On the link between mean square-radii and high-order toroidal moments

Multipole expansions of the source play an important role in a broad range of disciplines in modern physics, ranging from the description of exotic states of matter to the design of nanoantennas in photonics. Within the context of the latter, toroidal multipoles, a third group of multipoles complementing the well-known electric and magnetic ones, have been widely investigated since they lead to the formation of non-radiating sources. In the last years, however, the photonics community has brought to light the existence of a fourth type of multipoles that is commonly overlooked. Currently, different groups have provided different mathematical expressions to describe such sources, and they have been coined with different names; on the one hand mean-square radii, and on the other hand, as high order toroidal moments. Despite their clear physical similarity, a formal relation between the two has not yet been established. While explicit formulas for both types have been derived, they are not expressed in the same basis, and therefore it is not possible to draw a clear physical connection between them. In this contribution, we will bridge this gap and rigorously derive the connection between the two representations, taking as an example the cases of the nth order mean square radius of the electric dipole and the nth order electric toroidal dipole. Our results conclusively show that both types of representations are exactly equivalent up to a prefactor.

TOPICS, DOUBLE CODING AND FORM FUNCTIONALITY IN THOMAS ADÈS'S PIANO QUINTET

This article interrogates the formal and expressive roles of the opening horn-call topic in Thomas Adès's Piano Quintet (2001). Although William Caplin describes the relationship of topics to form as ‘rather tenuous’, he notes that some topics have a ‘likely’ formal relation.1 Within this, he includes the rising horn call as an initiating function. Drawing upon Charles Jencks’ influential concept of double coding, which describes a sign's ‘attempt to communicate with both the public and a concerned minority’,2 I show how the Piano Quintet's horn-call opening satisfies, on one level, the familiar (tonal) initiating formal function that Caplin describes but, understood in the context of two significant reversals of the horn call's characteristic rising contour to descending horn fifths (the openings of Beethoven's ‘Les Adieux’ sonata and Ligeti's Horn Trio), Adès's opening can be understood as transgressive. This Janus-faced interpretation of the opening bars engages both positively and critically with these references to the past, a double-coded understanding which points to Adès's continued popularity in both academic and concert spheres.

The Communicative Function of Non-Face Emoji "Folded Hands" in WhatsApp Interaction among Indonesians

This study aimed to examine the communicative functions of the non-face “folded hands” emoji that Indonesians use in WhatsApp interactions. Using descriptive qualitative, the data were analysed through the social semiotic approach proposed by Lemke (1998), the interactional sociolinguistic theory (Gumperz, 1982), and speech act theory. The data were taken from the messages that occurred naturally in several WhatsApp groups. It was re-transcribed and translated in English based on the theory by Dresner and Herring (2010). The findings revealed some functions of the non-face “folded hands” emoji in online communication. At the end of an utterance, it emphasizes message tone, politeness, and soft interaction. Furthermore, rather than this emoji expresses an emotion such as face emoji does, it performs illocutionary forces in communication such as thanking, apologizing, and asking. It is also performed in situational interaction in which the relation of speaker and interlocutor has a formal relation such as teacher-students and leader-staffs. This empirical research added to computer-mediated discourse literature by analyzing the communicative function of folded hands emoji in written discourse. Practically, it might help users interpret the emoji as an abstract concept in the messages.

A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory

A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section I.Many modifications of Turing machines cum quantum ones are researched in Section II for the Halting problem and completeness, and the model of two independent Turing machines seems to generalize them.Then, that pair can be postulated as the formal definition of reality therefore being complete unlike any of them standalone, remaining incomplete without its complementary counterpart. Representation is formal defined as a one-to-one mapping between the two Turing machines, and the set of all those mappings can be considered as “language” therefore including metaphors as mappings different than representation. Section III investigates that formal relation of “reality”, “representation”, and “language” modeled by (at least two) Turing machines.The independence of (two) Turing machines is interpreted by means of game theory and especially of the Nash equilibrium in Section IV.Choice and information as the quantity of choices are involved. That approach seems to be equivalent to that based on set theory and the concept of actual infinity in mathematics and allowing of practical implementations.

Inferential structures in old Romanian. The conditional and the concessive

The present study aims to highlight the fact that the conditional and concessive periods are two forms of manifestation of the hypothetical-deductive reasoning at the level of natural language. The evolution of the connectors has been described in diachrony, sometimes with the emphasis of the interference zones, with the semantic values imposed by the modal component of the predicativity and by the contextual determinism. The evolutionary analysis of the connectors has highlighted the fact that the old Romanian language, in order to impose the concessive procedural meaning, owns, like the other Romanic languages, a great area of creativity, but, unlike them, it also exercises its conservative character. The conception of the two syntactic relations as variants of the same system, studies the stylistic projection (the paradox and the oxymoron), the semantic and formal relation of the connectors and the implication of the adversative coordinating connectives in the polarization of the oppositions in the old Romanian language.

Thinking with and beyond the informal–formal relation in urban thought

This commentary to the special issue on ‘Transcending (in)formal urbanism’ reviews key threads common across the issue and opens up questions as to the work that the informal–formal dynamic does for urban studies. It points out the general agreement in that none of the papers rejects the utility of the category of informal and that the terms informal and formal still have value and utility. In doing so, the special issue articles offer three key contributions to demonstrate the ways in which the informal either composes or becomes a close partner to the formal, de-link informality from its more commonplace registers, and sketch how the formal and informal have always been blurred in practice. Centrally, this calls for a critical reflection on the structures of thought through which the informal–formal relation emerges. It advances an understanding of how informal and formal operate as a kind of ‘intellectual governmentality’ reiterating the same ways of seeing, carving up, and analysing the city, getting in the way of our ability to research urbanism differently. The appreciation of the informal–formal dynamic is situated as part of the challenge to build a more global urban studies that works with multiple ways of knowing and researching. To what extent does remaining within a structure of thought around the informal–formal relation enable or get in the way of that? Borrowing alternatives from movements to ‘provincialising’ that structure of thought, this commentary calls for a renewed interest in the potential, and limits, of the informal–formal inheritance in urban thought.

The Ruins of Inter-Americanism

During the early Cold War, inter-Americanism often took shape in the genre of postromantic meditations on pre-Columbian ruins. These ruin poems are usually understood as expressions of universal humanism, exercises in postmodern tourism, symptoms of neo-imperial fortune hunting, or preludes to 1970s ethnopoetics. By contrast, the chapter argues that ruin poems galvanized by Pablo Neruda’s “Heights of Macchu Picchu” and Charles Olson’s “The Kingfishers” respond to the rapid demise of the movement for hemispheric democracy. Through their identifications with indigenous civic histories, poets critiqued the collapse of political and cultural inter-Americanism. Moving beyond poets like Neruda and Olson who had previously maintained a formal relation to Good Neighbor diplomacy, it shows how even Allen Ginsberg’s poetic theories developed during sojourns in Mayan Mexico, and the tropes of ruin poetry subtend the “destroyed” generation in “Howl” (1956), as well as poems by writers in his cohort such as Philip Lamantia and Ernesto Cardenal.

On relation between constraint answer set programming and satisfiability modulo theories

Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link is obscured as the terminology and concepts used in these two research areas differ. In this paper, we connect these two research areas by uncovering the precise formal relation between them. We believe that this work will boost the cross-fertilization of the theoretical foundations and the existing solving methods in both areas. As a step in this direction, we provide a translation from constraint answer set programs with integer linear constraints to satisfiability modulo linear integer arithmetic that paves the way to utilizing modern satisfiability modulo theories solvers for computing answer sets of constraint answer set programs.

Enablers and inhibitors in causal justifications of logic programs

In this paper, we propose an extension of logic programming where each default literal derived from the well-founded model is associated to a justification represented as an algebraic expression. This expression contains both causal explanations (in the form of proof graphs built with rule labels) and terms under the scope of negation that stand for conditions that enable or disable the application of causal rules. Using some examples, we discuss how these new conditions, we respectively callenablersandinhibitors, are intimately related to default negation and have an essentially different nature from regular cause-effect relations. The most important result is a formal comparison to the recent algebraic approaches for justifications in logic programming:Why-not ProvenanceandCausal Graphs. We show that the current approach extends both Why-not Provenance and Causal Graphs justifications under the well-founded semantics and, as a byproduct, we also establish a formal relation between these two approaches.

Placebo Reforms

I study a dynamic model of strategic reform decisions that potentially affect the stochastic evolution of a publicly observed economic variable. Policy makers maximize their evaluation by a boundedly rational public. Specifically, the public follows a rule that attributes recent changes to the most recent intervention. I analyze subgame perfect equilibrium in this model when the economic variable follows a linear growth trend with noise. Equilibrium is essentially unique and stationary, bearing a subtle formal relation to optimal search models. Policy makers tend to act during crises, display risk aversion conditional on acting, and prefer interventions that induce permanent noise. (JEL D78, D83)