Dyadic Representation Research Articles

The Pitkinian public: representation in the eyes of citizens

Democracy is backsliding in Europe and around the world as citizens’ trust in elected representatives and institutions wanes. Representation theories and studies have mostly centred on the representatives, rather than the represented. But how do citizens perceive political representation? Are their perceptions of any consequence at all? In this paper, we set forth a framework of representation in the eyes of citizens, based on Pitkin’s classic concept of representation in conjunction with Weissberg’s distinction between dyadic and collective representations. We use Israel as a proof of concept for our theoretical framework, employing an original set of survey items. We find that, in keeping with Pitkin’s framework, citizens perceive representation as multidimensional and depreciate the descriptive and symbolic—the standing-for—dimensions. Furthermore, citizens’ democratic attitudes are shaped by collective representation by the parliament rather than by dyadic representation by an elected representative. We conclude with a call for a greater focus on representation from the citizens’ standpoint.

Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrödinger Equations

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R(t)) representing another observable. In the language of physics, the information carried by R(t)≠R†(t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ(t). From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ(t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the “kinematical input” operator R(t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a(t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R(t) mimicking the birth of the Universe (“Big Bang”) at t=0.

Orientations of golden-mean matroids

Bland and Las Vergnas proved that orientations of binary matroids are induced by totally unimodular representations. (A related result is due to Minty.) Lee and Scobee proved that orientations of ternary matroids are induced by dyadic representations. In this paper we prove that consistently ordered orientations of quaternary matroids are induced by golden-mean representations.

Mediated Representation at the Age of Social Media: How Connection with Politicians Contributes to Citizens’ Feelings of Representation. Evidence from a Longitudinal Study

ABSTRACT Modern democracies are built around the idea of representation: the electorate is represented, and perhaps more importantly, should feel represented. Yet recent decades have been marked by a growing gap between citizens and the political system. The emergence of new, more direct communication channels such as social media gave rise to expectations that the two sides can be brought closer together. This study investigates whether a connection with politicians and parties via social media platforms can enhance citizens’ feelings of being represented by a certain politician or party (dyadic representation), or by the entire parliament (collective representation). Our data come from a two-year panel study, covering four Israeli elections. Findings demonstrate that passive (receiving political information), but not active (producing political information) connection increases dyadic representation perceptions. Collective representation perceptions, by contrast, were not affected by either type of connection. Furthermore, our analysis does not demonstrate a reverse causal order; we did not find evidence supporting the idea that representation perceptions influence connection with politicians or parties. The upshot of our findings is that unidirectional communication between politicians and citizens on social media can foster citizens’ feelings of being represented in the political arena and of closeness with the political elites. That said, such effects were obtained only with regard to dyadic representation and are therefore limited in scope. The study contributes to the ongoing theoretical debate concerning the complex relations between new technologies, citizens, and political elites.

Dyadic representation in parliamentary democracy in Japan

AbstractThis study evaluates dyadic representation, that is, the link between the policy preferences of the constituencies and their representatives in the Japanese Lower House (LH). More specifically, this study examines how the within-party variation in policy positions among party candidates corresponds with that across their districts. By examining a series of candidate surveys conducted between 2003 and 2012 as well as the local employment structure, this study maps the association between the policy preferences of constituencies and those of their district candidates for two major parties. Specifically, candidates were found to take more rural-oriented positions on economic policies when running in districts with rural employment structures, while there remained a clear difference between parties. Moreover, this study demonstrates that constituencies accord more votes to candidates who better represent their preferences, strengthening the link by electing those who fulfill the responsibility beyond their party label.

The Dyadic Representation Theorem Using Smooth Wavelets with Compact Support

The representation of a general Calderón–Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the A_2 theorem, and it has found a number of other applications. In this paper we prove a new dyadic representation theorem by using smooth compactly supported wavelets in place of Haar functions. A key advantage of this is that we achieve a faster decay of the expansion when the kernel of the general Calderón–Zygmund operator has additional smoothness.

Near-field scattering from PEC wedge excited by electric dipole in lossy medium

PurposeThe purpose of this paper is to derive the dyadic representations of Green’s function in lossy medium because of the electric current dipole source radiating in close proximity of a PEC wedge and to reveal the effect of conductivity on the scattered electric field.Design/methodology/approachBy using the scalarization procedure, the paraxial fields are obtained first and then scalar Green’s functions are used to derive asymptotic forms of the dyadic Green’s functions. The problem is also analyzed by the image theory and analytical derivations are compared. However, analytically calculated results are validated with FEKO, a commercially available numerical electromagnetic field solver.FindingsThe results indicate that excellent agreement is observed between analytical and numerical results. Moreover, it is found that the presence of conductivity introduces a reduction in scattered electric fields.Originality/valueAsymptotically derived forms presented in this study can be used to calculate field distributions in the paraxial region of a wedge in a lossy medium.

Dyadic Representation in the American North and South: The Case of Prohibition

A persistent question in the study of American political history has been the capacity of one-party government in the American South to represent its voting citizens. In this article, we use county...

Friend of a Friend with Benefits ontology (FOAF+): extending a social network ontology for public health

BackgroundDyadic-based social networks analyses have been effective in a variety of behavioral- and health-related research areas. We introduce an ontology-driven approach towards social network analysis through encoding social data and inferring new information from the data.MethodsThe Friend of a Friend (FOAF) ontology is a lightweight social network ontology. We enriched FOAF by deriving social interaction data and relationships from social data to extend its domain scope.ResultsOur effort produced Friend of a Friend with Benefits (FOAF+) ontology that aims to support the spectrum of human interaction. A preliminary semiotic evaluation revealed a semantically rich and comprehensive knowledge base to represent complex social network relationships. With Semantic Web Rules Language, we demonstrated FOAF+ potential to infer social network ties between individual data.ConclusionUsing logical rules, we defined interpersonal dyadic social connections, which can create inferred linked dyadic social representations of individuals, represent complex behavioral information, help machines interpret some of the concepts and relationships involving human interaction, query network data, and contribute methods for analytical and disease surveillance.

Online Activism and Dyadic Representation: Evidence from the UK E‐Petition System

By making it easier for citizens to communicate their preferences, online forms of political participation have the potential to strengthen the representational link between politicians and voters. However, we know little about the effects of online advocacy on politicians’ behavior. Using new data from an e‐petition system in the United Kingdom, I show that support for a petition among a Member of Parliament’s constituents is associated with a substantial increase in the probability that the MP advocates for the petition in parliamentary debate, even when compared to MP behavior in counterfactual non‐petition debates which focus on the same policy issues. However, MP responsiveness is conditioned both by party discipline and electoral competition. These findings have important implications for our understanding of dyadic representation in parliamentary systems.

Dyadic Representation in the Japanese Parliament: Adaptation by Candidates and Selection by Constituencies

This paper examines basic but very important questions in the democratic process: do individual candidates represent the will of their own district constituency, even in a parliamentary system with well-disciplined legislative parties? The answer is clearly yes: this paper demonstrates dyadic representation, or the link between the policy preference of the constituencies and their representatives in the Japanese Lower House. I also demonstrate that constituencies provide more votes to candidates who better represent their preferences, which would strengthen the link by electing those better fulfilling the responsibility.

The Existence of Singular Traces on Simply Generated Operator Ideals

We present direct and self-contained proofs of the existence of singular traces on sufficiently large classes of operator ideals that live on the separable infinite-dimensional real Hilbert space. Our only tool is Banach’s version of the extension theorem of linear forms. Thanks to the use of dyadic representations of operators, all proofs have become straightforward.

Product formalisms for measures on spaces with binary tree structures: representation, visualization, and multiscale noise

Abstract In this paper, we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by optimization), and illustrate its applicability to a wide range of data types. The preprocessing step then consists of representing data sets as simple measures. The theoretical foundation consists of a dyadic product formula representation lemma, and a visualization theorem. We also define an additive multiscale noise model that can be used to sample from dyadic measures and a more general multiplicative multiscale noise model that can be used to perturb continuous functions, Borel measures, and dyadic measures. The first two results are based on theorems in [15, 3, 1]. The representation uses the very simple concept of a dyadic tree and hence is widely applicable, easily understood, and easily computed. Since the data sample is represented as a measure, subsequent analysis can exploit statistical and measure theoretic concepts and theories. Because the representation uses the very simple concept of a dyadic tree defined on the universe of a data set, and the parameters are simply and explicitly computable and easily interpretable and visualizable, we hope that this approach will be broadly useful to mathematicians, statisticians, and computer scientists who are intrigued by or involved in data science, including its mathematical foundations.

Bilinear Calderón–Zygmund theory on product spaces

We develop a wide general theory of bilinear bi-parameter singular integrals T. This includes general Calderón–Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach range, imply boundedness in the full bilinear range Lp×Lq→Lr, 1/p+1/q=1/r, 1<p,q≤∞, 1/2<r<∞, weighted estimates, mixed-norm estimates, and so on. We build this Calderón–Zygmund theory using the very useful perspective of dyadic representation theorems that hold under testing conditions. New weighted estimates are developed and used effectively throughout. We also develop commutator decompositions and use them to show estimates in the full range for commutators and iterated commutators, like [b1,T]1 and [b2,[b1,T]1]2, where b1 and b2 are little BMO functions. Our commutator method contains several novelties – one is that the new method can be used to simplify and improve linear commutator proofs, even in the two-weight Bloom setting. We also quickly show commutator lower bounds by using and developing the recent median method.

Dyadic interaction processing in the posterior temporal cortex

Recent behavioural evidence shows that visual displays of two individuals interacting are not simply encoded as separate individuals, but as an interactive unit that is 'more than the sum of its parts'. Recent functional magnetic resonance imaging (fMRI) evidence shows the importance of the posterior superior temporal sulcus (pSTS) in processing human social interactions, and suggests that it may represent human-object interactions as qualitatively 'greater' than the average of their constituent parts. The current study aimed to investigate whether the pSTS or other posterior temporal lobe region(s): 1) Demonstrated evidence of a dyadic information effect - that is, qualitatively different responses to an interacting dyad than to averaged responses of the same two interactors, presented in isolation, and; 2) Significantly differentiated between different types of social interactions.Multivoxel pattern analysis was performed in which a classifier was trained to differentiate between qualitatively different types of dyadic interactions. Above-chance classification of interactions was observed in 'interaction selective' pSTS-I and extrastriate body area (EBA), but not in other regions of interest (i.e. face-selective STS and mentalizing-selective temporo-parietal junction). A dyadic information effect was not observed in the pSTS-I, but instead was shown in the EBA; that is, classification of dyadic interactions did not fully generalise to averaged responses to the isolated interactors, indicating that dyadic representations in the EBA contain unique information that cannot be recovered from the interactors presented in isolation. These findings complement previous observations for congruent grouping of human bodies and objects in the broader lateral occipital temporal cortex area.

What Politicians Believe About Electoral Accountability

Despite legislators’ incentives to respond to their constituents’ opinions on salient issues, they often take positions at odds with public opinion in their districts. These gaps in dyadic representation can arise because of politicians’ perceptions of which constituents will hold them accountable for their actions in office and of their potential future electoral opponents. Using original survey data from more the 3,000 candidates running for state legislative office in 2014 and 2016, I document American politicians’ beliefs about important factors influencing electoral accountability. To test to whom politicians believe they must be responsive, I survey their perceptions of which citizens are most likely to vote and pay attention to their actions in office. I find asymmetries in politicians’ beliefs about to whom they must be accountable. Politicians perceive the partisan makeup of their districts fairly accurately but overestimate the Republican share of the district’s residents. Candidates from both parties underestimated Democratic turnout in 2014. In a conjoint experiment, candidates from both parties believed that Republicans and citizens with conservative issue positions were more likely to turn out and to pay attention to what they do in office. Republican candidates are also more likely to fear losing in future primary elections than Democrats are. Candidates’ perceptions suggest that they would strategically respond more to conservative constituents, possibly exacerbating asymmetric polarization.

National policy for local reasons: how MPs represent party and geographical constituency through initiatives on social security

In parliamentary systems of government, dyadic representation between MP and geographical constituency is considered to be of secondary importance and is typically understood as work related to particularised issues (e.g. constituency service, “pork” allocation and local matters). This paper argues that personal representation need not be particularistic. It may also come in the form of attention to national policy for local reasons, when issue salience varies across geographical constituencies due to the number of affected people or problem severity. The specific focus of the study lies on private members’ bills related to social security (pensions, unemployment, welfare). These three policies differ, among other things, in their alignment with class divisions and their link to the economic left–right dimension. They therefore allow for studying how both the party constituency and the geographical constituency shape MPs’ legislative work. The article develops specific predictions regarding how left–right position, electoral support among the affected group, and district-level recipient numbers affect legislative activity in the three policy fields. The empirical analysis uses data from Belgium (1999–2007). The results suggest that Belgian MPs represent party and geographical constituency in the case of pensions and unemployment benefits, but not in the same way as when it comes to social welfare.

Dyadic Representation and Boundedness of Nonhomogeneous Calderón–Zygmund Operators with Mild Kernel Regularity

We prove a new dyadic representation theorem with applications to the T(1) and A2 theorems. In particular, we obtain the nonhomogeneous T(1) theorem under weaker kernel regularity than in the earlier approaches.

Economic Decline and Extreme‐Right Electoral Threat: How District‐Level Factors Shape the Legislative Debate on Immigration

This research examines the degree to which legislators respond to their districts by analyzing immigration‐related legislative speeches from the Swedish parliament (2005–16). Using a text‐scaling method, we find that the immigration discourse fluctuates between “socioeconomic responsibility” and “cultural difference” poles. We argue that socioeconomic declines and extreme‐right party success serve as an indication to MPs that there is demand for “cultural difference” rhetoric on immigration. Our statistical analyses support the argument and demonstrate that district‐level economic declines can lead to an increase in the salience of cultural framing of migrants, especially in districts with a higher share of foreign residents. We also find that district‐level extreme‐right electoral success has a significant influence on legislative immigration discourse. Overall, the results have implications for studies of legislative texts, dyadic representation, and the impact of the populist right on legislative politics in Europe.

Dyadic representations of graphs

A graph G is dyadic provided it has a representation v→Sv from vertices v of G to subtrees Sv of a host tree T with maximum degree 3 such that (i)v and w are adjacent in G if and only if Sv and Sw share at least three nodes and (ii) each edge of T is used by exactly two representing subtrees. We show that a connected graph is dyadic if and only if it can be constructed from edges and cycles by gluing vertices to vertices and edges to edges.