Wholeness as a Hierarchical Graph to Capture the Nature of Space

According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness.Comment: 14 pages, 7 figures, 2 table

Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law

We quantise the massless vector potential A of electromagnetism in the presence of a classical electromagnetic (background) current, j, in a generally covariant way on arbitrary globally hyperbolic spacetimes M. By carefully following general principles and procedures we clarify a number of topological issues. First we combine the interpretation of A as a connection on a principal U(1)-bundle with the perspective of general covariance to deduce a physical gauge equivalence relation, which is intimately related to the Aharonov-Bohm effect. By Peierls' method we subsequently find a Poisson bracket on the space of local, affine observables of the theory. This Poisson bracket is in general degenerate, leading to a quantum theory with non-local behaviour. We show that this non-local behaviour can be fully explained in terms of Gauss' law. Thus our analysis establishes a relationship, via the Poisson bracket, between the Aharonov-Bohm effect and Gauss' law (a relationship which seems to have gone unnoticed so far). Furthermore, we find a formula for the space of electric monopole charges in terms of the topology of the underlying spacetime. Because it costs little extra effort, we emphasise the cohomological perspective and derive our results for general p-form fields A (p < dim(M)), modulo exact fields. In conclusion we note that the theory is not locally covariant, in the sense of Brunetti-Fredenhagen-Verch. It is not possible to obtain such a theory by dividing out the centre of the algebras, nor is it physically desirable to do so. Instead we argue that electromagnetism forces us to weaken the axioms of the framework of local covariance, because the failure of locality is physically well-understood and should be accommodated.Comment: Minor corrections to Def. 4.3, acknowledgements and typos, in line with published versio

An explicit relationship between time-domain noise correlation and spatial autocorrelation (SPAC) results

The success of recent ambient noise tomographic studies is now understood to arise due to cross-correlation properties documented in the acoustics community since the 1950s. However, despite the fact that Aki's 1957 spatial autocorrelation (SPAC) work yields identical analytical results to certain noise correlation results, the precise relationship between SPAC and time-domain cross-correlation remains not entirely transparent. Here, we present an explicit comparison of the two approaches and clarify that SPAC theory is indeed equivalent to the cross-correlation theory used for recent noise tomography studies. This equivalence allows theoretical work from each field to be applied to the other, and we illustrate a few examples of this

Level statistics across the many--body localization transition

Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing the effects due to Griffiths rare events for the former case. It is argued that the transition in the case of random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. The considered weighted short-range plasma model yields a very good agreement both for level spacing distribution including its exponential tail and the number variance up to tens of level spacings outperforming previously proposed models. In particular, our model grasps the critical level statistics which arise at disorder strength for which the inter-sample fluctuations are the strongest. Going beyond the paradigmatic examples of many-body localization in spin systems, we show that the considered model also grasps the level statistics of disordered Bose- and Fermi-Hubbard models. The remaining deviations for long-range spectral correlations are discussed and attributed mainly to the intricacies of level unfolding.Comment: 19pp. enlarged by including 1807.06983; version accepted in Phys. Rev.

An approach to preventing spam using Access Codes with a combination of anti-spam mechanisms

Spam is becoming a more and more severe problem for individuals, networks, organisations and businesses. The losses caused by spam are billions of dollars every year. Research shows that spam contributes more than 80% of e-mails with an increased in its growth rate every year. Spam is not limited to emails; it has started affecting other technologies like VoIP, cellular and traditional telephony, and instant messaging services. None of the approaches (including legislative, collaborative, social awareness and technological) separately or in combination with other approaches, can prevent sufficient of the spam to be deemed a solution to the spam problem. The severity of the spam problem and the limitations of the state-of-the-Art solutions create a strong need for an efficient anti-spam mechanism that can prevent significant volumes of spam without showing any false positives. This can be achieved by an efficient anti-spam mechanism such as the proposed anti-spam mechanism known as "Spam Prevention using Access Codes", SPAC. SPAC targets spam from two angles i.e. to prevent/block spam and to discourage spammers by making the infrastructure environment very unpleasant for them. In addition to the idea of Access Codes, SPAC combines the ideas behind some of the key current technological anti-spam measures to increase effectiveness. The difference in this work is that SPAC uses those ideas effectively and combines them in a unique way which enables SPAC to acquire the good features of a number of technological anti-spam approaches without showing any of the drawbacks of these approaches. Sybil attacks, Dictionary attacks and address spoofing have no impact on the performance of SPAC. In fact SPAC functions in a similar way (i.e. as for unknown persons) for these sorts of attacks. An application known as the "SPAC application" has been developed to test the performance of the SPAC mechanism. The results obtained from various tests on the SPAC application show that SPAC has a clear edge over the existing anti-spam technological approaches

STUDY OF GATE TURN OFF THYRISTOR STRUCTURE FOR POWER CONTROL APPLICATION USING SIMULATION

The turn-on and turn-off losses in a GTO thyristor must be properly accounted for because they can comprise upwards of 60% of the total losses. If a research can be done to remove the defect and reduce the losses and improved the performance of the GTO thyristor, it will be a great breakthrough to the semiconductor field. This report represents the study on the Gate Turn- Off (GTO) Thyristor using simulation software. This project which was done in 2 semesters (July 2006 semester and January 2007 semester) is the study on the method to improve the performance of the GTO thyristor by reducing it losses. During the first part of the project, familiarization with the TCAD SILVACO ATHENA and ATLAS is done in order to continue doing a critical evaluation to the device; furthermore this step is very important during the extraction process of the electrical performance for the conventional device. For the second semester, the review process of the researches done by other people began to takeplace. Each of the reference and research found will be carefully compared. The best design or steps is then being chosen to be adopted in the project

Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.Comment: 11 pages, typos corrected, added reference