Compact AC(σ)AC(\sigma) operators

All compact $AC(\sigma)$ operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the paper, we answer a number of questions about the decomposition of a compact $AC(\sigma)$ into real and imaginary parts

Securing The Root: A Proposal For Distributing Signing Authority

Management of the Domain Name System (DNS) root zone file is a uniquely global policy problem. For the Internet to connect everyone, the root must be coordinated and compatible. While authority over the legacy root zone file has been contentious and divisive at times, everyone agrees that the Internet should be made more secure. A newly standardized protocol, DNS Security Extensions (DNSSEC), would make the Internet's infrastructure more secure. In order to fully implement DNSSEC, the procedures for managing the DNS root must be revised. Therein lies an opportunity. In revising the root zone management procedures, we can develop a new solution that diminishes the impact of the legacy monopoly held by the U.S. government and avoids another contentious debate over unilateral U.S. control. In this paper we describe the outlines of a new system for the management of a DNSSEC-enabled root. Our proposal distributes authority over securing the root, unlike another recently suggested method, while avoiding the risks and pitfalls of an intergovernmental power sharing scheme

Regional Address Registries, Governance and Internet Freedom

Regional Internet Address Registries (RIRs) are private, nonprofit and transnational governance entities that evolved organically with the growth of the Internet to manage and coordinate Internet Protocol addresses. The RIR's management of Internet address resources is becoming more contentious and more central to global debates over Internet governance. This is happening because of two transformational problems: 1) the depletion of the IPv4 address space; and 2) the attempt to introduce more security into the Internet routing system. We call these problems "transformational" because they raise the stakes of the RIR's policy decisions, make RIR processes more formal and institutionalized, and have the potential to create new, more centralized control mechanisms over Internet service providers and users. A danger in this transition is that the higher stakes and centralized control mechanisms become magnets for political contention, just as ICANN's control of the DNS root did. In order to avoid a repeat of the problems of ICANN, we need to think carefully about the relationship between RIRs, governments, and Internet freedom. In particular, we need to shield RIRs from interference by national governments, and strengthen and institutionalize their status as neutral technical coordinators with limited influence over other areas of Internet governance

Reinventing Media Activism: Public Interest Advocacy in the Making of U.S. Communication-Information Policy, 1960-2002

This report is a long-term analysis of citizens' collective action to influence public policy toward communication and information. The work discusses in greater detail what is meant by communication and information policy (CIP) and why we think it is worthwhile to study it as a distinctive domain of public policy and citizen action. The report concentrates on citizen action in the United States and looks backwards, tracing the long-term evolutionary trajectory of communications-information advocacy in the USA since the 1960s. We focus on the concept of citizen collective action and explain its relevance to CIP.Research supported by the Ford Foundation's Knowledge, Creativity and Freedom Program. The views expressed are those of the author and do not necessarily represent the views of the School of Information Studies, Syracuse University, or the Ford Foundation

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

The practical success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad, Landau, Vazirani, and Vidick. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce an efficient implementation of the theoretical RRG procedure which finds MPS ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in situations of practical interest. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a tree-like manner. We evaluate the algorithm numerically, finding similar performance to DMRG in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, or large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.Comment: 13 pages, 10 figure

Deconfined quantum critical point in one dimension

We perform a numerical study of a spin-1/2 model with $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by Landau-Ginzburg-Wilson symmetry-breaking theory.Comment: 20 pages, 18 figure