Notion Of Duality Research Articles

Taste and Sentiment: Cartographies of Afropean Affiliation in Leonora Miano’s Soulfood Équatoriale (2009)1

Through a study of Soulfood Équatoriale (2009), a nostalgic collection of culinary short stories by Paris-based Cameroonian writer Leonora Miano (1973–), and her essay “Afropea” (Miano, Écrits pour la parole), this article relates culinary literary form to the AfroEuropean subjectivities. Located in the emergent field of foodways, the article examines the juxtaposition “Soulfood” as a signifier of histories of Afrodiasporic dispersal and African-American culinary tradition, with “Équatoriale” denoting the author’s personal trajectory from Cameroon to becoming a naturalized French citizen or AfroEuropean. Using the dual notions of taste and nostalgia to interrogate the affective multiple affiliation created by the translocation of soul food to the Francophone Afropean space, the article frames a nascent Afropean culinary culture as a site of subjectivation created by an entangled network of cultural roots and routes, which transcend cultural and linguistic borders.

Session types and subtyping for orchestrated interactions

In the setting of the π-calculus with binary sessions, we aim at relaxing the notion of duality of session types by the concept of retractable compliance developed in contract theory. This leads to extending session types with a new type operator of “speculative selection” including choices not necessarily offered by a compliant partner. We address the problem of selecting successful communicating branches by means of an operational semantics based on orchestrators, which has been shown to be equivalent to the retractable semantics of contracts, but clearly more feasible. A type system, sound with respect to such a semantics, is hence provided. The introduction of subtyping when interactions are orchestrated naturally leads to explicit subtyping, where coercions are functors on orchestrators. Besides, priority-governed selection policies (either at type- or process-level) are investigated in order to get rid of nondeterministic behaviours but those of the partner processes of the interactions.

Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations

We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential equations. We also develop applications concerning associated classes of stochastic partial differential equations (SPDEs). In particular, we study the support properties of probability laws corresponding to these SPDEs as well as provide applications concerning the ergodic and mixing properties of invariant measures for these stochastic systems.

Inertial properties in groups

‎‎Let $G$ be a group and $p$ be an endomorphism of $G$‎. ‎A subgroup $H$ of $G$ is called $p$-inert if $H^pcap H$ has finite index in the image $H^p$‎. ‎The subgroups that are $p$-inert for all inner automorphisms of $G$ are widely known and studied in the literature‎, ‎under the name inert subgroups‎. ‎The related notion of inertial endomorphism‎, ‎namely an endomorphism $p$ such that all subgroups of $G$ are $p$-inert‎, ‎was introduced in cite{DR1} and thoroughly studied in cite{DR2,DR4}‎. ‎The ``dual‎ ‎notion of fully inert subgroup‎, ‎namely a subgroup that is $p$-inert for all endomorphisms of an abelian group $A$‎, ‎was introduced in cite{DGSV} and further studied in cite{Ch+‎, ‎DSZ,GSZ}‎. ‎The goal of this paper is to give an overview of up-to-date known results‎, ‎as well as some new ones‎, ‎and show how some applications of the concept of inert subgroup fit in the same picture even if they arise in different areas of algebra‎. ‎We survey on classical and recent results on groups whose inner automorphisms are inertial‎. ‎Moreover‎, ‎we show how‎ ‎inert subgroups naturally appear in the realm of locally compact topological groups or locally linearly compact topological vector spaces‎, ‎and can be helpful for the computation of the algebraic entropy of continuous endomorphisms‎.

Schedulers and finishers: On generating and filtering the behaviours of an event structure

It is well known that every trace of a transition system can be generated using a scheduler. However, this basic completeness result does not hold in event structure models. The reason for this failure is that, according to its standard definition, a scheduler chooses which action to schedule and, at the same time, observes that the one scheduled last has occurred. Thus, scheduled events will never be able to overlap. We propose to separate scheduling from observing termination and introduce the dual notion of finishers which, together with schedulers, are enough to regain completeness. We then investigate all possible interactions between schedulers and finishers, concluding that simple alternating interactions are enough to express complex resolution. We also observe that when these interactions are independent, they may produce behaviours that are not satisfying some desired property that is intrinsic to the system. To filter these behaviours out, we extend our results by defining permissible pairs of schedulers and finishers. In contrast to independent interactions, this new concept allows us to control and observe concurrent executions with a granularity that is strictly higher than that provided by the bundle relation.

A dual approach to the theory of inverse split modules

Let [Formula: see text] be an arbitrary ring with identity, [Formula: see text] a right [Formula: see text]-module and [Formula: see text] a fully invariant submodule of [Formula: see text]. The notion of an [Formula: see text]-inverse split module [Formula: see text] has been defined and studied by the present authors recently. In this paper, we introduce its dual notion, namely, dual [Formula: see text]-inverse split module [Formula: see text]. This work is devoted to investigation of various properties and characterizations of a dual [Formula: see text]-inverse split module [Formula: see text]. We include applications for rings and cosingular submodules. We also deal with the notion of relatively dual inverse splitness to investigate direct sums of dual inverse split modules.

Subgroups generated by images of endomorphisms of Abelian groups and duality

Abstract A subgroup H of a group G is called endo-generated if it is generated by endo-images, i.e. images of endomorphisms of G. In this paper we determine the following classes of Abelian groups: (a) the endo-groups, i.e. the groups all of whose subgroups are endo-generated; (b) the endo-image simple groups, i.e. the groups such that no proper subgroup is an endo-image; (c) the pure-image simple, i.e. the groups such that no proper pure subgroup is an endo-image; (d) the groups all of whose endo-images are pure subgroups; (e) the ker-gen groups, i.e. the groups all of whose kernels are endo-generated. Some dual notions are also determined.

Cross-connections of linear transformation semigroups

Cross-connection theory developed by Nambooripad is the construction of a semigroup from its principal left (right) ideals using categories. We briefly describe the general cross-connection theory for regular semigroups and use it to study the {normal categories} arising from the semigroup $Sing(V)$ of singular linear transformations on an arbitrary vectorspace $V$ over a field $K$. There is an inbuilt notion of duality in the cross-connection theory, and we observe that it coincides with the conventional algebraic duality of vector spaces. We describe various cross-connections between these categories and show that although there are many cross-connections, upto isomorphism, we have only one semigroup arising from these categories. But if we restrict the categories suitably, we can construct some interesting subsemigroups of the {variant} of the linear transformation semigroup.

A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures

This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk (Synthese 12(2–3):228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation (the dual notion of connection). Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze (quasi-)separation structures and Grzegorczyk structures, and establish their properties which will be useful in the sequel. We prove that in the class of Urysohn spaces with countable chain condition, to every topologically interpreted representative of a point in the sense of Grzegorczyk’s corresponds exactly one point of a space. We also demonstrate that Tychonoff first-countable spaces give rise to complete Grzegorczyk structures. The results established below will be used in the second part devoted to points and topological spaces.

A formal approach to meaning

Building on the overlap between notions of duality and the principles of Formal Concept Analysis, we propose a way of quantifying the degree of meaningfulness of one aspect of a data set for defining another. Drawing on ideas from information theory, some familiar and some less familiar, we demonstrate not only how to maximize the meaningfulness in a dataset, but how to translate across datasets.

Doorway to the dharma of duality

One of the most exciting formal approaches in the sociology of culture involves the exploration of duality–that the meaning of any of one set of elements (for example, choices of cultural consumption) is the subset of persons to which it is linked (for example, the occupations of the persons who make this choice). We here generalize this notion of duality, which we call “Breiger classic,” to the case in which similarities between persons are constructed not on the basis of which cultural elements they choose or deploy, but how these cultural elements are themselves connected, which we call “Mega-Breiger.” We then consider how to look at the duality between cultural and social units within cultural formations, treating each cultural formation as a virtual social structure among cultural elements, which we call “Mondo Breiger.” We finally discuss the “Full Breiger” duality as the complete use of a person-to-person and person-to-cultural element data set to arrange relations among one set of cultural elements. We illustrate with an analysis of all the texts of the members of the first generation of the Frankfurt School of critical theory.

Session Types for Orchestrated Interactions

In the setting of the pi-calculus with binary sessions, we aim at relaxing the notion of duality of session types by the concept of retractable compliance developed in contract theory. This leads to extending session types with a new type operator of "speculative selection" including choices not necessarily offered by a compliant partner. We address the problem of selecting successful communicating branches by means of an operational semantics based on orchestrators, which has been shown to be equivalent to the retractable semantics of contracts, but clearly more feasible. A type system, sound with respect to such a semantics, is hence provided.

On the dual nature theory of bilateral series associated to mock theta functions

In recent work, Hickerson and Mortenson introduced a dual notion between Appell–Lerch sums and partial theta functions. In this sense, Appell–Lerch sums and partial theta functions appear to be dual to each other. In this paper, by making the substitution [Formula: see text] in the tail of the associated bilateral series of mock theta functions and universal mock theta functions, we demonstrate how to obtain duals of the second type in terms of Appell–Lerch sums defined by Mortenson for such functions. Then by using the substitution [Formula: see text] in duals of the second type of each bilateral series, we present how to translate between identities expressing [Formula: see text]-hypergeometric series in terms of Appell–Lerch sums and identities expressing [Formula: see text]-hypergeometric series in terms of partial theta functions. Indeed, we obtain only four duals in terms of partial theta functions of duals of the second type in terms of Appell–Lerch sums of bilateral series associated to mock theta functions. As an application, we construct Ramanujan radial limits by using these bilateral series with mock modular behavior in terms of Appell–Lerch sums for some order mock theta functions. This method is well-suited for the other order mock theta functions.

A trinity of duality: Non-separable planar maps, β(1,0)-trees and synchronized intervals

The dual of a map is a fundamental construction on combinatorial maps, but many other combinatorial objects also possess their notion of duality. For instance, the Tamari lattice is isomorphic to its order dual, which induces an involution on the set of so-called “synchronized intervals” introduced by Préville-Ratelle and the present author. Another example is the class of β(1,0)-trees, which has a mysterious involution h proposed by Claesson, Kitaev and Steingrímsson (2009). These two classes of combinatorial objects are all in bijection with the class of non-separable planar maps, which is closed under map duality. In this article, we show that we can identify the notions of duality in these three classes using previously known natural bijections, which leads to a bijective proof of a result from Kitaev and de Mier (2013).

Deconstructing high performance Nordic sport: the case study of women’s handball (the ‘team as method’)

The principal purpose of this study was to record and explore the changing coaching landscape within elite Norwegian women’s handball from 2003 to 2005. This was in relation to critically understanding the culture created within the context, and the precise role(s) of head coach Marit Breivik, the assistant coaches, and the athletes in question, in its creation. The significance of the paper lies in enhancing understanding the ‘Nordic model’ of society, inclusive of its emphasis on equality, tolerance, consensus and cooperation, and the ways in which this is constructed, explored and challenged within and through sport. When appointed in 1994, Breivik inherited a high performance system not unlike any other in international sport; one dominated by metrics, compliance and control. It was one she wanted to change to better reflect the Nordic values of integration, interdependence and egalitarianism. The study’s method comprised an in depth ethnography where the principal author spent two years embedded within the setting. The results, deduced from inductive analysis of the collected data, are discussed in terms of two principal themes. First, the initial attempts at culture change by Breivik and the inevitable resistance experienced; and second, the relational strategy she adopted to overcome such resistance (including that of establishing the ‘team as method’). Finally, a conclusion reflects on the meaning of such findings, touching on the dual explanatory notions of ‘progressive repair’ and that of the coach as a ‘virtuoso actor’.

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

SummaryA method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.

Duality for Graded Manifolds

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different category than the initial ones, namely graded polynomial (co)algebra bundles and free graded Weil (co)algebra bundles. Our results are then applied to obtain elegant characterizations of double vector bundles and graded bundles of degree 2. All these results have their supergeometric counterparts. For instance, we give a simple proof of a nice characterisation of $N$-manifolds of degree 2, announced in the literature.

Theatre and participation: Towards a holistic notion of participation

Abstract Participation is central to and essentialized in theatre and interactive arts. While scholars have articulated the importance of participation in arts, participation has also been considered a foundational principle in development discourse, and it is largely external. Beyond the notion of participation as an external force, which I term a verb-oriented notion of participation, is the noun-oriented notion of participation, which is innate and organically induced from within an individual and a group or community (collective). In this article, I discuss a dual notion of participation and a relational interaction between these notions, which can lead to a holistic insight on participation. Using a case study that deals with managing conflict and bullying in a secondary drama classroom, an applied theatre project among refugees in Australia, I explore how this holistic insight into participation can influence how participation is framed and conceptualized in any applied theatre project. I argue that participation has been framed using a onesided, verb-oriented approach, and I propose a holistic notion of participation as a tool to rethink, reposition, reconceptualize and re-evaluate participation in applied theatre practice.

All My Relatives: Exploring Nineteenth-Century Lakota Ontology and Belief

Abstract This article is a reinterpretation of the ethnohistorical literature on the Lakota or Western (Teton) Sioux from a Descolian animist perspective. Applying key insights from what has been called the “ontological turn,” in particular, the dual notions of interiority and physicality and an extended notion of personhood that includes nonhumans as well as humans, this article demonstrates how a new animist framework can connect and articulate otherwise disparate and obscure elements of Lakota ethnography, offering new and exciting insights, along with the potential for a deeper understanding of traditional Lakota culture.

Factorization of Observables

Categorical approach to probability leads to better understanding of basic notions and constructions in generalized (fuzzy, operational, quantum) probability, where observables—dual notions to generalized random variables (statistical maps)—play a major role. First, to avoid inconsistencies, we introduce three categories $\mathbb {L}$ , $\mathbb {S}$ , and $\mathbb {P}$ , the objects and morphisms of which correspond to basic notions of fuzzy probability theory and operational probability theory, and describe their relationships. To illustrate the advantages of categorical approach, we show that two categorical constructions involving observables (related to the representation of generalized random variables via products, or smearing of sharp observables, respectively) can be described as factorizing a morphism into composition of two morphisms having desired properties. We close with a remark concerning products.