Democratic Representations

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.Comment: Submitted to a Journa

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

Global value perceptions : the legitimising functions of western representations of democracy

This paper argues that a fundamental antagonism between democracy and nondemocracy organises lay thinking on global issues. We review key findings of a long-standing experimental research programme that examined the "Democracy-as-value" hypothesis across a variety of political and social contexts. This hypothesis contends that democracy is an ideological belief system that provides value to democratic individuals, groups, and institutions and thereby grants legitimacy to their actions. Based on procedural justice theories and social representations theory, we contend that western lay perceivers associate democracy with procedural equality and individual autonomy, whereas nondemocracy is associated with ingroup hierarchy and conformity. We discuss how idealised representations of democracy justify global power arrangements and emphasise the paradoxical justification function of democratic values through which nondemocratic forms of social regulation based on physical force are legitimised with the very democratic norms that call for peaceful resolution of conflicts

Picturing Teacher Agency: Developing Upstanding Heuristics in a Middle Grades Social Studies Methods Course

This paper presents a multi-case study of teacher candidates in a pre-service middle grades social studies methods course. The research aimed to understand how the middle grades teacher candidates viewed their future as upstanders with agency in middle grades settings. The focus of the research was on heuristic representations that the teacher candidates created to illustrate how they understood their role in supporting the democratic aims of middle grades social studies. Qualitative data was collected and analyzed through chordal triad of agency theory (Emirbayer & Mische, 1998). The findings indicate that preservice teachers best understand their future as change agents through their role of curriculum and instruction and their impact on students, additionally their conceptualizations of their intended agency were influenced by their past and present experiences as well as their projected goals for the future. This research also suggests that heuristics may be a powerful tool in the preparation of teacher candidates, helping them to think through their role in supporting the democratic aims of social studies, middle grades education and social justice education. Important constraints about teacher candidates’ perceptions (or lack thereof) of oppressive structures within middle schools settings are considered

Discrete Flavor Symmetry, Dynamical Mass Textures, and Grand Unification

Discrete flavor symmetry is explored for an intrinsic property of mass matrix forms of quarks and leptons. In this paper we investigate the S3 permutation symmetry and derive the general forms of mass matrices in various types of S3 theories. We also exhibit particular realizations of previous ansatze of mass matrices, which have often been applied in the literature to the standard model Yukawa sector. Discrete flavor symmetry is also advantageous for vanishing matrix elements being dynamically generated in the vacuum of scalar potential. This is due to the fact that group operations are discrete. While zero elements themselves do not explain mass hierarchies, we introduce an abelian flavor symmetry. A non-trivial issue is whether successful quantum numbers can be assigned so that they are compatible with other (non-abelian) flavor symmetries. We show typical examples of charge assignments which not only produce hierarchical orders of mass eigenvalues but also prohibit non-renormalizable operators which disturb the hierarchies in first-order estimation. As an explicit application, a flavor model is constructed in grand unification scheme with S3 and U(1) (or Z_N) flavor symmetries.Comment: 40 pages, references adde

Representation

About the book: This edited volume presents a unique challenge to mainstream political theory • Offers fourteen ‘think pieces’ by renowed international scholars • Presents a comprehensive examination of core political ideologies and core political concept

Embedding A4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy

We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left-right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A4 leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left-right flavor symmetry into the diagonal A4, it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a heavy 3rd family, the tribimaximal mixing for the leptons, and we suggest a possible origin of the Cabibbo and other mixing angles for the quarks.Comment: 9 pages, uses revtex4 and axodraw.st

Can the Subaltern Listen? Self-determination and the Provisioning of Expertise in Papua New Guinea

Voice is a major concern in contemporary liberal-democratic politics, one that stresses the political importance of speaking (“giving voice,” “speaking up”). But in the Yopno valley of Papua New Guinea, where NGO and government projects are expanding, people’s sense that they are losing control of their future has led them to worry about their capacity to listen, not their capacity to speak. In largely acephalous villages, people’s self-determination seems particularly threatened by their ignorance of the true nature of their own actions. From a perspective in which the antecedents and the consequences of action are deeply unclear—a perspective stressed in the provisioning of expertise prevalent in political discourse—self-determination hinges on listening and gaining the understanding needed to shape one’s future.Anthropolog

Regimes of Temporality: China, Tibet and the Politics of Time in the Post-2008 Era

While the politics of time are an important dimension of Chinese state discourse about Tibet, it remains insufficiently explored in theoretical and practical terms. This article examines the written and visual discourses of Tibetan temporality across Chinese state media in the post-2008 era. It analyses how these media discourses attempt to construct a ‘regime of temporality’ in order to manage public opinion about Tibet and consolidate Chinese rule over the region. While the expansion of online technologies has allowed the state to consolidate its discourses about Tibet’s place within the People’s Republic of China (PRC), they have also provided Tibetans a limited but valuable space to challenge these official representations through counter readings of Tibet’s past, present and future. In doing so, this article contributes new insights on the production of state power over Tibet, online media practices in China, and the disruptive potential of social media as sites of Tibetan counter discourses