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Fisher information matrix of binary time series

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arXiv 2017年

作者： Gao, Xu Ombao, Hernando Gillen, Daniel Department of Statistics University of California IrvineCA United States Department of Cognitive Sciences University of California IrvineCA United States Program on Applied Mathematics and Computational Science King Abdullah University of Science and Technology Saudi Arabia

A common approach to analyzing categorical correlated time series data is to fit a gen- eralized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T . Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to pro- vide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix. Copyright © 2017, The Authors. All rights reserved.

关键词： Time series

Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids

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arXiv 2018年

作者： Hirvonen, Petri Fan, Zheyong La Boissoniere, Gabriel Martine Achim, Cristian-Vasile Provatas, Nikolas Elder, Ken R. Ala-Nissila, Tapio Qtf Centre of Excellence Department of Applied Physics Aalto University School of Science P.O. Box 11000 Aalto EspooFIN-00076 Finland Department of Mathematics and Statistics McGill University MontrealQCH3A 0B9 Canada University of Concepcion Concepcion4030000 Chile Department of Physics and Centre for the Physics of Materials McGill University MontrealQCH3A 0B9 Canada Department of Physics Oakland University RochesterMI48309 United States Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences Loughborough University LeicestershireLE11 3TU United Kingdom

While the microscopic structure of defected solid crystalline materials has significant impact on their physical properties, eficient and accurate determination of a given polycrystalline microstructure remains a challenge. In this paper we present a highly generalizable and reliable variational method to achieve this goal for two-dimensional crystalline and quasicrystalline materials. The method is benchmarked and optimized successfully using a variety of large-scale systems of defected solids, including periodic structures and quasicrystalline symmetries to quantify their microstructural characteristics, e.g., grain size and lattice misorientation distributions. We find that many microstructural properties show universal features independent of the underlying symmetries. Copyright © 2018, The Authors. All rights reserved.

关键词： Large scale systems

Detection of RS Oph with LST-1 and modelling of its HE/VHE gamma-ray emission

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arXiv 2025年

作者： Abe, K. Abe, S. Abhishek, A. Acero, F. Aguasca-Cabot, A. Agudo, I. Alispach, C. Crespo, N. Alvarez Ambrosino, D. Antonelli, L.A. Aramo, C. Arbet-Engels, A. Arcaro, C. Asano, K. Aubert, P. Baktash, A. Balbo, M. Bamba, A. Larriva, A. Baquero de Almeida, U. Barres Barrio, J.A. Jiménez, L. Barrios Batkovic, I. Baxter, J. González, J. Becerra Bernardini, E. Bernete, J. Berti, A. Bezshyiko, I. Bhattacharjee, P. Bigongiari, C. Bissaldi, E. Blanch, O. Bonnoli, G. Bordas, P. Borkowski, G. Brunelli, G. Bulgarelli, A. Bunse, M. Burelli, I. Burmistrov, L. Buscemi, M. Cardillo, M. Caroff, S. Carosi, A. Carrasco, M.S. Cassol, F. Castrejón, N. Cerasole, D. Ceribella, G. Chai, Y. Cheng, K. Chiavassa, A. Chikawa, M. Chon, G. Chytka, L. Cicciari, G.M. Cifuentes, A. Contreras, J.L. Cortina, J. Costantini, H. Da Vela, P. Dalchenko, M. Dazzi, F. De Angelis, A. de Bony de Lavergne, M. De Lotto, B. de Menezes, R. Del Burgo, R. Del Peral, L. Delgado, C. Delgado Mengual, J. della Volpe, D. Dellaiera, M. Di Piano, A. Di Pierro, F. Di Tria, R. Di Venere, L. Díaz, C. Dominik, R.M. Dominis Prester, D. Donini, A. Dore, D. Dorner, D. Doro, M. Eisenberger, L. Elsässer, D. Emery, G. Escudero, J. Fallah Ramazani, V. Ferrarotto, F. Fiasson, A. Foffano, L. Freixas Coromina, L. Fröse, S. Fukazawa, Y. Garcia López, R. Gasbarra, C. Gasparrini, D. Geyer, D. Giesbrecht Paiva, J. Giglietto, N. Giordano, F. Gliwny, P. Godinovic, N. Grau, R. Green, D. Green, J. Gunji, S. Günther, P. Hackfeld, J. Hadasch, D. Hahn, A. Hassan, T. Hayashi, K. Heckmann, L. Heller, M. Herrera Llorente, J. Hirotani, K. Hoffmann, D. Horns, D. Houles, J. Hrabovsky, M. Hrupec, D. Hui, D. Iarlori, M. Imazawa, R. Inada, T. Inome, Y. Inoue, S. Ioka, K. Iori, M. Iuliano, A. Jahanvi, J. Jimenez Martinez, I. Jimenez Quiles, J. Jurysek, J. Kagaya, M. Kalashev, O. Karas, V. Katagiri, H. Kataoka, J. Kerszberg, D. Kobayashi, Y. Kohri, K. Kong, A. Kubo, H. Kushida, J. Lacave, B. Lainez, M. Lamanna, G. Lamastra, A. Lemoigne, L. Department of Physics Tokai University 4-1-1 Kita-Kaname Kanagawa Hiratsuka259-1292 Japan Institute for Cosmic Ray Research University of Tokyo 5-1-5 Kashiwa-no-ha Chiba Kashiwa277-8582 Japan Sezione di Fisica Via Roma 56 Siena53100 Italy Université Paris-Saclay Université Paris Cité CEA CNRS AIM Gif-sur-YvetteF-91191 Cedex France FSLAC IRL 2009 CNRS/IAC Tenerife La Laguna Spain Departament de Física Quàntica i Astrofísica Institut de Ciències del Cosmos Universitat de Barcelona IEEC-UB Martí i Franquès 1 Barcelona08028 Spain Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n Granada18008 Spain Department of Astronomy University of Geneva Chemin d’Ecogia 16 VersoixCH-1290 Switzerland IPARCOS-UCM Instituto de Física de Partículas y del Cosmos EMFTEL Department Universidad Complutense de Madrid Ciudad Universitaria Plaza de Ciencias 1 Madrid28040 Spain INFN Sezione di Napoli Via Cintia ed. G Napoli80126 Italy INAF - Osservatorio Astronomico di Roma Via di Frascati 33 Monteporzio Catone00040 Italy Max-Planck-Institut für Physik Föhringer Ring 6 München80805 Germany INFN Sezione di Padova Università degli Studi di Padova Via Marzolo 8 Padova35131 Italy Univ. Savoie Mont Blanc CNRS Laboratoire d’Annecy de Physique des Particules - IN2P3 Annecy74000 France Universität Hamburg Institut für Experimentalphysik Luruper Chaussee 149 Hamburg22761 Germany Graduate School of Science University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan Faculty of Science and Technology Universidad del Azuay Cuenca Ecuador Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud 150 RJ Rio de Janeiro22290-180 Brazil Instituto de Astrofísica de Canarias Departamento de Astrofísica Universidad de La Laguna C. Vía Láctea s/n Santa Cruz de Tenerife La Laguna38205 Spain CIEMAT Avda. Complutense 40 Madrid28040 Spain University of Geneva Département de physique nucléaire et corpusculaire 24 Quai Ernest Ansernet

Context. The recurrent nova RS Ophiuchi (RS Oph) underwent a thermonuclear eruption in August 2021. In this event, RS Oph was detected by the High Energy Stereoscopic System (H.E.S.S.), the Major Atmospheric Gamma Imaging Cherenkov (MAGIC), and the first Large-Sized Telescope (LST-1) of the future Cherenkov Telescope Array Observatory (CTAO) at very-high gamma-ray energies above 100 GeV. This means that novae are a new class of very-high-energy (VHE) gamma-ray emitters. Aims. We report the analysis of the RS Oph observations with LST-1. We constrain the particle population that causes the observed emission in hadronic and leptonic scenarios. Additionally, we study the prospects of detecting further novae using LST-1 and the upcoming LST array of CTAO-North. Methods. We conducted target-of-opportunity observations with LST-1 from the first day of this nova event. The data were analysed in the framework of cta-lstchain and Gammapy, the official CTAO-LST reconstruction and analysis packages. One-zone hadronic and leptonic models were considered to model the gamma-ray emission of RS Oph using the spectral information from Fermi-LAT and LST-1, together with public data from the MAGIC and H.E.S.S. telescopes. Results. RS Oph was detected at 6.6σ with LST-1 in the first 6.35 hours of observations following the eruption. The hadronic scenario is preferred over the leptonic scenario considering a proton energy spectrum with a power-law model with an exponential cutoff whose position increases from (0.26 ± 0.08) TeV on day 1 up to (1.6 ± 0.6) TeV on day 4 after the eruption. The deep sensitivity and low energy threshold of the LST-1/LST array will allow us to detect faint novae and increase their discovery rate. © 2025, CC BY.

关键词： Gamma radiography

GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run

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Physical Review X 2023年第4期13卷 041039-041039页

作者： R. Abbott T. D. Abbott F. Acernese K. Ackley C. Adams N. Adhikari R. X. Adhikari V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith S. Akcay T. Akutsu S. Albanesi A. Allocca P. A. Altin A. Amato C. Anand S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando T. Andrade N. Andres T. Andrić S. V. Angelova S. Ansoldi J. M. Antelis S. Antier S. Appert Koji Arai Koya Arai Y. Arai S. Araki A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud M. Arogeti S. M. Aronson K. G. Arun H. Asada Y. Asali G. Ashton Y. Aso M. Assiduo S. M. Aston P. Astone F. Aubin C. Austin S. Babak F. Badaracco M. K. M. Bader C. Badger S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai L. Baiotti J. Baird R. Bajpai M. Ball G. Ballardin S. W. Ballmer A. Balsamo G. Baltus S. Banagiri D. Bankar J. C. Barayoga C. Barbieri B. C. Barish D. Barker P. Barneo F. Barone B. Barr L. Barsotti M. Barsuglia D. Barta J. Bartlett M. A. Barton I. Bartos R. Bassiri A. Basti M. Bawaj J. C. Bayley A. C. Baylor M. Bazzan B. Bécsy V. M. Bedakihale M. Bejger I. Belahcene V. Benedetto D. Beniwal T. F. Bennett J. D. Bentley M. BenYaala F. Bergamin B. K. Berger S. Bernuzzi C. P. L. Berry D. Bersanetti A. Bertolini J. Betzwieser D. Beveridge R. Bhandare U. Bhardwaj D. Bhattacharjee S. Bhaumik I. A. Bilenko G. Billingsley S. Bini R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boer G. Bogaert M. Boldrini L. D. Bonavena F. Bondu E. Bonilla R. Bonnand P. Booker B. A. Boom R. Bork V. Boschi N. Bose S. Bose V. Bossilkov V. Boudart Y. Bouffanais A. Bozzi C. Bradaschia P. R. Brady A. Bramley A. Branch M. Branchesi J. Brandt J. E. Brau M. Breschi T. Briant J. H. Briggs A. Brillet M. Brinkmann P. Brockill A. F. Brooks J. Brooks D. D. Brown S. Brunett G. Bruno R. Bruntz J. Bryant T. Bulik H. J. Bulten A. Buonanno R. Buscicchio D. Buskulic C. Buy R. L. Byer G. S. Cabourn Davies L. Cadonati G. Cagn LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Louisiana State University Baton Rouge Louisiana 70803 USA Dipartimento di Farmacia Università di Salerno I-84084 Fisciano Salerno Italy INFN Sezione di Napoli Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 Victoria Australia LIGO Livingston Observatory Livingston Louisiana 70754 USA University of Wisconsin-Milwaukee Milwaukee Wisconsin 53201 USA OzGrav Australian National University Canberra Australian Capital Territory 0200 Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-30167 Hannover Germany Leibniz Universität Hannover D-30167 Hannover Germany Inter-University Centre for Astronomy and Astrophysics Pune 411007 India University of Cambridge Cambridge CB2 1TN United Kingdom Theoretisch-Physikalisches Institut Friedrich-Schiller-Universität Jena D-07743 Jena Germany University of Birmingham Birmingham B15 2TT United Kingdom Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Gravity Exploration Institute Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione di Pisa I-56127 Pisa Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India University College Dublin Dublin 4 Ireland Gravitational Wave Science Project National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan INFN Sezione di Torino I-10125 Torino Italy Università di Napoli “Federico II” Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy Université de Lyon Université Claude Bernard Lyon 1 CNRS Institut L

The third Gravitational-Wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, 15∶00 Coordinated Universal Time (UTC) and 27 March 2020, 17∶00 UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin pastro>0.5. Of these, 18 were previously reported as low-latency public alerts, and 17 are reported here for the first time. Based upon estimates for the component masses, our O3b candidates with pastro>0.5 are consistent with gravitational-wave signals from binary black holes or neutron-star–black-hole binaries, and we identify none from binary neutron stars. However, from the gravitational-wave data alone, we are not able to measure matter effects that distinguish whether the binary components are neutron stars or black holes. The range of inferred component masses is similar to that found with previous catalogs, but the O3b candidates include the first confident observations of neutron-star–black-hole binaries. Including the 35 candidates from O3b in addition to those from GWTC-2.1, GWTC-3 contains 90 candidates found by our analysis with pastro>0.5 across the first three observing runs. These observations of compact binary coalescences present an unprecedented view of the properties of black holes and neutron stars.

关键词： Gravitational waves

Correction to: A probiotic has differential effects on allergic airway inflammation in A/J and C57BL/6 mice and is correlated with the gut microbiome

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Microbiome 2021年第1期9卷 159页

作者： Mateus B Casaro Andrew M Thomas Eduardo Mendes Claudio Fukumori Willian R Ribeiro Fernando A Oliveira Amanda R Crisma Gilson M Murata Bruna Bizzarro Anderson Sá-Nunes Joao C Setubal Marcia P A Mayer Flaviano S Martins Angélica T Vieira Ana T F B Antiorio Wothan Tavares-de-Lima Niels O S Camara Rui Curi Emmanuel Dias-Neto Caroline M Ferreira Department of Pharmaceutics Sciences Institute of Environmental Chemistry and Pharmaceutical Sciences Universidade Federal de São Paulo R. São Nicolau 210 Diadema SP 09913-03 Brazil. Department CIBIO University of Trento Trento Italy. Medical Genomics Laboratory CIPE/A.C. Camargo Cancer Center São Paulo Brazil. Department of Biochemistry Institute of Chemistry Universidade de São Paulo São Paulo Brazil. Center for Mathematics Computing and Cognition (CMCC) Federal University of ABC - UFABC São Bernardo do Campo SP Brazil. Department of Clinical Analyses Universidade Federal do Paraná Curitiba Brazil. Department of Medical Clinic Faculty of Medicine University of São Paulo São Paulo 01246-903 Brazil. Department of Immunology Institute of Biomedical Sciences Universidade de São Paulo São Paulo Brazil. Department of Microbiology Institute of Biomedical Sciences University of São Paulo São Paulo SP Brazil. Department of Microbiology Institute of Biological Sciences Federal Universidade de Minas Gerais Belo Horizonte Brazil. Department of Biochemistry and Immunology Biological Science Institute Federal University of Minas Gerais Belo Horizonte Brazil. Department of Pathology School of Veterinary Medicine and Animal Science Universidade de São Paulo São Paulo Brazil. Department of Pharmacology Institute of Biomedical Sciences I Universidade de São Paulo São Paulo Brazil. Interdisciplinary Post-Graduate Program in Health Sciences Cruzeiro do Sul University São Paulo Brazil. Laboratory of Neurosciences (LIM-27) Institute of Psychiatry Medical School Universidade de São Paulo São Paulo Brazil. Department of Pharmaceutics Sciences Institute of Environmental Chemistry and Pharmaceutical Sciences Universidade Federal de São Paulo R. São Nicolau 210 Diadema SP 09913-03 Brazil. cferreira16@unifesp.br.

Correction to: Genes associated with survival of female bovine blastocysts produced in vivo

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Cell and tissue research 2020年第3期382卷 679页

作者： A M Zolini J Block M B Rabaglino G Rincon M Hoelker J J Bromfield D Salilew-Wondim P J Hansen Department of Animal Sciences D.H. Barron Reproductive and Perinatal Biology Research Program and Genetics Institute University of Florida PO Box 110910 Gainesville FL 32611-0910 USA. Zoetis Inc. Kalamazoo MI 49007 USA. Instituto de Investigación en Ciencias de La Salud CONICET Córdoba Argentina. Quantitative Genetics Bioinformatics and Computational Biology Group Department of Applied Mathematics and Computer Science Technical University of Denmark Kemitorvet 2800 Kgs. Lyngby Denmark. Institute of Animal Science Animal Breeding and Husbandry University of Bonn Bonn Germany. Teaching and Research Station Frankenforst Faculty of Agriculture University of Bonn Königswinter Germany. Center of Integrated Dairy Research University of Bonn Bonn Germany. Department of Animal Sciences D.H. Barron Reproductive and Perinatal Biology Research Program and Genetics Institute University of Florida PO Box 110910 Gainesville FL 32611-0910 USA. pjhansen@ufl.edu.

The first error is on page 5. A sentence lists two genes as SCNA1A and SCNA2A but they should be SCN1A and SCN2A.

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On the uniqueness of FROG methods

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arXiv 2017年

作者： Bendory, Tamir Sidorenko, Pavel Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Physics and Solid State Institute Technion-Israel Institute of Technology Haifa Israel Department of Electrical Engineering Technion-Israel Institute of Technology Haifa Israel

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultra-short laser pulse characterization in which the electromagnetic field is oscillating with ∼ 1015 Hz and phase information cannot be measured directly due to limitations of the electronic sensors. Phase retrieval is ill-posed in most cases as there are many different signals with the same Fourier transform magnitude. To overcome this fundamental ill-posedness, several measurement techniques are used in practice. One of the most popular methods for complete characterization of ultra-short laser pulses is the Frequency-Resolved Optical Gating (FROG). In FROG, the acquired data is the power spectrum of the product of the unknown pulse with its delayed replica. Therefore the measured signal is a quartic function of the unknown pulse. A generalized version of FROG, where the delayed replica is replaced by a second unknown pulse, is called blind FROG. In this case, the measured signal is quadratic with respect to both pulses. In this letter we introduce and formulate FROG-type techniques. We then show that almost all band-limited signals are determined uniquely, up to trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in addition we have access to the signals power spectrum. Copyright © 2017, The Authors. All rights reserved.

关键词： Power spectrum

Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number

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arXiv 2018年

作者： Wen, Baole Chini, Gregory P. Department of Geological Sciences Jackson School of Geosciences University of Texas at Austin AustinTX78712 United States Institute of Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States Program in Integrated Applied Mathematics University of New Hampshire W113 Kingsbury Hall 33 Academic Way DurhamNH03824 United States Center for Fluid Physics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States

Direct numerical simulations (DNS) indicate that at large values of the Rayleigh number (Ra) convection in porous media self-organizes into narrowly-spaced columnar flows, with more complex spatiotemporal features being confined to boundary layers near the top and bottom walls. In this investigation of high-Ra porous media convection in a minimal flow unit, two reduced modeling strategies are proposed that exploit these specific flow characteristics. Both approaches utilize the idea of decomposition since the flow exhibits different dynamics in different regions of the domain: small-scale cellular motions generally are localized within the thermal and vorticity boundary layers near the upper and lower walls, while in the interior, the flow exhibits persistent large-scale structures and only a few low (horizontal) wavenumber Fourier modes are active. Accordingly, in the first strategy, the domain is decomposed into two near-wall regions and one interior region. Our results confirm that suppressing the interior high-wavenumber modes has negligible impact on the essential structural features and transport properties of the flow. In the second strategy, a hybrid reduced model is constructed by using Galerkin projection onto a fully a priori eigenbasis drawn from energy stability and upper bound theory, thereby extending the model reduction strategy developed by Chini et al. (Physica D, vol. 240, 2011, pp. 241-248) to large Ra. The results indicate that the near-wall upper-bound eigenmodes can economically represent the small-scale rolls within the exquisitely-thin thermal boundary layers. Relative to DNS, the hybrid algorithm enables over an order-of-magnitude increase in computational efficiency with only a modest loss of accuracy. Copyright © 2018, The Authors. All rights reserved.

关键词： Porous materials

Bose polaron as an instance of quantum Brownian motion

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arXiv 2017年

作者： Lampo, Aniello Lim, Soon Hoe Garciá-March, Miguel Ángel Lewenstein, MacIej ICFO-Institut de Ciencies Fotoniques Barcelona Institute of Science and Technology Castelldefels08860 Spain Department of Mathematics Program in Applied Mathematics University of Arizona TucsonAZ85721-0089 United States ICREA-Institució Catalana de Recerca i Estudis Avancats Lluis Companys 23 BarcelonaE-08010 Spain

We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integro-differential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Degrees of freedom (mechanics)