Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0_0

Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.Comment: 30 page

Interventions for female drug-using offenders (Review)

Kumar KM,

Using the past to constrain the future: how the palaeorecord can improve estimates of global warming

Climate sensitivity is defined as the change in global mean equilibrium temperature after a doubling of atmospheric CO2 concentration and provides a simple measure of global warming. An early estimate of climate sensitivity, 1.5-4.5{\deg}C, has changed little subsequently, including the latest assessment by the Intergovernmental Panel on Climate Change. The persistence of such large uncertainties in this simple measure casts doubt on our understanding of the mechanisms of climate change and our ability to predict the response of the climate system to future perturbations. This has motivated continued attempts to constrain the range with climate data, alone or in conjunction with models. The majority of studies use data from the instrumental period (post-1850) but recent work has made use of information about the large climate changes experienced in the geological past. In this review, we first outline approaches that estimate climate sensitivity using instrumental climate observations and then summarise attempts to use the record of climate change on geological timescales. We examine the limitations of these studies and suggest ways in which the power of the palaeoclimate record could be better used to reduce uncertainties in our predictions of climate sensitivity.Comment: The final, definitive version of this paper has been published in Progress in Physical Geography, 31(5), 2007 by SAGE Publications Ltd, All rights reserved. \c{opyright} 2007 Edwards, Crucifix and Harriso

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Interventions for female drug-using offenders

Background This review represents one in a family of three reviews focusing on the effectiveness of interventions in reducing drug use and criminal activity for offenders. Objectives To assess the effectiveness of interventions for female drug‐using offenders in reducing criminal activity, or drug use, or both. Search methods We searched 12 electronic bibliographic databases up to February 2019. Selection criteria We included randomised controlled trials (RCTs). Data collection and analysis We used standard methodological procedures expected by Cochrane. Main results We included 13 trials with 2560 participants. Interventions were delivered in prison (7/13 studies, 53%) and community (6/13 studies, 47%) settings. The rating of bias was affected by the lack of clear reporting by authors, and we rated many items as 'unclear'. In two studies (190 participants) collaborative case management in comparison to treatment as usual did not reduce drug use (risk ratio (RR) 0.65, 95% confidence interval (CI) 0.20 to 2.12; 1 study, 77 participants; low‐certainty evidence), reincarceration at nine months (RR 0.71, 95% CI 0.32 to 1.57; 1 study, 77 participants; low‐certainty evidence), and number of subsequent arrests at 12 months (RR 1.11, 95% CI 0.83 to 1.49; 1 study, 113 participants; low‐certainty evidence). One study (36 participants) comparing buprenorphine to placebo showed no significant reduction in self‐reported drug use at end of treatment (RR 0.57, 95% CI 0.27 to 1.20) and three months (RR 0.58, 95% CI 0.25 to 1.35); very low‐certainty evidence. No adverse events were reported. One study (38 participants) comparing interpersonal psychotherapy to a psychoeducational intervention did not find reduction in drug use at three months (RR 0.67, 95% CI 0.30 to 1.50; low‐certainty evidence). One study (31 participants) comparing acceptance and commitment therapy (ACT) to a waiting list showed no significant reduction in self‐reported drug use using the Addiction Severity Index (mean difference (MD) ‐0.04, 95% CI ‐0.37 to 0.29) and abstinence from drug use at six months (RR 2.89, 95% CI 0.73 to 11.43); low‐certainty evidence. One study (314 participants) comparing cognitive behavioural skills to a therapeutic community programme and aftercare showed no significant reduction in self‐reported drug use (RR 0.86, 95% CI 0.58 to 1.27), re‐arrest for any type of crime (RR 0.73, 95% CI 0.52 to 1.03); criminal activity (RR 0.80, 95% CI 0.63 to 1.03), or drug‐related crime (RR 0.95, 95% CI 0.68 to 1.32). A significant reduction for arrested (not for parole) violations at six months follow‐up was significantly in favour of cognitive behavioural skills (RR 0.43, 95% CI 0.25 to 0.77; very low‐certainty evidence). A second study with 115 participants comparing cognitive behavioural skills to an alternative substance abuse treatment showed no significant reduction in reincarceration at 12 months (RR 0.70, 95% CI 0.43 to 1.12; low certainty‐evidence. One study (44 participants) comparing cognitive behavioural skills and standard therapy versus treatment as usual showed no significant reduction in Addiction Severity Index (ASI) drug score at three months (MD 0.02, 95% CI ‐0.05 to 0.09) and six months (MD ‐0.02, 95% CI ‐0.09 to 0.05), and incarceration at three months (RR 0.46, 95% CI 0.04 to 4.68) and six months (RR 0.51, 95% CI 0.20 to 1.27); very low‐certainty evidence. One study (171 participants) comparing a single computerised intervention versus case management showed no significant reduction in the number of days not using drugs at three months (MD ‐0.89, 95% CI ‐4.83 to 3.05; low certainty‐evidence). One study (116 participants) comparing dialectic behavioural therapy and case management (DBT‐CM) versus a health promotion intervention showed no significant reduction at six months follow‐up in positive drug testing (RR 0.67, 95% CI 0.43 to 1.03), number of people not using marijuana (RR 1.23, 95% CI 0.95 to 1.59), crack (RR 1.00, 95% CI 0.87 to 1.14), cocaine (RR 1.02, 95% CI 0.93 to 1.12), heroin (RR 1.05, 95% CI 0.98 to 1.13), methamphetamine (RR 1.02, 95% CI 0.87 to 1.20), and self‐reported drug use for any drug (RR 1.20, 95% CI 0.92 to 1.56); very low‐certainty evidence. One study (211 participants) comparing a therapeutic community programme versus work release showed no significant reduction in marijuana use at six months (RR 1.03, 95% CI 0.19 to 5.65), nor 18 months (RR 1.00, 95% CI 0.07 to 14.45), heroin use at six months (RR 1.59, 95% CI 0.49 to 5.14), nor 18 months (RR 1.92, 95% CI 0.24 to 15.37), crack use at six months (RR 2.07, 95% CI 0.41 to 10.41), nor 18 months (RR 1.64, 95% CI 0.19 to 14.06), cocaine use at six months (RR 1.09, 95% CI 0.79 to 1.50), nor 18 months (RR 0.93, 95% CI 0.64 to 1.35). It also showed no significant reduction in incarceration for drug offences at 18 months (RR 1.45, 95% CI 0.87 to 2.42); with overall very low‐ to low‐certainty evidence. One study (511 participants) comparing intensive discharge planning and case management versus prison only showed no significant reduction in use of marijuana (RR 0.79, 95% CI 0.53 to 1.16), hard drugs (RR 1.12, 95% CI 0.88 to 1.43), crack cocaine (RR 1.08, 95% CI 0.75 to 1.54), nor positive hair testing for marijuana (RR 0.75, 95% CI 0.55 to 1.03); it found a significant reduction in arrests (RR 0.19, 95% CI 0.04 to 0.87), but no significant reduction in drug charges (RR 1.07, 95% CI 0.75 to 1.53) nor incarceration (RR 1.09, 95% CI 0.86 to 1.39); moderate‐certainty evidence. One narrative study summary (211 participants) comparing buprenorphine pre‐ and post‐release from prison showed no significant reduction in drug use at 12 months post‐release; low certainty‐evidence. No adverse effects were reported. Authors' conclusions The studies showed a high degree of heterogeneity for types of comparisons, outcome measures and small samples. Descriptions of treatment modalities are required. On one outcome of arrest (no parole violations), we identified a significant reduction when cognitive behavioural therapy (CBT) was compared to a therapeutic community programme. But for all other outcomes, none of the interventions were effective. Larger trials are required to increase the precision of confidence about the certainty of evidence

Triangulation network of 1929-1944 of the first 1:500 urban map of València

[EN] Triangulation is a surveying method on which earlier maps made were based. Although the origins of the method can be traced back to the 16th century, it is still used today, with minor changes, to adjust networks observed with modern geodetic techniques. In this paper we present the geodetic survey work that was carried out for the primary triangulation network of the first 1:500 urban map of the city of València (Spain). It spanned from 1929 to 1944 and resulted in 421 maps covering about 174 square kilometres. We focus on four key elements to define the geometric framework of a map: (1) the geodetic network, (2) the cartographic projection, (3) the baseline measurements, and (4) the primary triangulation. The paper is based on the interpretation of original documents and field books recovered from the archives of the València City Council. In order to check the accuracy and consistency of the survey work, we recomputed all calculations directly from the field data, following the mathematical procedures of the time. We obtained a set of transformation parameters to convert the coordinates of 1929 to current coordinates based on the European Terrestrial Reference System of 1989 (ETRS89). Results showed that the 1929 primary triangulation angles and coordinates are accurate to 8 s of arc and 35 cm respectively, and that the coordinates transform well into the current reference system with average residuals of 26 cm across nine control points, demonstrating the high quality of the 1929 work.Villar-Cano, M.; Marqués-Mateu, Á.; Jiménez-Martínez, MJ. (2020). Triangulation network of 1929-1944 of the first 1:500 urban map of València. Survey Review (Online). 52(373):317-329. https://doi.org/10.1080/00396265.2018.1564599S31732952373Bitelli, G., Cremonini, S., & Gatta, G. (2014). Cartographic heritage: Toward unconventional methods for quantitative analysis of pre-geodetic maps. Journal of Cultural Heritage, 15(2), 183-195. doi:10.1016/j.culher.2013.04.003Blachut, T. J., Chrzanowski, A., & Saastamoinen, J. H. (1979). Urban Surveying and Mapping. doi:10.1007/978-1-4612-6145-2Brinker, R. C., & Minnick, R. (Eds.). (1987). The Surveying Handbook. doi:10.1007/978-1-4757-1188-2Gatta, G. 2010. Valorizzazione di cartografia storica attraverso moderne tecniche geomatiche: recupero metrico, elaborazione e consultazione in ambiente digitale [Valuation of historic cartography using modern geomatics techniques: metric recovering, making and use in digital environment]. Doctoral thesis. Bologna: Universitá di Bologna. 295 pages. (In Italian).Gorse, C., Johnston, D., & Pritchard, M. (2012). A Dictionary of Construction, Surveying and Civil Engineering. doi:10.1093/acref/9780199534463.001.0001Hotine, M. (1939). THE RE-TRIANGULATION OF GREAT BRITAIN IV—BASE MEASUREMENT. Empire Survey Review, 5(34), 211-225. doi:10.1179/sre.1939.5.34.211Kahmen, H., & Faig, W. (1988). Surveying. doi:10.1515/9783110845716Leick, A., Rapoport, L., & Tatarnikov, D. (2015). GPS Satellite Surveying. doi:10.1002/9781119018612Murdin, P. (2009). Full Meridian of Glory. doi:10.1007/978-0-387-75534-2Schofield, W., & Breach, M. (2007). Engineering Surveying. doi:10.1201/b12847Seeber, G. (2003). Satellite Geodesy. doi:10.1515/9783110200089Snyder, J. P. (1987). Map projections: A working manual. Professional Paper. doi:10.3133/pp139

Gravitational Lensing at Millimeter Wavelengths

With today's millimeter and submillimeter instruments observers use gravitational lensing mostly as a tool to boost the sensitivity when observing distant objects. This is evident through the dominance of gravitationally lensed objects among those detected in CO rotational lines at z>1. It is also evident in the use of lensing magnification by galaxy clusters in order to reach faint submm/mm continuum sources. There are, however, a few cases where millimeter lines have been directly involved in understanding lensing configurations. Future mm/submm instruments, such as the ALMA interferometer, will have both the sensitivity and the angular resolution to allow detailed observations of gravitational lenses. The almost constant sensitivity to dust emission over the redshift range z=1-10 means that the likelihood for strong lensing of dust continuum sources is much higher than for optically selected sources. A large number of new strong lenses are therefore likely to be discovered with ALMA, allowing a direct assessment of cosmological parameters through lens statistics. Combined with an angular resolution <0.1", ALMA will also be efficient for probing the gravitational potential of galaxy clusters, where we will be able to study both the sources and the lenses themselves, free of obscuration and extinction corrections, derive rotation curves for the lenses, their orientation and, thus, greatly constrain lens models.Comment: 69 pages, Review on quasar lensing. Part of a LNP Topical Volume on "Dark matter and gravitational lensing", eds. F. Courbin, D. Minniti. To be published by Springer-Verlag 2002. Paper with full resolution figures can be found at ftp://oden.oso.chalmers.se/pub/tommy/mmviews.ps.g

Observers and Locality in Everett Quantum Field Theory

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory [M. A. Rubin, Found. Phys. 32, 1495-1523 (2002)]. Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations of the results of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is applied to a calculation of the quintessential "nonlocal" quantum phenomenon, spin correlations in the Einstein-Podolsky-Rosen-Bohm experiment.Comment: Some changes to introduction and discussion sections, typos corrected, conclusions unchanged. To appear in Foundations of Physic