Noise in Grover's Quantum Search Algorithm

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA, December 199

Clebsch-Gordan and 6j-coefficients for rank two quantum groups

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as well as some other topological data associated with theories corresponding to rank-two quantum groups. Finally, we collect some useful properties of the fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica notebooks containing the various q-CG and 6j symbols, see http://arxiv.org/src/1004.5456/an

Multi-graviton theory, a latticized dimension, and the cosmological constant

Beginning with the Pauli-Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbor ``theory spaces'' lead to a discrete mass spectrum. Our model coincides with the Kaluza-Klein theory whose fifth dimension is latticized. We evaluate one-loop vacuum energy in models with a circular latticized extra dimension as well as with compact continuous dimensions. We find that the vacuum energy can take a positive value, if the dimension of the continuous space time is $6, 10,...$. Moreover, since the amount of the vacuum energy can be an arbitrary small value according to the choice of parameters in the model, our models is useful to explain the small positive dark energy in the present universe.Comment: 10 pages, No figure. Needs REVTeX4. citations are corrected and minor correction

Spin half fermions with mass dimension one: theory, phenomenology, and dark matter

We provide the first details on the unexpected theoretical discovery of a spin-one-half matter field with mass dimension one. It is based upon a complete set of dual-helicity eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity, it belongs to a non-standard Wigner class. Consequently, the theory exhibits non-locality with (CPT)^2 = - I. We briefly discuss its relevance to the cosmological `horizon problem'. Because the introduced fermionic field is endowed with mass dimension one, it can carry a quartic self-interaction. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate the new fermion as a prime dark matter candidate. Taking this suggestion seriously we study a supernova-like explosion of a galactic-mass dark matter cloud to set limits on the mass of the new particle and present a calculation on relic abundance to constrain the relevant cross-section. The analysis favours light mass (roughly 20 MeV) and relevant cross-section of about 2 pb. Similarities and differences with the WIMP and mirror matter proposals for dark matter are enumerated. In a critique of the theory we bare a hint on non-commutative aspects of spacetime, and energy-momentum space.Comment: 78 pages [Changes: referee-suggested improvements, additional important references, and better readability

Identifying habitation patterns in world heritage areas through social media and open datasets

Although cities with World Heritage (WH) areas worldwide are socially active, specific social and cultural complexities are associated primarily with the abandonment and decay of districts. Contemporary habitation patterns in historic districts require technology to understand parallel realities in protected areas. This stakeholders-based approach benefits significantly from cross-referencing locative social media and open data sources. Therefore, the concepts put forward in this paper use evidence from an empirical case of WH areas in selected Spanish urban sites. The cartographic correlation of data identifies hotspots of activities and coldspots around services within each site. The results present two significant findings. The first confirms the successful implementation of a digital method to support current transitions for the historic city. The second demonstrates that social networks and open datasets can mirror contemporary social interaction in historic cities. Finally, the study calls on further investigating Artificial Intelligence-based assessments for the future of WH areas

Functional divergence in the role of N-linked glycosylation in smoothened signaling

The G protein-coupled receptor (GPCR) Smoothened (Smo) is the requisite signal transducer of the evolutionarily conserved Hedgehog (Hh) pathway. Although aspects of Smo signaling are conserved from Drosophila to vertebrates, significant differences have evolved. These include changes in its active sub-cellular localization, and the ability of vertebrate Smo to induce distinct G protein-dependent and independent signals in response to ligand. Whereas the canonical Smo signal to Gli transcriptional effectors occurs in a G protein-independent manner, its non-canonical signal employs Gαi. Whether vertebrate Smo can selectively bias its signal between these routes is not yet known. N-linked glycosylation is a post-translational modification that can influence GPCR trafficking, ligand responsiveness and signal output. Smo proteins in Drosophila and vertebrate systems harbor N-linked glycans, but their role in Smo signaling has not been established. Herein, we present a comprehensive analysis of Drosophila and murine Smo glycosylation that supports a functional divergence in the contribution of N-linked glycans to signaling. Of the seven predicted glycan acceptor sites in Drosophila Smo, one is essential. Loss of N-glycosylation at this site disrupted Smo trafficking and attenuated its signaling capability. In stark contrast, we found that all four predicted N-glycosylation sites on murine Smo were dispensable for proper trafficking, agonist binding and canonical signal induction. However, the under-glycosylated protein was compromised in its ability to induce a non-canonical signal through Gαi, providing for the first time evidence that Smo can bias its signal and that a post-translational modification can impact this process. As such, we postulate a profound shift in N-glycan function from affecting Smo ER exit in flies to influencing its signal output in mice

Could dark energy be vector-like?

In this paper I explore whether a vector field can be the origin of the present stage of cosmic acceleration. In order to avoid violations of isotropy, the vector has be part of a ``cosmic triad'', that is, a set of three identical vectors pointing in mutually orthogonal spatial directions. A triad is indeed able to drive a stage of late accelerated expansion in the universe, and there exist tracking attractors that render cosmic evolution insensitive to initial conditions. However, as in most other models, the onset of cosmic acceleration is determined by a parameter that has to be tuned to reproduce current observations. The triad equation of state can be sufficiently close to minus one today, and for tachyonic models it might be even less than that. I briefly analyze linear cosmological perturbation theory in the presence of a triad. It turns out that the existence of non-vanishing spatial vectors invalidates the decomposition theorem, i.e. scalar, vector and tensor perturbations do not decouple from each other. In a simplified case it is possible to analytically study the stability of the triad along the different cosmological attractors. The triad is classically stable during inflation, radiation and matter domination, but it is unstable during (late-time) cosmic acceleration. I argue that this instability is not likely to have a significant impact at present.Comment: 28 pages, 6 figures. Uses RevTeX4. v2: Discussion about relation to phantoms added and additional references cite

A Practical Vision of Heritage Tourism in Low-Population- Density Areas. The Spanish Mediterranean as a Case Study

Heritage tourism bases its definition on searching for different, authentic, and somewhat unexplored places. Recent literature speaks of the growth of new forms of tourism based on the tradition that seeks to surprise visitors with popular culture, traditional activities, or actions that bring traditional culture closer to tourists. However, the reality is that the influx of tourists to small mountain villages is marked by the most “monumental” historical and architectural values, leaving aside some other minor attributes. This article uses the historical centres of rural villages to place inhabitants’ knowledge at the centre of tourism initiatives. The aim of the study was to develop cohesive and inclusive tourism activities in historic centres by analysing the built environment’s attributes and values. A participatory methodology marks the cultural change to enhance collaboration through transparent and ethical foundations and respect these places’ distinctive character. The study of values helped to conduct an in-depth analysis of local realities to document and map historical centres’ tangible attributes through crafts, traditional culture, and local heritage forms

The Heritagization of a Mediterranean Vernacular Mountain Landscape: Concepts, Problems and Processes

The concepts of heritage and landscape have always changed or been developed based on the social context of the time. For decades, attempts have been made to find a pragmatic definition for a changing setting where values, evolve or disappear in step with the changing ways and styles of life of each society. Heritage and landscape have inherent values such as identity, culture, authenticity or integrity, that is to say, landscape character. Current heritagization processes that lead to an understanding of the palimpsest of landscape and heritage layers need to be participatory and inclusive as their importance and sustainability depend on this. This article shows how the early stages of a heritagization process unfold in a small region of the western Mediterranean, Penyagolosa (Castellón). The current problems of the region - depopulation, abandonment and loss of culture and identity - are assessed in search of an understanding and appreciation of a heritage landscape. The research uses techniques such as photo elicitation in a workshops, GIS analysis and evaluates the different options to characterize the landscape offered by different researchers. The analysis explains the different phases of the research to establish the basis of the heritagization of this setting. The study also established a parallel perspective for valorization between researchers and local population - objective and subjective visions - thus encouraging the interest of the social majority linked to the landscape

A GIS-based methodology for the appraisal of historical, architectural, and social values in historic urban cores

Historic environments represent the evolution of materials and techniques that have been used for the construction these environments over the centuries. Entering into the study of this field entails working not only on the crafts that have constructed these environments but also on the people who made, used, and reinterpreted them by learning about the craftsmen and the idiosyncrasies of the place. The study has adopted several methodologies as reference to examine the material and cultural reality of the rural region of Valencia, Spain. Through the adaptation of international methodologies, researchers have carried out a digital database that compiles and maps out the results of the Local Character Assessment of ten Histotiric Urban Cores by incorporating the historical, architectural, and social values to reinforce the Territorial Heritage Action Plan. One of the critical innovations adopted by this form of assessment is the compulsory integration of tangible and intangible heritage through the active involvement of users and makers. Another innovation is to understand the values behind the dynamism and transformation of historic sites. Hence, this study advances theory and practice on the transmission of knowledge among artisans, researchers, and the population and how contemporary practices help acquire new meanings that overlap the past ones