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 of just studying Halakha, Louis Ginzberg wrote responsa, formal responses to questions of Jewish law.

Instead of groups, groupoids, the mathematical generalization of groups in category theory, is the appropriate tool for studying quasicrystals.

Instead of studying law, he tinkered with mechanical gadgets.

Instead, new and borrowed verbs and adjectives are conjugated periphrastically as verbal noun + suru ( e. g. benkyō suru ' do studying = study ') and adjectival noun + na.

Instead, he used his grandfather's legacy and a small borrowed sum to spend the next two years studying the educational systems of the Old World in Europe.

Instead, functional rather than geographical intelligence requirements came to the fore such as counter-proliferation ( via the agency's Production and Targeting, Counter-Proliferation Section ) which had been a sphere of activity since the discovery of Pakistani physics students studying nuclear-weapons related subjects in 1974 ; counter-terrorism ( via two joint sections run in collaboration with the Security Service, one for Irish republicanism and one for international terrorism ); counter-narcotics and serious crime ( originally set up under the Western Hemisphere Controllerate in 1989 ); and a ' global issues ' section looking at matters such as the environment and other public welfare issues.

Instead of studying hard or conducting military affairs, he was always in the presence of court officials in order to gain their support.

Instead, Hooper decided on a career in law, studying under James Otis, a popular attorney in Boston who was regarded as a radical.

Instead of studying the bass playing of someone like John Entwistle, which would have given me a foundation of how to play.

Instead of being only a worrisome problem, renormalization has become an important theoretical tool for studying the behavior of field theories in different regimes.

Instead of having to pay each year while studying, students are to be loaned the funds by the government and repayments will be made out of income once the graduate is earning more than £ 15000 per year.

Instead learner interest guides things, with students studying what they want to study.

Instead, Lane joined his brother Richard in London, studying engraving with him.

Instead of studying martial arts, like his fellow bodyguards, Ling Ling Fat makes unusual inventions, such as cannons fired from the mouth, helicopter blades, and magnets.

Instead of the expected `` annoyances '' due to the nature of his mission, he received many calling cards and invitations from `` gentlemen of mark, on whom I had no sort of claim, & have had many more invitations than I could accept ''.

Instead of nature as their teacher, Mannerist artists took art.

Instead, these depictions gave recognizable forms to the abstract deities by using symbolic imagery to indicate each god's role in nature.

Instead, it is first down converted to the lower frequency of 630 kHz, and the complex nature of the PAL sub carrier means that the down conversion must be done via heterodyning to ensure that information is not lost.

Instead of an elf with pointed ears and repulsive goat hooves, we face a child of nature, pure, but tame and fearless and brutal instincts necessary to enable it to defend itself against threats, and survives even without the help of modern civilization.

Instead he sought a middle ground, the pastoral realm that integrates both nature and culture.

Instead of focusing on what they eat, this system classifies predators by the way in which they eat, and the general nature of the interaction between predator and prey species.

Instead, dynamic changes of the landscape are now seen as an essential part of their nature.

Instead, the differences appear in the nature and value of various ' access ' bursaries that are on offer.

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, he taught how one should recognize one's nature and the nature of others, and then maximize the benefit that is there in reality, rather than wasting one's life trying to change oneself and others.

Instead, the former road connecting Birdsboro to Robeson Township would be used formally as a nature trail, as it had been informally used since the time of the flood.

Instead of reviving what he saw as an anachronistic institution with strong ties to the Roman Catholic Church, he aimed to create a new university, secular in nature and national in scope, that could reorganize higher education within the country, serve as a model of positivism and encompass the ideas of the dominant Mexican liberalism.

Instead of making reality solid, it reminds us of the world ’ s ever changing nature.

Instead, a cyan biochrome of unknown chemical nature is responsible.

Instead, Carlton chose to commission the vast majority of its production content from third-parties ; not only had ownership changed, but so too had the nature of a large part of ITV's operation.

Instead, the usual clinical practice is to offer hydration, nutrition, and comfort measures and to " let nature take its course ".

Instead of a constructed playground, allowing children to play in a natural environment such as open land or a park is sometimes recommended ; children gain a better sense of balance playing on uneven ground, and learn to interpret the complexity and signals of nature more effectively.

Instead of focusing on the individual's appraisal of so-called stressors in relation to his or her own coping skills ( as the transactional model does ), the health realization model focuses on the nature of thought, stating that it is ultimately a person's thought processes that determine the response to potentially stressful external circumstances.

Instead of returning to his wife, he engaged in promiscuous sex and what Epiphanius termed " sex practices against nature ".

Instead they exist within nature and thus, sexuality is an innate part of life itself.

Instead of formal instruction in reading and math there are lessons on nature, animals, and the “ circle of life ” and a focus on materials-based learning.

Instead, Janco was publicizing the idea that Dada and various other strands of modernism were the actual tradition, for being indirectly indebted to the absurdist nature of Romanian folklore.

Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of the operating system.

Instead it is part of the Intelligence and Security Directorate ( DIS ) which reports directly to the Minister of the Presidency.

Instead, it is the atoms in the fourth layer that are directly above the first layer.

Instead of looking at a blank lens, then, both Morris and his subject are looking directly at a human face.

Instead of directly modifying an FFT algorithm for these cases, DCTs / DSTs can also be computed via FFTs of real data combined with O ( N ) pre / post processing.

Instead, an equally historic area of streets directly to the south of the bridge, including part of the Corridoio Vasariano, was destroyed using mines.

Instead of addressing the situation directly, she foolishly lets her ignorance turn into pettiness and mistreatment of Adeline.

Instead, the final pattern is created directly from a digital representation on a computer, by controlling an electron beam as it scans across a resist-coated substrate.

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, a large hatch was cut into the stern, thereby allowing the tanks to drive directly into deep water before turning under their own motive power and heading towards shore.

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, one looks directly to the notation to discover which operator to evaluate first.

Instead, it may be that other underlying factors, like genes, diet and exercise, affect both HDL levels and the likelihood of having a heart attack ; it is possible that medicines may affect the directly measurable factor, HDL levels, without affecting the chance of heart attack.

Instead, proprietary graphical languages have been used to enable telecom engineers to create services directly.

Instead, the plaintiffs extended their argument on the copyright clause to note that the clause requires Congress to " promote the Progress of Science and useful Arts ," and argued that retroactive extensions do not directly serve this purpose in the standard quid pro quo previously required by the courts.

Instead of dialing directly “ into ” the host computer – which would require the host to have its own pool of modems and phone lines, and require non-local callers to make long-distance calls – the host could have an X. 25 connection to a network service provider.

Instead Poland was directly governed by a purely German administration known as the Generalgouvernement.

Instead, the matter would be directly determined by a meeting of the AFL Commission, and any punishment Hird would receive would result directly from that meeting.

Instead, it is about entities that we can create directly through mental activity.

Instead of appearing by hundred or by township, holdings appear under the names of the landholders ( tenentes ), i. e. those who held the lands directly of the crown in fee.

Instead, the infrared grill directly heats the food, not the air.

Instead of solving a sequence of broken down problems, this approach directly solves the problem as a whole.

Instead of going through traditional distribution channels, which had some type of intermediate ( such as a distributor, wholesaler, broker, or agent ), companies may now deal with every customer directly, for example via the Internet.