58 Sentences With "nonlinearly" | Random Sentence Generator

Furthermore, the power of a group increases nonlinearly with its size.

Earthquake Bird, told nonlinearly, opens with Lily's disappearance and spends 90% of its runtime heavily implying Lucy is the killer.

What's more, as software eats the world, one side effect is that rewards accrue nonlinearly to those with the best software.

Which of two interpretations of the Shang scene you buy will largely depend on how you believe experiencing time nonlinearly would affect the human brain.

Though the cross-references serve as a useful guide to experiencing the story nonlinearly, it is often difficult to parse the motivation behind which story redirects where.

Its central relationships weren't built solely around nuclear families, or any particular character's attempts to secure one; its story was told nonlinearly, through flashbacks and bottle episodes, in novel-like seasons.

The likelihood of extreme heat, like what we are seeing in the US Midwest this week, increases nonlinearly with the warming of average temperatures (caused by increases in anthropogenic greenhouse gas concentrations). pic.twitter.

When Season 4 debuted on Netflix in 2013, the stories were presented nonlinearly – that is, viewers could watch them in any order and piece together the story that way, as opposed to a traditional TV narrative.

You're probably willing to go with the idea that protagonist Louise (Amy Adams) suddenly starts seeing glimpses of her own future thanks to learning the language of the alien Heptapods (who experience time nonlinearly and know what's coming).

This nonlinear approach is no surprise coming from Nolan, who has a history of playing with time and viewer expectations in films ranging from Memento (which is told nonlinearly) to Interstellar (which utilizes cyclical time as part of its internal logic).

Thus, it can be viewed as a smoothing function which nonlinearly interpolates between a linear and the ReLU function.

Note, however, that the ratio allocation to each channel is not a fixed proportion but varies nonlinearly with the maximum average transmit power.

Self- organization requires a 'macroscopic' system, consisting of many nonlinearly interacting subsystems. Depending on the external control parameters (environment, energy-fluxes) self-organization takes place.

Optical gratings are less expensive, provide much higher resolution, and are easier to calibrate, due to their linear diffraction dependency. A prism's refraction angle varies nonlinearly with wavelength. On the other hand, gratings have significant intensity losses.

The MLP consists of three or more layers (an input and an output layer with one or more hidden layers) of nonlinearly-activating nodes. Since MLPs are fully connected, each node in one layer connects with a certain weight w_{ij} to every node in the following layer.

In particular, almost all standard RGB color spaces and file formats use a non- linear encoding (a gamma compression) of the intended intensities of the primary colors of the photographic reproduction; in addition, the intended reproduction is almost always nonlinearly related to the measured scene intensities, via a tone reproduction nonlinearity.

In human walking, net metabolic rate also increases nonlinearly with speed. These measures of walking energetics are based on how much oxygen people consume per unit time. Many locomotion tasks, however, require walking a fixed distance rather than for a set time. Dividing gross metabolic rate by walking speed results in gross cost of transport.

Many techniques such as carrier recovery, clock recovery, bit slip, frame synchronization, rake receiver, pulse compression, Received Signal Strength Indication, error detection and correction, etc., are only performed by demodulators, although any specific demodulator may perform only some or none of these techniques. Many things can act as a demodulator, if they pass the radio waves on nonlinearly.

Optical magnetometry makes use of various optical techniques to measure magnetization. One such technique, Kerr Magnetometry makes use of the magneto-optic Kerr effect, or MOKE. In this technique, incident light is directed at the sample's surface. Light interacts with a magnetized surface nonlinearly so the reflected light has an elliptical polarization, which is then measured by a detector.

Water is a fluid that does not obey the Boussinesq approximation. This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures. The density of water reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods.

In numerical analysis, stochastic tunneling (STUN) is an approach to global optimization based on the Monte Carlo method-sampling of the function to be objective minimized in which the function is nonlinearly transformed to allow for easier tunneling among regions containing function minima. Easier tunneling allows for faster exploration of sample space and faster convergence to a good solution.

Stochastic tunneling (STUN) is an approach to global optimization based on the Monte Carlo method- sampling of the function to be objectively minimized in which the function is nonlinearly transformed to allow for easier tunneling among regions containing function minima. Easier tunneling allows for faster exploration of sample space and faster convergence to a good solution.

Michael Heath earned his B.A. in Mathematics from the University of Kentucky in 1968. In 1974, Heath earned his M.S. in Mathematics from the University of Tennessee. Heath earned his Ph.D. in Computer Science from Stanford University in 1978; his Ph.D. dissertation was entitled Numerical Algorithms for Nonlinearly Constrained Optimization and was completed under the direction of Gene Golub.

Robert Geroch. During this time, he collaborated with Subrahmanyan Chandrasekhar on colliding plane waves. In particular, they discovered an exact solution which models two gravitational plane waves which collide, interact nonlinearly, and create in the interaction zone a curved region of spacetime which is locally isometric to the Kerr vacuum. This is now called the 'Chandrasekhar–Xanthopoulos colliding plane wave model.

At a concentration of 164 μg/L, chlorothalonil was found to kill a species of frog within a 24-hour exposure.Taegan McMahon, Neal Halstead, Steve Johnson, Thomas R. Raffel, John M. Romansic, Patrick W. Crumrine, Raoul K. Boughton, Lynn B. Martin, Jason R. Rohr "The Fungicide Chlorothalonil is Nonlinearly Associated with Corticosterone Levels, Immunity, and Mortality in Amphibians" Environ Health Perspectives, 2011, Online: 4 April.

The Rényi entropy as well as von Neumann entropy in quantum physics are not observables since they depend nonlinearly on the density matrix. Recently, Ansari and Nazarov proved an exact correspondence that reveals the physical meaning of the Rényi entropy flow in time. This correspondence is similar to the fluctuation-dissipation theorem in spirit and allows the measurement of quantum entropy using the full counting statistics (FCS) of energy transfers.

Energy minimization is widely considered a primary goal of the central nervous system. The rate at which an organism expends metabolic energy while walking (gross metabolic rate) increases nonlinearly with increasing speed. However, they also require a continuous basal metabolic rate to maintain normal function. The energetic cost of walking itself is therefore best understood by subtracting basal metabolic rate from total metabolic rate, yielding Final metabolic rate.

Another form taken by calcite is oolitic limestone, which can be recognized by its granular (oolite) appearance. The primary source of the calcite in limestone is most commonly marine organisms. Some of these organisms can construct mounds of rock known as reefs, building upon past generations. Below about 3,000 meters, water pressure and temperature conditions cause the dissolution of calcite to increase nonlinearly, so limestone typically does not form in deeper waters (see lysocline).

Y′ (with prime) is distinguished from Y, which is luminance, meaning that light intensity is nonlinearly encoded based on gamma corrected RGB primaries. Y′CbCr color spaces are defined by a mathematical coordinate transformation from an associated RGB color space. If the underlying RGB color space is absolute, the Y′CbCr color space is an absolute color space as well; conversely, if the RGB space is ill-defined, so is Y′CbCr.

Resistive loaded varactors. Regenerative varactors. Penfield. Frequency multipliers have much in common with frequency mixers, and some of the same nonlinear devices are used for both: transistors operated in Class C and diodes. In transmitting circuits many of the amplifying devices (vacuum tubes or transistors) operate nonlinearly and create harmonics, so an amplifier stage can be made a multiplier by tuning the tuned circuit at the output to a multiple of the input frequency.

Frequently Questioned Answers about Gamma. Gamma encoding of floating-point images is not required (and may be counterproductive), because the floating- point format already provides a piecewise linear approximation of a logarithmic curve. Although gamma encoding was developed originally to compensate for the input–output characteristic of cathode ray tube (CRT) displays, that is not its main purpose or advantage in modern systems. In CRT displays, the light intensity varies nonlinearly with the electron-gun voltage.

A mathematical introduction to this subject is given by Arnold & Khesin (1998) and recent survey articles and contributions may be found in Ricca (2009), and Moffatt, Bajer & Kimura (2013). Topology is also crucial to the structure of neutral surfaces in a fluid (such as the ocean) where the equation of state nonlinearly depends on multiple components (e.g. salinity and heat). Fluid parcels remain neutrally buoyant as they move along neutral surfaces, despite variations in salinity or heat.

POC is decomposed by a series of microbe-driven processes, such as methanogenesis and sulfate reduction, before burial in the seafloor. Degradation of POC also results in microbial methane production which is the main gas hydrate on the continental margins. Lignin and pollen are inherently resistant to degradation, and some studies show that inorganic matrices may also protect organic matter. Preservation rates of organic matter depend on other interdependent variables that vary nonlinearly in time and space.

The voltage noise Sv is considered to be a small signal outside the linewidth and thus can be accurately predicted using small-signal analyses. Conversely, the voltage noise within the linewidth is a large signal (it is large enough to cause the circuit to behave nonlinearly) and cannot be predicted with small-signal analyses. Thus, small-signal noise analysis, such as is available from RF simulators, is valid only up to the corner frequency (it does not model the corner itself).

The inner ear, for example, does significant signal processing in converting sound waveforms into neural stimuli, so certain differences between waveforms may be imperceptible. Data compression techniques, such as MP3, make use of this fact. In addition, the ear has a nonlinear response to sounds of different intensity levels; this nonlinear response is called loudness. Telephone networks and audio noise reduction systems make use of this fact by nonlinearly compressing data samples before transmission, and then expanding them for playback.

For amplitudes up to 15 or 20°, the velocity of a saccade linearly depends on the amplitude (the so-called saccadic main sequence, a term borrowed from astrophysics; see Figure). For amplitudes larger than 20°, the peak velocity starts to plateau (nonlinearly) toward the maximum velocity attainable by the eye at around 60°. For instance, a 10° amplitude is associated with a velocity of 300°/s, and 30° is associated with 500°/s."Sensory Reception: Human Vision: Structure and function of the Human Eye" vol.

Williams [1992] suggested that global temperature may be monitored with the Schumann resonances. The link between Schumann resonance and temperature is lightning flash rate, which increases nonlinearly with temperature. The nonlinearity of the lightning-to-temperature relation provides a natural amplifier of the temperature changes and makes Schumann resonance a sensitive "thermometer". Moreover, the ice particles that are believed to participate in the electrification processes which result in a lightning discharge have an important role in the radiative feedback effects that influence the atmosphere temperature.

Even so, it cannot be overemphasized that, regardless of its motivation, an extra margin added to the sampling frequency does not make the reconstructed waveform smoother, it merely prevents aliasing of the frequencies in the transition band to lower frequencies, which would distort the signal nonlinearly. DAWs today typically use 44.1 kHz or higher sample rates. Early digital gear used much lower sample rates to conserve memory for stored audio. A Speak & Spell from the 1979, for instance, used an 8 kHz sample rate.

In addition to the direct heating effect and the normal feedbacks, the methane breaks down to carbon dioxide and water. This water is often above the tropopause where little water usually reaches. Ramanathan (1988) notes that both water and ice clouds, when formed at cold lower stratospheric temperatures, are extremely efficient in enhancing the atmospheric greenhouse effect. He also notes that there is a distinct possibility that large increases in future methane may lead to a surface warming that increases nonlinearly with the methane concentration.

However, perturbation expansions are generally not reliable for questions of long-term existence and stability, in the case of nonlinear equations. The full field equation is highly nonlinear, so we really want to prove that the Minkowski vacuum is stable under small perturbations which are treated using the fully nonlinear field equation. This requires the introduction of many new ideas. The desired result, sometimes expressed by the slogan that the Minkowski vacuum is nonlinearly stable, was finally proven by Demetrios Christodoulou and Sergiu Klainerman only in 1993.

Urban soil contains higher concentrations of heavy metals (especially lead, copper, and nickel) and has lower pH than soil in comparable wilderness. Modern cities are known for creating their own microclimates, due to concrete, asphalt, and other artificial surfaces, which heat up in sunlight and channel rainwater into underground ducts. The temperature in New York City exceeds nearby rural temperatures by an average of 2–3 °C and at times 5–10 °C differences have been recorded. This effect varies nonlinearly with population changes (independently of the city's physical size).

Note the similarity with the observed light curve. From an analysis of the fixed points of the evolution operator a nice physical picture can be inferred, namely that the pulsations arise from the excitation of an unstable pulsation mode that couples nonlinearly to a second, stable pulsation mode which is in a 2:1 resonance with the first one, a scenario described by the Shilnikov theorem. This resonance mechanism is not limited to R Scuti, but has been found to hold for several other stars for which the observational data are sufficiently good.

The effect of this system is to nonlinearly amplify quiet sounds more than large ones so that a wide range of sound pressures can be reduced to a much smaller range of hair displacements. This property of amplification is called the cochlear amplifier. The molecular biology of hair cells has seen considerable progress in recent years, with the identification of the motor protein (prestin) that underlies somatic electromotility in the outer hair cells. Prestin's function has been shown to be dependent on chloride channel signaling and that it is compromised by the common marine pesticide tributyltin.

Transmutation flow in LWR Plutonium-242 is produced by successive neutron capture on 239Pu, 240Pu, and 241Pu. The odd-mass isotopes 239Pu and 241Pu have about a 3/4 chance of undergoing fission on capture of a thermal neutron and about a 1/4 chance of retaining the neutron and becoming the following isotope. The proportion of 242Pu is low at low burnup but increases nonlinearly. Plutonium-242 has a particularly low cross section for thermal neutron capture; and it takes three neutron absorptions to become another fissile isotope (either curium-245 or plutonium-241) and then one more neutron to undergo fission.

Interactive models of language processing assume that information flows both bottom-up and top-down, so that the representations formed at each level may be influenced by higher as well as lower levels. A framework called the interactive activation framework that embeds this key assumption among others, including the assumption that influences from different sources are combined nonlinearly. The nonlinearity means that information that may be decisive under some circumstances may have little or no effect under other conditions. In the interactive activation framework, the knowledge that guides processing is stored in the connections between units on the same and adjacent levels.

They transform nonlinearly (shift) under the action of these generators, and can thus be excited out of the asymmetric vacuum by these generators. Thus, they can be thought of as the excitations of the field in the broken symmetry directions in group space—and are massless if the spontaneously broken symmetry is not also broken explicitly. If, instead, the symmetry is not exact, i.e. if it is explicitly broken as well as spontaneously broken, then the Nambu–Goldstone bosons are not massless, though they typically remain relatively light; they are then called pseudo-Goldstone bosons or pseudo-Nambu–Goldstone bosons (abbreviated PNGBs).

If the law of mass action is applied to an enzyme-catalysed process it results in the Michaelis–Menten equation, from which Monod is inspired. This makes things difficult for in situ biosurfactant production because controlled experimentation is required to determine specific growth rate and Michaelis–Menten parameters of rate-limiting enzyme reaction. Modelling of bioclogging is complicated because the production of clogging metabolite is coupled nonlinearly to the growth of microbes and flux of nutrients transported in the fluid. The ecophysiology of the entire microbial microcosms at oil reservoir conditions is still unclear and thus not considered by the available models.

For electrophoresis of colloid particles under a small strength electric field, the force f(t) in the right-hand side of Eq. (5) is linearly proportional to the strength E(t) of the electric field applied. For a high strength, the linearity is broken due to nonlinear polarization. As a result, the force may depend nonlinearly on the applied field: : \qquad\qquad f(t)\sim E(t)+\alpha (E(t))^3. In the last expression, even if the applied field, E(t) has zero mean, the applied force f(t) may happen to have a constant component that can cause a directed drift.

For example, if a limb that is swinging forward reaches the end of swing in less time than the current CPG-generated flexor phase duration, sensory input would cause the CPG timer to terminate swing and start the stance phase. Furthermore, as body velocity increases, the pattern formation layer would increase muscle activation nonlinearly to provide increased load-bearing and thrust forces. It has been posited that in well-predicted movements, CPG- generated phase durations and muscle forces closely match those required by the evolving biomechanical events, minimizing the sensory corrections required. The term ‘‘neuromechanical tuning’’ has been coined to describe this process Fig. 1.

The map was presented nonlinearly, and some paths and interactions required a high statistic to successfully complete the task. Every statistic could unlock at least one, and usually several, crucial puzzles and solutions; but the player would find him or herself at a disadvantage in others. For example, an intelligent player character could read the words on magical scrolls, and use magical items, from early on in the game - this allowed the wide-ranging traversal of the map and the completion of many plot points; but the value required generally meant taking points away from the combat statistics. A dexterous character could traverse paths and enter rooms unavailable to the clumsy.

CHAPTER 1, LESS LIKE SWEDEN: Ellenberg encourages his readers to think nonlinearly, and know that “where you should go depends on where you are”. To develop his thought, he relates this to Voodoo economics and the Laffer curve of taxation. Although there are little to no numbers in this chapter, the point is that the overall concept still ties back to mathematical thinking. CHAPTER 2, STRAIGHT LOCALLY, CURVED GLOBALLY: This chapter puts an emphasis on recognizing that “not every curve is a straight line”, and makes reference to multiple mathematical concepts including the Pythagorean theorem, the derivation of Pi, Zeno's paradox, and non-standard analysis.

Saturation puts a practical limit on the maximum magnetic fields achievable in ferromagnetic-core electromagnets and transformers of around 2 T, which puts a limit on the minimum size of their cores. This is one reason why high power motors, generators, and utility transformers are physically large; to conduct the large amounts of magnetic flux necessary for high power production, they must have large magnetic cores. In applications in which the weight of magnetic cores must be kept to a minimum, such as transformers and electric motors in aircraft, a high saturation alloy such as Permendur is often used. In electronic circuits, transformers and inductors with ferromagnetic cores operate nonlinearly when the current through them is large enough to drive their core materials into saturation.

First, a new information carrier Inew created by the mutation must be better recognized by one of the hypercycle's members Ii than the chain Ii+1 that was previously recognized by it. Secondly, the new member Inew of the cycle has to better catalyse the formation of the polynucleotide Ii+1 that was previously catalysed by the product of its predecessor Ii. In theory, it is possible to incorporate into the hypercycle mutations that do not satisfy the second condition. They would form parasitic branches that use the system for their own replication but do not contribute to the system as a whole. However, it was noticed that such mutants do not pose a threat to the hypercycle, because other constituents of the hypercycle grow nonlinearly, which prevents the parasitic branches from growing.

IDA involves performing multiple nonlinear dynamic analyses of a structural model under a suite of ground motion records, each scaled to several levels of seismic intensity. The scaling levels are appropriately selected to force the structure through the entire range of behavior, from elastic to inelastic and finally to global dynamic instability, where the structure essentially experiences collapse. Appropriate postprocessing can present the results in terms of IDA curves, one for each ground motion record, of the seismic intensity, typically represented by a scalar Intensity Measure (IM), versus the structural response, as measured by an engineering demand parameter (EDP). Possible choices for the IM are scalar (or rarely vector) quantities that relate to the severity of the recorded ground motion and scale linearly or nonlinearly with its amplitude.

ReActive Transport (RAT) has been developed to solve reactive transport problems in subsurface porous media that involves highly nonlinearly coupled physical processes of fluid flow, solute transport, biogeochemical reactions and media-solution interactions. These problems are common in various subsurface-engineered systems, such as engineered environmental remediation, enhanced geothermal systems and carbon dioxide geological sequestration. Currently, the physics that could be coupled in RAT include: single-phase fluid flow in porous media, advection, dispersion and diffusion transport, aqueous kinetic reaction, aqueous equilibrium reaction, kinetic mineral precipitation/dissolution reaction, and Carmen-Kozeny porosity-permeability relationship. This software is not to be confused with the Reactor Analysis Tool (RAT) which is a toolkit based on ROOT and GEANT4 for microphysical simulations of scintillation detectors used in neutrino and dark matter experiments including Braidwood, SNO+, and DEAP-3600.

A transducer can be made to project a narrow beam of modulated ultrasound that is powerful enough, at 100 to 110 dBSPL, to substantially change the speed of sound in the air that it passes through. The air within the beam behaves nonlinearly and extracts the modulation signal from the ultrasound, resulting in sound that can be heard only along the path of the beam, or that appears to radiate from any surface that the beam strikes. This technology allows a beam of sound to be projected over a long distance to be heard only in a small well-defined area; for a listener outside the beam the Sound pressure decreases substantially. This effect cannot be achieved with conventional loudspeakers, because sound at audible frequencies cannot be focused into such a narrow beam.

In a paper on the acquisition of moral values by robots, Nayef Al-Rodhan mentions the case of neuromorphic chips, which aim to process information similarly to humans, nonlinearly and with millions of interconnected artificial neurons. Robots embedded with neuromorphic technology could learn and develop knowledge in a uniquely humanlike way. Inevitably, this raises the question of the environment in which such robots would learn about the world and whose morality they would inherit - or if they end up developing human 'weaknesses' as well: selfishness, a pro-survival attitude, hesitation etc. In Moral Machines: Teaching Robots Right from Wrong, Wendell Wallach and Colin Allen conclude that attempts to teach robots right from wrong will likely advance understanding of human ethics by motivating humans to address gaps in modern normative theory and by providing a platform for experimental investigation.

In photography, the differences between an "objective" and "subjective" tone reproduction, and between "accurate" and "preferred" tone reproduction, have long been recognized. Many steps in the process of photography are recognized as having their own nonlinear curves, which in combination form the overall tone reproduction curve; the Jones diagram was developed as a way to illustrate and combine curves, to study and explain the photographic process. The luminance range of a scene maps to the focal-plane illuminance and exposure in a camera, not necessarily directly proportionally, as when a graduated neutral density filter is used to reduce the exposure range to less than the scene luminance range. The film responds nonlinearly to the exposure, as characterized by the film's characteristic curve, or Hurter–Driffield curve; this plot of optical density of the developed negative versus the logarithm of the exposure (also called a D–logE curve) has central straight section whose slope is called the gamma of the film.