academic/bibletime: Updated for version 2.11.2.
academic/fet: Updated for version 5.36.1.
academic/gwyddion: Updated for version 2.51.
desktop/faba-icon-theme: Updated for version 20180624.
desktop/i3-gaps: Added (a tiling window manager for Linux).
desktop/oranchelo-icon-theme: Updated for version 0.7.7.1.
desktop/qtpass: Updated for version 1.2.3.
desktop/simplenote: Updated for version 1.1.6.
desktop/slack-wallpapers: Updated for version 1.0.
development/atom-amd64: Updated for version 1.28.0.
development/gambas3: Updated for version 3.11.3 + new maintainer.
development/jupyter-widgetsnbextension: Upgraded for version 3.2.1.
development/mrustc: Updated for version gitb03d61e.
development/pyvim: Updated for version 2.0.22.
development/qt-creator: Updated for version 4.6.2.
development/slibtool: Updated for version 0.5.20.
games/freeorion: Updated for version 0.4.7.1.
games/gzdoom: Updated for version 3.4.1.
games/maelstrom: Fix build on -current.
games/snes9x: Updated for version 1.56.2.
gis/google-earth: Updated for version 7.3.2.5481.
gis/ossim: Updated for version 2.4.1.
graphics/GraphicsMagick: Updated for version 1.3.30, script fixes.
graphics/feh: Updated for version 2.27.
libraries/CoinMP: Fixed building in sandbox.
libraries/agg: Updated for version r127.
libraries/gavl: Cleanups, added a license.
libraries/jbig2dec: Use new homepage/download URLs.
libraries/libtorrent-rasterbar: Updated for version 1.1.8.
libraries/libxlsxwriter: Added (C library for Excel XLSX files).
libraries/ulfius: Updated for version 2.3.7.
multimedia/devedeng: Updated for version 4.12.0.
multimedia/opera-developer-ffmpeg-codecs: Updated for v. 0.31.2.
multimedia/opera-ffmpeg-codecs: Updated for version 0.30.5.
network/WireGuard: Updated for version 0.0.20180625.
network/cicb: Updated for version 5.2.0b1+git20170501.
network/dovecot-pigeonhole: Updated for version 0.5.1.
network/dovecot: Updated for version 2.3.1.
network/newsboat: Updated for version 2.12.
network/opera-developer: Updated for version 55.0.2976.0.
network/opera: Updated for version 53.0.2907.106.
network/postfix: Updated for version 3.3.1.
network/slimjet: Updated for version 19.0.6.0.
network/vimb: Updated for version 3.2.0.
office/MasterPDFEditor: Updated for version 5.0.28.
office/libreoffice-helppack: Updated for version 6.0.5.
office/libreoffice-langpack: Updated for version 6.0.5.
office/libreoffice: Updated for version 6.0.5.
office/mupdf: Add support for shared libraries.
office/wps-office: Updated for version 10.1.0.5707~a21.
python/astroid: Updated for version 1.6.5.
python/blessings: Updated for version 1.7.
python/prompt_toolkit: Updated for version 2.0.3.
python/python-evdev: Updated for version 1.0.0.
python/python-progress: Updated for version 1.4.
python/python-twitter: Updated for version 3.4.2.
python/python3-ptyprocess: Updated for version 0.6.0.
python/python3-setuptools_autover: Added (version number generator).
python/python3-uth: Added (Python Unit Test Helpers).
python/requests-oauthlib: Updated for version 1.0.0.
system/borgbackup: Updated for version 1.1.6.
system/fr: Updated for version 1.38.
system/kbfs: Updated for version 2.3.0_20180622234805.
system/keybase: Updated for version 2.1.0.
system/kmscon: Minor fix for -current.
system/letsencrypt: Updated for version 0.25.1.
system/lynis: Updated for version 2.6.5.
system/phoronix-test-suite: Updated for version 8.0.1.
system/pytrash: Updated for version 1.1.2.
system/slpkg: Updated for version 3.3.8.
system/vagrant: Updated for version 2.1.2.
system/wine-staging: Updated for version 3.11.
academic/flexbar: Updated for version 3.4.0.
academic/pyCRAC: Updated for version 1.3.2.
academic/units: Updated for version 2.17.
audio/drumkv1: Updated for version 0.9.1, French man page.
audio/jack-keyboard: Updated for version 2.7.2.
audio/rubberband: Updated for version 1.8.2.
audio/samplv1: Updated for version 0.9.1, French man page.
audio/synthv1: Updated for version 0.9.1, French man page.
desktop/compton-conf: Updated for version 0.4.0.
desktop/enlightenment: Updated for version 0.22.3.
desktop/faba-icon-theme: Updated for version 4.3.
desktop/oomox: Update for moved downloads.
desktop/py3status: Updated for version 3.10.
desktop/redshift: Updated for version 1.12.
desktop/simplenote: Update SlackBuild & maintainer email.
desktop/slack-wallpapers: Update DOWNLOAD and EMAIL.
desktop/xmonad: Switch homepage to https.
desktop/zenity: Updated for version 3.28.0.
development/SQLAlchemy: Updated for version 1.2.9.
development/brotli: Updated for version 1.0.5.
development/diffoscope: Updated for version 98.
development/eclim: Updated for version 2.8.0.
development/eclipse-cpp: Updated for version 4.8.0.
development/eclipse-java: Updated for version 4.8.0.
development/eclipse-jee: Updated for version 4.8.0.
development/fpc-source: Updated for version 3.0.4.
development/glm: Updated for version 0.9.9.0.
development/mrustc: Updated for version gitc1d4b60.
development/pycharm: Updated for version 2018.1.4.
development/tea: Updated for version 45.0.2.
games/advancemame: Updated for version 3.8.
games/atari800: Updated for version 4.0.0.
games/freeciv: Updated for version 2.6.0_RC1.
games/mame: Updated for version 0.199.
games/vbam: Updated for version 2.1.0.
gis/GMT: Updated for version 5.4.4.
gis/google-earth: Updated for version 7.3.2.5483.
graphics/gource: Updated for version 0.49.
graphics/xli: New maintainer, various fixes.
graphics/yacreader: Updated for version 9.5.0.
libraries/cmark: Fix man directory, update maintainer email.
libraries/cpp-netlib: Switch homepage to https.
libraries/hdf: Updated for version 4.2.14.
libraries/libosinfo: Updated for version 1.2.0.
libraries/nltk: Updated for version 3.3.0.
libraries/pexpect: Updated for version 4.6.0.
libraries/re2: Added (Regular Expression Engine).
multimedia/QMPlay2: Updated for version 18.07.03.
multimedia/get_iplayer: Updated for version 3.16.
multimedia/opera-ffmpeg-codecs: Updated for version 0.31.2.
multimedia/smplayer: Updated for version 18.6.0.
network/atftp: New maintainer, expand README.
network/bozohttpd: New maintainer, many tweaks.
network/dante: Added (a free SOCKS client and server).
network/dropbox: Updated for version 52.4.60.
network/glewlwyd: Updated for version 1.4.6.
network/gui-ufw: Amend SlackBuild, new maintainer email.
network/luakit: Updated for version 2.0 + new maintainer.
network/nextcloud-server: Updated for version 13.0.4.
network/opera-developer: Updated for version 55.0.2991.0.
network/opera: Updated for version 54.0.2952.41.
network/prosody-mod-smacks: Updated for version hg3150.
network/qutebrowser: Updated for version 1.4.0.
network/riot-web: Updated for version 0.15.6.
network/signal-desktop: Updated for version 1.13.0.
network/skype4pidgin: Added (SkypeWeb Chat for Pidgin).
network/telegram: Updated for version 1.3.9.
network/tnftp: New maintainer, SOCKS5 support.
network/tor-browser: Updated for version 7.5.6.
network/twine: Updated for version 1.11.0.
network/vivaldi: Updated for version 1.15.1147.52.
network/yandex-browser-beta: Updated for version 18.6.0.2253.
network/youtube-dl: Updated for version 2018.06.25.
office/MasterPDFEditor: Updated for version 5.0.30.
office/MasterPDFEditor: Updated for version 5.0.32.
office/ProjectLibre: Updated for version 1.8.0.
office/ganttproject: Updated for version 2.8.8.
office/gnucash-docs: Added (Gnucash help and user guides).
office/gnucash-legacy-docs: Added (Gnucash help and user guides).
office/gnucash-legacy: Added (financial accounting application).
office/gnucash: Added (financial accounting application).
office/paps: New maintainer, expand README.
perl/perl-Math-Complex_C-L: Updated for version 0.06.
python/atomicwrites: Added (Python library for atomic file writes).
python/colored: Updated for version 1.3.93.
python/getdevinfo: Added (A device information gatherer).
python/ipython: Change dependency to prompt_toolkit1.
python/lxml: Switch homepage to https.
python/parso: Updated for version 0.3.0.
python/prompt_toolkit1: Added (interactive command lines).
python/ptyprocess: Updated for version 0.6.0.
python/pytest: Updated for version 3.6.2.
python/python-unicodedata2: Updated for version 11.0.0.
python/python3-jedi: Updated for version 0.12.1.
python/python3-parso: Updated for version 0.3.0.
python/s3cmd: Switch homepage to https.
system/ack: Updated for version 2.24.
system/alacritty: Updated for version git68b3d8a.
system/ansible: Updated for version 2.5.6.
system/apparmor: Added (Mandatory Access Control mechanism).
system/argyllcms: Updated for version 2.0.0.
system/ddrescue-gui: Updated for version 2.0.0.
system/dosbox-dev: Updated for version 0.74.r4122.
system/keybase: Updated for version 2.1.1.
system/lsb-release: Added (LSB version query program).
system/lynis: Updated for version 2.6.6.
system/osinfo-db-tools: Updated for version 1.2.0.
system/osinfo-db: Updated for version 20180612.
system/snapscreenshot: Added (screenshot program for text consoles).
system/terminology: Updated for version 0.22.3.
system/unicode-character-database: Updated for version 11.0.0.
academic/PhyML: Updated for version 3.3.20180621.
academic/gchemutils: Updated for version 0.14.17.
academic/genometools: Updated for version 1.5.10.
academic/hyphy: Updated for version 2.3.13.
academic/megax: Added (Molecular Evolutionary Genetics Analysis).
academic/pari: Added (a computer algebra system).
academic/perlprimer: Updated for version 1.2.3_f7d3bd0.
academic/primer3: Updated for version 2.4.0.
academic/treeview: Removed (renamed to treeviewx).
academic/treeviewx: Added (Program to display phylogenetic trees).
academic/zotero: Updated for version 5.0.52.
audio/calf: Updated for version 0.90.1.
audio/pianobar: Updated for version 2018.06.22.
audio/unsf: Added (convert .sf2 files to GUS-type patches).
desktop/jgmenu: Updated for version 1.1.
desktop/lemonbar-xft: Added (lightweight taskbar based on XCB).
desktop/murrine-themes: Updated for version 2.98.11.
desktop/sun: Updated for version 1.2.3.
development/afl: Updated for version 2.52b.
development/complexity: Updated for version 1.10.
development/diffoscope: Updated for version 99.
development/hopper: Updated for version 4.3.25.
development/slibtool: Updated for version 0.5.21.
games/commandergenius: Updated for version 2.2.2.
games/fizmo: Updated for version 0.8.5.
games/fuse-emulator: Updated for version 1.5.5.
games/jfsw: Updated for version 20180424_8fc2d54.
gis/rasterio: Updated for version 1.0.0.
gis/saga-gis: Updated for version 6.4.0.
graphics/jpeg2ps: Switch homepage to https.
graphics/ristretto: Updated for version 0.8.3.
graphics/screencloud: Switch homepage to http.
libraries/Kivy: Updated for version 1.10.1.
libraries/PyYAML: Switch homepage and download to https.
libraries/botocore: Updated for version 1.10.52.
libraries/glktermw: Added (library for text interactive fiction).
libraries/libsixel: Added (SIXEL encoder/decoder implementation).
libraries/libspectrum: Updated for version 1.4.4.
libraries/libxnvctrl: Updated for version 390.59.
libraries/npth: Updated for version 1.5.
libraries/python3-PyYAML: Switch homepage and download to https.
libraries/qca-qt5: Added (Qt Cryptographic Architecture for Qt5).
libraries/remglk: Added (RPC implementation of the Glk IF API).
multimedia/flashplayer-plugin: Updated for version 30.0.0.134.
multimedia/openshot: Removed paragraph from the README.
multimedia/opera-developer-ffmpeg-codecs: Updated for version 0.31.
multimedia/opera-ffmpeg-codecs: Updated for version 0.31.4.
multimedia/pepperflash-plugin: Updated for version 30.0.0.134.
network/WireGuard: Updated for version 0.0.20180708.
network/atheme: Updated for version v7.2.10_r2.
network/awscli: Updated for version 1.15.53.
network/brave: Updated for version 0.23.31.
network/bro: Updated for version 2.5.4.
network/cicb: Update homepage, rm obsolete .diff.
network/dokuwiki: Updated for version 20180422a + new maintainer.
network/mattermost-desktop: Added (open-source Slack alternative).
network/opera-developer: Updated for version 56.0.3003.0.
network/opera: Updated for version 54.0.2952.51.
network/psi-plus: Added (development branch of Psi IM client).
network/qutebrowser: Updated for version 1.4.1.
network/riot-web: Updated for version 0.15.7.
network/signal-desktop: Updated for version 1.14.0.
network/slimjet: Updated for version 19.0.7.0.
network/yle-dl: Updated for version 2.34.
network/youtube-dl: Updated for version 2018.07.04.
office/texlive-docs: Updated for version 2018.180630.
office/texlive-extra: Updated for version 2018.180630.
office/texlive-fonts: Removed (included in texlive-extra).
office/texlive: Updated for version 2018.180630.
perl/MoarVM: Added (virtual machine for Rakudo Perl 6 and NQP).
perl/nqp: Updated f/v 2018.06, moved from development/ + new maint.
perl/perl-Sidef: Updated for version 3.18.
perl/perl6-Readline: Added (Perl 6 interface to GNU Readline).
perl/zef: Added (module management for Perl 6).
python/python-setuptools-doc: Added (HTML docs for setuptools).
python/python2-sip: Added (Tool to generate Python bindings).
python/python3-django: Updated for version 2.0.7.
ruby/rubygem-rubocop: Updated for version 0.58.1.
system/autojump: Updated for version 22.5.1.
system/clamav: Updated for version 0.100.1.
system/fio: Updated for version 3.7.
system/fuse-emulator-utils: Updated for version 1.4.3.
system/haveged: Updated for version 1.9.2.
system/hh: Updated for version 1.25.
system/inxi: Updated for version 3.0.16.
system/mailfromd: Added (A General-Purpose Mail Filter).
system/nano-syntax-highlighting: Updated for version 20180705.
system/onerng: Updated for version 3.6.
system/openrc-services: Updated for version 20180617.
system/upx: Updated for version 3.94 + new maintainer.
system/wine-staging: Updated for version 3.12.
system/xonsh: Updated for version 0.6.9.
system/zstd: Updated for version 1.3.5.
academic/OpenFOAM: Updated for version 6.
desktop/cwp: Update homepage and download.
desktop/neutral: Update homepage and download.
desktop/nitrokey-app: Updated for version 1.3.1.
desktop/smaragd: Update homepage and download.
desktop/vbox-runner: Update homepage and download.
development/blassic: Support last alpha version.
development/jupyter-notebook: Updated for version 5.6.0.
development/kotlin: Updated for version 1.2.51.
development/mrustc: Updated for version git5d4bf9e.
development/sbcl: Updated for version 1.4.9.
development/slibtool: Updated for version 0.5.24.
development/smartgit: Switch homepage to https.
development/z88dk: Added (C cross compiler targetting the Z80).
games/jfsw: Enhance script and documentation.
games/jfsw_demo_data: Modified to coexist with jfsw_registered_data.
games/jfsw_registered_data: Added (Game data for Shadow Warrior).
games/jfsw_wanton_destruction: Added (Shadow Warrior expack).
gis/geopy: Updated for version 1.15.0.
gis/pgsql-ogr-fdw: Updated for version 1.0.6.
libraries/frei0r: Patch for the newer opencv.
libraries/libgme: Updated for version 0.6.2.
libraries/libuv: Updated for version 1.22.0.
misc/abgx360: Switch homepage and download to https.
misc/abgx360gui: Switch homepage and download to https.
misc/fcitx-qt5: Updated for version 1.2.3.
misc/jmri: Updated for version 4.12.
network/dirb: Switch homepage to http.
network/psi-plus: Updated for version 1.3.398.
network/signal-desktop: Updated for version 1.14.1.
network/sqlmap: Updated for version 1.2.7.
network/telegram: Updated for version 1.3.10.
network/tor: Updated for version 0.3.3.9.
network/tornado: Updated for version 5.1.0.
network/weechat: Updated for version 2.2.
network/youtube-dl: Updated for version 2018.07.10.
office/MasterPDFEditor: Updated for version 5.0.36.
perl/zef: Updated for version 0.4.5.
python/parso: Updated for version 0.3.1.
python/python-keyring: Updated for version 13.2.1.
python/python3-parso: Updated for version 0.3.1.
python/python3-tornado: Updated for version 5.1.0.
python/pyzmq: Updated for version 17.1.0.
system/keybase: Updated for version 2.3.0.
system/overpass-desktop-fonts: Updated for version 3.0.3.
system/overpass-webfonts: Updated for version 3.0.3.
system/pytrash: Updated for version 1.1.3.
system/salt: Updated for version 2018.3.2.
system/sandbox: Fixed build on 32 bit.
system/spman: Updated for version 2.0.0.
academic/R: Updated for version 3.5.1.
audio/jack2: Updated for version 1.9.12, new maintainer.
audio/snd: Updated for version 18.5.
audio/transcribe: Updated for version 8.72.
development/ChezScheme: Updated for version 9.5.1_fb826e5.
development/Sphinx: Updated for version 1.7.6.
development/cgit: Updated for version 1.2.
development/neovim: Updated for version 0.3.1.
development/p4d: Updated for version 2018.1.1673397.
development/pkgconf: Updated for version 1.5.2.
development/rustup: Updated for version 1.13.0.
games/ultimatestunts: Added (remake of DOS racing game 'Stunts').
gis/Fiona: Updated for version 1.7.13.
gis/google-earth: Updated for version 7.3.2.5487.
graphics/feh: Updated for version 2.27.1.
graphics/nomacs: Updated for version 3.10.0.
libraries/appstream-glib: Updated for version 0.7.10.
libraries/cfitsio: Updated for version 3.45.
libraries/log4shib: Updated for version 2.0.0.
libraries/opensaml: Updated for version 3.0.0.
libraries/xf86-input-libinput: Updated for version 0.28.0.
libraries/xml-security-c: Updated for version 2.0.0.
libraries/xmltooling: Updated for version 3.0.0.
multimedia/plexmediaserver: Updated for v 1.13.4.5251_2e6e8f841.
network/WireGuard: Updated for version 0.0.20180718.
network/autossh: Updated for version 1.4f, changed maintainer.
network/brave: Updated for version 0.23.39.
network/nextcloud-client: Updated for version 2.3.3.
network/prosody-mod-http-upload: Updated for version hg3176.
network/rclone: Updated for version 1.42.
network/shibboleth-sp: Updated for version 3.0.0.
network/signal-desktop: Updated for version 1.14.2.
network/signal-desktop: Updated for version 1.14.3.
network/slimjet: Updated for version 19.0.8.0.
office/pdf2djvu: Updated for version 0.9.9.
python/git-fame: Updated for version 1.5.0.
python/pygame: Updated for version 1.9.4.
python/stevedore: Updated for version 1.29.0.
ruby/rubygem-parser: Updated for version 2.5.1.2.
system/bit-babbler: Updated for version 0.8.
system/fwupdate: Updated for version 12.
system/kitchen-sync: Updated for version 1.1.
system/nvme-cli: Updated for version 1.6.
system/pspg: Updated for version 1.2.1.
academic/ess: Updated for version 17.11.
desktop/compton-conf: Update script; added lxqt_l10n sources.
desktop/gmrun: Updated for version 0.9.4w.
desktop/qtile: Updated for version 0.12.0.
development/autogen: Updated for version 5.18.14.
development/hugo: Updated for version 0.45.1.
development/mutagen: Updated for version 1.41.0.
development/obnc: Updated for version 0.13.3.
development/tig: Updated for version 2.4.1.
development/tiled: Updated for version 1.1.6.
development/yarn: Updated for version 1.9.2.
games/angband: Updated for version 4.1.3.
games/freeciv: Updated for version 2.6.0.
gis/opencpn-plugin-oesenc: Added (oeSENC Charts Plugin).
gis/ossim: Updated for version 2.4.2.
gis/rasterio: Updated for version 1.0.2.
graphics/gimp-plugin-export-layers: Added (Export Layers for GIMP).
graphics/teighafileconverter: Updated for v19.5.0.0, new maintainer.
graphics/teighaviewer: Updated for version 4.00.0.
libraries/libfilezilla: Updated for version 0.13.0.
libraries/libinput: Updated for version 1.11.2.
libraries/libsixel: Updated for version 1.8.2.
libraries/ntl: Updated for version 11.2.1.
libraries/wxSQLite3: Updated for version 4.0.4.
multimedia/opera-developer-ffmpeg-codecs: Updated for v 0.31.5.
multimedia/opera-ffmpeg-codecs: Updated for version 0.31.5.
multimedia/plexmediaserver: Updated for v 1.13.4.5271_200287a06.
network/autossh: Fixed download link and md5sum.
network/brave: Updated for version 0.23.72.
network/etcd: Added (key value store for shared configuration).
network/filezilla: Updated for version 3.35.1.
network/gophernicus: Updated for version 2.5v101, new maintainer.
network/megatools: Updated for version 1.10.1.
network/nextcloud-server: Updated for version 13.0.5.
network/opera-developer: Updated for version 56.0.3013.0.
network/opera: Updated for version 54.0.2952.60.
network/owncloud-client: Updated for version 2.4.2.
network/palemoon-bin: Updated for version 27.9.4.
network/palemoon: Updated for version 27.9.4.
network/persepolis: Added (Download Manager for aria2).
network/signal-desktop: Updated for version 1.14.4.
network/waterfox: Updated for version 56.2.2.
network/wireshark: Updated for version 2.6.2.
network/yandex-browser-beta: Updated for version 18.6.0.2300.
network/youtube-dl: Updated for version 2018.07.21.
office/anorack: Updated for version 0.2.4.
perl/perl-IO-Socket-SSL: Updated for version 2.058.
perl/perl-Path-Tiny: Updated for version 0.106.
perl/perl6-Readline: Updated for version 0.1.4.
python/python-fonttools: Updated for version 3.29.0.
python/python-requests: Updated for version 2.19.1.
ruby/rubygem-rubocop: Updated for version 0.58.2.
system/dosbox-dev: Updated for version 0.74.r4132.
system/elo-mt-usb: Added (elo USB multitouch controller driver).
system/forkstat: Updated for version 0.02.05.
system/inxi: Updated for version 3.0.19.
system/letsencrypt: Updated for version 0.26.1.
system/nano-syntax-highlighting: Updated for version 20180715.
system/noto-fonts: Updated for version 20180624.
system/omnidb-app: Updated for version 2.10.0.
system/pspg: Updated for version 1.2.2.
system/ttf-crosscorefonts: Updated for version 20180624.
system/wine-staging: Updated for version 3.13.
academic/copasi: Updated for version 4.24.197.
academic/scidavis: Patched to fix crashes.
academic/sundials: Updated for version 3.1.1.
audio/id3tool: New maintainer, minor tweaks.
audio/mp4tools: Updated for version 3.6.1.
audio/sunvox: Updated for version 1.9.4.
audio/tuxguitar: Updated for version 1.5.1.
desktop/docfetcher: Updated for version 1.1.21.
development/kotlin: Updated for version 1.2.60.
development/pkgconf: Updated for version 1.5.3.
development/rstudio-desktop: Updated for version 1.1.456.
development/rust: Updated for version 1.27.2.
development/yarn: Updated for version 1.9.4.
games/RetroArch: Allow building without PA.
games/dolphin-emu: Switch homepage to https.
games/fortune-starwars: Added (Star Wars fortune file).
games/gzdoom: Updated for version 3.5.0.
games/innoextract: Updated for version 1.7.
games/mame: Updated for version 0.200.
games/snes9x-libretro: Removed (please use snes9x).
gis/gdal: Switch homepage and download to https.
gis/geopy: Updated for version 1.16.0.
graphics/xcur2png: Added (convert idiotic Xcursor format files).
libraries/gupnp: Updated for version 1.0.3.
libraries/libinput: Updated for version 1.11.3.
libraries/libxnvctrl: Updated for version 390.77.
libraries/orcania: Updated for version 1.2.4.
libraries/sqliteodbc: Added (SQLite ODBC Driver).
libraries/ulfius: Updated for version 2.3.8.
libraries/yder: Updated for version 1.3.4.
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text:
\section{Introduction}
Mean-field approaches have been widely applied in theoretical astrophysics including for models of stellar structure, convection \citep{CoxGiuli1968}, accretion discs \citep{SS73}, magnetic dynamos \citep{RobertsSoward1975,KrauseRaedler1980}, and interpreting large-scale structure in the Universe.
In such approaches, physical quantities are typically decomposed into mean and fluctuating parts, and the former is explicitly solved for while the latter is modeled using closure methods.
To facilitate an analytically tractable theory, an infinite scale separation between the mean and fluctuating fields is often assumed, allowing for Reynolds averaging rules: linearity of averaging, interchangeability between averaging and differentiation, and invariance of mean quantities under subsequent averaging \cite[see, e.g.,][]{ZhouBlackmanChamandy2018}.

In contrast to this idealized assumption however, realistic astrophysical turbulent flows often exhibit finite and moderate scale separations. The ratio between the system and the turbulence scales is $\sim\mathcal{O}(10)$ to $\sim\mathcal{O}(100)$
 for geometrically thin accretion discs,
$\sim\mathcal{O}(10)$ for galaxies, $\sim\mathcal{O}(5)$ in the solar convection zone, and even lower for geometrically thick accretion discs.
Consequently, the assumption of infinite scale separation leads to at least two classes of discrepancies between theoretical predictions and observations \citep{ZhouBlackmanChamandy2018}:
First, mean-field equations need to be modified with correction to account for the violation of Reynolds rules because double averages are not necessarily equal to single averages.
It follows that the \textit{accuracy} of the theory is threatened if equations derived assuming infinite scale separation are applied to flows with finite scale separation.
Secondly, finite scale fluctuations in observational data do not necessarily average to zero.
This poses an incompatibility if comparing to theoretical predictions that assume fluctuations have zero means because disagreement may be misinterpreted as systematic inaccuracy rather than stochastic imprecision.

Previous work \citep{ZhouBlackmanChamandy2018}
offered a solution to the latter problem, by theoretically estimating the influence from stochastic fluctuations coming from all scales below the mean-field scales, in turn defining the \textit{precision} of a mean-field theory. The deviations between observations and the theory can then be determined to be within or without the precision error bars of the theory, and a better assessment of whether they are stochastic or systematic can be deduced.

The question of computing precision of mean-field predictions can be mathematically formulated as follows:
Let $\mathcal{A}(\bm\tau)$ be some field
with
(i) mean $A$ to predicted by some theory,
(ii) fluctuations $\delta \mathcal{A}$ that modeled statistically;
and $\bm\tau$ is a set of formal variables representing spatial coordinates, time, or any other parameters that $\mathcal{A}$ may depend on.
If $K$ is an observable related to $\mathcal{A}$ via
\begin{equation}
K=\int_{\mathcal V} k(\mathcal{A}(\bm\tau))\text{d}\bm\tau
\end{equation}
where $\mathcal V$ is some appropriate interval and $k$ is some function of $\mathcal{A}$, what is the fluctuation in $K$ due to that of $\mathcal{A}$?

\cite{ZhouBlackmanChamandy2018} focused on the context where $\mathcal{A}$ is a galactic magnetic field, $K$ is the Faraday rotation, and the integration is carried out over a line of sight.In this case, $k(\mathcal{A})$ is the density-weighted magnetic field along the line of sight, and thus a linear function of the mean magnetic field. The coherence length and the variance of the fluctuations were taken to be independent of $\tau$, the position along the line of sight.
The integral of $k$ above is then replaced by a discrete summation and the central limit theorem readily applies.
In the ensemble of different realizations of turbulence, the variance of $K$ is then simply $N$ times smaller than that of $k$ where $N$ is the number of turbulent eddies along the line of sight.

In the present work, we generalize the method to include cases where $k(\mathcal{A})$ is a nonlinear function of $\mathcal A$, and both the variance and the coherent scales of the fluctuations depend on $\bm\tau$.
We apply the formalism to accretion disc theories. For a wide range of accretion models, angular momentum transport is modeled by solving for the dynamics of the mean velocity field with angular momentum transport mediated by an imposed mean stress. These models are manifestly mean-field theories, and predictions from these models should therefore be presented with precision error bars.

Our method herein enables efficiently quantifying fluctuations about the mean-field predictions for the disc spectrum at all photon frequencies, thereby providing a quantitative way of accessing the precision of the models considered.
This is accomplished by propagating local disc perturbations with given amplitudes and coherent scales to the emission spectrum.
At a given photon frequency, this requires including contributions from the entire disc, superseding the local treatment of \cite{Blackman2010}.
Quantifying the theoretical precision
 becomes particularly important when comparing to snapshot observations of a source because then the observed fluctuations cannot be identified by their temporal characteristics.

In Section \ref{sec:error_prop} we introduce the needed method for computing fluctuations of an integral from local contributions with inhomogeneous amplitudes and coherent scales.
In Section \ref{sec:spectrum} we apply the method to a generic thermal disc spectrum,
and more specifically to
protoplanetary discs in
 Section \ref{sec:pd}, and dwarf novae in \ref{sec:dn}.
In Section \ref{sec:tel} we consider how the derived imprecision should be binned when taking into account comparison to observations with finite telescope resolving power.
We summarize in Section \ref{sec:discussion}.

\section{Imprecision in observables from local fluctuations}
\label{sec:error_prop}

\subsection{Propagating fluctuations from integrand to integral}
\label{sec:method1}
To demonstrate how to propagate fluctuations to an integrated quantity, suppose $K$ represents the total luminosity from a one dimensional object in a Cartesian geometry.
If this is given by $k(r)$ per unit length at position $r$, then
\begin{equation}
K=\int_a^b k(r)\text{d}r,
\end{equation}
where $a$ and $b$ specify the boundary.
Now consider a local luminosity fluctuation $\delta k(r)$ with a vanishing mean but allow for inhomogeneous variance $\var{k}(r)$, i.e., $\abra{\delta k^2(r)}=\var{k}(r)$, where the angle brackets denote an ensemble average over all possible realizations of the fluctuation.
We take the fluctuations in the neighborhood of position $r$ to be coherent over a scale $l(r)$, and assume that $l$ is much smaller than the local variation scales of $k$, $\var{k}$, and $l$ itself; that is $l\ll |k/(\text{d}k/\text{d}r)|$, $l\ll |\var{k}/(\text{d}\var{k}/\text{d}r)|$, and $l\ll |l/(\text{d}l/\text{d}r)|$.
In the simplest case, for which both $\var{k}$ and $l$ are independent of position, the total luminosity becomes the sum of $N=(b-a)/l$ number of independent and identically distributed random variables, and thus the variance of $K$ is
\begin{equation}
\var{K}=\frac{\var{k}}{N}=\frac{l}{b-a}\var{k}
\end{equation}
according to the central limit theorem.
We now generalize to cases where both $\var{k}$ and $l$ are smooth functions of $r$. We provide two methods which give identical results. We use the first method here and a second is given in Appendix \ref{appx:method2}.

We discretize the system into grids with the size of the $i$th cell being $l_i\equiv l(r_i)$, and the grid can be constructed in the following way:
\begin{equation}
r_1=a;\
r_{i+1}=r_i+l_i;\ i=1,2,\cdots.
\end{equation}
$K$ is given by the sum of contributions from fluctuating cells,
\begin{equation}
K=\int_a^b k(r)\text{d}r\simeq\sum_i k_i l_i,
\end{equation}
where $k_i=k(r_i)$.
Because $l(r)\ll |k/(\text{d}k/\text{d}r)|$,
$l_i$ can be the line element. The mean of $K^2$ is
\begin{equation}
\abra{K^2}
=\sum_{i,j}\abra{k_i k_j}l_il_j.
\end{equation}
Since each cell covers a local coherent length and varies independently, we have
\begin{align}
\abra{k_ik_j}
=&\left\{
\begin{aligned}
	&\abra{k_i}\abra{k_j},\ &i\neq j\\
	&\abra{k_i^2},\ &i=j
\end{aligned}
\right\}\notag\\
=&\abra{k_i}\abra{k_j}
+\delta_{ij}\left(
\abra{k_i^2}-\abra{k_i}\abra{k_j}
\right).
\end{align}
Thus
\begin{align}
\abra{K^2}
&=\sum_{i,j}\abra{k_i}\abra{k_j}l_il_j
+\sum_i \var{k_i}l_i^2\notag\\
&=\abra{K}^2+\sum_i\var{k_i}l_i^2\notag\\
&\simeq\abra{K}^2+\int_a^b \var{k}(r)l(r)\text{d}r,
\end{align}
where the last step we have used the condition $l(r)\ll |\var{k}/(\text{d}\var{k}/\text{d}r)|$.
The variance of $K$ is thus
\begin{equation}
\var{K}=\abra{K^2}-\abra{K}^2
\simeq\int_a^b\var{k}(r)l(r)\text{d}r.
 \label{eqn:varmethod1}
 \end{equation}

We test the analytical formula (\ref{eqn:varmethod1}) against stochastically generated data using an example
where we have $\var{k}(r)$ and $l(r)$. Specifically
 we take Equation (\ref{eqn:varF_DN}) for an accretion disc model, which is derived and explained in more detail in Section \ref{sec:dn}, but here this simply motivates use of the mathematical example
\begin{equation}
\var k(r)=\frac{r^{37/8}e^{0.2 r^{3/4}}}{\left(e^{0.1 r^{3/4}}-1\right)^4};\
l(r)=l_0r^{9/8}
\label{eqn:test16}
\end{equation}
with two choices $l_0=0.03$ or $l_0=0.05$.
Here length scales are in dimensionless units, normalized by the disc inner radius.
The form of $\var k(r)$ is derived based on a black-body spectrum with a mean disc surface temperature $\propto r^{-3/4}$, with $r$ being the non-dimensional disc radius.

Using Equation
 (\ref{eqn:test16}),
 we compare the prediction of $\var K$ from Equation
 (\ref{eqn:varmethod1}) with that derived from numerically generated data sets.
For the latter, we discretize the interval $[a,b]$ and assign each mesh point a random number (representing $k$) according to a multivariate Gaussian probability distribution function (PDF) with a zero mean and a covariance matrix
\begin{equation}
C_{ij}=\var{k}(r')e^{-\left[\frac{r_i-r_j}{l(r')/2}\right]^2},\ r'=\frac{r_i+r_j}{2},
\end{equation}
where $r_{i,j}$ are the coordinates of a pair of cells on the grid.
For each realization of $k$, its values on all mesh points are summed to give $K$, and different realizations of $k$ construct an ensemble, over which the variance of $K$ is then calculated.
With $a=1$ and different values of $b$, the results are plotted in Figure \ref{fig:var_test}.
Importantly, at a given $b$ the analytical formula is on average $\sim2000$ times faster than averaging over an ensemble with $512$ members\footnote{Both using Wolfram Mathematica on a personal computer with a quad-core CPU}, and provides an efficient way of estimating $\var K$.

Comparing the $l_0=0.03$ and $l_0=0.05$ cases,  it is evident that the larger deviation between data points and the theoretical curve at larger $b$ is due to the breakdown of the condition $l\ll|\var{K}/(\text{d}\var{K}/\text{d}r)|$.
In fact the two length scales becomes comparable at $b\gtrsim600$ with $l_0=0.03$, and $b\gtrsim400$ with $l_0=0.05$.
In general, when the correlation length becomes large enough to violate the aforementioned condition,  Equation (\ref{eqn:varmethod1}) delivers less accuate results.
In the current case and later examples, the main contribution to $\var{K}$ comes from the region where $l\ll|\var{K}/(\text{d}\var{K}/\text{d}r)|$ still holds, and therefore yields the correct order of magnitude.

\begin{figure}
\centering
\includegraphics[width=0.9\columnwidth]{figures/test9.eps}
\caption{A comparison between the variance of stochastically generated data(dots) and that from Equation (\ref{eqn:varmethod1}) (curves).}
\label{fig:var_test}
\end{figure}

Having verified Equation (\ref{eqn:varmethod1}) numerically,
we can use it to formulate the following rules for propagating precision to an integrated quantity from its integrand:
\begin{enumerate}
\item
Replace the integrand by the variance of the integrand multiplied by the correlation length.
\item
Keep the line element of the integration unchanged.
\end{enumerate}
The result can be readily extended to included coordinate-dependent metric factors in the integration measure.

\subsection{Application to accretion discs }
Applying the formalism to an
an axisymmetric disc, we have for the total luminosity
\begin{equation}
K=2\pi\int_a^b k(r)r\text{d}r,
\end{equation}
where $k(r)$ is the luminosity per unit area from an annulus at radius $r$.
Here the line element is $\text{d}r$, and the variance of the integrand is $4\pi^2r^2\var{k}$.
Therefore
\begin{equation}
\var{K}=4\pi^2\int_a^b \var{k}(r)l(r)r^2\text{d}r.
\label{eqn:var_disc1d}
\end{equation}

For a two-dimensional non-axisymmetric disc, the luminosity is given by
\begin{equation}
K=\int_0^{2\pi}\text{d}\phi \int_a^b k(r,\phi)r\text{d}r.
\end{equation}
Assuming statistical axisymmetry, let the fluctuations of $k$ be coherent over scales of $l_r(r)$ and $l_\phi(r)$ in the radial and azimuthal directions, respectively.
The luminosity per unit length of an annulus is
\begin{equation}
K_1(r)=\int_0^{2\pi} k(r,\phi)r\text{d}\phi,
\end{equation}
and its variance is
\begin{equation}
\var{K_1}=\int_0^{2\pi} \var k(r)l_\phi(r)r\text{d}\phi,
\end{equation}
Since $K=\int K_1(r)\text{d}r$, we obtain
\begin{equation}
\var{K}=\int_0^{2\pi}\text{d}\phi \int_a^b \var{k}(r)l_r(r)l_\phi(r)r\text{d}r.
\label{eqn:var_disc2d}
\end{equation}
Equation (\ref{eqn:var_disc2d}) recovers the one-dimensional case (\ref{eqn:var_disc1d}) by taking $l_\phi=2\pi r$.
For quantities involving an integration in time, the method can be similarly extended.
Equation (\ref{eqn:var_disc2d}) also reflects the intuitive expectation that the variance decreases with decreasing correlation lengths because neighboring fluctuations rapidly cancel out.
For vanishing correlation lengths,
our method is not valid and stochastic calculus must be invoked for a rigorous treatment.

Below we explore two applications of Equation (\ref{eqn:var_disc2d}), to the spectra of geometrically thin, optically thick discs.
We focus on finding spectral fluctuations at some given snapshot, where snapshot indicates a short time scale compared to eddy turnover times.

\section{Variance of predicted emission spectrum from a thermal disc}
\label{sec:spectrum}
Consider the thermal spectrum from a geometrically thin, optically thick disc.
Given some surface temperature $\mathscr{T}(r,\phi)$ that includes both a mean and a fluctuating part, the black-body emission per unit frequency per unit area is
\begin{equation}
f(\mathscr{T})=\frac{2{h_\text{P}} \nu^3/c^2}{e^{{h_\text{P}}\nu/k_\text{B} \mathscr{T}}-1},
\label{eqn:f}
\end{equation}
where ${h_\text{P}}$ is the Planck constant, $\nu$ is the photon frequency, $c$ is the speed of light, and $k_\text{B}$ is Boltzmann's constant.
The total power per unit frequency from one side of the disc is
\begin{equation}
F=\int_0^{2\pi}\text{d}\phi \int_{r_*}^{r_\text{out}} f\ r\text{d}r,
\label{eqn:F}
\end{equation}
where ${r_*}$ and ${r_\text{out}}$ are the inner and outer radii of the disc, respectively.

We separate the total temperature $\mathscr{T}$ into a mean $T$ and fluctuating part $\delta\Ttot$.
The mean part $T$ is assumed to be modeled by some mean-field theory which we assume to be axisymmetric and stationary so that $T=T(r)$.
The residual $\delta\Ttot$ varies on turbulent time and length scales.
All fluctuations are assumed to obey statistical axisymmetry although this can be generalized.
In what follows, we give a unified formalism of calculating precision errors using the error propagation formula (\ref{eqn:var_disc2d}).
A more formal and systematic description of three important different types of errors is presented in Appendix \ref{appx:error}.

For any local fluctuation in $\mathscr{T}$ at location $(r,\phi)$, whether from $T$ or $\delta\Ttot$, with a variance $\var{\mathscr{T}}(r)$ of its amplitude, the variance of the local fluctuation in $f$ is
\begin{equation}
\var{f}=\left[\frac{\partial f(T)}{\partial T}\right]^2\var{\mathscr{T}}.
\end{equation}
As we are computing the expected variance of fluctuations around the mean, the term inside the angle brackets is evaluated at its mean value $\mathscr{T}=T$.

We assume that the fluctuation in $f$ has the same coherent scales as those of fluctuations in $\mathscr{T}$, as determined by the physical processes causig the latter.
If the fluctuation of $f$ is coherent over lengths $l_r(r)$ in the radial direction and $l_\phi(r)$ in the azimuthal direction, the variance of the fluctuation in $F$ will be determined by Equation (\ref{eqn:var_disc2d}) and given by
\begin{align}
\var{F}&=\int_0^{2\pi}\text{d}\phi \int_{r_*}^{r_\text{out}}
\var{f}(r) l_r(r) l_\phi(r){r\text{d}r}\notag\\
&=2\pi\int_{r_*}^{r_\text{out}}
\left(T\frac{\partial f}{\partial T}\right)^2
\frac{\var \mathscr{T}}{T^2}
l_rl_\phi{r\text{d}r}.
\label{eqn:varF}
\end{align}
Here, $T\partial f/\partial T$ as a function of $T$ is determined by Planck's law (\ref{eqn:f}), whereas the exact expressions of $T$ itself, $\var{\mathscr{T}}$, $l_r$, and $l_\phi$, will be model dependent.

We can also determine the fluctuation in the total luminosity for a frequency bandwidth over which fluctuations in the disc spectrum are coherent, in analogy to $l_r$ and $l_\phi$ which are coherent scales in configuration space.
Since the total luminosity is $L=2\int_0^\infty F\text{d}\nu$, the variance of its fluctuation is
\begin{equation}
\var{L}=4\int_0^\infty \var{F}\Delta \nu\text{d}\nu,
\label{eqn:varL}
\end{equation}
where $\Delta\nu$ is a frequency-dependent coherent bandwidth.
One such example is given in Section \ref{sec:dn}.

For convenience we define several dimensionless variables here for later use.
The dimensionless disc radius is $\tilde r=r/{r_*}$.
The mean temperature can be written as $T=T_*\tilde T(\tilde r)$, where $T_*$ is the mean temperature at ${r_*}$ and includes all dependence on other disc parameters such as the central object mass, mass accretion rate, etc.
The dimensionless frequency is then
\begin{equation}
\beta=\frac{{h_\text{P}}\nu}{k_\text{B} T_*}.
\label{eqn:beta}
\end{equation}
We denote the disc scale height by $h(r)$, and the height-to-radius ratio at the inner boundary by $\theta=h({r_*})/{r_*}$.

\section{Application to protoplanetary discs}
\label{sec:pd}
Gas in protoplanetary discs is subject to turbulence, as indicated by molecular line observations \citep{Hughes2011,Guilloteau2012} and dust distributions \citep{Pinte2016}.
The underlying turbulence drivers include MRI \citep{Velikhov1959,Chandrasekhar1960,BalbusHawley1991}, self-gravitation \citep{Toomre1964,Shlosman1987}, and hydrodynamic instabilities.
The driving mechanism may also vary  between young and old objects, and between inner and outer regions, or midplane and surface layers in a single object.
Regardless of the origin, if we assume that the  eddy turnover timescale of dominant eddies is comparable to the local Keplerian timescale, the eddy turnover time can reach $\sim 30\ \text{yr}$ just at 10 AU with a central solar-mass object.
Thus for most parts of a protoplanetary disc, the turbulence timescale exceeds exposure timescales of telescopes, or even timescales of multi-epoch observations.

For such a ``snapshot'' image, some turbulent eddies are brighter and some are dimmer than the average profile predicted by a mean-field theory, and they contribute to the observed thermal spectrum at all wavelengths.
It is therefore necessary to ask, whether a  deviation between observations and theory at a specific wavelength has a truly systematic or a merely  stochastic origin.
In this section, we quantitatively incorporate the effect of turbulent fluctuations on the mean-field prediction of the disc thermal spectrum.
We isolate this turbulent effect by assuming all other parameters in the problem, e.g., mass accretion rate and the $\alpha$ parameter, remain time-independent.

Let a fluctuation in the surface temperature due to turbulence be $\delta\Ttot$, which also generates a fluctuation in the luminosity ${L_\text{ed}}$ of a turbulent eddy.
Although a   realistic probability distribution description for turbulence is still lacking,  we capture  the properties of $\delta\Ttot$
by assuming that  the luminosity ${L_\text{ed}}$ for each turbulent eddy,  is drawn from an ensemble with a uniform PDF,
\begin{equation}
P_{{L_\text{ed}}}(x)=\frac{1}{2 L},\ 0,\leq x\leq 2L,
\end{equation}
so that $P_{L_\text{ed}}(x)\text{d}x$ is the probability to find ${L_\text{ed}}$ between $x$ and $x+\text{d}x$.
Here $L$ is the mean of ${L_\text{ed}}$, and equals the luminosity of the mean-field disc model from an area equal to that of the eddy.
In general, $L$ depends on the disc radius in a mean-field model, and so does $P_{L_\text{ed}}$.
This simple uniform PDF allows us to proceed simply, but more comprehensive statistical prescriptions may also be used \citep[e.g.,][]{LeeGammie2021}.

For optically thick discs, the PDF of $\mathscr{T}$ can be deduced from the relation ${L_\text{ed}}={\sigma_\text{SB}} \mathscr{T}^4$, so that
\newcommand{T_\text{max}}{T_\text{max}}
\begin{equation}
P_{\mathscr{T}}(x)=\frac{2 x^3}{ T_\text{max}^4},\ 0\leq x\leq 2^{1/4} T_\text{max},
\label{eqn:PT}
\end{equation}
where $\SBT_\text{max}^4=L$, and $T_\text{max}=5T/2^{9/4}$, with $T$ being the mean temperature field solved from a mean-field theory.
Equation (\ref{eqn:PT}) then defines a PDF for the disc surface temperature whose mean is $T$.
For a given mean-field disc model, $P_{\mathscr{T}}(x)$ is known at all radii and the mean and the variance of $f$ in the ensemble can be calculated by
\begin{equation}
\abra{f}=\int P_{\mathscr{T}}(x)\frac{2{h_\text{P}} \nu^3/c^2}{e^{{h_\text{P}}\nu/k_\text{B} x}-1} \text{d}x
\end{equation}
and
\begin{equation}
\var f=\int P_{\mathscr{T}}(x)
\left(\frac{2{h_\text{P}} \nu^3/c^2}{e^{{h_\text{P}}\nu/k_\text{B} x}-1}\right)^2\text{d}x
-\abra{f}^2,
\end{equation}
respectively.

Note that the ensemble mean of $f$ is different from the flux obtained by using the mean of $\mathscr{T}$, namely
\begin{equation}
\abra{f}\neq \frac{2{h_\text{P}} \nu^3/c^2}{e^{{h_\text{P}}\nu/k_\text{B} T}-1}.
\end{equation}
Consequently, there is a difference between the ensemble mean of $F$, and the value that would be obtained using first the mean of $\mathscr{T}$. The latter is what is done for  most mean-field disc models.
The difference between these two approaches leads to what we call the ``mismatch error'' (ME):
\begin{equation}
\Delta F=\int \abra{f}r\text{d}r \text{d}\phi-\left.F\right|_{\mathscr{T}=T},
\label{eqn:ME}
\end{equation}
where $F$ is given by Equation (\ref{eqn:F}).

The ME reflects the disagreement between the fluxes that arise from  the following two theoretical approaches:
(i) solve for mean fields such as the mean disc temperature $T$, and then calculate the disc spectrum using $\left.F\right|_{\mathscr{T}=T}$;
(ii) solve for both the mean and the fluctuation in temperature, the latter statistically in a mean-field model, then combine to obtain total temperature $\mathscr{T}$ and the associated total spectrum, and  take the average to get $\abra{F}$.
Approach (i) is commonly adopted, but approach (ii) is what should be used by theorists to more accurately compare to what observations measure.

The variance of $F$ can be computed by propagating that of $f$.
The correlation length of the latter is assumed to be isotropic and identified with the turbulence scale $l$ in the model.
In an $\alpha$ disc model we have
\begin{equation}
l\simeq\frac{\alpha{c_\text{S}} h}{v}\simeq\frac{\alpha\Omega h^2 }{l\Omega},
\end{equation}
and thus $l\simeq\alpha^{1/2}h$ \citep{Blackman1998}.
The variance of $F$ is then
\begin{equation}
\var{F}=2\pi\alpha\int \var{f}h^2 r\text{d}r,
\label{eqn:varF_PD}
\end{equation}
using Equation (\ref{eqn:var_disc2d}).

We now adopt a specific profile of $T$ to qualitatively compute ME and FE.   In mean-field models the mean temperature is typically related to  the disc radius via a power-law relation, $T=T_*\tilde r^{p}$.
In the context of protoplanetary discs, $p$ varies from $-1$ to $\sim-1/2$ depending on whether disc heating is dominated by star irradiation or viscous heating.
The exponent also likely varies with the disc radius if a transition of heating source occurs.
For simplicity, we consider a constant $p$ here.
A particular model is taken from \cite{Edgar2007} for which the heat of the central plane is solely due to viscous dissipation, and the mean surface temperature $T$ and scale height $h$ are solved to be
\begin{equation}
T=T_* \tilde r^{-21/40},\ h=h_* \tilde r^{21/20}.
\label{eqn:disc_model}
\end{equation}
Combining Equations (\ref{eqn:ME}), (\ref{eqn:varF_PD}), and (\ref{eqn:disc_model}), we compute the ME and the FE as shown in Figure \ref{fig:PD}.

While FE originates from  turbulence  and measures the corresponding stochastic fluctuation around the mean spectrum, ME is systematic as is clear from Equation (\ref{eqn:ME}).
Consequently, fitting averaged observational data (approximately $\abra{F}$) with typical theoretical predictions that amount to $\left.F\right|_{\mathscr{T}=T}$, introduces a bias of inferred parameters.
In the present   protoplanetary disc example
the bias in the maximum temperature at the disk inner radius $T=T(r_*)$ is $6.5\%$, that in the exponent $-\partial\ln T/\partial\ln r$ is $1.0\%$, and that for the disc outer radius is $-5.4\%$.
The numerical values are relatively small.  They do depend on the choice of the PDF for $\mathscr{T}$, but
the result shows that the thin disk mean field model in this context
are  quite precise, inasmuch as   observational uncertainties
are larger.

\begin{figure}
\centering
\includegraphics[width=0.9\columnwidth]{figures/FE.eps}
\caption{Relative errors in the disc spectrum:
that from comparing mean of the total spectrum versus the spectrum of the mean temperature (upper),
and that from turbulent fluctuations of the surface temperature (lower).
$\beta$ is the dimensionless photon frequency defined in Equation (\ref{eqn:beta}).
The disc model uses $\alpha=0.01$, ${r_\text{out}}/{r_*}=150$, and $\theta=0.01$.
}
\label{fig:PD}
\end{figure}

\section{Application to dwarf novae}
\label{sec:dn}
Dwarf novae (DNe) are characterized by their regular outbursts, and
 thought to  result from accretion disk instability \citep{Osaki1974,Hoshi1979,Lasota2001,Hameury2020}.
The standard disk instability model relies on thermal instability
and the fact that the disc opacity changes rapidly and nonlinearly with temperature at $\sim 10^4\text{ K}$ where hydrogen ionization takes place.
The temperature is directly connected to  the accretion rate and so  where the temperature  vs. surface density equilibrium  curve is unstable, so is the accretion rate.  Once the accretion rate increases in the disk to a value larger than the outer supply rate
can accommodate the surface density and temperature drop
until matter again builds up and the cycle repeats.
How  exactly the disc viscosity depends  on heating is model dependent. Recently, \cite{HeldLatter2021} demonstrated that if convection results from the strong opacity
increase, its combined effect with the magneto-rotational instability (MRI) may lead to a significant increase in angular momentum transport, characterized by cyclic bursts of $\alpha$, the stress-to-pressure parameter. The strengthened angular momentum transport  in the simulations is speculated to result from convection generated magnetic fields reseeding the MRI, an effect  most prevalent  in cases with long cooling times and short resistive times.
In these so-called strong MRI/convection cycles, $\alpha$ is enhanced in the MRI phase by approximately one order of magnitude.
Several studies have also reported similar $\alpha$ bursts in stratified shearing boxes
\citep{Simon2011,Bodo2012,Hirose2014,Coleman2018}, albeit some with different origins argued.
In this section, we build our model based on the results of \cite{HeldLatter2021}, and explore how such fluctuations in $\alpha$ can  affect the disc spectrum in the quiescent phase, during which the strong MRI/convection cycle is most likely because of the high resistivity.

We assume that the representative temporal and spatial fluctuations in $\alpha$ are local, focusing on circumstances  that apply before  they lead to   any global coherent structure over the entire disc.
The typical cycle periods of DN bursts are observed to be $\mathcal{O}(10)$ orbital times in simulations, and therefore may occur multiple times during one hot or cold phase of the disc.
The ratio between the Keplerian timescale at the outer radius and the quiescence time of the disc can be estimated from Equations (52) or (53) in \cite{Lasota2001} as
\begin{align}
\frac{t_\text{Kep,out}}{t_\text{quiesc,oi}}\simeq&
0.0126
\left(\frac{\alpha}{0.01}\right)
\left(\frac{\dot M}{10^{17}\text{ g s}^{-1}}\right)^{2}\notag\\
&\left(\frac{{T_\text{c}}}{3000\text{ K}}\right)
\left(\frac{M}{M_\odot}\right)^{0.76}
\left(\frac{{r_\text{out}}}{10^{10}\text{ cm}}\right)^{-4.3}
\end{align}
for an outside-in outburst, or
\begin{align}
\frac{t_\text{Kep,out}}{t_\text{quiesc,io}}\simeq&
0.00005\delta
\left(\frac{\alpha}{0.01}\right)
\left(\frac{T_c}{3000\text{ K}}\right)\notag\\
&
\left(\frac{M}{M_\odot}\right)^{-1}
\left(\frac{{r_\text{out}}}{10^{10}\text{ cm}}\right).
\end{align}
for an inside-out burst with large disc radii.
Here, ${T_\text{c}}$ is the disc mid-plane temperature, and $\delta$ is the difference between the logarithm of the maximum surface density in the lower equilibrium branch of temperature vs. surface density during the quiescent phase;
typically $\delta\lesssim2$ \citep[c.f. Figure 11 in][]{Lasota2001}.
As such, at all radii the cycle period of the bursty $\alpha$ is much shorter than the disc quiescent time.

The relatively short cycle period leads to axisymmetric fluctuations, and accordingly the azimuthal coherence length is $l_\phi=2\pi r$.
The radial viscous diffusion time is much larger than the orbital time because
\begin{equation}
\frac{t_\text{viscous}}{t_\text{Kep}}
\simeq
\frac{r^2}{\nu_\text{T}\Omega^{-1}}
\simeq\alpha^{-1}\left(\frac{h}{r}\right)^{-2}\gg1,
\end{equation}
which suggests that the $\alpha$ fluctuation can also be considered local in radius.
In the simulations exhibiting the strong MRI/convection cycles \cite{HeldLatter2021}, $\alpha$ is defined by a volume average over a box of radial length $4h$, based on which we assume a coherent scale $l_r=nh$ with a fiducial $n=5$ in the radial direction.
For the standard Shakura-Sunyaev model $h/r=\theta \tilde r^{1/8}$ \citep[e.g.,][]{Frank2002book}, and thus $l_r=n\theta r \tilde r^{1/8}$.

We now derive the temperature and flux fluctuations.
For DNe in the quiescent state, the disc is not necessarily in the global viscous equilibrium  \citep{Lasota2001},
but we assume that local  equilibrium between the mean surface black-body flux and the turbulent viscous dissipation holds, i.e.,
\begin{equation}
\sigma T^4(r)
=\frac{1}{2}\nu_T\Sigma\left(r\partial_r\Omega\right)^2
=\frac{1}{2}\alpha {c_\text{S}} h\Sigma\left(r\partial_r\Omega\right)^2.
\end{equation}
Since $h$, $\Sigma$, and $r\partial_r\Omega$ change on the viscous time scale, which is much longer than $10$ Keplerian orbit times, an $\alpha$ burst event that spans a timescale of $\mathcal{O}(10)$ orbits causes a mean surface temperature fluctuation  $T\propto\alpha^{1/4}$.
If the variance of fluctuations in $\alpha$ is $\var\alpha$, we have
\begin{equation}
\frac{\var{T}}{T^2}=\frac{1}{16}\frac{\var\alpha}{\alpha^2}.
\label{eqn:ie:varT}
\end{equation}
We  take $\sigma_\alpha/\alpha=0.5$ as estimated from \cite{HeldLatter2021}.
Since $\var{\mathscr{T}}=\var{T}$ in this case, combining Equation (\ref{eqn:ie:varT}), $l_r=n\theta r\tilde r^{1/8}$, and $l_\phi=2\pi r$, we obtain from Equation (\ref{eqn:varF}) that
\begin{equation}
\var{F}=\frac{\pi^2 n\theta}{16}
\int_{r_*}^{r_\text{out}}\left(T\frac{\partial f}{\partial T}\right)^2
\tilde r^{1/8} r^3\text{d}r.
\label{eqn:varF_DN}
\end{equation}
For a standard Shakura-Sunyaev model we have $T\simeq T_*\tilde r^{-3/4}$.
The integral can be numerically carried out, and we show in Figure \ref{fig:DN} the relative fluctuation $\sigma_F/F$ and also the $1\sigma$ uncertainty around $F$ by plotting $F$ and $F\pm\sigma_{F}$ together.

To quantify the corresponding variation in the total luminosity, we need to determine  the photon frequency range over which fluctuations in the disc spectrum are  coherent.
A reasonable estimate is obtained by assuming that photons at a  frequency $\nu$ are emitted by a single annulus whose position is determined by Wien's displacement law:
\begin{equation}
\frac{{h_\text{P}}\nu}{k_\text{B} T(r)}\simeq 2.8
\ \Rightarrow\
\beta=2.8{\tilde r}^{-3/4},
\label{eqn:Dbeta_coh}
\end{equation}
where $\beta={h_\text{P}}\nu/k_\text{B}T_*$ is the dimensionless frequency defined.
The coherence length $l_r$ of the temperature fluctuations is propagated to a coherent frequency width $\Delta\beta_\text{coh}$ by
\begin{equation}
\Delta\beta_\text{coh}=\left|\frac{\partial \beta}{\partial \tilde r}\right|\frac{l_r}{{r_*}}
=2.1n\theta\tilde r^{-5/8}
=0.89n\theta\beta^{5/6}.
\end{equation}
One can verify that $\Delta\beta_\text{coh}<F/|\partial F/\partial\beta|$ for all $\beta\in[10^{-3},10]$.
Using Equation (\ref{eqn:varL}), the relative fluctuation in the luminosity is found to be $\delta L/L=1\%$.
If we identify the variation time $t_L$ of $L$ as that of $\alpha$ for the most luminous annulus, we find $t_L/t_\text{Kep,out}=0.0016\times\mathcal{O}(10)$ where $t_\text{Kep,out}$ is the Keplerian timescale at the disc outer radius.

\begin{figure}
\centering
\includegraphics[width=0.9\columnwidth]{figures/IE.eps}
\caption{In dimensionless units, the relative error (upper) and the corresponding error bars overplotted on the spectrum (lower) induced by $\alpha$ bursts in strong MRI/convection cycles.
$\beta$ is the dimensionless photon frequency defined in Equation (\ref{eqn:beta}).
Variation in the luminosity is $\delta L/L=0.01$.
The disc model uses ${r_\text{out}}/{r_*}=600$ and $\theta=0.01$.
}
\label{fig:DN}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.9\columnwidth]{figures/FT.eps}
\caption{
The same model as in Figure \ref{fig:DN}, but showing the relative error in the spectrum after it is binned by the telescope resolving power.
}
\label{fig:FT}
\end{figure}

\section{Role of telescope resolving power in determining falsifiability}
\label{sec:tel}
The imprecision we have computed above
is independent of  the finite resolving power and binning of data by given telescope that observational data is subjected to before
it can be compared against  theoretical predictions.
We now show  how to incorporate this.

Let the spectral resolving power of a telescope be
\begin{equation}
\text{RP}=\frac{\nu}{\Delta \nu},
\end{equation}
where $\Delta\nu$ is the telescope resolving bandwidth at photon frequency $\nu$.
For snapshot measurements, defined by  exposure time being smaller than flux fluctuation timescales, the observed flux $F^\text{T}$ is binned using the resolved bandwidth $\Delta\nu=\nu/\text{RP}$, i.e.,
\begin{equation}
F^\text{T}(\nu)=\frac{\text{RP}}{\nu}\int_\nu^{\nu\left(1+\text{RP}^{-1}\right)}
F(\nu')\text{d}\nu'.
\end{equation}

The flux spectral fluctuations are fully  resolved when the resolved bandwidth is smaller than the coherent bandwidth of the fluctuations, i.e., when $\text{RP}>\nu/\Delta\nu_\text{coh}$ where $\Delta\nu_\text{coh}=\Delta\beta_\text{coh}k_\text{B} T_*/{h_\text{P}}$.
The fluctuation in $F^\text{T}$ is then $\sigma^\text{T}=\sigma_F$ from Equation (\ref{eqn:varF_DN}).
In the opposite limit of $\text{RP}< \nu/\Delta\nu_\text{coh}$, every neighboring number $\Delta\nu/\Delta\nu_\text{coh}$  of fluctuating bandwidths are binned.
Identifying $K$ with $F^\text{T}$ and $k$ with $F$ in Equation (\ref{eqn:var_disc2d})
we have
\begin{equation}
\sigma^\text{T}
\simeq \frac{\text{RP}}{\nu}
\left[\int_\nu^{\nu\left(1+\text{RP}^{-1}\right)}
\sigma^2(\nu')\Delta \nu'_\text{coh}\text{d}\nu'
\right]^{1/2}.
\label{eqn:varFT}
\end{equation}

In Figure \ref{fig:FT} we plot the relative precision $\sigma^T/F^\text{T}$ for different constant $\text{RP}$ values by evaluating Equation (\ref{eqn:varFT}).
The critical dimensionless photon frequencies above which $\text{RP}>\beta/\Delta\beta_\text{coh}$ are $10^{-3.9}$, $10^{-0.3}$, and $10^{5.7}$ for the $\text{RP}=5,20,200$ cases, respectively.
Smaller RP reduces the effect of fluctuations because more fluctuation cells are averaged within a single resolving bandwidth.

\section{Conclusion}
\label{sec:discussion}
The scale separations between mean and fluctuating fields in astrophysical flows are finite, in contrast to the idealized assumption of infinity, which affects both the accuracy and the precision of a given mean-field theory.
In particular, spatially or temporally averaged observational data unavoidably includes contributions from small-scale fluctuations, and thus when fitting data, the inferred model may fail to match those from an accurate theory, or misleadingly appear to agree with an inaccurate theory, if fluctuations around mean-field results are not properly estimated.
Falsifiability of mean-field theories by comparing to observations requires careful distinction between disagreements that result from accuracy with those that result from imprecision.

While improving accuracy means increasing the fidelity of the input physics that account for the finite scale separation, in this work we focus on calculations of precision of mean-field theories, defined as the variance of the fluctuations of mean-fields propagated from small-scale fields.
We have considered the general case of statistically inhomogeneous small-scale fluctuations, and the derived Equation (\ref{eqn:varmethod1}) is shown to be consistent with data from a numerically realized ensemble, yet significantly preceding the latter in terms of efficiency.

We then exemplified the method by computing imprecision in the prediction of accretion disc thermal spectra, induced by (i) turbulent fluctuations, and (ii) meso-scale fluctuations in $\alpha$, respectively.
For both, we imposed fluctuations in temperature and its coherence length allowing both to be local functions of space.
The consequent error propagation of these fluctuations to global observables, namely spectra and luminosity, were then derived.
Although with small magnitudes, the derived spectra fluctuations indeed depend on photon frequency, and suggests that accurate falsification of a mean-field theory may require a likelihood function or data weighting that reflects the fidelity of the theoretical mean-field values in different regions of the parameter space, as the photon frequency in the current examples.

In contrast to previous dynamical models \citep{Lyubarskii1997,DexterAgol2011,CowperthwiteReynolds2014,TurnerReynolds2021}, each of which considers  different models for the time evolution of imposed surface density or temperature fluctuations and pursues their observational signature, our work focuses on an efficient semi-analytical method of computing the propagation of inhomogeneous fluctuations to synthetic observables to compare with snapshot observations.
We have assessed how precise the predictions of standard mean-field disc theories are when subjected to such fluctuations of a given amplitude.

In addition to the stochastic contributions, we have also shown that the nonlinear relation between basic physical quantities solved in theories (i.e., surface temperature) and observables (i.e., disc spectrum) can lead to a finite systematic mismatch between the meaning of the quantity that is predicted and that is observed and then averaged.
This leads to a systematic bias when backing out disc parameters of a few per cent, and a more comprehensive treatment of turbulence would offer a more accurate determination of this bias.

\section*{Acknowledgements}
We thank Jing Yang and Alexandra Veledina for useful discussions, and we also thank the referees for helpful suggestions.
HZ acknowledges support from Horton Fellowship from the Laboratory for Laser Energetics at U. Rochester.
EB acknowledges support from NSF grants AST-1813298, PHY-2020249; DOE grants DE-SC0020432 and DE-SC0020103; KITP UC Santa Barbara funded by NSF Grant PHY-1748958.

redpajama_set_name: RedPajamaArXiv


text:
Creative Arts Practices
Spin Ins
Spin Outs
Thinktech launched by Minister Simon Coveney T.D.
Posted by: Andrew on: 22 June 2016
Minister Simon Coveney T.D. Launches €1 million Thinktech initiative to use technology for social good in Ireland.
21st June 2016: THINKTECH, a €1 million project to support and grow ideas for a better Ireland, was today officially launched at Google Foundry by Minister for Environment, Community & Local Government, Simon Coveney, T.D. Created by Social Innovation Fund Ireland with support from Google.org and the Department of Environment, Community & Local Government, the unique THINKTECH challenge will identify innovative ideas that use technology to create positive social impact in Ireland.
Social Innovation Fund Ireland and Google.org believe that technology has the power to transform our lives for the better. Successful participants will have access to an award fund of up to €750,000, which consists of €600,000 in grants and up to €150,000 worth of support and mentoring, plus a package of Google supports. They will also enter a five-month programme with Social Innovation Fund Ireland with support from Google.org.
CEO, Social Innovation Fund Ireland, Deirdre Mortell said: "We are delighted to team up with Google.org for THINKTECH. This project shines a light on the potential for social enterprises to use technology to solve critical social issues and create a better Ireland. Since Social Innovation Fund Ireland's launch in January this year, the organisation has grown from strength-to-strength, and through this collaboration with Google.org & the Department of Environment, Community & Local Government, we have been able to provide a €1 million Fund and a unique platform to promote social innovations. This project also highlights the benefits of private and public sector organisations working together to make a better Ireland."
Jacquelline Fuller, Director of Google.org said "We are proud to support THINKTECH, which is the first of its kind in Ireland and look forward to seeing great projects and supporting the winners through the five-month programme which Social Innovation Fund Ireland will run in 2017."
CONNECT is the world leading Science Foundation Ireland Research Centre for Future Networks and Communications. CONNECT is funded under the Science Foundation Ireland Research Centres Programme and is co-funded under the European Regional Development Fund. We engage with over 35 companies including large multinationals, SMEs and start-ups. CONNECT brings together world-class expertise from ten Irish academic institutes to create a one-stop-shop for telecommunications research, development and innovation.
Postdoc opportunities – EDGE call
Up to 17 postdoctoral fellowships are now open with the EDGE programme. Application deadline: 6 April 2020.
Homepage Feature
CONNECT's Marco Ruffini partners in €3.6 million DTIF win
The FreeSpace project is a consortium between industry and academic partners including CONNECT's Prof Marco Ruffini at Trinity College Dublin.
Colm Browning to lead new optical technologies research project
Dr Colm Browning, CONNECT Research Fellow at Dublin City University, has been awarded an SFI Investigator Research Grant (SIRG) to work on radio and optical communications.
CONNECT Centre
Dunlop Oriel House
34 Westland Row
Trinity College Dublin, the
University of Dublin
@connect_ie
CONNECT is funded under the Science Foundation Ireland Research Centres Programme and is co-funded under the European Regional Development Fund. Website © CONNECT Centre 2020. All rights reserved.

redpajama_set_name: RedPajamaCommonCrawl


A very tired traveler came to the banks of a river.
There was no bridge by which he could cross. It was winter, and the surface of the river was covered with ice. It was getting dark, and he wanted to reach the other side while there was enough light to see. He debated about whether or not the ice would bear his weight.
Finally, after much hesitation and fear, he got down on his knees and began very cautiously to creep across the surface of the ice. He hoped that by disturbing the weight of his body, the ice would be less apt to break under the load.
After he made his slow and painful journey about halfway across the river, he suddenly heard the sound of singing behind him. Out of the dusk, there came a 4-horse load of coal driven by a man singing merrily as he went to his carefree way. Here was the traveler, fearfully inching his way on his hands and knees. And there, as if whisked along by the winter's wind, went the driver, his horses, his sled, and the heavy load of coal over the same river!
The story illustrates how many of us go through life.
Some stand on the bank of decisions unable to make up their minds about the course to take. Others stand on the banks trying to muster enough courage to cross over to the other side of the task or problem encountered. On the other hand, some individuals crawl and creep through life for fear of thin ice.
Their faith is not strong enough to hold them up.
Still there are those who whisked along whistling as they go. Their faith is UNSHAKABLE.
……When we face the river of difficulties, we do not have to fear, nor do we creep through life. God has promised to help, and with God's help we can merrily make our way to the other side safely.


Posted on November 3, 2015 in My Blog.
Balance with each other, totally resolved.
No matter of what balance they are in.
Cleansing in all area's of these 3 situations.
In this area of growth.
Lead to "fear" as we make this next shift.
It really is each for their own right now.
Effort, love into another whom is NOT.
Full power to the human being in all aspects.
Action is required of each soul on EARTH..
The ends results are POWERFUL!!!!!
Let "me" be of "guidance" in this final stage.


text:
Решетниково () — присілок Гагарінського району Смоленської області Росії. Входить до складу Єльнинського сільського поселення.
Населення — 19 осіб (2007 рік).

Примітки

Населені пункти Гагарінського району

redpajama_set_name: RedPajamaWikipedia


text:
Wednesday, Jan 12 2022
CMS To Seek More Private Partnerships To Lower Medicare, Medicaid Expenses
CMS Administrator Chiquita Brooks-LaSure tells a financial conference that the federal Medicare and Medicaid programs need to "align goals" with private companies to help lower drug costs and other health expenses.
Modern Healthcare: CMS: We Will Lean On Private Sector To Address Costs, Disparities
The federal government will increase its partnerships with private companies and community groups in 2022 to bridge health disparities and reduce costs for publicly-covered patients, the Centers for Medicare and Medicaid Administrator Chiquita Brooks-LaSure said during the J.P. Morgan Healthcare Conference on Tuesday. "Our role with the private sector is really partnering and trying to align goals," Brooks-LaSure said, adding that companies like Walmart "absolutely" play a role in lowering drug costs for Medicare, Medicaid, Children's Health Insurance Program and the Affordable Care Act exchange customers. (Tepper, 1/11)
In other Medicaid news —
WICS/WRSP: After Legalizing Midwives, Illinois Lawmakers Look To Cover The Service With Medicaid
Springfield lawmakers want to expand Medicaid to cover in-home birthing services. A bill that has already passed in the House would expand Medicaid coverage for midwife services. The voucher program would include coverage for home birth services, in-home prenatal care, and postpartum services from certified professional midwives. In December, Gov. JB Pritzker, D-Illinois, signed a law that allows for the professional regulation of midwives in Illinois, a practice that had been illegal in the state since 1992. (Emerson, 1/11)
Missouri Independent: Timing Unclear For $5.3B Bill To Support Missouri Medicaid Expansion, State Pay Raises
Gov. Mike Parson is in a hurry to get a $5.3 billion spending bill passed by Feb. 1, but exactly when the bill will reach the House floor for debate is uncertain. The House Budget Committee spent about five hours Monday digging through the details of the bill that will fund Medicaid for the remainder of the year, give pay raises to state employees and distribute federal pandemic aid for schools. (Keller, 1/11)
Austin American-Statesman: Fact-Check: Did Texas Turn Down $100 Billion When Republicans Rejected Medicaid Expansion?
Announcing his candidacy for governor, former U.S. Rep. Beto O'Rourke said Texas has left billions of dollars on the table by failing to expand Medicaid during Gov. Greg Abbott's tenure. "Expanding Medicaid, which if we had done at the beginning of the Abbott administration, would have brought in $100 billion to this state's economy," O'Rourke said at a Nov. 19 rally in Houston. Texas is one of 12 states that hasn't expanded Medicaid coverage, which is backed mostly by federal funding. (Mizan, 1/9)
KHN: Left Behind: Medicaid Patients Say Rides To Doctors Don't Always Come
Tranisha Rockmore and her daughter Karisma waited at an Atlanta children's hospital in July for their ride home. Karisma had been at Children's Healthcare of Atlanta to have her gastrostomy tube fixed, Rockmore said. The 4-year-old, who has several severe medical conditions, has insurance coverage from Medicaid, which provides transportation to and from nonemergency medical appointments through private vendors. After being told that a ride would not be available for hours, Rockmore said, she finally gave up and called her sister to drive them home to the South Georgia town of Ashburn, more than 160 miles away. (Grapevine and Miller, 1/12)
Axios: Scoop: Medicaid-Focused Circulo Acquires Primary Care Startup Huddle
Circulo Health, an Ohio-based insurance startup focused on people who use Medicaid, has quietly acquired primary care provider Huddle Health, Axios has learned. Circulo is also said to have partnered with telehealth startup Brave Health to deliver tele-psychiatry services. Much of the recent healthcare buzz has focused on using tech to provide affluent people with more convenient, comprehensive care. That's left people who use Medicaid or Medicare — notably, those most in need of care — behind. (Brodwin, 1/11)


text:
Watch Dennis Hopper Movies | Watch Dennis Hopper TV Shows
Dennis Hopper Wiki
Real Name: Dennis Lee Hopper
Birth Place: Dodge City, Kansas, USA
Birth Date: May 17, 1936
Occupation: Actor, Director, Writer
Dennis Hopper Biography
Multi-talented and unconventional actor/director regarded by many as one of the true "enfant terribles" of Hollywood who has led an amazing cinematic career for more than five decades, Dennis Hopper was born on May 17, 1936 in Dodge City, Kansas. The young Hopper expressed interest in acting from a young age and first appeared in a slew of 1950s television series, including "Medic" (1954), "Cheyenne" (1955) and "Sugarfoot" (1957). His first film role was in Johnny Guitar (1954), which was quickly followed by roles in Rebel Without a Cause (1955), Giant (1956) and Gunfight at the O.K. Corral (1957). Hopper actually became good friends with James Dean and was shattered when Dean was killed in a car crash on September 30, 1955.Hopper portrayed a young Napoléon Bonaparte (!) in the star-spangled The Story of Mankind (1957) and regularly appeared on screen throughout the 1960s, often in rather undemanding parts, usually as a villain in westerns such as True Grit (1969) and Hang 'Em High (1968). However, in early 1969, Hopper, fellow actor Peter Fonda and writer Terry Southern, wrote a counterculture road movie script and managed to scrape together $400,000 in financial backing. Hopper directed the low-budget film, titled Easy Rider (1969), starring Fonda, Hopper and a young Jack Nicholson. The film was a phenomenal box-office success, appealing to the anti-establishment youth culture of the times. It changed the Hollywood landscape almost overnight and major studios all jumped onto the anti-establishment bandwagon, pumping out low-budget films about rebellious hippies, bikers, draft dodgers and pot smokers. However, Hopper's next directorial effort, The Last Movie (1971), was a critical and financial failure, and he has admitted that during the 1970s he was seriously abusing various substances, both legal and illegal, which led to a downturn in the quality of his work. He appeared in a sparse collection of European-produced films over the next eight years, before cropping up in a memorable performance as a pot-smoking photographer alongside Marlon Brando and Martin Sheen in Francis Ford Coppola's Vietnam War epic Apocalypse Now (1979). He also received acclaim for his work in both acting and direction for Out of the Blue (1980).With these two notable efforts, the beginning of the 1980s saw a renaissance of interest by Hollywood in the talents of Dennis Hopper and exorcising the demons of drugs and alcohol via a rehabilitation program meant a return to invigorating and provoking performances. He was superb in Rumble Fish (1983), co-starred in the tepid spy thriller The Osterman Weekend (1983), played a groovy school teacher in My Science Project (1985), was a despicable and deranged drug dealer in River's Edge (1986) and, most memorably, electrified audiences as foul-mouthed Frank Booth in the eerie and erotic David Lynch film Blue Velvet (1986). Interestingly, the offbeat Hopper was selected in the early 1980s to provide the voice of "The StoryTeller" in the animated series of "Rabbit Ears" children's films based upon the works of Hans Christian Andersen!Hopper returned to film direction in the late 1980s and was at the helm of the controversial gang film Colors (1988), which was well received by both critics and audiences. He was back in front of the cameras for roles in Super Mario Bros. (1993), got on the wrong side of gangster Christopher Walken in True Romance (1993), led police officer Keanu Reeves and bus passenger Sandra Bullock on a deadly ride in Speed (1994) and challenged gill-man Kevin Costner for world supremacy in Waterworld (1995). The enigmatic Hopper has continued to remain busy through the 1990s and into the new century with performances in The Night We Called It a Day (2003), The Keeper (2004) and Land of the Dead (2005).As well as his acting/directing talents, Hopper was a skilled photographer and painter, having had his works displayed in galleries in both the United States and overseas. He was additionally a dedicated and knowledgeable collector of modern art and has one of the most extensive collections in the United States. Dennis Hopper died of prostate cancer on May 29, 2010, less than two weeks after his 74th birthday.
Dennis Hopper Movies / TV-Shows
The Last Film Festival (2016)
Magician: The Astonishing Life and Work of Orson Welles (2014)
Corman's World: Exploits of a Hollywood Rebel (2011)
The 83rd Annual Academy Awards (2011)
Alpha and Omega (2010)
The 62nd Primetime Emmy Awards (2010)
Beautiful Darling (2010)
Swing Vote (2008)
Elegy (2008)
Hell Ride (2008)
Palermo Shooting (2008)
An American Carol (2008)
Sleepwalking (2008)
Not Quite Hollywood: The Wild, Untold Story of Ozploitation! (2008)
Bananaz (2008)
Pioneers of Television (2008)
No Subtitles Necessary: Laszlo & Vilmos (2008)
Chelsea on the Rocks (2008)
AFI's 100 Years... 100 Movies: 10th Anniversary Edition (2007)
The Brothers Warner (2007)
The Graham Norton Show (2007)
Hoboken Hollow (2006)
10th & Wolf (2006)
Memory (2006)
The Art of Football from A to Z (2006)
Ban the Sadist Videos! Part 2 (2006)
Gorillaz: Live in Manchester (2006)
The Drug Years (2006)
The Late Late Show with Craig Ferguson (2005)
Land of the Dead (2005)
The Crow: Wicked Prayer (2005)
House of 9 (2005)
American Masters Sketches of Frank Gehry (2005)
Inside Deep Throat (2005)
E-Ring (2005)
Midnight Movies: From the Margin to the Mainstream (2005)
Howard Stern on Demand (2005)
Out of Season (2004)
The Last Ride (2004)
Entourage (2004)
Jimmy Kimmel Live! (2003)
The Night We Called It a Day (2003)
Easy Riders, Raging Bulls: How the Sex, Drugs and Rock 'N' Roll Generation Saved Hollywood (2003)
A Decade Under the Influence (2003)
Willie Nelson & Friends: Live and Kickin' (2003)
Las Vegas (2003)
The Piano Player (2002)
1 Giant Leap (2002)
Last Call with Carson Daly (2002)
I Don't Know Jack (2002)
Knockaround Guys (2001)
Ticker (2001)
L.A.P.D.: To Protect and to Serve (2001)
The Prophet's Game (2000)
Jason and the Argonauts (2000)
Lured Innocence (2000)
Luck of the Draw (2000)
The Apostate (2000)
Held for Ransom (2000)
Jesus' Son (1999)
Edtv (1999)
Tycus (1999)
The Source: The Story of the Beats and the Beat Generation (1999)
Straight Shooter (1999)
Independent Lens (1999)
Meet the Deedles (1998)
E! Mysteries & Scandals (1998)
Welcome to Hollywood (1998)
The Blackout (1997)
Top of the World (1997)
James Dean: Race with Destiny (1997)
Pretty as a Picture: The Art of David Lynch (1997)
The View (1997)
Cannes Man (1997)
King of the Hill (1997)
Road Ends (1997)
Carried Away (1996)
Basquiat (1996)
The Last Days of Frankie the Fly (1996)
Samson and Delilah (1996)
The Daily Show (1996)
Waterworld (1995)
Search and Destroy (1995)
MADtv (1995)
Speed (1994)
Chasers (1994)
Witch Hunt (1994)
Inside the Actors Studio (1994)
True Romance (1993)
Red Rock West (1993)
Late Night with Conan O'Brien (1993)
WWE Raw (1993)
Late Show with David Letterman (1993)
Sunset Heat (1992)
The Heart of Justice (1992)
Nails (1992)
Paris Trout (1991)
The Indian Runner (1991)
Hearts of Darkness: A Filmmaker's Apocalypse (1991)
The Hot Spot (1990)
Catchfire (1990)
Flashback (1990)
Superstar: The Life and Times of Andy Warhol (1990)
Blood Red (1989)
Chattahoochee (1989)
Colors (1988)
Running Out of Luck (1987)
Straight to Hell (1987)
The Pick-up Artist (1987)
Biography (1987)
Blue Velvet (1986)
Hoosiers (1986)
River's Edge (1986)
The Texas Chainsaw Massacre 2 (1986)
My Science Project (1985)
O.C. and Stiggs (1985)
American Masters (1985)
Slagskämpen (1984)
Jungle Warriors (1984)
The Osterman Weekend (1983)
Rumble Fish (1983)
Live with Kelly and Ryan (1983)
King of the Mountain (1981)
Out of the Blue (1980)
Saturday Night Live (1975)
Arena (1975)
The Last Movie (1971)
Easy Rider (1969)
Hang 'Em High (1968)
Head (1968)
The Trip (1967)
The Glory Stompers (1967)
Queen of Blood (1966)
The Time Tunnel (1966)
The Sons of Katie Elder (1965)
The Big Valley (1965)
Petticoat Junction (1963)
Combat! (1962)
Night Tide (1961)
The Young Land (1959)
The Twilight Zone (1959)
From Hell to Texas (1958)
Naked City (1958)
The Rifleman (1958)
The Story of Mankind (1957)
Gunfight at the O.K. Corral (1957)
Sayonara (1957)
The James Dean Story (1957)
Wagon Train (1957)
Giant (1956)
Zane Grey Theater (1956)
Rebel Without a Cause (1955)
Gunsmoke (1955)
Cheyenne (1955)
Studio One in Hollywood (1948)