Conjugacy in Garside Groups III: Periodic braids

An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B_n are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known isomorphisms between Garside structures in the braid group B_n and other Garside groups. This allows us to obtain a polynomial solution to the original problem in the spirit of the previously known algorithms. This paper is the third in a series of papers by the same authors about the conjugacy problem in Garside groups. They have a unified goal: the development of a polynomial algorithm for the conjugacy decision and search problems in B_n, which generalizes to other Garside groups whenever possible. It is our hope that the methods introduced here will allow the generalization of the results in this paper to all Artin-Tits groups of spherical type.Comment: 33 pages, 13 figures. Classical references implying Corollaries 12 and 15 have been added. To appear in Journal of Algebr

Conjugacy in Garside groups I: Cyclings, powers, and rigidity

In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where 'rigid' means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given X in a Garside group, if some power X^m is conjugate to a rigid element, then m can be bounded above by ||\Delta||^3. In the particular case of braid groups, this implies that a pseudo-Anosov braid has a small power whose ultra summit set consists of rigid elements. This solves one of the problems in the way of a polynomial solution to the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in braid groups. In addition to proving the rigidity theorem, it will be shown how this paper fits into the authors' program for finding a polynomial algorithm to the CDP/CSP, and what remains to be done.Comment: 41 page

Single Stellar Populations in the Near-Infrared - I. Preparation of the IRTF spectral stellar library

We present a detailed study of the stars of the IRTF spectral library to understand its full extent and reliability for use with Stellar Population (SP) modeling. The library consist of 210 stars, with a total of 292 spectra, covering the wavelength range of 0.94 to 2.41 micron at a resolution R = 2000. For every star we infer the effective temperature (Teff), gravity (logg) and metallicity ([Z/Zsun]) using a full-spectrum fitting approach in a section of the K band (2.19 to 2.34 micron) and temperature-NIR colour relations. We test the flux calibration of these stars by calculating their integrated colours and comparing them with the Pickles library colour-temperature relations. We also investigate the NIR colours as a function of the calculated effective temperature and compared them in colour-colour diagrams with the Pickles library. This latter test shows a good broad-band flux calibration, important for the SP models. Finally, we measure the resolution R as a function of wavelength. We find that the resolution increases as a function of lambda from about 6 angstrom in J to 10 angstrom in the red part of the K-band. With these tests we establish that the IRTF library, the largest currently available general library of stars at intermediate resolution in the NIR, is an excellent candidate to be used in stellar population models. We present these models in the next paper of this series.Comment: 17 pages, 19 figures. Accepted for publication in Astronomy and Astrophysic

Energy poverty, crisis and austerity in Spain

Despite clear indications about its significance, a systematic examination of the connection between the European debt crisis and domestic energy affordability trends is still missing in the academic and policy literature. This paper seeks to provide an empirically-grounded investigation of crisis and austerity as macro-scale driving factors of energy poverty, taking Spain as a case study. For this, a range of data and indicators are presented for the period 2004-2012. They provide evidence of the increase in domestic energy deprivation levels in Spain since 2008 that occurred in parallel with a rapid surge in unemployment rates and domestic energy prices, especially of electricity. Collected evidence also indicates substantial differences in energy poverty levels across Spanish regions (Autonomous Communities) linked to disparities in climatic and socio-economic conditions, including unemployment. Resulting energy poverty levels are understood as a consequence of structural and short-term factors operating along pre-existing socio-spatial cleavages exacerbated by the crisis

Comunidades vegetales de los bofedales de la Cordillera Real (Bolivia) bajo el calentamiento global

Los humedales altoandinos (bofedales) son uno de los más amenazados frente al calentamiento global. Dada la estrecha relación entre bofedales y agua, el retroceso glacial podrá causar su contracción. Con tres proxis del cambio climático (área de bofedales, influencia glaciar y altitud) se infirió indirectamente cómo éstos pueden afectar a las comunidades vegetales. Las hipótesis fueron 1) que la reducción del área del bofedal podría afectar negativamente la diversidad de plantas - la influencia glaciar y la altitud podrían afectar ésta relación por su efectos en la heterogeneidad ambiental y la diversidad – y 2) que el retroceso glacial puede afectar indirectamente la diversidad a través de cambios en las especies dominantes. Se midió la diversidad α y β aditiva de plantas en 20 bofedales (>4.400 m) de la Cordillera Real (Bolivia). Se encontraron 63 especies (riqueza especifica: 5-22/cuadrante 1m²). Variaciones del área e influencia glacial no se relacionaron con cambios en la vegetación, pero la diversidad fue menor a mayor altitud. Las hojas de Oxychloe andina son más resistentes al estrés ambiental por su mayor masa foliar seca, a diferencia de Distichia spp., indicando que los bofedales dominados por O. andina son más secos. Además tienen más especies que también se pueden encontrar en las laderas. Mientras, las comunidades de Distichia spp. son menos tolerantes al déficit hídrico. Si el retroceso glacial reducirá el agua en las próximas décadas, el bofedal de O. andina podrá ser más abundante a expensas de los de Distichia spp., generando desafíos para la conservación. Oxychloe andina , Retroceso glacial

Analysis of Pedestrian Performance by Integrating both Quantitative and Qualitative Factors

The importance of non-motorized movements, explicitly walking, and its corresponding impact on social, economic, and environmental aspects has always been overlooked due to the convenience brought by motorized vehicles. An automobile-dependent society mirrors the rise and worsening of several transportation problems, such as road-wide traffic congestion, massive fuel consumption, and excessive CO2emissions. In response to these aggravating situations and in support of various national and international calls, the main objective of this study was to extract the significant factors influencing the pedestrian level of service and walkability and to subsequently develop a predictive mathematical model for evaluating pedestrian conditions. Factors influencing the pedestrian level of service and walkability were initially identified through an extensive review and evaluation of existing studies, literature, and other relevant resources. A cause-and-effect analysis was used to develop an Ishikawa Diagram tackling pedestrian performance. The finalized factors were incorporated into the development of the Pedestrian Performance Assessment Questionnaire (PPAQ), which was utilized for data acquisition. Survey responses were then subjected to factor analysis after satisfying several tests for assumptions and suitability to extract the root causes influencing pedestrian performance. The validated root causes were then integrated to form the Pedestrian Performance Audit Tool (PPAT), a tool used in evaluating pedestrian areas in Tarlac City, Philippines. Data was analyzed through ordinal regression analysis to develop the multi-objective pedestrian performance prediction model. Results showed that there are six critical predictors of pedestrian performance unified in the final mathematical model: Pedestrian Space (PS), Official’s Intervention (OI), Ambiance (A), Vibrance (V), Street Vendors (SV), and Trash Bins (TB), and is the most significant contribution of the study. The model's validity was ascertained through a confusion matrix, which resulted in an acceptable rating. The comparison between calculated and perceived values together with the use of odds ratios served as the basis for the interpretation of some of the key results and findings. Finally, recommendations were also presented which can be a basis for the development of sustainable programs and interventions for the improvement of the pedestrian system. Doi: 10.28991/CEJ-2022-08-06-02 Full Text: PD