More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

More sophisticated space elevator designs reduce the energy cost per trip by using counterweights, and the most ambitious schemes aim to balance loads going up and down and thus make the energy cost close to zero.

More sophisticated techniques will show proportional differences in optical density.

More sophisticated models can be made using a combination of etched sheets of brass and low temperature castings.

More modern and sophisticated approaches seek to maintain the idea of the morpheme while accommodating non-concatenative, analogical, and other processes that have proven problematic for Item-and-Arrangement theories and similar approaches.

More problematic, and never properly addressed by Cumont or his successors, is how real-life Roman Mithraists subsequently maintained a quite complex and sophisticated Iranian theology behind an occidental facade.

More sophisticated versions may make specific desired changes to the deck's order, while still appearing to be an innocuous normal cut.

More recently, structural equation modeling and path analysis represent more sophisticated approaches to working with large covariance matrices.

More sophisticated methods of signal processing are also used in order to recover useful radar signals.

More sophisticated routers, such as enterprise routers, connect large business or ISP networks up to the powerful core routers that forward data at high speed along the optical fiber lines of the Internet backbone.

Other biographers, such as Peter Ackroyd, have offered a more sympathetic picture of More as both a sophisticated philosopher and man of letters, as well as a zealous Catholic who believed in the authority of the Holy See over Christendom.

More sophisticated transformations include set operations on closed shapes ( union, difference, intersection, etc.

More sophisticated tests use a torsion balance of a type invented by Eötvös.

More sophisticated attackers use DDoS tools for the purposes of extortioneven against their business rivals.

More sophisticated cryptographic systems, such as Anonymous Digital credentials, enable users to communicate pseudonymously ( i. e., by identifying themselves by means of pseudonyms ).

More sophisticated methods may be used to optimize resources across campaigns so that one may predict to which channel and to which offer an individual is most likely to respond ( across all potential offers ).

More sophisticated methods are used in practice for natural language generation.

More recent studies using more sophisticated methodologies have generally refuted these findings: density, land use and public transport accessibility can influence travel behaviour, although social and economic factors, particularly household income, usually exert a stronger influence.

More sophisticated devices which use a graphical screen with touch sensing or screen-edge buttons provide flexibility while minimizing space used: the meaning of the buttons can change with the screen, and selection involves the natural behavior of pointing at what's desired.

More experienced players understand the power of the bishop, but a more sophisticated understanding is required.

More sophisticated tools, worked on both sides of the stone and dating to 600, 000 BC, were found in the Cave of Escale at Saint Estėve-Janson, and tools from 400, 000 BC and some of the first fireplaces in Europe were found at Terra Amata in Nice.

More sophisticated forecasting can include other aspects of traveler decisions, including auto ownership, trip chaining ( the decision to link individual trips together in a tour ) and the choice of residential or business location ( known as land use forecasting ).

More sophisticated systems allow for more information such as lateral and longitudinal acceleration ( or G-force ), throttle position, steering wheel position and brake pressure.

More sophisticated methods were developed and later adopted elsewhere.

More sophisticated turbines ( such as those found in modern jet engines ) may have multiple shafts ( spools ), hundreds of turbine blades, movable stator blades, and a vast system of complex piping, combustors and heat exchangers.

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

More and more specialized algorithms are used in 3D programs that can effectively simulate the global illumination.

* More efficient in practice than most other simple quadratic ( i. e., O ( n < sup > 2 </ sup >)) algorithms such as selection sort or bubble sort ; the best case ( nearly sorted input ) is O ( n )

More recent Unix or Unix like systems ( e. g., Linux or the various BSD systems ) use more secure password hashing algorithms such as PBKDF2, bcrypt and scrypt which have large salts and an adjustable cost or number of iterations.

More people can review the details of such algorithms, identify flaws, and fix the flaws sooner.

More recent instances of PRNGs with strong randomness guarantees are based on computational hardness assumptions, and include the Blum Blum Shub, Fortuna, and Mersenne Twister algorithms.

More esoterically, nondeterministic algorithms have been employed in the theoretical investigation of hypercomputation.

More advanced algorithms that are even faster while still being able to compute the exact minimax value are known, such as SCOUT, Negascout and MTD-f.

More sophisticated MCMC-based algorithms such as coupling from the past can produce exact samples, at the cost of additional computation and an unbounded ( though finite in expectation ) running time.

More sophisticated algorithms use some method of preventing the walker from doubling back.

More specific algorithms are often available as publicly-available scripts or third-party add-ons.

More complicated algorithms include the Luhn algorithm ( 1954 ), which captures 98 % of single digit transposition errors ( it does not detect 90 ↔ 09 ), while more sophisticated is the Verhoeff algorithm ( 1969 ), which catches all single digit substitution and transposition errors, and many ( but not all ) more complex errors.

More recent examples of research results from CWI include the development of scheduling algorithms for the Dutch railway system, the Nederlandse Spoorwegen ( one of the busiest rail networks in the world ), or the development of the Python programming language by Guido van Rossum.

More advanced implementations would employ algorithms similar to block motion compensation used in video compression ; deinterlacers that use this technique are often superior because they can use information from many fields, as opposed to just one or two.

More complex algorithms can be formed by mixing substitution and transposition in a product cipher ; modern block ciphers such as DES iterate through several stages of substitution and transposition.

More practically, the Chernoff bound is used in randomized algorithms ( or in computational devices such as quantum computers ) to determine a bound on the number of runs necessary to determine a value by majority agreement, up to a specified probability.

More generally, addition-chain exponentiation may also refer to exponentiation by non-minimal addition chains constructed by a variety of algorithms ( since a shortest addition chain is very difficult to find ).

More complex scheduling constraints may require more complex algorithms.

More complex algorithms are necessary to detect motion when the camera itself is moving, or when the motion of a specific object must be detected in a field containing other movement which can be ignored.

More efficient probabilistic encryption algorithms include Elgamal, Paillier, and various constructions under the random oracle model, including Optimal Asymmetric Encryption Padding ( OAEP ).

More recently, attempts have been made to construct mathematical models of the stereolithography process and design algorithms to determine whether a proposed object may be constructed by the process.

More complex algorithms can be used which use more samples ' errors ' worth of feedback in order to create more complex curves.

More recently, digital conversion methods have used algorithms which preserve the original pitch of the soundtrack, although the frame rate conversion still results in faster playback.

More efficient algorithms, that require examining only of the edges, are known.