Quantum cellular automata quantum computing with endohedral fullerenes

We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of Group V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a Hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state $S=3/2$. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automata is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum celluar automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automata operation and obtain a rough figure of merit for the the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes towards meeting the fifth criteria: qubit readout.Comment: 16 pages, Latex, 5 figures, See http://planck.thphys.may.ie/QIPDDF/ submitted to Phys. Rev.

Group Minds and the Case of Wikipedia

Group-level cognitive states are widely observed in human social systems, but their discussion is often ruled out a priori in quantitative approaches. In this paper, we show how reference to the irreducible mental states and psychological dynamics of a group is necessary to make sense of large scale social phenomena. We introduce the problem of mental boundaries by reference to a classic problem in the evolution of cooperation. We then provide an explicit quantitative example drawn from ongoing work on cooperation and conflict among Wikipedia editors, showing how some, but not all, effects of individual experience persist in the aggregate. We show the limitations of methodological individualism, and the substantial benefits that come from being able to refer to collective intentions, and attributions of cognitive states of the form "what the group believes" and "what the group values".Comment: 21 pages, 6 figures; matches published versio

Uniqueness of certain polynomials constant on a line

We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let $p(x,y)$ be a polynomial of degree $d$ with $N$ positive coefficients and no negative coefficients, such that $p=1$ when $x+y=1$. A sharp estimate $d \leq 2N-3$ is known. In this paper we study the $p$ for which equality holds. We prove some new results about the form of these "sharp" polynomials. Using these new results and using two independent computational methods we give a complete classification of these polynomials up to $d=17$. The question is motivated by the problem of classification of CR maps between spheres in different dimensions.Comment: 20 pages, latex; removed section 10 and address referee suggestions; accepted to Linear Algebra and its Application

Medium practices

In this essay I develop a topic addressed in my book, Film Art Phenomena: the question of medium specificity. Rosalind Krauss's essay 'Art In the Age of the Post-Medium Condition' has catalysed a move away from medium specificity to hybridity. I propose that questions of medium cannot be ignored, since they carry their own history and give rise to specific formal traits and possibilities. The research involves close critical analysis of four moving image works that have not previously been written about: two made with film, and one each with computer and mobile phone. The analyses are conducted by reference to my ideas about how technological peculiarities inform and inflect practice: I see the work's material composition, its form and final meaning as intricately bound up with each other. Film, video and the computer give rise to specific forms of moving image, partly because artists exploit a medium’s peculiarities, and because certain media lend themselves to some methodologies and not others. I do not seek hard distinctions between these media, but discuss them in terms of predispositions. For example, I discuss a 16mm cine film in which the shifting visibility of grain raises ideas around movement and stillness. The aim is to develop a definition of medium specificity, in relation to the moving image, that is not essentialist in the way previous versions were criticised for being, that is, based on ideas of "material substrate" (Wollen). I argue that film is a medium of stages, in contrast to the modern tapeless camcorder, in which all functions of recording, storage, playback and even editing are contained in a single device. Supported by a travel grant, I presented a version of this essay at the International Conference of Experimental Media Congress, Toronto, in April 2011, along with a selection of works: http://www.experimentalcongress.org/full-schedule

Generating Worthwhile Mathematical Tasks in Order to Sustain and Develop Mathematical Thinking

Making use of a phenomenological stance which first and foremost values the lived experience of learners, six tasks are used to illustrate what it might mean for a mathematical task to be deemed worthy of being offered to learners. These take the form of encounters with, and opportunities to develop, pervasive mathematical themes, use of mathematical powers and experience of mathematical concepts and topics. Comments about how worthwhile mathematical tasks can evolve centre around developing the propensity, the habit of mind to extend, vary and generalise for oneself. Mathematical thinking is sustained by developing this disposition

Conflict and Computation on Wikipedia: a Finite-State Machine Analysis of Editor Interactions

What is the boundary between a vigorous argument and a breakdown of relations? What drives a group of individuals across it? Taking Wikipedia as a test case, we use a hidden Markov model to approximate the computational structure and social grammar of more than a decade of cooperation and conflict among its editors. Across a wide range of pages, we discover a bursty war/peace structure where the systems can become trapped, sometimes for months, in a computational subspace associated with significantly higher levels of conflict-tracking "revert" actions. Distinct patterns of behavior characterize the lower-conflict subspace, including tit-for-tat reversion. While a fraction of the transitions between these subspaces are associated with top-down actions taken by administrators, the effects are weak. Surprisingly, we find no statistical signal that transitions are associated with the appearance of particularly anti-social users, and only weak association with significant news events outside the system. These findings are consistent with transitions being driven by decentralized processes with no clear locus of control. Models of belief revision in the presence of a common resource for information-sharing predict the existence of two distinct phases: a disordered high-conflict phase, and a frozen phase with spontaneously-broken symmetry. The bistability we observe empirically may be a consequence of editor turn-over, which drives the system to a critical point between them.Comment: 23 pages, 3 figures. Matches published version. Code for HMM fitting available at http://bit.ly/sfihmm ; time series and derived finite state machines at bit.ly/wiki_hm

Eloquent fragments: French fiction film and globalization

French (and Franco-Belgian) cinema has witnessed a return to the real since the middle of the 1990s and should thus successfully have pinned down the impact of the globalizing economy on the sociopolitical sphere. Yet neoliberal globalization is deeply resistant to representation within the frame of conventional fictions. Condemned to be a cinema of fragments by the shattering of the old leftist imaginary, has French cinema merely tracked globalization's local consequences, always letting systemic causes escape its grasp? Or has it identified successful strategies with which to restore eloquence to social struggle and suffering that otherwise seemed condemned to silence? Engaging with important films by the Dardenne brothers, Robert Guédiguian, Bertrand Tavernier, Manuel Poirier, Matthieu Kassovitz and others, this paper argues the latter. French film, it suggests, has found ways to make the fragments speak to the totality, to short-circuit neoliberal triumphalism and to interpellate a nation that no longer plays its erstwhile integrational role. While none of these strategies can provide totalizing systemic critique, they do show that cinema is playing an active role in the rebuilding of a radical oppositional imaginary

The Only Undoable CRDTs are Counters

In comparing well-known CRDTs representing sets that can grow and shrink, we find caveats. In one, the removal of an element cannot be reliably undone. In another, undesirable states are attainable, such as when an element is present -1 times (and so must be added for the set to become empty). The first lacks a general-purpose undo, while the second acts less like a set and more like a tuple of counters, one per possible element. Using some group theory, we show that this trade-off is unavoidable: every undoable CRDT is a tuple of counters