-equations that axiomatise the dual categories. We also show that there is a natural connection between the duality we construct for finite quasi-ordered sets and Birkhoff’s representation theorem for finite ordered sets [2], and between the dualities constructed for quasi-ordered sets and equivalence-relationed sets.

Art as a ‘thing-in-between’: Negotiating boundaries and values in an art circuit event

By introducing the analytical concept ‘thing-in-between’, in other words a mediating entity acting from a border position between dual categories, the dynamics and processes of value creation and boundary work in an art circuit event in the south of Sweden is analysed. Drawing on nondualistic notions of the social-material world and more specifically on two paths of the works of Georg Simmel — his sociological theory of value and his concept of the triad as a social form — it is argued that art objects act as the third part in the art circuit experience. As intermediaries with subjective as well as objective qualities, they (re)order boundaries in the cultural/economic nexus of the art-trail: between the commercial and non-commercial; the public and private; between and among consumers and visitors, and between gazing and doing/touching modes of experiencing. Through the boundary work of the art circuit, three types of value emerge: ‘aesthetic consumption’, ‘vicarious life style consumption’, and ‘the value of being together’. It is further argued that these values are more or less socially consolidated, and more or less articulated in different communicative contexts, thus pointing at the situated, performative character of value construction.