scholarly journals Mathematical Study of the Verhulst and Gompertz Growth Functions and Their Contemporary Applications

2021 ◽  
Vol 0 (34) ◽  
pp. 73-102
Author(s):  
Cemil İskender
Keyword(s):  
Mathematical Study ◽  
Growth Functions

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

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 Evolution of ribosomal protein network architectures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Youri Timsit ◽  
Grégoire Sergeant-Perthuis ◽  
Daniel Bennequin
Keyword(s):  
Selective Pressure ◽  
Experimental Studies ◽  
Protein Networks ◽  
Network Architectures ◽  
Mathematical Study ◽  
Remote Communication ◽  
Aromatic Residues ◽  
Peptidyl Transfer ◽  
Exit Tunnel ◽  
Long Range Communication

AbstractTo perform an accurate protein synthesis, ribosomes accomplish complex tasks involving the long-range communication between its functional centres such as the peptidyl transfer centre, the tRNA bindings sites and the peptide exit tunnel. How information is transmitted between these sites remains one of the major challenges in current ribosome research. Many experimental studies have revealed that some r-proteins play essential roles in remote communication and the possible involvement of r-protein networks in these processes have been recently proposed. Our phylogenetic, structural and mathematical study reveals that of the three kingdom’s r-protein networks converged towards non-random graphs where r-proteins collectively coevolved to optimize interconnection between functional centres. The massive acquisition of conserved aromatic residues at the interfaces and along the extensions of the newly connected eukaryotic r-proteins also highlights that a strong selective pressure acts on their sequences probably for the formation of new allosteric pathways in the network.

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