However, Apple's designs included quite a few concepts that were not part of ( or were non-trivial advances to ) the prototype developed at PARC.

However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time.

However, self-localization requires that the underlying product first be engineered to support such activities, which is a non-trivial endeavor.

However, if gcd ( v, n ) is neither 1 nor n, then the-addition will not produce a meaningful point on the curve, which shows that our elliptic curve is not a group ( mod n ), but, more importantly for now, gcd ( v, n ) is a non-trivial factor of n.

However, the non-trivial QCD vacuum effects ( instantons ) spoil the Peccei – Quinn symmetry explicitly and provide a small mass for the axion.

However, there can be non-trivial " propagation " ( or tunneling amplitudes ) from to through an intervening manifold with ; this reflects the topology of.

However, the falsity of an h-principle is also an interesting statement, intuitively this means the objects being studied have non-trivial geometry that cannot be reduced to topology.

However, there are aftermarket tuners that have already accomplished non-trivial engine transplants in Solstices.

However, for mappings with values in more general Banach spaces than, the situation is quite more complicated ; the first non-trivial result in this direction is the Kirszbraun theorem.

However, the most interesting and surprising results occur when i > n. The first such surprise was the discovery of a mapping called the Hopf fibration, which wraps the 3-sphere S < sup > 3 </ sup > around the usual sphere S < sup > 2 </ sup > in a non-trivial fashion, and so is not equivalent to a one-point mapping.

However, if the language of formulae representing beliefs itself includes the counterfactual conditional connective, the Ramsey test leads to the Gardnefors triviality result: there is no non-trivial revision operator that satisfies both the AGM postulates for revision and the condition of the Ramsey test.

However, algorithms are also implemented by other means, such as in a biological neural network ( for example, the human brain implementing arithmetic or an insect looking for food ), in an electrical circuit, or in a mechanical device.

However, the government resisted calls for the nationalisation of the network ( first proposed by William Ewart Gladstone as early as the 1830s ).

However, if business and government are entwined, then the government can maintain the small-hub network.

However, according to 2005 data reported by the Colombian government, the road network totaled 163, 000 kilometers, 68 percent of which were paved and in good condition.

However, as the Morris worm and Mydoom showed, even these " payload free " worms can cause major disruption by increasing network traffic and other unintended effects.

However, frequently they are built with dedicated tracks within that right-of-way to prevent delays, especially where service densities have converged in the inner parts of the network.

However, this simple model ends with the bandwidth of the network: Then congestion comes on the network and not with the peers.

However, this avoids the need for a separate DECT radio network.

However, DSN tracking requires many skilled operators, and the DSN is overburdened by its use as a communications network.

However, this scalability is difficult to test without a very large network.

However, remoter areas along the coast and in the east are often not connected to the road network.

However, since network news use of the term pertained primarily to the criminal activities despite this attempt by the technical community to preserve and distinguish the original meaning, the mainstream media and general public continue to describe computer criminals with all levels of technical sophistication as " hackers " and does not generally make use of the word in any of its non-criminal connotations.

However, all these activities have died out during the 1980s, when the phone network switched to digitally controlled switchboards, causing network hacking to shift to dialing remote computers with modems, when pre-assembled inexpensive home computers were available, and when academic institutions started to give individual mass-produced workstation computers to scientists instead of using a central timesharing system.

However, the network of dams and locks on the Columbia River and Snake River make the city of Lewiston the farthest inland seaport on the Pacific coast of the contiguous United States.

However, a single computer network may be converted into an internetwork by dividing the network into segments and logically dividing the segment traffic with routers.

However, in late 2010 the government announced an economic relief package and following the 2011 Jordanian protests it was decided to reduce the expected three year capital investment plan in the national railway network by 72 percent, partly to fund the relief package.

However, in contrast to the countries in the Anglo-Saxon system category, this is a much more widespread network of collective agreements, which covers most industries and most firms.

However, a rudimentary network begun under French colonial rule and continued from the 1950s has provided an important means of increased intervillage communication, movement of market goods, and a focus for new settlements.

However, the newer and less centralised Libyana network held copies of the HLR and engineers were able to restore some local services.

However, for supercomputing, the low latency of Myrinet is even more important than its throughput performance, since, according to Amdahl's law, a high-performance parallel system tends to be bottlenecked by its slowest sequential process, which in all but the most embarrassingly parallel supercomputer workloads is often the latency of message transmission across the network.

However it evolved in Generalized MPLS ( GMPLS ) to allow the creation of label-switched paths ( LSPs ) also in not native IP networks, such as SONET / SDH networks and wavelength switched optical network.

However, the scale of the city is far below a typical Arcology, having fewer than a thousand residents.

However, one group of researchers have found that carob seeds in fact have typical variability compared to the seeds of other species.

However, the wavelength of visible light ( about 4000 to 7000 angstroms ) is three orders of magnitude longer than the length of typical atomic bonds and atoms themselves ( about 1 to 2 angstroms ).

However, it is considerably more potent ( 5-MeO-DMT typical smoked dose: 5 – 20 mg ), and care should be taken to clearly differentiate between the two drugs to avoid accidental overdose.

However, about 80 % of his plays have been lost and even the extant plays don't present a fully consistent picture of his ' spiritual ' development ( for example, Iphigenia at Aulis is dated with the ' despairing ' Bacchae, yet it contains elements that became typical of New Comedy ).

However, in Cyclops ( the only complete satyr-play that survives ) Euripides structured the entertainment more like a tragedy and introduced a note of critical irony typical of his other work.

However, many see his monumental work, Don Carlo, as a response to Wagner's typical epics that often spanned over four hours.

However, typical daytime VFR minimums for most airspace is 3 statute miles of flight visibility and a cloud distance of 500 ' below, 1, 000 ' above, and 2, 000 ' feet horizontally.

However, even a minimal lock can delay a typical intruder for a time, and the disturbance generated in circumventing a high-quality lock, for example by breaking windows or doors, can deter many attackers, causing them to direct their attacks against weaker targets.

However, neighboring target neurons called ON bipolar cells are instead inhibited by glutamate, because they lack the typical ionotropic glutamate receptors and instead express a class of inhibitory metabotropic glutamate receptors.

However, the discovery of the object 1996 PW, an asteroid in an orbit more typical of a long-period comet, suggests that the cloud may also contain rocky objects.

However, this has been disputed, primarily on the basis that oxycodone produces effects typical of μ-opioid agonists.

However, other terms, such as Gothic architecture, used to refer to a style typical of the High Middle Ages have largely lost the negative connotations they initially had, acquiring new meanings over time ( see Gothic architecture and Goth subculture ).

However, English is typical as many languages show ambivalence in this regard.

However, of this metropolitan population, in 2001 nearly half lived in low-density neighborhoods, with only one in five living in a typical " urban " neighborhood.

However, there are some typical symptoms that can be objectively measured.

However, Hall thrusters operate at the high specific impulses that is typical of electric propulsion.

However, the growth rate is dependent on local soil and climatic conditions, as well as species, and a more typical growth rate for many commonly cultivated bamboos in temperate climates is in the range of 3 – 10 cm ( 1 – 4 inches ) per day during the growing period.

However, typical availability values are specified in decimal ( such as 0. 9998 ).

However, more typical, or frequent, " CISC " instructions merely combine a basic ALU operation, such as " add ", with the access of one or more operands in memory ( using addressing modes such as direct, indirect, indexed etc .).

However, these findings have been slow to move into typical classroom practice.

However, a typical temperate climate is one of the four climate zones in the world, beside polar regions ( subarctic climate, arctic climate, tundra climate, ice cap climate ) and the subtropics, tropics.

However the theory has been criticized because symptoms which would be typical of such effects are rare compared with prevalence of homosexuality

However, the typical pop-up indicator only shows that the cooker has pressure inside, which does not reliably signal that the cooker has reached the selected pressure.