There was an under-current of unsated coquetry.
"Gala-days" by Gail Hamilton
The lightnings, unsated in their wrath, flared and flickered on and out across the eastward sea.
"The Mississippi Bubble" by Emerson Hough
Beaulieu, Wuermser, and Alvintzy were not rivals in war; they were tiresome hindrances to his unsated love.
"The Life of Napoleon I (Volumes, 1 and 2)" by John Holland Rose
There was an under-current of unsated coquetry.
"Atlantic Monthly, Vol. XII. July, 1863, No. LXIX." by Various
None need leave this feast unsated!
"Count Hannibal A Romance of the Court of France" by Stanley J. Weyman
I came away untired, unsated; and with a delightful and distinct impression of all I had seen.
"The Diary of an Ennuyée" by Anna Brownell Jameson
The imagination, still unsated, seems the only active principle of the mind.
"The Best of the World's Classics, Restricted to Prose, Vol. IV (of X)--Great Britain and Ireland II" by Various
All my designs are lost, my love unsated, my revenge unfinished, and fresh cause of fury from unthought of plagues.
"The Comedies of William Congreve Volume 1 [of 2]" by William Congreve
When neither hunger now nor thirst remain'd Unsated, thus Gerenian Nestor spake.
"The Odyssey of Homer" by Homer
The sun sank, day departed, but the ill-will of the Day was still unsated.
"The Wagnerian Romances" by Gertrude Hall
Long life might lapse, age unperceived come on; And find the soul unsated with her theme.
"Young's Night Thoughts" by Edward Young
Then indeed all Spring Valley well-nigh choked of its own unsated curiosity.
"The Broken Gate" by Emerson Hough
She clasps him to her cheek, her lip, her breast, And looks with eye unsated on her child.
"Mystery and Confidence, Vol. 2" by Elizabeth Pinchard
Then wheel'd they round full knightly; each well the bridle sway'd Again they met unsated, and with blade encounter'd blade.
"The Nibelungenlied" by Unknown
None need leave this feast unsated!
"Historical Romances: Under the Red Robe, Count Hannibal, A Gentleman of France" by Stanley J. Weyman
I was not sorry now that the plenitude of happiness had so long been denied me; I was glad that fate had kept me unsated.
"The Closed Book" by William Le Queux
***
“’Not spare unsated thought her food—
No, not one rustle of the fold,
Nor scent of eastern sandal-wood,
Nor gleam of gold;
"The Letter L" by Jean Ingelow
In mid-way of your path you heard that cry—
And from his quiver of gold,
The last arrow, stinging hot and cold,
Unsealed your blood no longer frozen dry
Kindling the fires unsated,
Passionate, unabated.
"Epitaph for a Careless Beauty" by Marya Zaturenska
Yet virgin in her god-impelled approach
To Graeco-Roman ravishment, she waits
While the unsated python slides to crush
Her lust-eluding fleetness. Envious Jove
Rumbles Olympus. All the classic world
Leans breathless toward the legend she creates.
"Solar Eclipse" by Siegfried Sassoon
The leaf removal procedure allows to prove that a sharp transition between the sat and unsat phases indeed exists, to compute the value of αs (k) at which it occurs, and to characterize the geometry of the solutions [56, 57].
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
Table 3.1: Threshold values for the clustering and sat/unsat transitions and backbone size bc (at the clustering transition) for various values of k and (to the leading order) for k → ∞.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The existence of a sat/unsat transition in k-sat has been proved rigorously, but the proof of its sharpness remains an open problem.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
This theorem doesn’t imply that the sat/unsat transition is sharp, but it proves that it exists.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
As α increases further, the value of the maximum of Σ(si ) decreases, until it vanishes at α = αs (k), the sat/unsat transition.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The sat/unsat transition occurs when this bound is saturated.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The ﬁrst curve shows that the formula is in the unclustered phase; the second curve corresponds to the clustering transition; the third to a clustered formula; the fourth to the sat/unsat transition; ﬁnally, the formula is unsat.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
Each one of the cj ’s varies in [0, 1], because if some cj ′ > 1 then the sub-formula containing only the clauses of length j ′ is unsat(and therefore so is the complete formula).
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The suﬃx ‘k’ stands for critical (the ‘c’ being used for clustering ), because Σk is the surface where the discontinuous phase transitions (both the clustering and the sat/unsat ones) become continuous, which is traditionally called critical point in statistical mechanics.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
To summarize, in this paragraph I have shown that the tra jectories described by poissonian heuristics can cross the clustering transition surface Σc and the sat/unsat transition surface Σs only once.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The same happens with the sat/unsat transition at α = αs ≃ 0.918.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
Feige considers a class of algorithms that take a 3-sat formula as an input and have two possible outputs: either sat or unsat.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
One can set a ﬁxed maximum number of iterations Ni and stop the execution if it is reached; the output will then be unsat, and this will possibly be wrong.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
Therefore WP is an asymmetric algorithm, which never outputs sat to an unsat formula, but which sometimes outputs unsat to a sat formula.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
The algorithm described in Hypothesis 1 is different in this regard, as it must never return unsat to a sat formula.
Theoretical analysis of optimization problems - Some properties of random k-SAT and k-XORSAT
***