On Fragments and Geometry: The International Legal Order as Metaphor and How it Matters

This article engages the narrative of fragmentation in international law by asserting that legal academics and professionals have failed to probe more deeply into ‘fragmentation’ as a concept and, more specifically, as a spatial metaphor. The contention here is that however central fragmentation has been to analyses of contemporary international law, this notion has been conceptually assumed, ahistorically accepted and philosophically under-examined. The ‘fragment’ metaphor is tied historically to a cartographic rationality – and thus ‘reality’ – of all social space being reducible to a geometric object and, correspondingly, a planimetric map. The purpose of this article is to generate an appreciation among international lawyers that the problem of ‘fragmentation’ is more deeply rooted in epistemology and conceptual history. This requires an explanation of how the conflation of social space with planimetric reduction came to be constructed historically and used politically, and how that model informs representations of legal practices and perceptions of ‘international legal order’ as an inherently absolute and geometric. This implies the need to dig up and expose background assumptions that have been working to precondition a ‘fragmented’ characterization of worldly space. With the metaphor of ‘digging’ in mind, I draw upon Michel Foucault’s ‘archaeology of knowledge’ and, specifically, his assertion that epochal ideas are grounded by layers of ‘obscure knowledge’ that initially seem unrelated to a discourse. In the case of the fragmentation narrative, I argue obscure but key layers can be found in the Cartesian paradigm of space as a geometric object and the modern States’ imperative to assert (geographic) jurisdiction. To support this claim, I attempt to excavate the fragment metaphor by discussing key developments that led to the production and projection of geometric and planimetric reality since the 16th century

Constructions and Noise Threshold of Hyperbolic Surface Codes

We show how to obtain concrete constructions of homological quantum codes based on tilings of 2D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in two-dimensional quantum codes whose tradeoff of encoding rate versus protection is more favorable than for the surface code. These surface codes would require variable length connections between qubits, as determined by the hyperbolic geometry. We provide numerical estimates of the value of the noise threshold and logical error probability of these codes against independent X or Z noise, assuming noise-free error correction

A Compact Codimension Two Braneworld with Precisely One Brane

Building on earlier work on football shaped extra dimensions, we construct a compact codimension two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and magnetic flux. The torus has positive constant curvature almost everywhere, except for a single conical singularity at the location of the brane. In contradistinction to the football shaped case, there is no fine-tuning required for the brane tension. We also present some plausibility arguments why the model should not suffer from serious stability issues.Comment: 13 pages, 2 figures; references added, typos fixes; essentially the version published in PR

Space-Time Circuit-to-Hamiltonian Construction and Its Applications

The circuit-to-Hamiltonian construction translates dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev construction uses one global clock for all qubits while we consider a different construction in which a clock is assigned to each interacting qubit. This makes it possible to capture the spatio-temporal structure of the original quantum circuit into features of the circuit Hamiltonian. The construction is inspired by the original two-dimensional interacting fermionic model (see http://link.aps.org/doi/10.1103/PhysRevA.63.040302) We prove that for one-dimensional quantum circuits the gap of the circuit Hamiltonian is appropriately lower-bounded, partially using results on mixing times of Markov chains, so that the applications of this construction for QMA (and partially for quantum adiabatic computation) go through. For one-dimensional quantum circuits, the dynamics generated by the circuit Hamiltonian corresponds to diffusion of a string around the torus.Comment: 27 pages, 5 figure

The Small Stellated Dodecahedron Code and Friends

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges resp. vertices of a small stellated dodecahedron, making this code suitable for 3D connectivity. This code encodes 8 logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) as compared to 1 logical qubit into 9 physical qubits (plus 8 ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold.Comment: 19 pages, 14 figures, comments welcome! v2 includes updates which conforms with the journal versio

Local Decoders for the 2D and 4D Toric Code

We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 .Comment: 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,

Developing a Ketamine Infusion Protocol to Treat Complex Regional Pain Syndrome

Complex Regional Pain Syndrome (CRPS) has been studied under different names dating back to the American Civil War. Despite being studied for over 100 years, CRPS is still not a very well understood disease process and there is no consensus on the best way to treat it (O’Connell, Wand, McAuley, Marston, & Moseley, 2016). One treatment that has shown to be effective in reducing pain scores in patients with chronic CRPS is a multiple day infusion of ketamine (Sigtermans et al., 2009). The purpose of this doctor of nursing practice project was to develop a ketamine infusion protocol for anesthesia providers at community hospital in the Midwest. The implementation of this project was carried out through an educational inservice and evaluated using a short survey, which was filled out by the audience anonymously. Based upon the responses, it is reasonable to assume that this project can be effective in educating anesthesia providers on the topic of using ketamine infusions to treat CRPS. The protocol developed for this project can be used as a sample or guideline for facilities that are considering implementing a ketamine infusion protocol to treat CRPS. The protocol can be changed to fit the needs and constraints of a facility

Cognitive Origin of Reported Goals

Goal setting theory assumes that goals that drive self-regulation exist in ‘goal structures’ and that asking participants to report their goals draws from these pre-existing structures. This study tested this assumption of pre-existing goals against the notion that goals are generated by goal-setters at the time they are requested to report their goals. A model of working memory was used to differentiate between goals existing in memory or goals generated on the spot. Participants were 211 students from a large Midwestern public university, randomly assigned to one of two groups. The experimental group participants reported their career goals while also performing a working memory distraction task, while those in the control group reported their goals undistracted. Students in both groups shortly re-reported their goals (undistracted) by constructing a career ‘goal structure.’ The proportion of goals matching between reporting times, over total goals reported, could be used to infer whether goals were generated on demand or were drawn from pre-existing structures. After appropriate controls, the distracted group reported a significantly lower ratio of matching goals. No significant interaction effects were found for the secondary hypotheses that goal commitment and specificity were relevant to goal reporting. These results provide evidence that reported goals are not solely extracted from pre-existing mental structures

Performing Legality in the Theatre of Hostilities: Asymmetric Conflict, Lawfare and the Rise of Vicarious Litigation

This Article explores the extent of the change by looking at the ways in which asymmetric conflict and legalization have reshaped the theatre of hostilities and the implications for the institution of war itself. The shift from one literal battlefield to multiple and disaggregated battlespaces has led to a reconfigured theatre of hostilities, which now involves a complex mix of local and global spaces as well as kinetic and narrative forms of combat. This re-making of armed hostilities in geographical, material, and social terms has increased access to the drama, stage, and audience of military theatres. Further, the more globalized and publicized character of hostilities has allowed a higher number of actors, and actors of higher quality, to participate in and observe hostilities, whether kinetic, narrative, or both. This has given a powerful platform for law to mediate the conduct of warfare, and it is thus unsurprising that the notion of legality regularly occupies center stage in a reconstructed theatre of hostilities. Accordingly, military actors, whether state or non-state, are producing performances of legality in combat to influence not only their adversaries but also, crucially, formal and informal judgments across the theatre’s more expansive and global audience. The term “performances” does not imply cynical theatrics, but rather concerted actions to display legality or illegality as an integral part of warfare. In this way, such performances of legality have become a crucial strategic asset for interacting kinetic and narrative confrontations. This has led to a distinctive struggle between adversaries over appearances of legality and illegality, which has produced an institutional and narrative battlespace of growing importance that this Article conceptualizes as vicarious litigation. The Article is organized in five sections. Section I introduces and elaborates on the related notions of legal performances and vicarious litigation by bridging sociological theorizing on social performances with noted developments in asymmetric warfare. This conceptual effort draws insight from Performative Sociology and the so-called “practice turn” in international relations theory. Section II describes the origin of vicarious litigation as flowing from the asymmetric warfare’s disruption of the institutional bargain behind modern war and, consequently, International Humanitarian Law (IHL). To understand that institutional disruption, Section II discusses Andrew Mack’s under-examined inquiry into and conceptualization of “asymmetric conflict.” Sections III and IV look at how international lawyers, and specifically IHL scholars, have struggled to grasp the rise of asymmetric conflict and how the dominant “lawfare” literature has suffered from conceptual straining and the incapacity to theorize institutional change precipitated by the prevalence of asymmetric conflict. Section V focuses on the novel notions of legal performances and vicarious litigation and examines how these novel notions provide alternatives to the hobbled semantics of lawfare by offering greater insight into institutional mutations that now define the legalization of contemporary warfare