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Concept in stochastic analysis
In stochastic analysis, a rough path is a generalization of the classical notion of a smooth path. It extends calculus and differential equation theory
Rough_path
Differential equations involving stochastic processes
using rough paths theory, while adding a chosen definition of iterated integrals of Brownian motion, it is possible to define a deterministic rough integral
Stochastic differential equation
Stochastic_differential_equation
Operation in mathematical calculus
of unbounded variation. The rough path integral, which is defined for functions equipped with some additional "rough path" structure and generalizes stochastic
Integral
Transportation route connecting one location to another
turning and through traffic onto a one-way circular roadway Trail/track, a rough path through more wild or remote territory Many other types of road Strait
Thoroughfare
Non-linear stochastic partial differential equation
awarded the Fields Medal for this work on the KPZ equation, along with rough paths theory and regularity structures. There were 6 different analytic self-similar
Kardar–Parisi–Zhang_equation
Green sand beach in Kaʻū district, Hawai'i, US
surrounded by pasturelands and is only legally accessible by foot. The paths are rugged due to both illegal vehicular traffic and erosion. The land owner
Papakōlea_Beach
Austrian mathematician
awarded an ERC Consolidator Grant. with Hairer, Martin (2020). A Course on Rough Paths. Universitext (2nd ed.). Springer Cham. doi:10.1007/978-3-030-41556-3
Peter_Friz
Headland in County Wicklow, Ireland
person. The footpath, after the initial section with cut steps, is a rough path formed by rainwater and ascending through natural woodland. A more gradual
Bray_Head
Monolith in Mauritania
road that runs from Atar to Zouerrat. Drivers can be hired in Atar. The rough path runs parallel to the tracks for the Iron Ore Train before crossing it
Ben_Amera
Historic migration route spanning Independence, MO–Oregon City, OR
where they split from the main trail and followed (and improved) the rough path known as Hastings Cutoff, used by the ill-fated Donner Party in 1846.
Oregon_Trail
Mountain on the Isle of Man
railway station (last railway stop before the summit) from which there is a rough path to the peak. The trail has sections of gravel, slate stones, grass and
Snaefell
Greenock, Inverclyde, Scotland
Cross of Lorraine combined with an anchor. Across the road, steps and a rough path lead up to a viewpoint at Craigs Top with views up the River Clyde as
Lyle_Hill
Collection of random variables
In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic processes and other
Stochastic_process
2000 Bollywood drama film
and this breaks his heart. He decides to shed his innocence, takes the rough path to propose her, and ends up being a don in town. Manoj Bajpayee as Ram
Dil_Pe_Mat_Le_Yaar!!
Y = f ( Y ) d X {\displaystyle dY=f(Y)\,dX} driven by the path X. The theory of rough paths generalises the Young integral and Young differential equations
P-variation
Lebanese based writer, activist, attorney, and professor (born 1972)
fundamentalist past and to finally pursue his ultimate goal of personal freedom. A rough path that leaves him a traitor to Hezbollah, a suspected terrorist to the United
Rami_Ollaik
British mathematician
finance. In particular he developed what is now known as the theory of rough paths. Together with Patrick Kidger he proved a universal approximation theorem
Terry_Lyons_(mathematician)
Hiking trail in Bhutan
ends in Trongsa and from there to Bumthang District, taking through the rough paths of the Himalayas and up to as high as 5000m above sea level. The route
Snowman_Trek
Hill (486m) in Monmouthshire, Wales
reached. The main path follows the crest of the mountain north to the trig point and chapel remains which mark the summit. A rough path follows the perimeter
Skirrid_Fawr
US Army cavalry regiment (1898)
The Rough Riders was a nickname given to the 1st United States Volunteer Cavalry, one of three such regiments raised in 1898 for the Spanish–American
Rough_Riders
Mountain of the southern Scottish Highlands
ridge to the Bealach an Dubh Choirein. From this bealach a series of rough paths cut very steeply up the right side of the prominent buttress, involving
Stùc_a'_Chroin
Valley in Highland, Scotland
of waterfalls. The top of the path leads out onto the shoulder formed by the ancient landslip, with views and a rough path to the flat corrie floor. This
Coire_Gabhail
Hill in Snowdonia, Wales
from Nantmor Mountain Centre at Gelli-Iago. From this an intermittent rough path runs from West of Clogwyn Coch up to the two small lakes. The hill can
Yr_Arddu_(South)
Mathematician
projections. In a similar vein, and with rough differential equations in mind, the study of non-geometric rough paths on manifolds has been approached in Armstrong
Damiano_Brigo
Tamil Hindu saint and poet
equivalent to performing abhisekam and puja. Once, while walking on a rough path, a thorn pricked and pierced Pamban Swami’s foot, causing him intense
Pamban_Swamigal
Chapel in Knaresborough, North Yorkshire, England
dedicated to St Mary, is a Grade I Listed Building that is reached via a narrow path and steps from Abbey Road. The Chapel has a carved altar with a canopied
Chapel of Our Lady of the Crag
Chapel_of_Our_Lady_of_the_Crag
Computer graphics method
Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic
Path_tracing
Online action role-playing game
Path of Exile is a 2013 free-to-play action role-playing video game developed and published by Grinding Gear Games. Following an open beta phase, the game
Path_of_Exile
Sequence of data points over time
complexity Kolmogorov complexity estimates Hidden Markov model states Rough path signature Surrogate time series and surrogate correction Loss of recurrence
Time_series
Objects that generalize functions
(simplified) algebra is maybe the most popular in use today. Inspired by Lyons' rough path theory, Martin Hairer proposed a consistent way of multiplying distributions
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
American football player and coach (born 1992)
Tommy Rees stats. Sports.espn.go.com. Retrieved on August 9, 2012. "A Rough Path: The Tale of Tommy Rees". Down the Tunnel. November 18, 2013. Watson,
Tommy Rees (American football)
Tommy_Rees_(American_football)
Narrow strip of land in Afghanistan
There is a rough road from Ishkashim to Sarhad, Afghanistan built in the 1960s and improved in the 2020s, but only rough paths beyond. These paths run some
Wakhan_Corridor
Mountain in Scotland
livestock from raiders or hide cattle they themselves had stolen. The steep rough path up from Glen Coe skirts a wooded ravine and is a popular short walk (around
Bidean_nam_Bian
German schlager musician and songwriter
Wolfgang Petry 1983 Wahnsinn Madness Wolfgang Petry 1984 Rauhe Wege Rough Paths Wolfgang Petry 1987 Mit offenen Armen With Open Arms Wolfgang Petry 1988
Wolfgang_Petry
Reconstructed historic site in Fort Lee, New Jersey, United States
Washington, Cornwallis marched his men up the cliffs of the Palisades via a rough path, and southward through the Northern Valley. The landing was long erroneously
Fort_Lee_Historic_Park
stopped at Kurumalai station from where the villagers used to take a rough path to reach their homes. Of late, buses do ply into the village and pass
Kalugasalapuram
Unincorporated community in Washington, United States
his growing customer base, James Longmire's son, Elcaine, constructed a rough path from the resort to Paradise Park around 1885. In 1892 (or possibly 1895)
Paradise,_Washington
National news agency of Taiwan
ISBN 9789004227699. Wu, Wan-yu (May 1, 1994). "改革路上多崎嶇 — 唐盼盼與中央社" [The rough path of reform: Tang Pan-pan and the Central News Agency]. Commonwealth Magazine
Central_News_Agency_(Taiwan)
South Korean musician (born 2001)
Korean shoegaze musician. He has released four solo albums: Let's Walk on the Path of a Blue Cat (2020), To See the Next Part of the Dream (2021), After the
Parannoul
British mathematician (1905–2000)
also is named after him and has now been generalised in the theory of rough paths. Laurence Chisholm Young was born in Göttingen, the fifth of the six
Laurence_Chisholm_Young
Fingeroth Oct. 1993 Trial by Jury Part 2. Spider-Man pleads guilty. 385 Rough Justice Michelinie/Bagley Danny Fingeroth Nov. 1993 Trial by Jury Part 3
List of The Amazing Spider-Man issues
List_of_The_Amazing_Spider-Man_issues
City in Massachusetts, United States
(5 km) stretch with Massachusetts Route 2. Route 2, which follows the rough path of (and is nicknamed after) the Mohawk Trail, enters over the Fall River
Greenfield,_Massachusetts
Granite monolith in Queensland, Australia
different routes to the top, by road or by goat track. The Goat Track is a rough path that consists of 758 individual stairs from start to finish. Castle Hill
Castle_Hill,_Townsville
Suburban trail in Melbourne, Australia
The EastLink Trail is a shared use path for cyclists and pedestrians in the outer eastern/southeastern suburbs of Melbourne, Victoria, Australia. The trail
EastLink_Trail
Expedition from south to north poles using only surface transport
Scott Polar Research Institute. Rough map of the expedition (based on the official route graphic). Red shows the rough path; cyan shows the 0- and 180-degree
Transglobe_Expedition
Journalist A K Astbury (1987) also examines the word roddin, which means a rough path or a track trodden by sheep. He says that in north Lincolnshire, a roading
Roddon
Austrian-British mathematician
analysis techniques, theory of homogenisation, theory of path sampling and theory of rough paths and, in 2014, on his theory of regularity structures. Under
Martin_Hairer
1990 studio album by Sandra Mihanovich and Celeste Carballo
although perhaps not directly. I still believe that it left us a less rough path for those of us who came much later. It is a very brave album today. To
Mujer_contra_mujer_(album)
Census-designated place in South Carolina, United States
near the plantation houses) for horse and wagons. These dirt paths were crude rough paths that bore no resemblance to today's modern highways. Highway
Murrells Inlet, South Carolina
Murrells_Inlet,_South_Carolina
Technique used for determining crystal structures and identifying mineral compounds
Since it is difficult to visualize all the atoms at once, the ribbon shows the rough path of the protein's backbone from its N-terminus to its C-terminus.
X-ray_crystallography
Mountain in Lombardy, Italy
From Bondone to the lock of this pass are five miles of arduous and rough path for laden horses... The other is Count Gerolamo di Conces also of the
Monte_Cingolo_Rosso
2005 video game
Fire Emblem: Path of Radiance is a 2005 tactical role-playing game developed by Intelligent Systems and Nintendo SPD, and published by Nintendo for the
Fire_Emblem:_Path_of_Radiance
followed what is now M-123 and M-28 while the southern route followed the rough path of today's US 2. The highway was designated as a memorial following Theodore
Theodore Roosevelt International Highway
Theodore_Roosevelt_International_Highway
American baseball player (born 1988)
Nation. Retrieved May 2, 2015. Davis, Craig (August 29, 2013). "Dyson took rough path to Marlins". Sun-Sentinel. Archived from the original on December 23,
Sam_Dyson
Alternate name for Vale of Neath, Wales
Carboniferous Coal Measures. The falls are difficult of access with only a rough path reaching them from the vicinity of Sgwd Gwladus downstream and requiring
Waterfall_Country_(Wales)
Footpath in Northern Catalonia
ISBN 9780679032168. Retrieved 28 October 2012. Guides, Rough; Lloyd, Chris (2002-09-01). The Rough Guide to Costa Brava. Rough Guides. pp. 153–. ISBN 9781858288024. Retrieved
Camí_de_Ronda
without being seen") Fallschirmaufklärer: Per aspera ad astra (Latin for "Rough paths lead to the stars") Panzergrenadiere: in corde veritas (Latin for "truth
List of military unit mottoes by country
List_of_military_unit_mottoes_by_country
Long-distance footpath in England
The South West Coast Path is England's second-longest waymarked long-distance footpath, after the King Charles III England Coast Path, and is designated
South_West_Coast_Path
Nucleus of the rostral midbrain involved in motor coordination
human midbrain at the level of the superior colliculus, that shows the rough path of each nervus oculomotorius from its nucleus toward the eye and the relative
Magnocellular_red_nucleus
American journalist
behind. Bryant's group took the Hastings Cutoff, a shorter but much rougher path that took them through the Great Salt Lake Desert. Bryant was concerned
Edwin_Bryant_(alcalde)
Tor on Bodmin Moor, Cornwall, England
Rough Tor (/ˈraʊtər/), or Roughtor, is a tor on Bodmin Moor, Cornwall, England, United Kingdom. The site comprises the tor summit and logan stone, a Neolithic
Rough_Tor
Dynamical study of growth of a surface
Popular tools include statistical mechanics, renormalization group, rough path theory, etc. Kinetic Monte Carlo (KMC) is a form of computer simulation
Surface_growth
Cave in province of Chieti, Italy
stalagmites, flowstone, and rimstone pools. It has electric lighting with rough paths, concrete steps, and iron bridges. Gabriele D'Annunzio employed the cave
Grotta_del_Cavallone
Research institute in Bangalore, India
differential equations Probability theory Ergodic Theory and dynamical systems Rough path theory, stochastic analysis Random Geometry, point processes Complex analysis
TIFR Centre for Applicable Mathematics
TIFR_Centre_for_Applicable_Mathematics
an alliance between Britain and France and ending their historic rivalry Rough Riders 1997 1898 Depicts The Battle of San Juan Hill, part of the Spanish–American
List of historical films set in Near Eastern and Western civilization
List_of_historical_films_set_in_Near_Eastern_and_Western_civilization
Scottish mathematician
S2CID 118678520. Davie, A. M. (2007). "Differential equations driven by rough paths: An approach via discrete approximation". arXiv:0710.0772 [math.PR].
Alexander_Munro_Davie
Interstate 84 travels east–west, following the Columbia River and the rough path of the old Oregon Trail from Portland east to Idaho. For this reason,
Transportation_in_Oregon
2025 Indian TV series or programme
her to be a traditional housewife. Unhappy with this arrangement, Nila's path crosses with Chozhan, a driver hailing from a modest background. Chozhan
Ayyanar_Thunai
State highway in Colorado, United States
the Ute people. The future eastern half of Highway 82 came first, as a rough path over Independence Pass that soon reached Aspen. A private company improved
Colorado_State_Highway_82
wheel Talbot 700 Tripoli Tripoli Grand Prix Practice Car bounced on the rough surface of the road, went into the right embankment, hit a small wall, rolled
List of driver deaths in motorsport
List_of_driver_deaths_in_motorsport
Hiking trail in Highland, Scotland
North Highland Way varies hugely, crossing beaches, forests, road and rough paths as well as some remote areas.[citation needed] The Herald reported in
North_Highland_Way
1955 film by Satyajit Ray
Pather Panchali (Bengali pronunciation: [pɔtʰer pãtʃali] , transl. Song Of The Little Road) is a 1955 Indian drama film written and directed by Satyajit
Pather_Panchali
Extinct breed of horse
frugality. Paul Diffloth praised its ability to trot at 12 km/h (7.5 mph) on rough paths. Maturing late, it was suitable for work after age seven. Compact like
Bidet_horse
2010. Bloom did kill two other women (drug addicts who did not survive rough sex), gives the location of their bodies, and kills himself. Another Honduran
List_of_Elementary_episodes
12, 2014 June 20, 2014 Hugo: Magic In The Troll Woods Attractive Games Rough Trade 2009-11-27EU Unreleased Unreleased Unreleased November 27, 2009 Hula
List_of_Wii_games
Indian religion and philosophy
century. According to tradition, the Buddha instructed his followers in a path of cultivation that leads to awakening and full liberation from dukkha (lit
Buddhism
American singer-songwriter (born 1941)
announced a series of tours which were billed as the "Rough and Rowdy Ways World Wide Tour". The Rough and Rowdy Ways World Tour replaced Dylan's varied set
Bob_Dylan
Interstate Highway in Michigan, United States
the Michigan Legislature; at the time, Division 6 corresponded to the rough path of today's I-94. In 1919, the Michigan State Highway Department (MSHD)
Interstate_94_in_Michigan
United States Navy commander (1886–1941)
two months that Koehler spent on Sims' staff were far removed from the rough seas and fumes of the subchasers. "I have landed among the very smart and
Hugo_W._Koehler
American animation studio and production company
Capo Press. 0306-80917-6. Pg. 81–83 Holz, Jo (2017). Kids' TV Grows Up: The Path from Howdy Doody to SpongeBob. Jefferson, NC: McFarland. pp. 81–85, 124–126
Hanna-Barbera
Poem by Du Mu
(Chinese: 杜牧; pinyin: Dù Mù). Going to a distant mountain to climbing the stone path, people reside in the depth of white clouds. I had to stop my carriage to
Shan_Xing
Mountain in Colorado, United States
a trail for about 2 miles (3.2 km) to treeline. From there, there's a rough path on talus (scree) up the southwest ridge of the peak for an additional
West_Spanish_Peak
History of law enforcement for Queensland, Australia
Hagarty of Finch Hatton: "he is an exceptional good man in a rough place among a very rough class of people. He made seventy-one arrests single handed this
History of the Queensland Police
History_of_the_Queensland_Police
South Vietnamese military officer and politician (1924–2020)
young immediate superior Ho Ba, also from a mandarin family. Châu lived the rough life as a guerrilla soldier, entering combat many times. Yet he saw what
Trần_Ngọc_Châu
2025 American drama film
the courthouse. Many years later, Tony and Richard coincidentally cross paths at a bakery, wordlessly going their separate ways. An epilogue reveals that
Dead_Man's_Wire
conversion to atheism, She wrote, "The path from Christianity to Atheism is a long one, and its first steps are very rough and very painful." Wilfrid Scawen
List_of_atheist_authors
Icelandic magical stave intended as a wayfinder
Icelandic magical stave intended to help the bearer find their way through rough weather. The symbol is attested in the Huld Manuscript (1860), and does
Vegvísir
Civil parish in Derbyshire, England
as Grassmore in Chesterfield parish registers from 1568. Only a few rough paths crossed the "moor" at this time, from north to south diagonally one ran
Grassmoor, Hasland and Winsick
Grassmoor,_Hasland_and_Winsick
American television series
Green Producer Stephanie Laing Running time 30 minutes Production companies Rough House Pictures Gary Sanchez Productions Enemy MIGs Productions Original
Eastbound_&_Down
Accusations that Trump's ideology is fascist
speech directed at law-enforcement officers, Trump encouraged them to be "rough" on suspects. Trump has described, in 2016, instances of violence at his
Donald_Trump_and_fascism
International men's soccer tournament in North America
"Atlanta marks one year until FIFA World Cup with sponsors, projects". Rough Draft Atlanta. Archived from the original on June 7, 2025. "FIFA announces
2026_FIFA_World_Cup
Fictional character in the NBC medical drama
from the pilot episode until the eleventh-season finale. Carter's career path is one of the main story arcs of the series, beginning as a third-year medical
John_Carter_(ER)
Dellago, Christoph; Geissler, Phillip L. (2002). "TRANSITION PATH SAMPLING: Throwing Ropes Over Rough Mountain Passes, in the Dark". Annual Review of Physical
Transition_path_sampling
German composer (1838–1910)
the opportunity to finish his Der Ring des Nibelungen. So, instead of the rough journey to the Alps, Wagner went on 3 May 1864 to Munich, and after the
Wendelin_Weißheimer
1594 Portuguese military campaign against the Kingdom of Kandy
exhausted by days of fighting, were forced to fight for each step along rough paths through thick forests. One by one they fell. Captain Álvaro de Souza
Campaign_of_Danture
killed every man in the after engine room and was unable to move in the rough seas. As the ship was being abandoned, Leary was hit by two additional torpedoes
List of U.S. Navy ships sunk or damaged in action during World War II
List_of_U.S._Navy_ships_sunk_or_damaged_in_action_during_World_War_II
Signal attenuation in telecommunications
Path loss, or path attenuation, is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is
Path_loss
Prime Minister of Nepal since 2026
Nepali and Maithili. In the cramped quarters of the family home he recorded rough tracks on a basic computer microphone, which he initially shared with friends
Balen_Shah
Computer graphics technique
applications using shaders or offline applications using ray tracing or path tracing. Starting in the 1980s, a number of rendering researchers worked
Physically_based_rendering
Australian 2/16th Infantry Battalion's flanks and threatened to isolate it. A rough path, circling to the east and back to Dump 1, was found. Dump 1 is the first
First Battle of Eora Creek–Templeton's Crossing
First_Battle_of_Eora_Creek–Templeton's_Crossing
ROUGH PATH
ROUGH PATH
Boy/Male
Gaelic Irish
Rough.
Surname or Lastname
English (Cornwall)
English (Cornwall) : unexplained.
Boy/Male
Gaelic
Rough.
Boy/Male
Irish
Rough peace.
Boy/Male
Gaelic, Hindu, Indian, Irish
Rough; Small Rough One
Boy/Male
Gaelic
Rough.
Surname or Lastname
English and Irish (pronounced Bow)
English and Irish (pronounced Bow) : variant spelling of Bow.English (pronounced Boff) : from a Norman form of Old French boeuf ‘bull’, ‘ox’, hence a nickname for a powerfully built man, or in some cases a metonymic occupational name for a herdsman.
Boy/Male
Gaelic
Rough.
Surname or Lastname
English
English : habitational name from any of various places called Brough, of which there are several in Yorkshire and Derbyshire as well as elsewhere. The place name is from Old English burh ‘fortress’ and in most cases these are the sites of Roman fortifications. The pronunciation is usually ‘bruff’.Possibly an altered spelling of German Brauch.
Boy/Male
Gaelic
Rough.
Surname or Lastname
English
English : habitational name from any of various places, for example in Cheshire and Derbyshire, so named from Old English hÅh ‘spur of a hill’ (literally ‘heel’). This widespread surname is especially common in Lancashire.Irish (County Limerick) : variant of Haugh 1.
Boy/Male
Hindu
Rough, Rugged
Boy/Male
Irish
Rough.
Surname or Lastname
English
English : habitational name from a place so named in Humberside. Recorded in Domesday Book as Rutha, the place name may derive from Old Norse hrúedhr ‘rough shaly ground’.
Boy/Male
Gaelic Irish
Rough.
Boy/Male
Gaelic
Rough.
Surname or Lastname
Scottish
Scottish : variant of Tulloch. In Scotland it is pronounced tyookh.English : nickname for a valiant or stubborn person, from Middle English togh, tow(e) ‘steadfast’.
Boy/Male
Tamil
Rough, Rugged
Boy/Male
Irish
Rough; rugged.
Boy/Male
Australian, British, Christian, English, French, Irish
Spear-friend; Rough; Little Rough One
ROUGH PATH
ROUGH PATH
Girl/Female
Hindu, Indian, Traditional
Favourite Diety
Girl/Female
Indian, Tamil
Good
Girl/Female
Indian
Sweet or sabine
Girl/Female
Biblical
Destroying, wearing out.
Boy/Male
Hindu, Indian, Marathi
Lord Karthikeya
Female
English
Pet form of English Adelaide, LADY means "noble sort."Â In some instances it may be derived from the vocabulary word, meaning simply "lady."
Girl/Female
Hindu
Goddess Durga
Boy/Male
African, Hindu, Indian
Love
Surname or Lastname
English
English : occupational name denoting the servant (Middle English man) of someone called Hudde (see Hutt).
Boy/Male
Indian
The benign, The source of all-goodness
ROUGH PATH
ROUGH PATH
ROUGH PATH
ROUGH PATH
ROUGH PATH
a.
Feather-footed; as, a rough-footed dove.
superl.
Severe; violent; as, a tough storm.
v. t.
To cut or make in a hasty, rough manner; -- with out; as, to rough out a carving, a sketch.
v. t.
To tint with rouge; as, to rouge the face or the cheeks.
n.
Not polished; uncut; -- said of a gem; as, a rough diamond.
n.
Loud and hoarse; offensive to the ear; harsh; grating; -- said of sound, voice, and the like; as, a rough tone; rough numbers.
adv.
In a rough manner; rudely; roughly.
n.
Having inequalities, small ridges, or points, on the surface; not smooth or plain; as, a rough board; a rough stone; rough cloth.
v. t.
To render rough; to roughen.
superl.
Not easily separated; viscous; clammy; tenacious; as, tough phlegm.
n.
Hastily or carelessly done; wanting finish; incomplete; as, a rough estimate; a rough draught.
n.
Not courteous or kind; harsh; rude; uncivil; as, a rough temper.
n.
Marked by coarseness; shaggy; ragged; disordered; -- said of dress, appearance, or the like; as, a rough coat.
n.
Tempestuous; boisterous; stormy; as, rough weather; a rough day.
n.
Marked by severity or violence; harsh; hard; as, rough measures or actions.
superl.
Stiff; rigid; not flexible; stubborn; as, a tough bow.
a.
Like dough; soft.
v. i.
To paint the face or cheeks with rouge.
n.
Austere; harsh to the taste; as, rough wine.