Thus, the Kolmogorov complexity of the raw file encoding this bitmap is much less than 1. 62 million.

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

Thus, two drawbacks to elution mode chromatography, especially at the preparative scale, are operational complexity, due to gradient solvent pumping, and low throughput, due to low column loadings.

Thus the complexity of a digital filter and the computing time involved, grows inversely with, placing a higher cost on filter functions which better approximate the desired behavior.

Thus it has arithmetic complexity of O ( n < sup > 3 </ sup >).

Thus, the eventually attainable perfection and complexity of manufactured products, while they can be calculated in theory, cannot be predicted with confidence.

Thus, the eventually attainable perfection and complexity of

Thus the challenge of making sense of all this complexity is formidable.

Thus, the so-called blub paradox ( after a hypothetical programming language of average complexity called ' Blub ') says that anyone preferentially using some particular programming language will ' know ' that it is more powerful than some, but not that it is less powerful than others.

Thus the division between " hardware " and " software " began with abstraction being used to deal with the complexity of computing.

Thus, two drawbacks to elution mode chromatography, especially at the preparative scale, are operational complexity, due to gradient solvent pumping, and low throughput, due to low column loadings.

Thus Teilhard postulates the Omega Point as this supreme point of complexity and consciousness, which in his view is the actual cause for the universe to grow in complexity and consciousness.

Thus, as God creates, the universe evolves towards higher forms of complexity, consciousness, and finally with humans, personality, because God, who is drawing the universe towards Him, is a person.

Thus, the eventually attainable perfection and complexity of manufactured products, while they can be calculated in theory, cannot be predicted with confidence.

Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.

To understand the full sweep and complexity of cultures across all of human history, anthropology draws and builds upon knowledge from the social and biological sciences as well as the humanities and physical sciences .” Thus, the field is divided into four subareas: Sociocultural Anthropology, Biological ( or Physical ) Anthropology, Archaeology, and Linguistic Anthropology.

Thus the need for services as much larger units of functionality than traditional functions or classes, lest the sheer complexity of thousands of such granular objects overwhelm the application designer.

Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous — and therefore plausible as a source of natural complexity — rather than something that was only possible in the lab ( or lab computer ) where it was possible to tune control parameters to precise values.

Thus the number of quantifier alternations required to define a set gives a measure of the complexity of the set.

Thus, Dumont ’ s pleasure in the expansion of power, Roux ’ s internal struggle, Nägeli ’ s drive towards complexity, and Rolph ’ s principle of insatiability and assimilation are fused together into the biological side of Nietzsche ’ s theory of will to power, which is developed in a number of places in his published writings.

Thus, this maintenance is desired to be performed infrequently, even when such increased intervals cause increased complexity and cost to the overhaul.

Thus, barring continual conquest of your neighbors ( which is always subject to diminishing returns ), innovation that increases productivity is – in the long run – the only way out of the dismal science dilemma of declining marginal returns on added investments in complexity.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.