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 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 describing what behaviour is most commonly done, an injunctive norm is what is approved or disapproved of by society.

Instead symptoms like bodily deformity, neurologic abnormalities, tight hamstrings, and abnormal gait are often the reason for consultation.

Instead of transferring the weight of the bridge and traffic loads into thrust forces into the abutments, the ends of the arches are restrained by tension in the bottom chord of the structure.

Instead, these substances are discussed in terms of formula units or unit cells as the smallest repeating structure within the substance.

Instead of focusing merely on the individual objects ( e. g., groups ) possessing a given structure, category theory emphasizes the morphisms – the structure-preserving mappings – between these objects ; by studying these morphisms, we are able to learn more about the structure of the objects.

Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

Instead, its existence and properties are inferred from its gravitational effects on visible matter, radiation, and the large scale structure of the universe.

Instead, in yeast, it has been shown to be dependent on a multiprotein tethering structure termed the ER-mitochondria encounter structure, or ERMES, although it remains unclear whether this structure directly mediates lipid transfer or is required to keep the membranes in sufficiently close proximity to lower the energy barrier for lipid flipping.

Instead, the entire structure is assembled, inserted into its metal envelope, sealed and processed in a large vacuum chamber with simple robotic devices.

Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, and by simulating stellar structure using computer models.

Instead the Winteraceae were considered to be a primitive family ( due to the structure of the xylem and carpel, a structure which now seems to be derived from xylem and carpels more typical of the angiosperms as a whole ).

Instead, the Phoenix entity copied Grey's identity and form, keeping her safe in a cocoon-like structure beneath Jamaica Bay.

Instead, the contestant was allowed to play for a minimum of $ 500 as a consolation ; this was doubled to $ 1000 once the payoff structure for the Audience Match was changed.

Instead, in the center building of the Temple of Heaven, in a structure called the " Imperial Vault of Heaven ", a " spirit tablet " ( 神位, or shénwèi ) inscribed with the name of Shangdi is stored on the throne, Huangtian Shangdi ( 皇天上帝 ).

Instead of phrase structure rules ATNs used an equivalent set of finite state automata that were called recursively.

Instead, substrate-binding at one subunit only slightly alters the structure of other subunits so that their binding sites are more receptive to substrate.

Instead, Wyatt added a tower-like structure ( a hamper ) to provide bedrooms for the servants.

Instead of positing a rich innate and universal syntactic structure ( see Universal Grammar ), Van Valin suggests that the only truly universal parts of a sentence are its nucleus, generally a predicating element such as a verb or adjective, and the arguments, normally noun phrases, that the nucleus requires.

Instead of following the original ad hoc layout ( seven churches around the central core ), Ivan's architects opted for a more symmetrical floor plan with eight side churches around the core, producing " a thoroughly coherent, logical plan " despite the erroneous latter " notion of a structure devoid of restraint or reason " influenced by the memory of Ivan's irrational atrocities.

Instead, the most anterior portion ends in a funnel-shaped structure called the infundibulum, which collects eggs as they are released by the ovary into the body cavity.

Instead of just a listing of provisions, it had a structure of chapters, sections, and articles.

Instead the structure is designed to aid the playing of chords, which makes sense when one considers the origin of the instrument and its intended purpose.

Instead, the position of a voxel is inferred based upon its position relative to other voxels ( i. e., its position in the data structure that makes up a single volumetric image ).

Instead of having a pulp cavity, each tooth has a cluster of thin, upright, parallel tubes of vasodentin ( a modified form of dentine ), with individual pulp canals, held together by cementum.

Instead it was considered as a late Roman form of the Corinthian order.

Instead, a very vivid feeling can form.

Instead of adopting a form of eliminativism or mental fictionalism, positions that deny that inner mental phenomena exist, a behaviorist was able to adopt epiphenomenalism in order to allow for the existence of mind.

Instead, they gradually merge to form a single, larger galaxy.

" Instead, he advocates a form of tolerance that is intolerant of right wing political movements:

Instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary ( diatomic ) hydrogen gas, H < sub > 2 </ sub >.

Instead a form of organisation that pre-dated the Russian state was used during national emergencies called Narodnoe Opolcheniye ( People's Regimentation ).

Instead of analyzing a word form as a set of morphemes arranged in sequence, a word form is said to be the result of applying rules that alter a word form or stem in order to produce a new one.

Instead, part or all of the glans is usually kept and reshaped as a clitoris, while the skin of the penile shaft may also be inverted to form the vagina ( some more recently-developed procedures, such as that used by Dr. Suporn Watanyusakul use the scrotum to form the vaginal walls, and the skin of the penile shaft to form the labia majora ).

Instead, these updates can be estimated by sampling methods, without ever having to calculate form factors explicitly.

Instead of wasting time and money in patent disputes on the start-stop method, Kleinschmidt and the Morkrum Company decided to merge and form the Morkrum-Kleinschmidt Company in 1924.

Instead, the position of the small board where that player won is marked on a 3x3 grid, and a player wins when they form 3-in-a-row on that grid.

Instead it has generally provided guidance to Bahá ' ís around the world ; this guidance has generally been through the form of letters and messages, much like Shoghi Effendi's communications.

Instead Byng called upon the Conservative Party leader, Arthur Meighen, to form a government.

Instead, the law compelled the authorities to sell gold bullion on demand at a fixed price, but only in the form of bars containing approximately four hundred troy ounces of fine gold.

Instead, each ant reacts to stimuli in the form of chemical scent from larvae, other ants, intruders, food and build up of waste, and leaves behind a chemical trail, which, in turn, provides a stimulus to other ants.

Instead, the eggs form layers called " rafts " that float on the water.

Instead, they hold that moral claims are derived either from an unsupported belief that there are objective moral facts ( error theory, a form of moral nihilism ); the speakers ' sentiments ( emotivism, a form of moral relativism ); or any one of the norms prevalent in society ( ethical subjectivism, another form of moral relativism ).