266 Note: A Method for Obtaining Initial Estimates of the Parameters in Exponential Curve Fitting

Biometrics ◽  
1969 ◽  
Vol 25 (3) ◽  
pp. 580 ◽  
Author(s):  
S. D. Foss
Keyword(s):  
Curve Fitting ◽  
Exponential Curve

Exponential Modeling of Frequency-Following Responses in American Neonates and Adults

2018 ◽  
Vol 29 (02) ◽  
pp. 125-134 ◽  
Author(s):  
Fuh-Cherng Jeng ◽  
Brandie Nance ◽  
Karen Montgomery-Reagan ◽  
Chia-Der Lin
Keyword(s):  
Time Constant ◽  
Curve Fitting ◽  
Speech Processing ◽  
Phase Locking ◽  
Pitch Contour ◽  
Frequency Error ◽  
Tracking Accuracy ◽  
Exponential Curve ◽  
Adult Participants ◽  
Fitting Model

AbstractThe scalp-recorded frequency-following response (FFR) has been widely accepted in assessing the brain’s processing of speech stimuli for people who speak tonal and nontonal languages. Characteristics of scalp-recorded FFRs with increasing number of sweeps have been delineated through the use of an exponential curve-fitting model in Chinese adults; however, characteristics of speech processing for people who speak a nontonal language remain unclear.This study had two specific aims. The first was to examine the characteristics of speech processing in neonates and adults who speak a nontonal language, to evaluate the goodness of fit of an exponential model on neonatal and adult FFRs, and to determine the differences, if any, between the two groups of participants. The second aim was to assess effective recording parameters for American neonates and adults.This investigation employed a prospective between-subject study design.A total of 12 American neonates (1–3 days old) and 12 American adults (24.1 ± 2.5 yr old) were recruited. Each neonate passed an automated hearing screening at birth and all adult participants had normal hearing and were native English speakers.The English vowel /i/ with a rising pitch contour (117–166 Hz) was used to elicit the FFR. A total of 8,000 accepted sweeps were recorded from each participant. Three objective indices (Frequency Error, Tracking Accuracy, and Pitch Strength) were computed to estimate the frequency-tracking acuity and neural phase-locking magnitude when progressively more sweeps were included in the averaged waveform. For each objective index, the FFR trends were fit to an exponential curve-fitting model that included estimates of asymptotic amplitude, noise amplitude, and a time constant.Significant differences were observed between groups for Frequency Error, Tracking Accuracy, and Pitch Strength of the FFR trends. The adult participants had significantly smaller Frequency Error (p < 0.001), better Tracking Accuracy (p = 0.001), and larger Pitch Strength (p = 0.003) values than the neonate participants. The adult participants also demonstrated a faster rate of improvement (i.e., a smaller time constant) in all three objective indices compared to the neonate participants. The smaller time constants observed in adults indicate that a larger number of sweeps will be needed to adequately assess the FFR for neonates. Furthermore, the exponential curve-fitting model provided a good fit to the FFR trends with increasing number of sweeps for American neonates (mean r 2 = 0.89) and adults (mean r 2 = 0.96).Significant differences were noted between the neonatal and adult participants for Frequency Error, Tracking Accuracy, and Pitch Strength. These differences have important clinical implications in determining when to stop a recording and the number of sweeps needed to adequately assess the frequency-encoding acuity and neural phase-locking magnitude in neonates and adults. These findings lay an important foundation for establishing a normative database for American neonates and adults, and may prove to be useful in the development of diagnostic and therapeutic paradigms for neonates and adults who speak a nontonal language.

Analysis of kinetic data of antibody-antigen interaction from an optical biosensor by exponential curve fitting

1996 ◽  
Vol 48 (1-2) ◽  
pp. 117-127 ◽  
Author(s):  
Andrew Gill ◽  
Robin J Leatherbarrow ◽  
Mike Hoare ◽  
Denise V Pollard-knight ◽  
peter A Lowe ◽  
...  
Keyword(s):  
Curve Fitting ◽  
Kinetic Data ◽  
Optical Biosensor ◽  
Exponential Curve ◽  
Antigen Interaction

scholarly journals VisBio: a Flexible Open-Source Visualization Package for Multidimensional Image Data

2006 ◽  
Vol 14 (3) ◽  
pp. 6-11
Author(s):  
Curtis T. Rueden ◽  
Kevin W. Eliceiri
Keyword(s):  
Open Source ◽  
Curve Fitting ◽  
Image Data ◽  
Time Lapse ◽  
Dramatic Improvement ◽  
Exponential Curve ◽  
Lifetime Imaging ◽  
The Past ◽  
Resultant Data ◽  
Fitting Algorithm

Over the past few years there has been a dramatic improvement in microscopy acquisition techniques, in effective imaging modalities as well as raw hardware performance. As the microscopist's available tools become more sophisticated and diverse—e.g., time-lapse, Z sectioning, multispectra, lifetime, nth harmonic, polarization, and many combinations thereof—we face a corresponding increase in complexity in the software for understanding and interpreting the resultant data. With lifetime imaging, for example, it is overwhelming to study the raw numbers; instead, an exponential curve-fitting algorithm must be applied to extract meaningful lifetime values from the mass of photon counts recorded by the instrument.

Double-exponential curve fitting of isometric relaxation: a new measure for myocardial lusitropism

1995 ◽  
Vol 269 (4) ◽  
pp. 1-1
Author(s):  
Kouichi Tamiya ◽  
Toshiyuki Beppu ◽  
Kazuaki Ishihara
Keyword(s):  
Curve Fitting ◽  
Exponential Curve ◽  
Double Exponential

Pages H393–H406: Kouichi Tamiya, Toshiyuki Beppu, and Kazuaki Ishihara. “Double-exponential curve fitting of isometric relaxation: a new measure for myocardial lusitropism.” Page H402: Figure 10 should appear as the following. (See PDF)

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