Instead of describing a process which can only evolve in one way ( as in the case, for example, of solutions of an ordinary differential equation ), in a stochastic or random process there is some indeterminacy: even if the initial condition ( or starting point ) is known, there are several ( often infinitely many ) directions in which the process may evolve.

Instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Instead, for the purposes of describing their anatomy and enumerating their bones, mammalian and human skulls are divided differently: They are deemed to consist of two categorical parts, the neurocranium and the viscerocranium.

Instead of Raymond Briggs describing how much it had snowed the winter he made The Snowman, while walking through the field that morphed into the animation of the same landscape, David Bowie was shown reciting the same speech after walking into the attic of ' his ' childhood home and discovering a scarf in a drawer.

Instead of describing events, using straight forward images and icons, the collection was painted in allegories used to enthrone the Stadholder as heroic and virtuous.

Instead, in 1995, Bill Landis, who had been an associate of Anger's in the early 1980s, wrote an unofficial biography of him, which Anger himself condemned, describing Landis as " an avowed enemy ".

Instead of describing the fundamental differences of class in terms of property, Dahrendorf claims that we must “ replace the possession, or nonpossesion, of effective private property by the exercise of, or exclusion from, authority as the criterion of class formation ”.

Instead of frequency response, system performance may be specified in terms of parameters describing time-dependence of response.

Instead of using two vector fields describing the electric and magnetic fields, a tensor field representing these two fields together is used.

Instead of describing the abnormalities in structure and form, research focuses nowadays at decoding the molecular interactions that underlie them.

Instead of describing the Feit – Thompson theorem directly, it is easier to describe Suzuki's CA theorem and then comment on some of the extensions needed for the CN-theorem and the odd order theorem.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Instead of asking how a man's actions and experiences result from what he saw, remembered, or believed, the dynamic psychologist asks how they follow from the subject's goals, needs, or instincts.

Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.

Instead of attempting to defend all of southern China, Li ordered what remained of the Nationalist armies to withdraw to Guangxi and Guangdong, hoping that he could concentrate all available defenses on this smaller, and more easily defensible, area.

Instead — much like in his earlier film, Videodrome — he consistently blurred the lines between what appeared to be reality and what appeared to be hallucinations brought on by the main character's drug addiction.

Instead, he stated that what gods there may be, do not concern themselves with us, and thus would not seek to punish us either in this or any other life.

Instead, Bordwell promotes what he describes as " neoformalism.

Instead, what is demonstrated in the definition of Hīnayāna given by Yijing, is that the term referred to individuals based on doctrinal differences with the Mahāyāna tradition.

Instead, he improvised: " He says more than he should, something different from what his advisers had recommended, and is more provocative than he had intended to be.

Instead, they argued that the resolution simply declared what the Assembly's powers already were, according to the UN Charter, in the case of a dead-locked Security Council.

Instead of having meta-consciousness, these humans were constituted by what Jaynes calls the " bicameral mind ".

Instead, it referred to the process of one's training-the strengthening of the body and the mind, the learning and the perfection of one's skills-rather than to what was being trained.

Instead he proposed that a revolutionary society should “ transform itself immediately into a communist society ,” that is, should go immediately into what Marx had regarded as the “ more advanced ,” completed, phase of communism.

Instead, it is a cogent philosophy that directly challenges the notion of progress and what may be considered the faith-based claims of optimism.

Instead, what matters is the connectedness of the cloud.

Instead, what Bardeen, Brattain, and Shockley invented in 1947 was the first bipolar point-contact transistor.

Instead, they see this teaching as the same teaching in the Bible's reports of what Christ himself and Paul the Apostle taught.

Instead, what would be required to avoid paradoxes is that unlike any known particle, tachyons do not interact in any way and can never be detected or observed, because otherwise a tachyon beam could be modulated and used to create an anti-telephone or a " logically pernicious self-inhibitor ".

Mill notes that, contrary to what its critics might say, there is “ no known Epicurean theory of life which does not assign to the pleasures of the intellect … a much higher value as pleasures than to those of mere sensation .” However, he accepts that this is usually because the intellectual pleasures are thought to have circumstantial advantages, i. e. “ greater permanency, safety, uncostliness, & c .” Instead, Mill will argue that some pleasures are intrinsically better than others.

Instead, one has a single, holistic continuum, wherein what were formerly called discrete, separable particles of matter are instead the infinite number of distinguishable, though correlated manifestations of this continuum, that in principle is the universe.

what evil looksHad I from old and young! Instead of the cross, the AlbatrossAbout my neck was hung.

Instead, the proceedings became notorious for the large number of demonstrators and the use of force by the Chicago police during what was supposed to be, in the words of the Yippie activist organizers, “ A Festival of Life .” Rioting took place between demonstrators and the Chicago Police Department, who were assisted by the Illinois National Guard.

Instead of looking into what was to come, he argued, America was " daydreaming of past while the rest of the world was building its future.

Instead, we must ask what each player would do, taking into account the decision-making of the others.

Instead, if firms have different cost structures then each will have different maximizing behaviour, so they will have an incentive to set a different price or quantity.

Instead a component implements a behaviour whose side effect contributes to the global functionality [...] Each behaviour has a side effect and the sum of the side effects gives the desired functionality ".

Instead, Bujinkan training mostly consists of spur-of-the-moment, slow motion and dynamic ' techniques ' during which the " defender " ( tori ) hit, lock, choke and / or throw the " attacker " ( uke ); this slow motion simulated fighting is made possible by the nature of the ' attacker's ' behaviour after the initial ' attack '.

Instead of direct delegation of tasks and results demanding, employees are in this case, induced into a behaviour of self propelled performance and innovation, by comparison feelings towards their peers.

Instead, its news coverage indulged more in yellow journalism, with an emphasis on celebrities, bad behaviour and toilet humour.

Instead, a child's behaviour is shaped by " democratic interaction " and by deepening parent-child communication.

Instead they are keen to privilege the experience of the victim and the real effects of criminal behaviour.

Instead, the lodger's strange behaviour arises because he is a vigilante, trying to catch the real killer.