Thus in the presence of large quantum computers an n-bit key can provide at least n / 2 bits of security.

Thus, presence of high levels of peptidoglycan is the primary determinant of the characterisation of bacteria as gram-positive.

Thus in strong alkali at high pH, it forms the dually charged full urate ion, but at biological pH or in the presence of carbonic acid or carbonate ions, it forms the singly charged hydrogen or acid urate ion as its pKa < sub > 1 </ sub > is lower than the pKa < sub > 1 </ sub > of carbonic acid.

Thus, for example, the presence of an extra chromosome 21, which is found in Down syndrome, is called trisomy 21.

Thus an important influence upon the Dalcassians was the presence of the Hiberno-Norse city of Limerick on an isthmus around which the Shannon River winds ( known today as King's Island or the Island Field ).

Thus CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity, and the presence of various cofactors.

Thus a consensus definition of what constitutes the presence of a phenotype is essential for determining the penetrance of an allele.

Thus there is a reciprocal link between the god of beginnings and unending motion, who bestows life to the beings of this world ( Cerus Manus ) as well as presiding over its end, and the goddess of the hearth of man, which symbolises through fire the presence of life.

Thus a very high gas pressure of oxygen can be obtained, which can even account for the presence of gas in the swim bladders of deep sea fish like the eel, requiring a pressure of hundreds of bars.

Thus PIE ( traditional ) * anti " in front of and facing " > Greek antí " against "; Latin ante " in front of, before "; ( Sanskrit ánti " near ; in the presence of ").

Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of R < sup > n </ sup > under dot product.

Thus the presence or absence of gamma rays in a borehole is an indication of the amount of shale or clay in the surrounding formation.

Thus he secured the continued Roman presence in the areas of Gaul and Germania.

Thus Akhenaten extended even further the heretical belief that Aten was not the disc or orb of the sun ( the Egyptian sun god Ra ) but a universal spiritual presence ( see Akhenaten and Atenism ).

Thus, in a sequence alignment, the presence of these features may be an indication of a loop.

Thus in June 2003, the Indianapolis Star reported that the Army, in a March 31 letter to Buyer signed by Army Secretary Thomas White, had rejected Buyer's offer to serve in the Iraq War because " we are able to meet the need without your participation ," and " we are concerned that your presence would put in jeopardy the safety of those serving around you.

Thus the presence of y does not imply the presence of x.

Thus, iodine tincture solutions are characterized by the presence of alcohol, and about the same amount ( weight % content ) of elemental iodine as iodide.

Thus in the presence of h-principle, a differential topological problem reduces to an algebraic topological problem.

Thus, in the motivational example, above, the fact that the sum of residual values is equal to zero it is not accidental but is a consequence of the presence of the constant term, α, in the model.

Thus, when overall estimates are plotted against the variance ( sample size ), a symmetrical funnel is usually formed in the absence of publication bias, while a skewed asymmetrical funnel is observed in presence of potential publication bias.

Thus any two CPP-compatible presence protocol suites are automatically interoperable.

Thus an elevated IgM titre indicates recent primary infection, while the presence of IgG suggests past infection or immunization.

Thus the Congress marks a formal recognition of the political system that was central to world politics for a century.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

Thus, central to Zoroastrianism is the emphasis on moral choice, to choose between the responsibility and duty for which one is in the mortal world, or to give up this duty and so facilitate the work of druj.

Thus, a central conclusion of Keynesian economics is that, in some situations, no strong automatic mechanism moves output and employment towards full employment levels.

Thus, the attack on the Soviet Union ( which together with Germany had partitioned central Europe in 1939 – 1940 ) was not pressed with sufficient strength.

Thus, Regensburg was one of the central towns of the Empire, attracting visitors in large numbers.

Thus, starting from 1817, the central Merina kingdoms, Betsileo, Bezanozano, and Sihanaka, unified by Radama I was known to the outside world as the Kingdom of Madagascar.

Thus the contest was joined on the central issue which was to dominate all American history for the next dozen years, the disposition of the Territories.

Thus the long and exciting discussion touching the removal of Williams College and the location of a college in some more central town of old Hampshire County at length came to an end, and the contending parties now directed all their energies to building up the institutions of their choice.

Thus, the Maasai, according to their own oral history, migrated south from the lower Nile valley north of Lake Turkana in about the 15th century, arriving in a long trunk of land stretching from what is now northern Kenya to what is now central Tanzania during the 17th and 18th centuries.

Thus according to the central limit theorem, we can model jitter as a gaussian random variable.

Thus, Perseus's descendants played a central role in the Homeric epics and the pre-history of Greece.

Thus, some scholars have suggested that this may have been intended to signify the absence of a central authority in Kish for a time.

Thus the Lingnan language began to develop more significant differences with central Chinese.

Thus, contrasted with a carillon, in which a large number of bells are struck by hammers, all tied in to a central framework so that one carillonneur can control them all, a set of such bells is comparatively unwieldy — hence the emergence of permutations rather than melody as an organizing principle.

Thus, in 1808 he was placed by Napoleon upon the council of the Imperial University, and in this capacity he presided ( in the years 1809, 1811 and 1813 ) over commissions charged to examine the state of the higher educational establishments in the districts beyond the Alps and the Rhine which had been annexed to France, and to report upon the means by which these could be affiliated with the central university.

Thus Cologne's central location on the Rhine river placed it at the intersection of the major trade routes between east and west and was the basis of Cologne's growth.

Thus AGN-like characteristics are expected whenever a supply of material for accretion comes within the sphere of influence of the central black hole.

Thus, based on the fueros and their Statute of Autonomy, Basques have their own police body and manage their own public finances with virtually no intervention from the central government of Spain.

Thus is contradicted by the Aboriginal people of central Australia, who knew it well and reported that if disturbed, it was capable of running with considerable speed by breaking into a smooth, galloping sprint.

Thus Paris closed its central churchyards and relocated its burials during the Napoleonic period, creating cemeteries such as Père Lachaise.

Thus the central business district of a North American city, or the historical core of the city, is often the " down " part of the city.

Thus many buildings which once had a central pulpit now have a pulpit to the side.

Thus, he combined central figures in the founding of Judaism and Christianity.