Alphabetic points in restricted growth functions

2022 ◽  
Vol 309 ◽  
pp. 130-137
Author(s):  
Aubrey Blecher ◽  
Arnold Knopfmacher ◽  
Toufik Mansour
Keyword(s):  
Growth Functions

scholarly journals Effect of Chronological Age on Pulse Rate Discrimination in Adult Cochlear-Implant Users

2021 ◽  
Vol 25 ◽  
pp. 233121652110073
Author(s):  
Kelly C. Johnson ◽  
Zilong Xie ◽  
Maureen J. Shader ◽  
Paul G. Mayo ◽  
Matthew J. Goupell
Keyword(s):  
Pulse Rate ◽  
Compound Action Potential ◽  
Action Potential Amplitude ◽  
Growth Functions ◽  
Evoked Compound Action Potential ◽  
Rate Discrimination ◽  
Amplitude Growth ◽  
Temporal Pulse ◽  
Compound Action Potential Amplitude ◽  
Compound Action

Cochlear-implant (CI) users rely heavily on temporal envelope cues to understand speech. Temporal processing abilities may decline with advancing age in adult CI users. This study investigated the effect of age on the ability to discriminate changes in pulse rate. Twenty CI users aged 23 to 80 years participated in a rate discrimination task. They attempted to discriminate a 35% rate increase from baseline rates of 100, 200, 300, 400, or 500 pulses per second. The stimuli were electrical pulse trains delivered to a single electrode via direct stimulation to an apical (Electrode 20), a middle (Electrode 12), or a basal location (Electrode 4). Electrically evoked compound action potential amplitude growth functions were recorded at each of those electrodes as an estimate of peripheral neural survival. Results showed that temporal pulse rate discrimination performance declined with advancing age at higher stimulation rates (e.g., 500 pulses per second) when compared with lower rates. The age-related changes in temporal pulse rate discrimination at higher stimulation rates persisted after statistical analysis to account for the estimated peripheral contributions from electrically evoked compound action potential amplitude growth functions. These results indicate the potential contributions of central factors to the limitations in temporal pulse rate discrimination ability associated with aging in CI users.

scholarly journals Deriving loudness growth functions from categorical loudness scaling data

2017 ◽  
Vol 142 (6) ◽  
pp. 3660-3669 ◽  
Author(s):  
Marcin Wróblewski ◽  
Daniel M. Rasetshwane ◽  
Stephen T. Neely ◽  
Walt Jesteadt
Keyword(s):  
Growth Functions ◽  
Loudness Scaling ◽  
Loudness Growth

scholarly journals ON THE GROWTH OF GROUPS AND AUTOMORPHISMS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Finitely Generated ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Growth Functions ◽  
Growth Of Groups

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.

Medial Olivocochlear Reflex Effects on Amplitude Growth Functions of Long- and Short-Latency Components of Click-Evoked Otoacoustic Emissions in Humans

2021 ◽  
Author(s):  
Shawn Goodman ◽  
Sriram Boothalingam ◽  
Jeffery T Lichtenhan
Keyword(s):  
Otoacoustic Emissions ◽  
Dynamic Range ◽  
Short Latency ◽  
Medial Olivocochlear Reflex ◽  
Time Frequency ◽  
Growth Functions ◽  
Sound Levels ◽  
Amplitude Attenuation ◽  
Slope Change ◽  
Medial Olivocochlear

Functional outcomes of medial olivocochlear reflex (MOCR) activation, such as improved hearing in background noise and protection from noise damage, involve moderate to high sound levels. Previous noninvasive measurements of MOCR in humans focused primarily on otoacoustic emissions (OAEs) evoked at low sound levels. Interpreting MOCR effects on OAEs at higher levels is complicated by the possibility of the middle-ear muscle reflex and by components of OAEs arising from different locations along the length of the cochlear spiral. We overcame these issues by presenting click stimuli at a very slow rate and by time-frequency windowing the resulting click-evoked (CE)OAEs into short-latency (SL) and long-latency (LL) components. We characterized the effects of MOCR on CEOAE components using multiple measures to more comprehensively assess these effects throughout much of the dynamic range of hearing. These measures included CEOAE amplitude attenuation, equivalent input attenuation, phase, and slope of growth functions. Results show that MOCR effects are smaller on SL components than LL components, consistent with SL components being generated slightly basal of the characteristic frequency region. Amplitude attenuation measures showed the largest effects at the lowest stimulus levels, but slope change and equivalent input attenuation measures did not decrease at higher stimulus levels. These latter measures are less commonly reported and may provide insight into the variability in listening performance and noise susceptibility seen across individuals.

A description of the growth of sheep

1998 ◽  
Vol 1998 ◽  
pp. 47-47
Author(s):  
R.M. Lewis ◽  
G.C. Emmans ◽  
G. Simm ◽  
W.S. Dingwall ◽  
J. FitzSimons
Keyword(s):  
Growth Curves ◽  
Growth Function ◽  
Single Equation ◽  
Rate Parameter ◽  
Growth Functions ◽  
Gompertz Equation ◽  
Lumped Parameter ◽  
Highly Correlated ◽  
Mature Size

The idea that an animal of a given kind has, and grows to, a final or mature size is a useful one and several equations have been proposed that describe such growth to maturity (Winsor, 1932; Parks, 1982; Taylor, 1982). The Gompertz is one of these growth functions and describes in a comparatively simple, single equation the sigmoidal pattern of growth. It has 3 parameters, only 2 of which are important - mature size A and the rate parameter B. Estimates of A and B, however, are highly correlated. Considering A and B as a lumped parameter (AB) may overcome this problem. A Gompertz, or any other, growth function is not expected to describe all growth curves. When the environment (e.g., feed, housing) is non-limiting, it may provide a useful and succinct description of growth. The objectives of this study were to examine: (i) if the Gompertz equation adequately describes the growth of two genotypes of sheep under conditions designed to be non-limiting; and, (ii) if the lumped parameter AB has more desirable properties for estimation than A and B separately.

scholarly journals ROLES OF LOG-CONCAVITY, LOG-CONVEXITY, AND GROWTH ORDER IN WHITE NOISE ANALYSIS

2001 ◽  
Vol 04 (01) ◽  
pp. 59-84 ◽  
Author(s):  
NOBUHIRO ASAI ◽  
IZUMI KUBO ◽  
HUI-HSIUNG KUO
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Holomorphic Functions ◽  
Legendre Transform ◽  
Legendre Functions ◽  
Growth Order ◽  
White Noise Analysis ◽  
Systematic Method ◽  
Growth Functions ◽  
Natural Way

In this paper we will develop a systematic method to answer the questions (Q1) (Q2) (Q3) (Q4) (stated in Sec. 1) with complete generality. As a result, we can solve the difficulties (D1) (D2) (discussed in Sec. 1) without uncertainty. For these purposes we will introduce certain classes of growth functions u and apply the Legendre transform to obtain a sequence which leads to the weight sequence {α(n)} first studied by Cochran et al.6 The notion of (nearly) equivalent functions, (nearly) equivalent sequences and dual Legendre functions will be defined in a very natural way. An application to the growth order of holomorphic functions on ℰc will also be discussed.

scholarly journals The Precision of eCAP Thresholds Derived From Amplitude Growth Functions

2018 ◽  
Vol 39 (4) ◽  
pp. 701-711 ◽  
Author(s):  
Jan Dirk Biesheuvel ◽  
Jeroen J. Briaire ◽  
Johan H. M. Frijns
Keyword(s):  
Growth Functions ◽  
Amplitude Growth
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