Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

The Age of Artificial Intelligence: Use of Digital Technology in Clinical Nutrition

Purpose of review Computing advances over the decades have catalyzed the pervasive integration of digital technology in the medical industry, now followed by similar applications for clinical nutrition. This review discusses the implementation of such technologies for nutrition, ranging from the use of mobile apps and wearable technologies to the development of decision support tools for parenteral nutrition and use of telehealth for remote assessment of nutrition. Recent findings Mobile applications and wearable technologies have provided opportunities for real-time collection of granular nutrition-related data. Machine learning has allowed for more complex analyses of the increasing volume of data collected. The combination of these tools has also translated into practical clinical applications, such as decision support tools, risk prediction, and diet optimization. Summary The state of digital technology for clinical nutrition is still young, although there is much promise for growth and disruption in the future

Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Archeological Survey and Testing of Selected Prehistoric Sites along FM 481, Zavala County, Texas

Between April 1981 and December 1982, Texas Department of Transportation (TxDOT) personnel conducted archeological fieldwork along an approximately 13-km segment of FM 481 in northwest Zavala County. The work was part of an evaluation of the impacts of road improvements to a series of sites along the right-of-way. All of the sites but one (41ZV202) were found not to be eligible for listing on the National Register of Historic Places and not to warrant designations as State Archeological Landmarks. Additional work, not reported here, was later conducted at 41ZV202. As part of Work Authorization #57015PD004, the Environmental Affairs Division of TxDOT contracted with the Center for Archaeological Research (CAR) of The University of Texas at San Antonio to report on the fieldwork carried out at the sites during the early 1980s, identify data types warranting additional research, and conduct the appropriate analyses. The current document provides descriptions of the work undertaken along FM 481, assesses the analytical utility of the data types recovered, and reports the results of limited new research of selected data types. Note that all documentation of the project, including notes, photographs, and a sample of recovered artifacts are curated at the Center for Archaeological Research. The sample includes all projectile points, as well as other chipped and ground stone tools, and the debitage recovered for a 10% sample of proveniences

Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Rationale and design: telepsychology service delivery for depressed elderly veterans

BACKGROUND: Older adults who live in rural areas experience significant disparities in health status and access to mental health care. "Telepsychology," (also referred to as "telepsychiatry," or "telemental health") represents a potential strategy towards addressing this longstanding problem. Older adults may benefit from telepsychology due to its: (1) utility to address existing problematic access to care for rural residents; (2) capacity to reduce stigma associated with traditional mental health care; and (3) utility to overcome significant age-related problems in ambulation and transportation. Moreover, preliminary evidence indicates that telepsychiatry programs are often less expensive for patients, and reduce travel time, travel costs, and time off from work. Thus, telepsychology may provide a cost-efficient solution to access-to-care problems in rural areas. METHODS: We describe an ongoing four-year prospective, randomized clinical trial comparing the effectiveness of an empirically supported treatment for major depressive disorder, Behavioral Activation, delivered either via in-home videoconferencing technology ("Telepsychology") or traditional face-to-face services ("Same-Room"). Our hypothesis is that inhome Telepsychology service delivery will be equally effective as the traditional mode (Same-Room). Two-hundred twenty-four (224) male and female elderly participants will be administered protocol-driven individual Behavioral Activation therapy for depression over an 8-week period; and subjects will be followed for 12-months to ascertain longer-term effects of the treatment on three outcomes domains: (1) clinical outcomes (symptom severity, social functioning); (2) process variables (patient satisfaction, treatment credibility, attendance, adherence, dropout); and (3) economic outcomes (cost and resource use). DISCUSSION: Results from the proposed study will provide important insight into whether telepsychology service delivery is as effective as the traditional mode of service delivery, defined in terms of clinical, process, and economic outcomes, for elderly patients with depression residing in rural areas without adequate access to mental health services. TRIAL REGISTRATION: National Institutes of Health Clinical Trials Registry (ClinicalTrials.gov identifier# NCT00324701)

Archeological Testing and Data Recovery at 41ZV202, Zavala County, Texas

At the request of the Texas Department of Transportation, Environmental Affairs Division (TxDOT-ENV), the Center for Archaeological Research (CAR) of The University of Texas at San Antonio (UTSA) conducted archeological significance testing at 41ZV202, a prehistoric site located in northwestern Zavala County, in March of 2003. The work, conducted under Texas Antiquities Permit No. 3071 issued to Dr. Steven A. Tomka, was done in anticipation of the potential widening by TxDOT of FM 481. While materials dating to the Archaic were also present, the testing demonstrated the presence of significant Late Prehistoric (Austin Interval) deposits with good integrity within a portion of the TxDOT right-of-way (ROW). As TxDOT construction could not avoid these deposits, and as both the Texas Historical Commission (THC) and TxDOT concurred with CAR’s recommendations that the deposits were eligible for listing on the National Register of Historic Places (NRHP) under criterion d of 36CFR 60.4, data recovery investigations were initiated. CAR began that work in July and August of 2003. The testing permit was amended to include the data recovery efforts. Dr. Russell Greaves served as project archeologist for both the testing and data recovery effort at 41ZV202. The testing and data recovery work consisted of the excavation of a 53-m-long Gradall trench, exposing and profiling a 75-m-long road cut, and the hand excavation of 52 1 x 1 meter units that removed approximately 34.6 m3 of soil. Testing identified two large, dark stained areas designated Features 4 and 5, an associated hearth (Feature 7), and a small cluster of FCR (Feature 6). Just over 1,000 chipped stone items were recovered, including several Scallorn points, one reworked dart point, several bifaces, and two flake tools. Eleven AMS radiocarbon dates were submitted from deposits, with eight clustering around 1000 BP. Data recovery efforts defined FCR features 8 through 13. In addition, 24 arrow points, several dart points, a variety of unifacial and bifacial tools, a small number of cores, roughly 6,000 pieces of debitage, and a variety of burned sandstone, were recovered. We also collected small quantities of bone and mussel shell along with about 14,350 gastropod shells, and a variety of soil samples. Finally, all calcium carbonate nodules were retained from the screens. Following the completion of data recovery efforts, the CAR was directed by TxDOT to develop a research design for the analysis of the material from 41ZV202. TxDOT and THC accepted that research design in November of 2004, at which time the CAR began analysis and report production. Unfortunately, by 2005 project archeologist Russell Greaves had left the CAR. At that point, CAR assistant director Dr. Raymond Mauldin took over the project. The analysis of the 41ZV202 Late Prehistoric data outlined in this report is conducted in the context of a large-scale, theoretically driven model of adaptation for hunters and gatherers loosely based on aspects of Optimal Foraging Theory. In addition to 41ZV202, the approach relies on comparative data sets from Late Archaic and other Late Prehistoric sites from South and South-Central Texas to investigate shifts in subsistence, technology, and mobility across this broad region. At this time, discard decisions have not been made. However, all artifacts and associated samples collected and retained during this project, along with all project-associated documentation, are to be permanently curated at the CAR according to Texas Historical Commission guidelines

The driving factors of new particle formation and growth in the polluted boundary layer

New particle formation (NPF) is a significant source of atmospheric particles, affecting climate and air quality. Understanding the mechanisms involved in urban aerosols is important to develop effective mitigation strategies. However, NPF rates reported in the polluted boundary layer span more than 4 orders of magnitude, and the reasons behind this variability are the subject of intense scientific debate. Multiple atmospheric vapours have been postulated to participate in NPF, including sulfuric acid, ammonia, amines and organics, but their relative roles remain unclear. We investigated NPF in the CLOUD chamber using mixtures of anthropogenic vapours that simulate polluted boundary layer conditions. We demonstrate that NPF in polluted environments is largely driven by the formation of sulfuric acid&ndash;base clusters, stabilized by the presence of amines, high ammonia concentrations and lower temperatures. Aromatic oxidation products, despite their extremely low volatility, play a minor role in NPF in the chosen urban environment but can be important for particle growth and hence for the survival of newly formed particles. Our measurements quantitatively account for NPF in highly diverse urban environments and explain its large observed variability. Such quantitative information obtained under controlled laboratory conditions will help the interpretation of future ambient observations of NPF rates in polluted atmospheres. Full List of Authors: Mao Xiao1, Christopher R. Hoyle1,2, Lubna Dada3, Dominik Stolzenburg4, Andreas K&uuml;rten5, Mingyi Wang6, Houssni Lamkaddam1, Olga Garmash3, Bernhard Mentler7, Ugo Molteni1, Andrea Baccarini1, Mario Simon5, Xu-Cheng He3, Katrianne Lehtipalo3,8, Lauri R. Ahonen3, Rima Baalbaki3, Paulus S. Bauer4, Lisa Beck3, David Bell1, Federico Bianchi3, Sophia Brilke4, Dexian Chen6, Randall Chiu9, Ant&oacute;nio Dias10, Jonathan Duplissy3,11, Henning Finkenzeller9, Hamish Gordon6, Victoria Hofbauer6, Changhyuk Kim13,14, Theodore K. Koenig9,a, Janne Lampilahti3, Chuan Ping Lee1, Zijun Li15, Huajun Mai13, Vladimir Makhmutov16, Hanna E. Manninen17, Ruby Marten1, Serge Mathot17, Roy L. Mauldin18,19, Wei Nie20, Antti Onnela17, Eva Partoll7, Tuukka Pet&auml;j&auml;3, Joschka Pfeifer5,17, Veronika Pospisilova1, Lauriane L. J. Qu&eacute;l&eacute;ver3, Matti Rissanen3,b, Siegfried Schobesberger15, Simone Schuchmann17,c, Yuri Stozhkov16, Christian Tauber4, Yee Jun Tham3, Ant&oacute;nio Tom&eacute;21, Miguel Vazquez-Pufleau4, Andrea C. Wagner5,9,d, Robert Wagner3, Yonghong Wang3, Lena Weitz5, Daniela Wimmer3,4, Yusheng Wu3, Chao Yan3, Penglin Ye6,22, Qing Ye6, Qiaozhi Zha3, Xueqin Zhou5, Antonio Amorim10, Ken Carslaw12, Joachim Curtius5, Armin Hansel7, Rainer Volkamer9,19, Paul M. Winkler4, Richard C. Flagan13, Markku Kulmala3,11,20,23, Douglas R. Worsnop3,22, Jasper Kirkby5,17, Neil M. Donahue6, Urs Baltensperger1, Imad El Haddad1, and Josef Dommen1 1Laboratory of Atmospheric Chemistry, Paul Scherrer Institute, 5232 Villigen, Switzerland 2Institute for Atmospheric and Climate Science, ETH Zurich, 8092 Zurich, Switzerland 3Institute for Atmospheric and Earth System Research (INAR)/Physics, University of Helsinki, 00014 Helsinki, Finland 4Faculty of Physics, University of Vienna, 1090 Vienna, Austria 5Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany 6Center for Atmospheric Particle Studies, Carnegie Mellon University, Pittsburgh, PA 15213, USA 7Institute of Ion Physics and Applied Physics, University of Innsbruck, 6020 Innsbruck, Austria 8Atmospheric Composition Research Unit, Finnish Meteorological Institute, 00560 Helsinki, Finland 9Department of Chemistry &amp; CIRES, University of Colorado Boulder, Boulder, CO 80309, USA 10CENTRA and FCUL, University of Lisbon, 1749-016 Lisbon, Portugal 11Helsinki Institute of Physics, University of Helsinki, 00014 Helsinki, Finland 12School of Earth and Environment, University of Leeds, LS2 9JT Leeds, United Kingdom 13Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA 14School of Civil and Environmental Engineering, Pusan National University, 46241 Busan, Republic of Korea 15Department of Applied Physics, University of Eastern Finland, 70211 Kuopio, Finland 16Solar and Cosmic Ray Physics Laboratory, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russian Federation 17CERN, 1211 Geneva, Switzerland 18Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA 19Department of Oceanic and Atmospheric Sciences, University of Colorado Boulder, Boulder, CO 80309, USA 20Joint International Research Laboratory of Atmospheric and Earth System Sciences, School of Atmospheric Sciences, Nanjing University, Nanjing, Jiangsu Province, China 21IDL-Universidade da Beira Interior, Covilh&atilde;, Portugal 22Aerodyne Research Inc., Billerica, MA 01821-3976, USA 23Aerosol and Haze Laboratory, Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing, China anow at: College of Environmental Sciences and Engineering, Peking University, 100871 Beijing, China bnow at: Aerosol Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, 33720 Tampere, Finland cnow at: Experimentelle Teilchen- und Astroteilchenphysik, Johannes Gutenberg University Mainz, 55128 Mainz, Germany dnow at: Department of Chemistry &amp; CIRES, University of Colorado Boulder, Boulder, CO 80305, USA Correspondence: Urs Baltensperger ([email protected]) and Imad El Haddad ([email protected])</p

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co