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Computer simulation method
Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting
Parallel_tempering
Branch of mathematics
exploration of sample space and faster convergence to a good solution. Parallel tempering, also known as replica exchange MCMC sampling, is a simulation method
Global_optimization
American engineer, scientist, inventor, and entrepreneur
biochemical and genetic engineering, and for his contributions to parallel tempering methods in computational science. Deem received a Bachelor of Science
Michael_W._Deem
Scientific computer simulation method
bias-exchange MTD, and the collective-variable tempering MTD. The last three are similar to the parallel tempering method and use replica exchanges to improve
Metadynamics
Optimization method
Anatoly Zhigljavsky (1991) Informational search stochastic tunneling parallel tempering a.k.a. replica exchange stochastic hill climbing swarm algorithms
Stochastic_optimization
1983 young adult novel by Gloria Skurzynski
portal The Tempering is a young adult novel by the American writer Gloria Skurzynski set in 1911 in the fictional mill town of Canaan (a parallel to the author's
The_Tempering
Italian theoretical and computational physicist
introducing several new algorithms in computational physics, such as Parallel Tempering, the SU(N) updating method and Constraint Allocation Flux Balance
Enzo_Marinari
Monte Carlo algorithm
particle methods Metropolis light transport Multiple-try Metropolis Parallel tempering Sequential Monte Carlo Simulated annealing Kalos, Malvin H.; Whitlock
Metropolis–Hastings_algorithm
Probabilistic optimization technique and metaheuristic
the behavior of natural water drops to solve optimization problems Parallel tempering is a simulation of model copies at different temperatures (or Hamiltonians)
Simulated_annealing
Technique used in heat treating
differential tempering, that is, by heating it evenly to red-hot and then quenching it, turning it into martensite, and then tempering part of it by
Differential_heat_treatment
Number of available physical states per energy unit
over other common algorithms such as multicanonical simulations and parallel tempering. For example, the density of states is obtained as the main product
Density_of_states
Computer simulations to discover and understand chemical properties
with the slow dynamics of disordered spin systems. It is also called parallel tempering. The replica exchange MD (REMD) formulation tries to overcome the
Molecular_dynamics
Method in computational chemistry
thermodynamic integration. Free energy perturbation Bennett acceptance ratio Parallel tempering Kirkwood, John G. (1935). "Statistical Mechanics of Fluid Mixtures"
Thermodynamic_integration
Type of safety glass processed to increase its strength
thermal tempering and can be applied to glass objects of complex shapes. Tempered glass must be cut to size or pressed to shape before tempering, and cannot
Tempered_glass
Collection of keyboard music by J.S. Bach
Werckmeister ( 1 /4), with the same general pattern tempering the naturals, and concluding with a tempered fifth B–F♯. Mark Lindley, a researcher of historical
The_Well-Tempered_Clavier
sequence Constructions of low-discrepancy sequences Event generator Parallel tempering Umbrella sampling — improves sampling in physical systems with significant
List of numerical analysis topics
List_of_numerical_analysis_topics
Five crystals arranged around a common axis
"Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics". Nanoscale. 16 (23): 11146–11155. doi:10.1039/D4NR00317A
Fiveling
(or parallel tempering), as it performs a non-local update on a fraction of the sites between the two replicas at the same temperature, while parallel tempering
Replica_cluster_move
Stochastic method of global optimization
of determining if trapped at a local minimum. Simulated annealing Parallel tempering Genetic algorithm Differential evolution K. Hamacher (2006). "Adaptation
Stochastic_tunneling
Algorithm for estimating the difference in free energy between two systems
Python-based code for MBAR and BAR is available for download at [2]. Parallel tempering Charles H. Bennett (1976) Efficient estimation of free energy differences
Bennett_acceptance_ratio
Structure found in atomic clusters and nanoparticles
"Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics". Nanoscale. 16 (23): 11146–11155. doi:10.1039/D4NR00317A
Icosahedral_twins
German mathematical physicist (born 1945)
Turvani, G. (2023). "Integration of simulated quantum annealing in parallel tempering and population annealing for heterogeneous-profile QUBO exploration"
Hajo_Leschke
Overjustification effect - Overlearning Pair by association - Parallel education - Parallel tempering - Parents' Rights Coalition - Parent-Teacher Association
Index_of_education_articles
Israeli biochemist and nanotechnologist
(2005) Energy Landscape of Amyloidogenic Peptide Oligomerization by Parallel-tempering Molecular Dynamics Simulation: Significant Role of Asn Ladder. Proc
Ehud_Gazit
Pseudorandom number generator
tempering bitmasks s , t {\displaystyle s,t} : TGFSR(R) tempering bit shifts u , d , l {\displaystyle u,d,l} : additional Mersenne Twister tempering bit
Mersenne_Twister
Touzai News encounters his son Takashi in the street and his story seems parallel the rakugo. Dainippon TV requires that the list of dishes for the competition
List_of_Oishinbo_episodes
German philosopher (1788–1860)
are evident in his criticism of contemporaneous attempts to prove the parallel postulate in Euclidean geometry. Writing shortly before the discovery of
Arthur_Schopenhauer
Type of steel used in Middle Eastern swordmaking
an article in the November 4, 1894 issue of the Chicago Tribune titled Tempering Damascus Blades. The note asserts that a certain "Prof. von Eulenspiegel"
Damascus_steel
List of characters in the Dexter franchise
analysis for the fictional Miami Metro Police Department, who leads a secret parallel life as a vigilante serial killer, hunting down murderers who have not
List_of_Dexter_characters
shell-tempered wares towards entirely sand tempered wares. The shell-and-sand tempered wares produced during this time period developed in parallel with
Shelly-sandy_ware
English actor and comedian (born 1971)
column called "Skater vs. Instigator", which illustrates various amusing "parallels" between Baron Cohen and figure skater Sasha Cohen, ranging from their
Sacha_Baron_Cohen
American adult animated television series
near lack of any form of morality. Jackknife is depicted as being short-tempered, violent, and misogynistic. He escapes often from the jail and is brought
Superjail!
Relationship among tones of the chromatic scale
and tuning systems were developed to address these issues. By changing (tempering) the 3:2 ratio, these systems produce a sequence of perfect fifths that
Circle_of_fifths
Country in South Asia
as far north as the Satpura and Vindhya ranges in central India. These parallel chains run from the Arabian Sea coast in Gujarat in the west to the coal-rich
India
Keyboard composition by Johann Sebastian Bach
4 (second inversion) minor chord with C as its root borrowed from the parallel harmonic minor. The A♭ may be considered as its enharmonic, G♯, which creates
Prelude and Fugue in C major, BWV 846
Prelude_and_Fugue_in_C_major,_BWV_846
Story plot device
maint: ref duplicates default (link) Lowe, Nick (July 1986). "The Well-Tempered Plot Device". Ansible (46). Berkshire, England. ISSN 0265-9816. Archived
MacGuffin
Composition by J. S. Bach
minor, BWV 883, is the fourteenth piece of the second book of The Well-Tempered Clavier by Johann Sebastian Bach, compiled between 1739 and 1744. Unable
Prelude and Fugue in F-sharp minor, BWV 883
Prelude_and_Fugue_in_F-sharp_minor,_BWV_883
1976 film
"a lively, spontaneously funny entertainment" that "could rally a large parallel audience seeking less innocuous and stereotyped pictures with and about
The_Bad_News_Bears
Season of television series
drunk while seeking to track down Rick Prime, a version of himself from a parallel universe who killed his first wife and daughter. Harry Belden as Morty
Rick_and_Morty_season_7
Electric pickup truck
in parallel for compatibility with widespread 400 V DC charging infrastructure. The service menu shows the current state of "Series" or "Parallel" (High
Tesla_Cybertruck
Fictional character from The Boondocks
from Return of the Jedi is used as a musical theme for Ruckus, drawing a parallel between the two characters. In the episode "The Story of Jimmy Rebel",
Uncle_Ruckus
Chinese five elements
Wuxing was first translated into English as "the Five Elements", drawing parallels with the Greek and Indian Vedic static, solid or formative arrangement
Wuxing_(Chinese_philosophy)
2024 anime television series
daughter), disapprove of their adventures. As Morty meets "time warrior" Elle, parallel storylines set sometime during the events of the sixth season of the main
Rick_and_Morty:_The_Anime
Indian drama television series
Hai: Ghum Hai Kisikey Pyaar Meiin fame Sumit Singh comes on board as the parallel lead". Moneycontrol. Retrieved 2 June 2026. Bharti, Anamika (5 June 2026)
Seher_–_Hone_Ko_Hai
Special period of exile in Mahabharata
New Year often involved role reversals and transgressive behaviors, paralleling the Pandavas’ temporary shifts in status and identity. Additionally,
Ajnatavasa
Shah of Iran from 1941 to 1979
great Shah who had reformed the country and built an empire with obvious parallels to himself. Alongside this change in image, Mohammad Reza started to speak
Mohammad_Reza_Pahlavi
Use of racial theories for and against Zionism
389–427. Doron, Joachim (1983). "Classic zionism and modern anti-semitism: Parallels and influences (1883-1914)". Studies in Zionism. 4 (2): 169–204. doi:10
Racial conceptions of Jewish identity in Zionism
Racial_conceptions_of_Jewish_identity_in_Zionism
Group of fictional characters
Stupidest He-Man Characters' by Total Film. Orko is a magician from the parallel world of Trolla. Orko's magical abilities vary, depending on his location
List of He-Man and the Masters of the Universe characters
List_of_He-Man_and_the_Masters_of_the_Universe_characters
2017 murder of a cadet officer in Malaysia
established by the government, UPNM should make sure that no similar tragedies parallel to the murder of Zulfarhan should happen again, as the university was a
Murder of Zulfarhan Osman Zulkarnain
Murder_of_Zulfarhan_Osman_Zulkarnain
Fictional character
nickname "Gian" (「ジャイアン」, "Jaian"; English: Big G) is a strong and quick-tempered local bully. He frequently steals other children's stuff (especially Nobita's
List_of_Doraemon_characters
discrimination against persons employed at educational institutions. A parallel law, Title VI, had also been enacted in 1964 to prohibit discrimination
History of civil rights in the United States
History_of_civil_rights_in_the_United_States
Series of Gothic horror novels by Anne Rice
success of Rice's Vampire Chronicles reinforced the "widely recognized parallel between the queer and the vampire." He notes that in particular "gay and
The_Vampire_Chronicles
Setting of works by Jane Austen
long-established reputation as one of Britain’s greatest writers, developing in parallel yet distinct trajectories. In contrast, her standing in the French-speaking
Jane Austen's literary universe
Jane_Austen's_literary_universe
2009 film directed by Susi Ganesan
along, until where they fall in love with each other in reality. In a parallel comedic role, Thengakadai Thenappan/Kobarikayala Subbayya is also sought
Kanthaswamy
2026 Indian film by Harish Shankar
cast to play a pivotal role with a character poster, and stated to be a parallel female lead role as Shloka, it marks her first collaboration with Kalyan
Ustaad_Bhagat_Singh
2005 film by Tim Burton
the elaborate playground built by an adult for the child inside" as parallels between the two. Depp was surprised by the comparisons and stated that
Charlie and the Chocolate Factory (film)
Charlie_and_the_Chocolate_Factory_(film)
price, ensuring she would be sold to a man she genuinely loved. Drawing a parallel, Maomao concludes that Fuyou intentionally mirrored this behavior. Upon
List of The Apothecary Diaries episodes
List_of_The_Apothecary_Diaries_episodes
Town in Shetland, Scotland
produces an extremely narrow difference for an area north of the 60th parallel. In average monthly precipitation, October to January are the year's wettest
Lerwick
Love focused on feelings
Young, Larry J. (2012). "The behavioral, anatomical and pharmacological parallels between social attachment, love and addiction". Psychopharmacology. 224
Romance
2010 DreamWorks Animation film
transported back to the original timeline at the moment before he lost his temper at the party. Instead of lashing out, Shrek embraces his family and friends
Shrek_Forever_After
Knife used to remove body hair
tempering stage follows the hardening process, where the blade is heated in a bath of oil at a temperature between 200–400 °C (392–752 °F). Tempering
Straight_razor
Haseki Sultan of Ottoman Empire
between Hafsa's stipend and Hurrem's stipend of 2,000 aspers a day at a parallel point in her career only forty years later further underlines the exceptional
Hürrem_Sultan
Jewish-American writer (1884–1965)
Fleischhauer's Welt-Dienst distributed these propagandistic reprints (in parallel with other antisemitic pamphlets) at least in England, France, and Germany
Marcus_Eli_Ravage
Supervillain appearing in DC Comics
Joker is arrested, and then-Robin Damian Wayne beats him with a crowbar, paralleling Todd's murder. When the Joker escapes, he attacks the Black Glove, burying
Joker_(character)
German fairy tale
the examples of Bachstelze, Wasserstelze (names of birds; stilt) as paralleling examples. However, this was not the etymology hinted at by Jacob Grimm
Rumpelstiltskin
1847 novel by Emily Brontë
such as The Romance of the Forest and The Mysteries of Udolpho. The parallels are especially marked in the second volume, where Cathy is abducted by
Wuthering_Heights
Prime Minister of Australia since 2022
attributed Albanese's victory to anti-Donald Trump sentiment and drew parallels to the 2025 Canadian federal election, which saw similar results for the
Anthony_Albanese
2021 film by Malcolm D. Lee
Lowry of CNN wrote: "The first Space Jam was hardly a classic, which should temper expectations. Yet even by that standard, this marketing-driven exercise
Space_Jam:_A_New_Legacy
2010 American TV series or program
season who wants to destroy the guardians and the NFL. He has a very short temper and hates losing more than anything. In the episode "The Mystery Guardian"
NFL_Rush_Zone
Measure of a substance's ability to resist or conduct electric current
across the sample, and the electric field and current density are both parallel and constant everywhere. Many resistors and conductors do in fact have
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
Fictional character from The Simpsons franchise
Simpsons version of the Cincinnati Bengals-Dallas Cowboys game, which paralleled the events on the field. In November 2025, Homer appeared in the Fortnite
Homer_Simpson
Romantic fantasy film by Matthew Vaughn
because, in my head, that's just the Earth-Two version of Stardust. It's a parallel Earth version of Stardust, which has Robert De Niro and stuff. And I get
Stardust_(2007_film)
"unruly" format was abandoned again in 1993 in favor of bound books. In parallel with this change, the 2nd edition introduced colored images for each monster
List of Advanced Dungeons & Dragons 2nd edition monsters
List_of_Advanced_Dungeons_&_Dragons_2nd_edition_monsters
1856 treaty between the United States and Siam
concluded the similar American–Siamese Roberts Treaty in 1833, which, in parallel to the Burney Treaty, abolished Siam's royal monopoly on Western trades
American–Siamese Treaty of 1856
American–Siamese_Treaty_of_1856
Kashmiri folktale
titled Nágray and Himál, a poor brahmin named Soda Ram, who has an "ill-tempered" wife, laments his luck. One day, he decides to go on a pilgrimage to Hindustan
Himal_and_Nagaray
DC Comics character
Loeb stated in an interview that he paralleled the Falcone family to that of the Corleone family, with Sofia's temper matching that of Sonny Corleone.[citation
Sofia_Falcone
2015 Marvel Studios film
story dynamics are fundamentally silly and the family stuff, with its parallel father-daughter melodrama, is elemental button-pushing, a good cast led
Ant-Man_(film)
Film by Paul Thomas Anderson
took issue not only with this statement, but with the way it supposedly paralleled L. Ron Hubbard Jr.'s conflict with his own father. While church members
The_Master_(2012_film)
Glass object created by dripping molten glass into cold water
doi:10.1063/1.4971339. Narayanaswamy, O. S.; Gardon, Robert (1998). "Tempering glass spheres and related topics". Glass Science and Technology. 71: 120–128
Prince_Rupert's_drop
List of Crusader historians after the fall of Acre
the Names of Books and the Arts. Published in the original Arabic with parallel Latin translation by German orientalist Gustav Flügel and in a French translation
List of early modern works on the Crusades
List_of_early_modern_works_on_the_Crusades
Abbreviations and symbols used in engineering drawing
in GD&T. It typically tells you what sort of geometric condition (e.g., parallel, perpendicular, round, concentric), followed by what size (and maybe shape)
Engineering drawing abbreviations and symbols
Engineering_drawing_abbreviations_and_symbols
1993 film directed by John McTiernan
premiere. Frank McRae as Lieutenant Dekker, Slater's immediate and ill-tempered supervisor, who is always screaming at him. Anthony Quinn as Tony Vivaldi
Last_Action_Hero
16th-century novel by Wu Cheng'en
series Doraemon released a movie named Doraemon: The Record of Nobita's Parallel Visit to the West which is based on the same story. In 1997, Brooklyn-based
Journey_to_the_West
1994 American animated film
is a prequel in showing how Timon and Pumbaa met each other, and also a parallel in that it also depicts what the characters were retconned to have done
The_Lion_King
Crossover published in prestige format by DC Comics and Marvel Comics
that Superman and Captain America become paranoid, irritable, and short-tempered; their emotions flare to the point where they blame each other for everything
JLA/Avengers
South Korean television series
글로리 우영우 평행이론?...김히어라 뿐만 아니다 두작품 성공 이끈 배우들 [The Glory and Woo Young-woo parallel theory?... It's not just Kim Hee-ra Actors who led the success of the two
Extraordinary_Attorney_Woo
Season of television series
Daily Beast, the season alludes to Pizzolatto's childhood and creates a parallel between Christianity and the supernatural theology of "Carcosa": "Both
True_Detective_season_1
Australian zoologist, palaeontologist, and museum curator
like a shark, which had hitherto been known only from fossil teeth": a parallel to the (1994) recognition of the true identity of the Wollemi pine as a
Gerard_Krefft
English philosopher and statesman (1561–1626)
influences and to establish magic as a field of study and application paralleling Bacon's vision of science. Furthermore, Josephson-Storm argues that Bacon
Francis_Bacon
Chinese historical period
at least temporarily. Initially, the rice husk and stalk were used as tempering agents in pottery, later replaced by sand. Clues visible to botanists
Neolithic_in_China
British writer and journalist (1903–1966)
Stinson, John J (September 2008). "Evelyn Waugh and Anthony Burgess: Some Parallels as Catholic Writers". Evelyn Waugh Newsletter and Studies. 38 (2). Archived
Evelyn_Waugh
Neurodevelopmental disorder
marketed as EndeavourRx. The paediatric STARS-ADHD randomised, double-blind, parallel-group, controlled trial demonstrated that AKL-T01 significantly improved
Attention deficit hyperactivity disorder
Attention_deficit_hyperactivity_disorder
2006 video game
disk real estate" than Morrowind's partially recorded dialogue. Rolston tempered his criticism with the suggestion that voice acting "can be a powerful
The Elder Scrolls IV: Oblivion
The_Elder_Scrolls_IV:_Oblivion
noted that while Rudeus gets into less fights, he is contrasted by the parallel adventures of Roxy. Roxy' figurine that Rudeus creates in the series was
List of Mushoku Tensei characters
List_of_Mushoku_Tensei_characters
English playwright and poet (1564–1616)
Julius Caesar—based on Sir Thomas North's 1579 translation of Plutarch's Parallel Lives—which introduced a new kind of drama. According to the Shakespearean
William_Shakespeare
(February 20, 2026). "Guided by Voices' Doug Gillard Announces New Solo Album Parallel Stride: Hear "Face of Smiles"". Stereogum. Retrieved February 20, 2026
List_of_2026_albums
Enterprise resource planning by SAP SE
October 2015. "SAP Q3 2015 results: On-premises [sic] and cloud grow in parallel, says Cohen". ComputerWeekly. 20 October 2015. McKenna, Brian. "SAP Q2
SAP_S/4HANA
Polish-British writer (1857–1924)
insights and discoveries in his fiction." Said found especially close parallels between Conrad's letters and his shorter fiction. "Conrad ... believed
Joseph_Conrad
American general (born 1952)
against the Taliban. In an interview with Brian Kilmeade Petraeus drew parallels between the U.S. withdrawal from Afghanistan, the Dunkirk evacuation,
David_Petraeus
Movable barrier that allows ingress and egress
from the doorway/portal, by sliding on a plane parallel to the frame, by folding in angles on a parallel plane, or by spinning along an axis at the center
Door
PARALLEL TEMPERING
PARALLEL TEMPERING
Boy/Male
Shakespearean
All's Well That Ends Well.' A follower of Bertram, Count of Rousillon.
Biblical
parables; governing
Girl/Female
Biblical
A parable, governing.
Surname or Lastname
English
English : occupational name from Middle English combere, an agent derivative of Old English camb ‘comb’, referring perhaps to a maker or seller of combs, or to someone who used them to prepare wool or flax for spinning. This was an alternative process to carding, and caused the wool fibers to lie more or less parallel to one another, so that the cloth produced had a hard, smooth finish without a nap.English : variant of Coomber.Probably an Americanized spelling of German Kommer or Kammer.
Girl/Female
Biblical
Parables, governing.
Biblical
a parable; governing
Girl/Female
Muslim
Example, Allegory, Parable
Girl/Female
Arabic, Muslim
Example; Allegory; Parable
PARALLEL TEMPERING
PARALLEL TEMPERING
Boy/Male
Muslim
Favor
Boy/Male
Danish, German, Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Darkness; Twin
Female
Norse
Old Norse name derived from the ancient element freyja (Old High German frouwa), FREYJA means "lady, mistress." In mythology, this is the name of the goddess of beauty and love.
Boy/Male
Tamil
Courteous
Boy/Male
Tamil
Achiever, Blue lotus
Male
English
English name derived from the vocabulary word, from the Middle English word sterrling, STERLING means "little star."Â
Surname or Lastname
English
English : from the Old English personal name Hereweald, its Old Norse equivalent Haraldr, or the Continental form Herold introduced to Britain by the Normans. These all go back to a Germanic personal name composed of the elements heri, hari ‘army’ + wald ‘rule’, which is attested in Europe from an early date; the Roman historian Tacitus records a certain Cariovalda, chief of the Germanic tribe of the Batavi, as early as the 1st century ad.English : occupational name for a herald, Middle English herau(l)d (Old French herau(l)t, from a Germanic compound of the same elements as above, used as a common noun).German : from a personal name equivalent to 1.Irish : this name is of direct Norse origin (see 1), but is also occasionally a variant of Harrell and Hurrell.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Learned
Male
Polish
Polish form of Roman Latin Maurice, MAURYCY means "dark-skinned; Moor."Â
Girl/Female
Hindu, Indian
Daughter of Emperor Mughal
PARALLEL TEMPERING
PARALLEL TEMPERING
PARALLEL TEMPERING
PARALLEL TEMPERING
PARALLEL TEMPERING
p. pr. & vb. n.
of Parallel
v. t.
To produce or adduce as a parallel.
v. i.
To be parallel; to correspond; to be like.
n.
A line which, throughout its whole extent, is equidistant from another line; a parallel line, a parallel plane, etc.
n.
One of the imaginary circles on the surface of the earth, parallel to the equator, marking the latitude; also, the corresponding line on a globe or map.
a.
Extended in the same direction, and in all parts equally distant; as, parallel lines; parallel planes.
imp. & p. p.
of Parallel
v. t.
To represent by parable.
adv.
In a parallel manner; with parallelism.
v. t.
To place or set so as to be parallel; to place so as to be parallel to, or to conform in direction with, something else.
v. t.
To equal; to match; to correspond to.
a.
Having opposite surfaces exactly plane and parallel, as a piece of glass.
a.
Meeting and intersecting, as lines; not parallel; -- opposed to parallel.
v. t.
Fig.: To make to conform to something else in character, motive, aim, or the like.
n.
A comparison; a similitude; specifically, a short fictitious narrative of something which might really occur in life or nature, by means of which a moral is drawn; as, the parables of Christ.
n.
One of a series of long trenches constructed before a besieged fortress, by the besieging force, as a cover for troops supporting the attacking batteries. They are roughly parallel to the line of outer defenses of the fortress.
n.
A character consisting of two parallel vertical lines (thus, ) used in the text to direct attention to a similarly marked note in the margin or at the foot of a page.
v. t.
To render parallel.
n.
A comparison made; elaborate tracing of similarity; as, Johnson's parallel between Dryden and Pope.
a.
Continuing a resemblance through many particulars; applicable in all essential parts; like; similar; as, a parallel case; a parallel passage.