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Network analysis of synonymous codon usage

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arXiv 2019年

作者： Newaz, Khalique Wright, Gabriel Piland, Jacob Li, Jun Clark, Patricia Emrich, Scott Milenković, Tijana Department of Computer Science and Engineering University of Notre Dame Notre DameIN46556 United States Interdisciplinary Center for Network Science and Applications University of Notre Dame Notre DameIN46556 United States Eck Institute for Global Health University of Notre Dame Notre DameIN46556 United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Department of Chemistry and Biochemistry University of Notre Dame Notre DameIN46556 United States Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States

Most amino acids are encoded by multiple synonymous codons. For an amino acid, some of its synonymous codons are used much more rarely than others. Analyses of positions of such rare codons in protein sequences revealed that rare codons can impact co-translational protein folding and that positions of some rare codons are evolutionary conserved. Analyses of positions of rare codons in proteins' 3-dimensional structures, which are richer in biochemical information than sequences alone, might further explain the role of rare codons in protein folding. We analyze a protein set recently annotated with codon usage information, considering non-redundant proteins with sufficient structural information. We model the proteins' structures as networks and study potential differences between network positions of amino acids encoded by evolutionary conserved rare, evolutionary non-conserved rare, and commonly used codons. In 84% of the proteins, at least one of the three codon categories occupies significantly more or less network-central positions than the other codon categories. Different protein groups showing different codon centrality trends (i.e., different types of relationships between network positions of the three codon categories) are enriched in different biological functions, implying the existence of a link between codon usage, protein folding, and protein function. Copyright © 2019, The Authors. All rights reserved.

关键词： Protein folding

A Lagrangian Method for Reactive Transport with Solid/Aqueous Chemical Phase Interaction i

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arXiv 2018年

作者： Schmidt, Michael J. Pankavich, Stephen D. Navarre-Sitchler, Alexis Benson, David A. Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States

A significant drawback of Lagrangian (particle-tracking) reactive transport models has been their inability to properly simulate interactions between solid and liquid chemical phases, such as dissolution and precipitation reactions. This work addresses that problem by implementing a mass-transfer algorithm between mobile and immobile sets of particles that allows aqueous species of reactant that are undergoing transport to interact with stationary solid species. This mass-transfer algorithm is demonstrated to solve the diffusion equation for an arbitrarily small level of diffusion and thus does not introduce any spurious mixing. The algorithm can be combined with random walks to simulate the desired total level of diffusion in a reactive transport system. Copyright © 2018, The Authors. All rights reserved.

关键词： Diffusion

SPT clusters with DES and HST weak lensing. I. Cluster lensing and Bayesian population modeling of multiwavelength cluster datasets

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Physical Review D 2024年第8期110卷 083509页

作者： S. Bocquet S. Grandis L. E. Bleem M. Klein J. J. Mohr M. Aguena A. Alarcon S. Allam S. W. Allen O. Alves A. Amon B. Ansarinejad D. Bacon M. Bayliss K. Bechtol M. R. Becker B. A. Benson G. M. Bernstein M. Brodwin D. Brooks A. Campos R. E. A. Canning J. E. Carlstrom A. Carnero Rosell M. Carrasco Kind J. Carretero R. Cawthon C. Chang R. Chen A. Choi J. Cordero M. Costanzi L. N. da Costa M. E. S. Pereira C. Davis J. DeRose S. Desai T. de Haan J. De Vicente H. T. Diehl S. Dodelson P. Doel C. Doux A. Drlica-Wagner K. Eckert J. Elvin-Poole S. Everett I. Ferrero A. Ferté A. M. Flores J. Frieman J. García-Bellido M. Gatti G. Giannini M. D. Gladders D. Gruen R. A. Gruendl I. Harrison W. G. Hartley K. Herner S. R. Hinton D. L. Hollowood W. L. Holzapfel K. Honscheid N. Huang E. M. Huff D. J. James M. Jarvis G. Khullar K. Kim R. Kraft K. Kuehn N. Kuropatkin F. Kéruzoré S. Lee P.-F. Leget N. MacCrann G. Mahler A. Mantz J. L. Marshall J. McCullough M. McDonald J. Mena-Fernández R. Miquel J. Myles A. Navarro-Alsina R. L. C. Ogando A. Palmese S. Pandey A. Pieres A. A. Plazas Malagón J. Prat M. Raveri C. L. Reichardt J. Roberson R. P. Rollins A. K. Romer C. Romero A. Roodman A. J. Ross E. S. Rykoff L. Salvati C. Sánchez E. Sanchez D. Sanchez Cid A. Saro T. Schrabback M. Schubnell L. F. Secco I. Sevilla-Noarbe K. Sharon E. Sheldon T. Shin M. Smith T. Somboonpanyakul B. Stalder A. A. Stark V. Strazzullo E. Suchyta M. E. C. Swanson G. Tarle C. To M. A. Troxel I. Tutusaus T. N. Varga A. von der Linden N. Weaverdyck J. Weller P. Wiseman B. Yanny B. Yin M. Young Y. Zhang J. Zuntz University Observatory Faculty of Physics Universität Innsbruck Institut für Astro- und Teilchenphysik Technikerstr. 25/8 6020 Innsbruck Austria Argonne National Laboratory 9700 South Cass Avenue Lemont Illinois 60439 USA Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Max Planck Institute for Extraterrestrial Physics Gießenbachstr. 1 85748 Garching Germany Laboratório Interinstitucional de e-Astronomia - LIneA Rua Gal. José Cristino 77 Rio de Janeiro RJ-20921-400 Brazil Fermi National Accelerator Laboratory P. O. Box 500 Batavia Illinois 60510 USA Kavli Institute for Particle Astrophysics and Cosmology Stanford University 452 Lomita Mall Stanford California 94305 USA Department of Physics Stanford University 382 Via Pueblo Mall Stanford California 94305 USA SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo Park California 94025 USA Department of Physics University of Michigan Ann Arbor Michigan 48109 USA Institute of Astronomy University of Cambridge Madingley Road Cambridge CB3 0HA United Kingdom Kavli Institute for Cosmology University of Cambridge Madingley Road Cambridge CB3 0HA United Kingdom School of Physics University of Melbourne Parkville Victoria 3010 Australia Institute of Cosmology and Gravitation University of Portsmouth Portsmouth PO1 3FX United Kingdom Department of Physics University of Cincinnati Cincinnati Ohio 45221 USA Physics Department 2320 Chamberlin Hall University of Wisconsin-Madison 1150 University Avenue Madison Wisconsin 53706-1390 USA Department of Astronomy and Astrophysics University of Chicago Chicago Illinois 60637 USA Fermi National Accelerator Laboratory Batavia Illinois 60510-0500 USA Department of Physics and Astronomy University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Physics and Astronomy University of Missouri 5110 Rockhill Road Kansas City Missouri 64110 USA Department of Physics and Astronomy University Coll

We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at z=0.25 to 10% at z=0.95, to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multiobservable likelihood for the Sunyaev-Zel’dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset.

关键词： Cosmological parameters Gravitational lenses Large scale structure of the Universe

Changing life expectancy in European countries 1990–2021: a subanalysis of causes and risk factors from the Global Burden of Disease Study 2021

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The Lancet Public Health 2025年第3期10卷 e172-e188页

作者： Steel, Nicholas Bauer-Staeb, Clarissa Maria Mercedes Ford, John A. Abbafati, Cristiana Abdalla, Mohammed Altigani Abdelkader, Atef Abdi, Parsa Zuñiga, Roberto Ariel Abeldaño Abiodun, Olugbenga Olusola Abolhassani, Hassan Abu-Gharbieh, Eman Abukhadijah, Hana J. Abu-Zaid, Ahmed Addo, Isaac Yeboah Addolorato, Giovanni Adekanmbi, Victor Adetunji, Juliana Bunmi Adeyeoluwa, Temitayo Esther Agardh, Emilie E. Agyemang-Duah, Williams Ahmad, Danish Ahmed, Ayman Ahmed, Syed Anees Akinosoglou, Karolina Akkaif, Mohammed Ahmed Al Awaidy, Salah Al Hasan, Syed Mahfuz Al Zaabi, Omar Ali Mohammed Aldridge, Robert W. Algammal, Abdelazeem M. Al-Gheethi, Adel Ali Saeed Ali, Abid Ali, Mohammed Usman Ali, Syed Shujait Ali, Waad Alicandro, Gianfranco Alif, Sheikh Mohammad Al-Jumaily, Adel Allebeck, Peter Alrawashdeh, Ahmad Al-Rifai, Rami H. Alsabri, Mohammed A. Alshahrani, Najim Z. Aluh, Deborah Oyine Al-Wardat, Mohammad Al-Zyoud, Walid A. Amiri, Sohrab Anderlini, Deanna Andrei, Catalina Liliana Anil, Abhishek Anvari, Saeid Anyasodor, Anayochukwu Edward Appiah, Seth Christopher Yaw Aquilano, Michele Arabloo, Jalal Arafat, Mosab Areda, Demelash Aremu, Abdulfatai Armani, Keivan Armocida, Benedetta Ärnlöv, Johan Asaduzzaman, Muhammad Astell-Burt, Thomas Aujayeb, Avinash Ausloos, Marcel Azadnajafabad, Sina Aziz, Shahkaar Azzam, Ahmed Y. Babu, Giridhara Rathnaiah Badache, Andreea Corina Badiye, Ashish D. Bahramian, Saeed Baig, Atif Amin Baker, Jennifer L. Bansal, Hansi Bärnighausen, Till Winfried Barone, Mark Thomaz Ugliara Barrow, Amadou Barteit, Sandra Bashir, Shahid Bashiru, Hameed Akande Basso, João Diogo Bastan, Mohammad-Mahdi Basu, Sanjay Batra, Kavita Bauckneht, Matteo Baune, Bernhard T. Beghi, Massimiliano Beiranvand, Maryam Béjot, Yannick Bell, Michelle L. Bello, Olorunjuwon Omolaja Belo, Luis Beloukas, Apostolos Beneke, Alice A. Bettencourt, Paulo J.G. Bhagavathula, Akshaya Srikanth Bhala, Neeraj Bhaskar, Sonu Bisulli, Francesca Bjørge, Tone Bodunrin, Aadam Olalekan Carvajal, Alejandro Botero Bouaoud, Souad Brayne, Carol Brenner, H Department of Primary Care and Public Health University of East Anglia Norwich United Kingdom Office for Health Improvement and Disparities Department of Health and Social Care London United Kingdom Department of Legal and Economic Studies La Sapienza University Rome Italy Rome Italy Hull York Medical School University of Hull Hull United Kingdom Department of Mathematics and Sciences Ajman University Ajman United Arab Emirates Department of Medicine Memorial University St. John's NL Canada Postgraduate Department University of Sierra Sur Miahuatlan de Porfirio Diaz Mexico Yhteiskuntadatatieteen keskus (Centre for Social Data Science) Helsinki Finland Department of Internal Medicine Federal Medical Centre Abuja Nigeria Research Center for Immunodeficiencies Tehran University of Medical Sciences Tehran Iran Department of Medical Biochemistry and Biophysics Karolinska Institutet (Karolinska Institute) Stockholm Sweden Department of Clinical Sciences University of Sharjah Sharjah United Arab Emirates Department of Biopharmaceutics and Clinical Pharmacy University of Jordan Amman Jordan Medical Research Center Hamad Medical Corporation Doha Qatar Department of Biochemistry and Molecular Medicine Alfaisal University Riyadh Saudi Arabia College of Graduate Health Sciences University of Tennessee Memphis TN United States School of Medicine Sydney NSW Australia Centre for Social Research in Health University of New South Wales Sydney NSW Australia Internal Medicine and Alcohol Related Disease Unit Fondazione Policlinico Universitario A. Gemelli IRCCS Rome Italy Department of Medical and Surgical Sciences Università Cattolica di Roma (Catholic University of Rome) Rome Italy Department of Obstetrics and Gynecology University of Texas Medical Branch Galveston TX United States Department of Biochemistry Osun State University Osogbo Nigeria Department of Pharmacology and Therapeutics University of Medical Sciences Ondo Ondo Nigeria Department of Veteri

Background: Decades of steady improvements in life expectancy in Europe slowed down from around 2011, well before the COVID-19 pandemic, for reasons which remain disputed. We aimed to assess how changes in risk factors and cause-specific death rates in different European countries related to changes in life expectancy in those countries before and during the COVID-19 pandemic. Methods: We used data and methods from the Global Burden of Diseases, Injuries, and Risk Factors Study 2021 to compare changes in life expectancy at birth, causes of death, and population exposure to risk factors in 16 European Economic Area countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, and Sweden) and the four UK nations (England, Northern Ireland, Scotland, and Wales) for three time periods: 1990–2011, 2011–19, and 2019–21. Changes in life expectancy and causes of death were estimated with an established life expectancy cause-specific decomposition method, and compared with summary exposure values of risk factors for the major causes of death influencing life expectancy. Findings: All countries showed mean annual improvements in life expectancy in both 1990–2011 (overall mean 0·23 years [95% uncertainty interval [UI] 0·23 to 0·24]) and 2011–19 (overall mean 0·15 years [0·13 to 0·16]). The rate of improvement was lower in 2011–19 than in 1990–2011 in all countries except for Norway, where the mean annual increase in life expectancy rose from 0·21 years (95% UI 0·20 to 0·22) in 1990–2011 to 0·23 years (0·21 to 0·26) in 2011–19 (difference of 0·03 years). In other countries, the difference in mean annual improvement between these periods ranged from –0·01 years in Iceland (0·19 years [95% UI 0·16 to 0·21] vs 0·18 years [0·09 to 0·26]), to –0·18 years in England (0·25 years [0·24 to 0·25] vs 0·07 years [0·06 to 0·08]). In 2019–21, there was an overall decrease in mean annual life expectancy a

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Nonadiabatic Effect on the Rescattering Trajectories of Electrons in Strong Laser Field Ionization Process

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Chinese Physics Letters 2016年第9期33卷 29-31页

作者：涂心海郝小雷李卫东胡师林陈京 Institute of Theoretical Physics and Department of Physics Shanxi University Institute of Applied Physics and Computational Mathematics

The important features of the rescattering trajectories in strong field ionization process such as the cutoff of the return energy at 3.17Up and that of the final energy at 10Up are obtained, based on the adiabatic approximation in which the initial momentum of the electron is assumed to be zero. We theoretically study the nonadiabatic effect by assuming a nonzero initial momentum on the rescattering trajectories based on the semiclassical simpleman model. We show that the nonzero initial momentum will modify both the maximal return energy at collision and the final energy after backward scattering, but in different ways for odd and even number of return trajectories. The energies are increased for even number of returns but are decreased for odd number of returns when the nonzero （positive or negative） initial momentum is applied.

关键词： of it in Nonadiabatic Effect on the Rescattering Trajectories of Electrons in Strong Laser Field Ionization Process on is that for

On a generalization of the Rogers generating function

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arXiv 2018年

作者： Cohl, Howard S. Costas-Santos, Roberto S. Wakhare, Tanay Applied and Computational Mathematics Division National Institute of Standards and Tech-Nology Mission ViejoCA92694 United States Departamento de Física y Matemáticas Universidad de Alcalá c.p. 28871 Alcalá de Henares Spain Department of Mathematics University of Maryland College ParkMD20742 United States

We derive a generalized Rogers generating function and corresponding definite integral, for the continuous q-ultraspherical polynomials by applying its connection relation and utilizing orthogonality. Using a recent generalization of the Rogers generating function by Ismail & Simeonov expanded in terms of Askey-Wilson polynomials, we derive corresponding generalized expansions for the continuous q-Jacobi, and Wilson polynomials with two and four free parameters respectively. Comparing the coefficients of the Askey-Wilson expansion to our continuous q-ultraspherical/Rogers expansion, we derive a new quadratic transformation for basic hypergeometric series connecting 2φ1 and 8φ7.33C45, 05A15, 33C20, 34L10, 30E20 Copyright © 2018, The Authors. All rights reserved.

关键词： Orthogonal functions

Investigating the Nature of the Luminous Ambiguous Nuclear Transient ASASSN-17jz

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arXiv 2021年

作者： Holoien, Thomas W.-S. Neustadt, Jack M.M. Vallely, Patrick J. Auchettl, Katie Hinkle, Jason T. Romero-Cañizales, Cristina Shappee, Benjamin J. Kochanek, Christopher S. Stanek, K.Z. Chen, Ping Dong, Subo Prieto, Jose L. Thompson, Todd A. Brink, Thomas G. Filippenko, Alexei V. Zheng, Weikang Bersier, David Bose, Subhash Burgasser, Adam J. Channa, Sanyum De Jaeger, Thomas Hestenes, Julia Im, Myungshin Jeffers, Benjamin Jun, Hyunsung D. Lansbury, George Post, Richard S. Ross, Timothy W. Stern, Daniel Tang, Kevin Tucker, Michael A. Valenti, Stefano Yunus, Sameen Zhang, Keto D. The Observatories of the Carnegie Institution for Science 813 Santa Barbara St. PasadenaCA91101 United States Department of Astronomy The Ohio State University 140 West 18th Avenue ColumbusOH43210 United States School of Physics The University of Melbourne ParkvilleVIC3010 Australia Department of Astronomy and Astrophysics University of California Santa CruzCA95064 United States Institute for Astronomy University of Hawai'i 2680 Woodlawn Drive HonoluluHI96822 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Roosevelt Rd Taipei10617 Taiwan The Ohio State University 191 W. Woodruff Ave. ColumbusOH43210 United States Kavli Institute for Astronomy and Astrophysics Peking University Yi He Yuan Road 5 Hai Dian District Beijing100871 China Núcleo de Astronomía de la Facultad de Ingeniería y Ciencias Universidad Diego Portales Av. Ejército 441 Santiago Chile Millennium Institute of Astrophysics Santiago Chile Department of Astronomy University of California BerkeleyCA94720-3411 United States Miller Institute for Basic Research in Science University of California BerkeleyCA94720 United States Astrophysics Research Institute Liverpool John Moores University 146 Brownlow Hill LiverpoolL3 5RF United Kingdom Center for Astrophysics and Space Sciences University of California San Diego La Jolla CA92093 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027-6623 United States SNU Astronomy Research Center Astronomy Program Dept. of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of School of Physics Korea Institute for Advanced Study 85 Hoegiro Dongdaemun-gu Seoul02455 Korea Republic of European Southern Observatory Karl-Schwarzschild-Strasse 2 GarchingD-85748 Germany Post Observatory LexingtonMA02421 United States Jet Propulsion Laboratory California Institute of Technology 4800 Oa

We present observations of the extremely luminous but ambiguous nuclear transient (ANT) ASASSN-17jz, spanning roughly 1200 days of the object's evolution. ASASSN-17jz was discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) in the galaxy SDSS J171955.84+414049.4 on UT 2017 July 27 at a redshift of z = 0:1641. The transient peaked at an absolute B-band magnitude of MB,peak=-22:81, corresponding to a bolometric luminosity of Lbol,peak= 8.3×1044erg s-1, and exhibited late-time ultraviolet emission that was still ongoing in our latest observations. Integrating the full light curve gives a total emitted energy of Etot= (1.36±0.08)×1052erg, with (0.80±0.02)×1052erg of this emitted within 200 days of peak light. This late-time ultraviolet emission is accompanied by increasing X-ray emission that becomes softer as it brightens. ASASSN-17jz exhibited a large number of spectral emission lines most commonly seen in active galactic nuclei (AGNs) with little evidence of evolution. It also showed transient Balmer features which became fainter and broader over time, and are still being detected > 1000 days after peak brightness. We consider various physical scenarios for the origin of the transient, including supernovae (SNe), tidal disruption events (TDEs), AGN outbursts, and ANTs. We find that the most likely explanation is that ASASSN-17jz was an SN IIn occurring in or near the disk of an existing AGN, and that the late-time emission is caused by the AGN transitioning to a more active state. Copyright © 2021, The Authors. All rights reserved.

关键词： Supernovae

Accuracy of the semiclassical picture of photoionization in intense laser fields

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arXiv 2019年

作者： Guo, Li Hu, Shilin Liu, Mingqing Shu, Zheng Liu, XiWang Li, Jie Yang, Weifeng Lu, Ronghua Han, ShenSheng Chen, Jing Key laboratory for Quantum Optics and Center for Cold Atom Physics Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai201800 China Laboratory of Quantum Engineering and Quantum Metrology School of Physics and Astronomy Sun Yat-Sen University Zhuhai Campus Zhuhai519082 China HEDPS Center for Applied Physics and Technology Collaborative Innovation Center of IFSA Peking University Beijing100084 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing100088 China Department of Physics College of Science Shantou University Shantou Guangdong515063 China

In the semiclassical picture of photoionization process in intense laser fields, the ionization rate solely depends on the amplitude of the electric field and the final photoelectron momentum corresponds to the instant of ionization of the photoelectron, however, this picture has never been checked rigorously. Recently an attosecond angular streaking technique based on this semiclassical perspective has been widely applied to temporal measurement of the atomic and molecular dynamics in intense laser fields. We use a Wigner-distribution-like function to calculate the time-emission angle distribution, angular distribution and ionization time distribution for atomic ionization process in elliptically polarized few-cycle laser fields. By comparing with semiclassical calculations, we find that the two methods always show discrepancies except in some specific cases and the offset angles are generally not consistent with the offset times of the ionization time distributions obtained by the two methods even when the non-adiabatic effect is taken into account, indicating that the "attoclock" technique is in principle inaccurate. Moreover, calculations for linearly polarized laser fields also show similar discrepancies between two methods in the ionization time distribution. Our analysis indicates that the discrepancy between the semiclassical and quantum calculations can be attributed to correlation, i. e., temporal nonlocalization effect. Copyright © 2019, The Authors. All rights reserved.

关键词： Angular distribution

A Simple Network of Nodes Moving on the Circle

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arXiv 2018年

作者： Cheliotis, Dimitris Kontoyiannis, Ioannis Loulakis, Michail Toumpis, Stavros Department of Mathematics Panepistimiopolis Athens15784 Greece Department of Engineering University of Cambridge Trumpington Street CambridgeCB2 1PZ United Kingdom Department of Informatics Athens University of Economics and Business Patission 76 Athens10434 Greece School of Applied Mathematical and Physical Sciences National Technical University of Athens Poly-technioulopis Zographou Athens15780 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Greece

Two simple Markov processes are examined, one in discrete and one in continuous time, arising from idealized versions of a transmission protocol for mobile networks. We consider two independent walkers moving with constant speed on the discrete or continuous circle, and changing directions at independent geometric (respectively, exponential) times. One of the walkers carries a message that wishes to travel as far and as fast as possible in the clockwise direction. The message stays with its current carrier unless the two walkers meet, the carrier is moving counter-clockwise, and the other walker is moving clockwise. Then the message jumps to the other walker. Explicit expressions are derived for the long-term average clockwise speed and number of jumps made of the message, via the solution of associated boundary value problems. The tradeoff between speed and cost (measured as the rate of jumps) is also examined. Copyright © 2018, The Authors. All rights reserved.

关键词： Markov processes