Academic literature on the topic 'Nonmonotonicity degree'

In this article, a new nonmonotone line search technique is proposed for solving a system of nonlinear equations. We attempt to answer this question how to control the degree of the nonmonotonicity of line search rules in order to reach a more efficient algorithm? Therefore, we present a novel algorithm that can avoid the increase of unsuccessful iterations. For this purpose, we show the robust behavior of the proposed algorithm by solving a few numerical examples. Under some suitable assumptions, the global convergence of our strategy is proved.

Cortical neurons selective for the direction of motion often exhibit some limited response to motion in their nonpreferred directions. Here we examine the dependence of neuronal direction selectivity on stimulus contrast, both for first-order (luminance-modulated, sine-wave grating) and second-order (contrast-modulated envelope) stimuli. We measured responses from single neurons in area 18 of cat visual cortex to both kinds of moving stimuli over a wide range of contrasts (1.25–80%). Direction-selective contrast response functions (CRFs) were calculated as the preferred-minus-null difference in average firing frequency as a function of contrast. We also applied receiver operating characteristic analysis to our CRF data to obtain neurometric functions characterizing the potential ability of each neuron to discriminate motion direction at each contrast level tested. CRFs for sine-wave gratings were usually monotonic; however, a substantial minority of neurons (35%) exhibited nonmonotonic CRFs (such that the degree of direction selectivity decreased with increasing contrast). The underlying preferred and nonpreferred direction CRFs were diverse, often having different shapes in a given neuron. Neurometric functions for direction discrimination showed a similar degree of heterogeneity, including instances of nonmonotonicity. For contrast-modulated stimuli, however, CRFs for either carrier or envelope contrast were always monotonic. In a given neuron, neurometric thresholds were typically much higher for second- than for first-order stimuli. These results demonstrate that the degree of a cell's direction selectivity depends on the contrast at which it is measured, and therefore is not a characteristic parameter of a neuron. In general, contrast response functions for first-order stimuli were very heterogeneous in shape and sensitivity, while those for second-order stimuli showed less sensitivity and were quite stereotyped in shape.

1. Several studies of auditory cortex have examined the competitive inhibition that can occur when appropriate sounds are presented to each ear. However, most cortical neurons also show both excitation and inhibition in response to presentation of stimuli at one ear alone. The extent of such inhibition has not been described. Forward masking, in which a variable masking stimulus was followed by a fixed probe stimulus (within the excitatory response area), was used to examine the extent of monaural inhibition for neurons in primary auditory cortex of anesthetized cats (barbiturate or barbiturate-ketamine). Both the masking and probe stimuli were 50-ms tone pips presented to the contralateral ear. Most cortical neurons showed significant forward masking at delays beyond which masking effects in the auditory nerve are relatively small compared with those seen in cortical neurons. Analysis was primarily concerned with such components. Standard rate-level functions were also obtained and were examined for nonmonotonicity, an indication of level-dependent monaural inhibition. 2. Consistent with previous reports, a wide range of frequency tuning properties (excitatory response area shapes) was found in cortical neurons. This was matched by a wide range of forward-masking-derived inhibitory response areas. At the most basic level of analysis, these were classified according to the presence of lateral inhibition, i.e., where a probe tone at a neuron's characteristic frequency was masked by tones outside the limits of the excitatory response area. Lateral inhibition was a property of 38% of the sampled neurons. Such neurons represented 77% of those with nonmonotonic rate-level functions, indicating a strong correlation between the two indexes of monaural inhibition; however, the shapes of forward masking inhibitory response areas did not usually correspond with those required to account for the "tuning" of a neuron. In addition, it was found that level-dependent inhibition was not added to by forward masking inhibition. 3. Analysis of the discharges to individual stimulus pair presentations, under conditions of partial masking, revealed that discharges to the probe occurred independently of discharges to the preceding masker. This indicates that even when the masker is within a neuron's excitatory response area, forward masking is not a postdischarge habituation phenomenon. However, for most neurons the degree of masking summed over multiple stimulus presentations appears determined by the same stimulus parameters that determine the probability of response to the masker.(ABSTRACT TRUNCATED AT 400 WORDS)

Heil, Peter. Auditory cortical onset responses revisited. II. Response strength. J. Neurophysiol. 77: 2642–2660, 1997. Most neurons of the auditory pathway discharge spikes locked to the onset of an acoustic stimulus, but it is largely unknown in which way the acoustic parameters of sound onsets shape the neuronal responses. In this paper is analyzed the number of spikes discharged by single neurons in primary auditory cortex of barbiturate-anesthetized cats to the onsets of tones of characteristic frequency. The time course of the peak pressure (i.e., the envelope) was altered by parametrically varying sound pressure level (SPL), rise time, and rise function (linear or cosine-squared). For both rise functions, rise time had manifold, and in some cases dramatic, effects on conventional spike count–level functions. In general, threshold SPL, dynamic range, and the lowest SPL at which monotonic spike count functions saturated increased with prolongation of the rise time. In neurons with mostly nonmonotonic spike count–level functions, “best SPL” increased and the descending high-SPL arms flattened, so that functions obtained with long rise times were often monotonic whereas those obtained with shorter rise times were highly nonmonotonic. Consequently, the “tuning” to SPL was less sharp for longer rise time tones, and spike count versus rise time functions changed from “short-pass” to “long-pass” with an increase in SPL. Systematic effects of rise time persisted when spike counts were plotted against the rate of change of peak pressure or against the maximum acceleration of peak pressure. However, when spike counts were plotted as a function of the instantaneous peak pressure at the time of response initiation, the functions obtained with different rise times, and even with different rise functions, were in close register. This suggests that the stimulus-dependent component of first-spike latency can be viewed as an integration window, during which rate of change of peak pressure is integrated. The window commences with tone onset and its duration is inversely related to the maximum acceleration (or, for linear rise functions, the rate of change) of peak pressure and the neuron's transient sensitivity. The present findings seriously question, for onset responses, the usefulness of the spike count–level function and measures derived from it, such as threshold SPL, dynamic range, best SPL, or degree of nonmonotonicity. They further cast doubt onto the validity of current concepts of intensity coding at cortical levels, because most neurons' onset responses are not indicative of a signal's steady-state SPL. However, they suggest a mechanism by which a neuronal population will sample a given transient in an orderly, sensitivity-dependent, temporal sequence. The sampling rate is automatically adjusted to, and adjusted by, the rapidity of the signal's change. And the instantaneous properties of the transient could be represented by the ratios and spatial distribution of responses across the simultaneously active subpopulation. Such a mechanism could provide the basis for the demonstrated capability of discrimination of rapid transients.

1. We examined the temporal and mean rate discharge characteristics of 514 single units recorded extracellularly from the dorsal cochlear nucleus (DCN) of anesthetized guinea pigs. A mean rate response area (receptive field) was measured for the majority of units in this study. Each response area was placed in one of seven categories (type I to type V and the intermediate types I/III and IV-T) as defined by previous workers. The shape of the best frequency (BF) rate-level function has been used to aid in the distinction between type IV and type IV-T units, and the classification of type II units is based on their relative response to noise and tone bursts. 2. The threshold of single units was normalized to the cochlear action potential (CAP) threshold (a negative relative threshold indicates that the unit's threshold was more sensitive than the corresponding CAP threshold). There were significant differences (P < 0.05; 1-way analysis of variance--Duncan test) between the mean relative thresholds of type IV units (-12 dB) and those of type I (-6.52 dB), type II (-3 dB), and type I/III units (-4.25 dB). There were also significant differences between the relative thresholds of types III and IV-T and those of types I/III and II. 3. Rate-level functions at a unit's BF were divided into groups according to shape and degree of nonmonotonicity. Six units responded with a decrease in firing rate at all suprathreshold sound levels. However, most units increased their discharge rate over approximately the first 20 dB above BF threshold. Units were further subdivided by the change in slope 20 dB above BF threshold. The majority of units (60%) showed monotonic increases in discharge rate with sound level: some rate-level functions clearly resembled the sloping saturation rate-level functions observed in intermediate-threshold auditory nerve fibers. An unexpected finding was the relatively large number of nonmonotonic rate-level functions (40%). Among a relatively homogenous group of projection neurons (predominantly type IV and pause/build units) with nonmonotonic rate-level functions, the range of "best intensities" (the sound level evoking the highest discharge rate) was < 50 dB. This range of best intensities is narrower than found in higher auditory nuclei. 4. Units were also classified by their temporal activity pattern in response to suprathreshold BF tones. The most common pattern identified is the pause/build pattern (n = 294). This temporal activity pattern has been associated with the principal output neuron of the DCN, the fusiform cell. Our definition of pause/build units includes units with an almost constant steady-state discharge rate. Nonmonotonic rate-level functions were observed in 42% (99 of 233) of pause/build units. A measure of discharge regularity (the SD of the interspike interval/mean interspike interval: coefficient of variation, CV) revealed that the majority (82%) of units classified as pause/build and with steady-state discharge rates > 75 spikes/s (n = 142) were characterized by regular discharge patterns (CV = 0.41 +/- 0.15, mean +/- SD). 5. Units characterized by chopper or onset-type discharges were the next most frequently encountered units. The chopper units (n = 75) showed a regular discharge (CV = 0.39 +/- 0.17) similar to that found in recordings from the ventral division of the cochlear nucleus (VCN). One difference between many chopper units in the DCN compared with those recorded in the VCN was the relatively high value (> 5 ms) of the mean interspike interval (and thus the low steady-state discharge rate). The majority (44 of 59; 75%) of chopper units had monotonic rate-level functions. Onset units (n = 47) may represent several response types, linked by the predominance of discharges in response to stimulus onset, and the majority of onset units reported here bear little resemblance to onset units recorded in the VCN of the guinea pig. Approximately 10% of units did not fit easily into any of th

Abstract The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

The focus of this thesis is the study and the application of nonmonotone strategies. These techniques are basically introduced to improve numerical results of existing optimization algorithms. Their first aim is that of relaxing the monotone requirement imposed by the globalization techniques. In fact, these monotone conditions might slow down the convergence rate of inher- ently nonmonotone optimization methods. This relaxation must not harm global convergence results. In this thesis we apply nonmonotone strategies to both line search and trust-region globalization techniques. We first considered Generalized Nash Equilibrium Problems (GNEPs) and their KKT reformulation into a highly nonlinear constrained smooth system of equations. In order to obtain global and fast local convergence, we take into account an existing trust-region method that is locally superlinear under an error bound condition only. A nonmonotone strategy has been applied, showing that the resulting algo- rithm performs significantly better than the original one. Global conver- gence properties have been proved for the new algorithm, while superlinear convergence is directly inherited from the existing method. The resulting algorithm is competitive with a standard software for nonlinear equations, not only on GNEPs, but also on quasi-variational inequalities. The second contribution of this thesis is the development of a framework for nonmonotone line search based decomposition methods. This is the first time in which nonmonotonicity is combined with decomposition methods for general constrained problems. Note that the choice of the direction and the line search are not fixed in advance, in fact the framework proves conver- gence for all those combinations of directions and line searches that are able to satisfy some mild assumptions. A specific realization of this abstract algo- rithm has been implemented in two versions, monotone and nonmonotone. The two algorithms have been compared on a set of network equilibrium problems. Also on this application, the nonmonotone version outperformed its monotone counterpart both on the total number of iterations and the function evaluations. In the end, a new family of nonmonotone techniques is proposed to build algorithms that are able to control the amount of nonmonotonicity intro- duced in each of the phases of the optimization procedure. This tool might be very helpful to understand in which combination of methods, problems and phases is more important to apply a nonmonotone strategy.