Hausdorff dimension of a quantum string

In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum mechanical path of a relativistic string and find that the ``trajectory'', in this case, is a fractal surface with Hausdorff dimension three. Depending on the resolution of the detecting apparatus, the extra dimension is perceived as ``fuzziness'' of the string world-surface. We give an interpretation of this phenomenon in terms of a new form of the uncertainty principle for strings, and study the transition from the smooth to the fractal phase.Comment: 18 pages, non figures, ReVTeX 3.0, in print on Phys.Rev.

\u3ci\u3eBreard\u3c/i\u3e, \u3ci\u3ePrintz\u3c/i\u3e, and the Treaty Power

This article considers whether the anti-commandeering principle of New York v. United States and Printz v. United States applies to exercises of the Treaty Power. It illustrates the problem with an analysis of the treaty provision involved in Breard v. Greene, 118 S. Ct. 1352 (1998), which requires state officials to notify certain aliens they arrest that they have a right to consult with their consul. Whether exercises of the treaty power are subject to the commandeering prohibition depends on the resolution of two ambiguities in the Supreme Court\u27s anti-commandeering doctrine. The first concerns the distinction between commandeering and mere encouragement. Specifically, can a treaty such as the one involved in Breard be upheld as an exercise of conditional preemption, on the theory that it gives the state the choice between providing notification and refraining from arresting aliens? The answer to that question depends on whether a treaty barring states from arresting aliens would be valid, and the answer to that question turns on where the line falls between commandeering and valid preemption. If, as some lower courts have found, Printz and New York prohibit legislation that imposes obligations on states but not individuals, or regulates the states in their roles as governments, then a treaty barring the arrest of aliens would contravene the anti-commandeering principle. But, if so, the anti-commandeering principle could not be applicable to the treaty power, as it would call into question too much Supreme Court precedent. If the anti-commandeering principle is narrower, there would appear to be no reason to exempt the Treaty Power from its scope. Under the narrow interpretation of Printz and New York, the sorts of obligations to which the treaty-makers would legitimately want to subject the states would be valid encouragement under the conditional preemption doctrine. The anti-commandeering principle, narrowly construed, would thus not represent much of a burden on the Treaty Power. (Whether the anti-commandeering principle is broad or narrow is before the Supreme Court this Term in Condon v. Reno.

Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics – A Logical Extension to Quantum Entanglement

Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality

Time Delay in Tunnelling Ionization

A promising new method of attosecond spectroscopy, the attoclock, offers attosecond resolution without requiring attosecond laser pulses. However, it requires knowledge of the ionization time, opening up a long standing conceptual problem in physics (“how much time does tunnelling take?”). In this work, the time delay in the tunnel ionization process is considered. It is shown that a delay of the peak of the tunnelling wavefunction exists as a matter of principle, and is caused by the interference of transmitted and reflected components of the wavefunction. If sub-barrier reflections are neglected from the wavefunction, the delay in the peak vanishes and tunnelling is seen to be instantaneous. This is shown by considering a series of models of increasing complexity: the square barrier, an adiabatically tunnelling electron, and a wavefunction based on the Strong Field Approximation. This work has implications on the interpretation of attoclock experiments: treatments based on instantaneous tunnelling should be adjusted in order to achieve appropriate calibration of the attoclock

Article 31(3)(c) of the VCLT and the principle of systemic integration

PhDThe proliferation of international courts and tribunals combined with the expansion of the areas and density of regulation of international law has given rise to a debate on the issue of fragmentation of international law. Within this context and as a possible response to this fear of fragmentation, the issue of interpretation with specific reference to Article 31(3)(c) of the Vienna Convention on the Law of Treaties has come to the forefront. The overarching aim of the present thesis entitled ‘Article 31(3)(c) of the VCLT and the Principle of Systemic Integration’ is to provide a comprehensive analysis of the content and the function of Article 31(3)(c) both as a conventional and as a customary rule (i.e. as principle of systemic integration). To this end, the thesis adopts a two-pronged approach. In the first Part of this thesis the analysis is based on the text of the provision itself, both on its written and unwritten elements (intertemporal law considerations). This analysis demonstrates that a proper understanding of Article 31(3)(c) leads us to the adoption of the proximity criterion as the only appropriate in the application of Article 31(3)(c). Having concluded the textual analysis, the thesis then, in the second Part, considers Article 31(3)(c) from a different vantage point. It examines Article 31(3)(c) from the more general perspective of the system as a whole and analyses what the effects of more systemic considerations to the content of Article 31(3)(c) are. Within these parameters two issues arise: i) The principles of conflict resolution, which the thesis proves can be applied, in certain scenarios, in the interpretative process of Article 31(3)(c) and ii) more importantly the notion of interpretation of customary law. The relevant Chapter establishes that customary international law can be the object of interpretation and in such an interpretation Article 31(3)(c), as custom, plays a pivotal role. Through this approach, both from a textual and a systemic perspective, the thesis offers a new and complete understanding of Article 31(3)(c) in all its manifestations and spheres of application

Flow Analysis And Leak Detection With The CFPD Method In The Paris Drinking Water Distribution System

With significant drinking water loss rates \u3e10% during distribution at many drinking water utilities worldwide, the detection of new leaks, especially small and slowly growing leaks, remains an important challenge for the water sector. Time series of flow rates into isolated or completely metered distribution areas (e.g. District Metered Areas) contain signals of all existing and new leaks in that area, and also of all other processes taking place, e.g. changes in demand, operations, etc. Therefore, in principle these data can provide valuable information about new leaks, unregistered changes in valve status, etc. However, distinguishing one from the others is often difficult. The CFPD (Comparison of Flow Pattern Distributions) method is a flow time series data transformation which facilitates the identification, quantification, and interpretation of changes in the amounts of water supplied. Contrary to the often applied minimum night flow analysis, it uses all available flow data (24 hours per day, resolution of 1 measurement per hour or better) and recognizes different types of changes. In this way, it helps to distinguish e.g. new leaks from operational signals and demand changes. In the past year, it has been successfully applied at several Dutch drinking water companies. In this paper, we illustrate the application of the CFPD method by presenting selected results from CFPD analyses of flow data for 16 of 30 DMAs in the city of Paris. The findings are compared to a list of registered leaks

An Emerging Norm - Determining the Meaning and Legal Status of the Responsibility to Protect

The responsibility to protect, from its recent nativity in the 2001 report of the International Commission on Intervention and State Sovereignty (ICISS), is the latest round in an old debate pitting the principle of nonintervention in the internal affairs of states against allowing such intervention to prevent gross and systematic violations of human rights. Advocates for the concept see it as an important new commitment by the international community, injecting new meaning into the tragically threadbare promise to never again allow mass atrocities to occur unchallenged. ICISS offered the concept of responsibility to protect as a new way to confront these calamities that addressed the concerns of some nations that humanitarian intervention was merely a license to invade. This idea made its way in four short years from the 2001 ICISS Report into the 2005 Summit Outcome Document (Summit Outcome), unanimously adopted by the Sixtieth Session of the U.N. General Assembly. A frequently repeated phrase in the commentary on responsibility to protect is that it is an emerging norm, representing the coalescence of a new international consensus around the duties and powers of the international community in confronting massive human rights violations. While many advocates and commentators have been cautious on this subject, one interpretation is that, as an emerging norm, responsibility to protect is somewhere on the path to becoming customary international law. [W]ith the weight behind it of a unanimous General Assembly resolution at head of state and government level, the responsibility to protect can already be properly described as a new international norm: a new standard of behavior . . . for every state

An Emerging Norm - Determining the Meaning and Legal Status of the Responsibility to Protect

The responsibility to protect, from its recent nativity in the 2001 report of the International Commission on Intervention and State Sovereignty (ICISS), is the latest round in an old debate pitting the principle of nonintervention in the internal affairs of states against allowing such intervention to prevent gross and systematic violations of human rights. Advocates for the concept see it as an important new commitment by the international community, injecting new meaning into the tragically threadbare promise to never again allow mass atrocities to occur unchallenged. ICISS offered the concept of responsibility to protect as a new way to confront these calamities that addressed the concerns of some nations that humanitarian intervention was merely a license to invade. This idea made its way in four short years from the 2001 ICISS Report into the 2005 Summit Outcome Document (Summit Outcome), unanimously adopted by the Sixtieth Session of the U.N. General Assembly. A frequently repeated phrase in the commentary on responsibility to protect is that it is an emerging norm, representing the coalescence of a new international consensus around the duties and powers of the international community in confronting massive human rights violations. While many advocates and commentators have been cautious on this subject, one interpretation is that, as an emerging norm, responsibility to protect is somewhere on the path to becoming customary international law. [W]ith the weight behind it of a unanimous General Assembly resolution at head of state and government level, the responsibility to protect can already be properly described as a new international norm: a new standard of behavior . . . for every state

Query Evaluation in Deductive Databases

It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up