On the Hausdorff distance between the Heaviside step function and Verhulst logistic function

Kyurkchiev, Nikolay; Markov, Svetoslav

doi:10.1007/s10910-015-0552-0

Cited by 63 publications

(41 citation statements)

References 17 publications

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“…In this example a descent sequence of intervals {F (x k )} is generated starting with randomly chosen initial point. At every iteration, α k is selected according to (6). d k is determined using Remark 2.…”

Section: Generating a Descent Sequence Of Interval Functionmentioning

confidence: 99%

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On Critical Point for Functions with Bounded Parameters

Roy

Panda

2019

2019 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT)

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Selection of descent direction at a point plays an important role in numerical optimizationfor minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a critical point. First, sufficient condition for the existence of descent direction is studied for this function and then a set of descent directions at a point is determined using linear expansion. Using these results a descent sequence of intervals is generated and critical point is characterized. This theoretical development is justified with numerical example.keywords Line search technique, Markov difference, Interval ordering, Descent direction, Critical point.

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Section: Generating a Descent Sequence Of Interval Functionmentioning

confidence: 99%

“…An example of such type function is F (x, y) = e [−3,3]x 3 ⊕ [4, 5]xy 5 . In the literature of interval analysis, Markov is the pioneer who has studied different areas of modern mathematics using interval analysis ( see [5], [6], [10], [11], [12], [13] etc. ).…”

Section: Introductionmentioning

confidence: 99%

On Critical Point for Functions with Bounded Parameters

Roy

Panda

2019

2019 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT)

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“…5. Graphs of the solutions m, f of model (23) ues for the rate parameters and the initial conditions by fitting (some of) the solutions to available time course experimental measurements. Computational tools for the solution of this problem are proposed in [10], [11].…”

Section: Denoting the Concentrationsmentioning

confidence: 99%

Building reaction kinetic models for amiloid fibril growth

Markov

2016

BIOMATH

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Abstract-In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We propose several reaction network models for the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using the computer algebra system Mathematica.

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“…logistic functions in Hausdorff metric. The Hausdorff approximation of the Heaviside step function by sigmoid functions is discussed from various computational and modelling aspects in [28], [29], [30].…”

Section: Propositionmentioning

confidence: 99%

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Илиев

Kyurkchiev²,

Markov³

2015

BIOMATH

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Abstract-We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued step function is discussed using Hausdorff metric. Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

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On the Hausdorff distance between the Heaviside step function and Verhulst logistic function

Cited by 63 publications

References 17 publications

On Critical Point for Functions with Bounded Parameters

On Critical Point for Functions with Bounded Parameters

Building reaction kinetic models for amiloid fibril growth

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

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