The geometry of the double gyroid wire network: quantum and classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.Comment: pdflatex 9 Figures. Minor changes, some typos and formulation

Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the Gyroid wire network

We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)-commutative geometries. By selecting gauging data, these geometries are realized by matrices through an explicit construction or a Kan extension. We describe the changes in gauge via the action of a re-gauging groupoid. It acts via matrices that give rise to a noncommutative 2-cocycle and hence to a groupoid extension (gerbe). We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of re-gaugings. In the commutative case, we deduce that the extended symmetries act via a projective representation. This yields isotypical decompositions and super-selection rules. We apply these results to the primitive cubic, diamond, gyroid and honeycomb wire networks using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the G(yroid) and the honeycomb systems

"Seize the state, seize the day": state capture, corruption, and influence in transition

The main challenge of the transition has been to redefine how the state interacts with firms, but little attention has been paid to the flip side of the relationship : how firms influence the state - especially how they exert influence on, and collude with public officials to extract advantages. Some firms in transition economies have been able to shape the rules of the game to their own advantage, at considerable social cost, creating what the authors call a"capture economy"in many countries. In the capture economy, public officials, and politicians privately sell under-provided public goods, and a range of rent-generating advantages"a la carte"to individual firms. The authors empirically investigate the dynamics of the capture economy, on the basis of new firm-level data from the 1999 Business Environment and enterprise performance survey (BEEPS), which permits the unbundling of corruption into meaningful, and measurable components. they contrast state capture (firms shaping, and affecting formulation of the rules of the game through private payments to public officials, and politicians) with influence (doing the same without recourse to payments), and with administrative corruption ("petty"forms of bribery in connection with the implementation of laws, rules, and regulations). They develop economy-wide measures for these phenomena, which are then subject to empirical measurement utilizing the BEEPS data. State capture, influence, and administrative corruption are all shown to have distinct causes, and consequences. Large incumbent firms with formal ties to the state tend to inherit influence as a legacy of the past, and tend to enjoy more secure property, and contractual rights, and higher growth rates. To compete against these influential incumbents, new entrants turn to state capture as a strategic choice - not as a substitute for innovation, but to compensate for weaknesses in the legal, and regulatory framework. When the state under-provides the public goods needed for entry and competition,"captor"firms purchase directly from the state, such private benefits as secure property rights, and removal of obstacles to improved performance - but only in a capture economy. Consistent with empirical findings in previous research on petty corruption, administrative corruption - unlike both capture and influence - is not associated with specific benefits for the firm. The focus of reform should be shifted toward channeling firms'strategies in the direction of more legitimate forms of influence, involving societal"voice", transparency reform, political accountability, and economic competition, Where state capture has distorted reform to create (or preserve) monopolistic structures, supported by powerful political interests, the challenge is particularly daunting.Roads&Highways,Corruption&Anitcorruption Law,Decentralization,Economic Theory&Research,National Governance,National Governance,Governance Indicators,Economic Theory&Research,Corruption&Anitcorruption Law,Microfinance