Single-channel neural signal recordings were obtained from deep brain region in normal rats and r... more Single-channel neural signal recordings were obtained from deep brain region in normal rats and rats conditioned as an animal model for human obsessive-compulsive disorder (OCD), both in anesthetized condition. Artifact noise of consistent 70Hz repetition frequency and its ...
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear ... more From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the local generalizations of derivatives assuming the usual topology of the real line. The concept of derivative is generalized in terms of the class of the modulus of continuity of the primitive function. This definition is suitable for applications involving continuous but possibly non-absolutely continuous functions of a real variable. The main application of the approach is the generalization of the Lebesgue monotone differentiation theorem. On the second place, the conditions of continuity of generalized derivative are also demonstrated.
Multiples lines of evidence indicate that spatial 3D organisation nuclear DNA is critical in adap... more Multiples lines of evidence indicate that spatial 3D organisation nuclear DNA is critical in adapting to different environmental conditions and the Impact of Nuclear Domains On Gene Expression and Plant Traits (INDEPTH) network aims to decipher how nuclear architecture, chromatin organisation and gene expression are connected and modified in response to internal and external cues.
Image segmentation still represents an active area of research since no universal solution can be... more Image segmentation still represents an active area of research since no universal solution can be identified. Traditional image segmentation algorithms are problem-specific and limited in scope. On the other hand, machine learning offers an alternative paradigm where predefined features are combined into different classifiers, providing pixel-level classification and segmentation. However, machine learning only can not address the question as to which features are appropriate for a certain classification problem. The article presents an automated image segmentation and classification platform, called Active Segmentation, which is based on ImageJ. The platform integrates expert domain knowledge, providing partial ground truth, with geometrical feature extraction based on multi-scale signal processing combined with machine learning. The approach in image segmentation is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application we demonstrate whole ima...
Abstract In their article, N. A. Kudryashov, M. A. Chmykhov, M. Vigdorowitsch, “Analytical featur... more Abstract In their article, N. A. Kudryashov, M. A. Chmykhov, M. Vigdorowitsch, “Analytical features of the SIR model and their applications to COVID-19”, Applied Mathematical Modelling 90 (2021) 466–473, aimed to establish the relationships among S, I and R populations, as well as to suggest a form for the exact solution of the SIR model. One of the equations given there is not correct, which leads to an error in the solution. The objective of the present letter is to present the correct parametric solution and to discuss its numerical approximation by direct quadrature.
H\"older functions represent mathematical models of nonlinear physical phenomena. This work ... more H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the exponent order. Fractional velocity is defined as the limit of the difference quotient of the function's increment and the difference of its argument raised to a fractional power. A relationship to the point-wise H\"older exponent of a function, its point-wise oscillation and the existence of fractional velocity is established. It is demonstrated that wherever the fractional velocity of non-integral order is continuous then it vanishes. The work further demonstrates the use of fractional velocity as a tool for characterization of the discontinuity set of the derivatives of functions thus providing a natural characterization of strongly non-linear local behavior. Finally the equivalence with the Kolwankar-Gangal local fractional derivativ...
The chapter introduces multiscale methods for image analysis and their applications to segmentati... more The chapter introduces multiscale methods for image analysis and their applications to segmentation of microscopic images. Specifically, it presents mathematical morphology and linear scale-space theories as overarching signal processing frameworks without excessive mathematical formalization. The chapter introduces several differential invariants, which are computed from parametrized Gaussian kernels and their derivatives. The main application of this approach is to build a multidimensional multiscale feature space, which can be subsequently used to learn characteristic fingerprints of the objects of interests. More specialized applications, such as anisotropic diffusion and detection of blob-like and fiber-like structures, are introduced for two-dimensional images, and extensions to three-dimensional images are discussed. Presented approaches are generic and thus have broad applicability to time-varying signals and to twoand three-dimensional signals, such as microscopic images. T...
Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, wh... more Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still not understood well. Recent experimental and theoretical results point out possible role of the diffusion species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries -- a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, which is derived from physically realistic assumptions using a fractional calculus approach. The derived fractional-order distribution morphs into regular order diffusion in the case of integer fractional exponents. The...
Single-channel neural signal recordings were obtained from deep brain region in normal rats and r... more Single-channel neural signal recordings were obtained from deep brain region in normal rats and rats conditioned as an animal model for human obsessive-compulsive disorder (OCD), both in anesthetized condition. Artifact noise of consistent 70Hz repetition frequency and its ...
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear ... more From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the local generalizations of derivatives assuming the usual topology of the real line. The concept of derivative is generalized in terms of the class of the modulus of continuity of the primitive function. This definition is suitable for applications involving continuous but possibly non-absolutely continuous functions of a real variable. The main application of the approach is the generalization of the Lebesgue monotone differentiation theorem. On the second place, the conditions of continuity of generalized derivative are also demonstrated.
Multiples lines of evidence indicate that spatial 3D organisation nuclear DNA is critical in adap... more Multiples lines of evidence indicate that spatial 3D organisation nuclear DNA is critical in adapting to different environmental conditions and the Impact of Nuclear Domains On Gene Expression and Plant Traits (INDEPTH) network aims to decipher how nuclear architecture, chromatin organisation and gene expression are connected and modified in response to internal and external cues.
Image segmentation still represents an active area of research since no universal solution can be... more Image segmentation still represents an active area of research since no universal solution can be identified. Traditional image segmentation algorithms are problem-specific and limited in scope. On the other hand, machine learning offers an alternative paradigm where predefined features are combined into different classifiers, providing pixel-level classification and segmentation. However, machine learning only can not address the question as to which features are appropriate for a certain classification problem. The article presents an automated image segmentation and classification platform, called Active Segmentation, which is based on ImageJ. The platform integrates expert domain knowledge, providing partial ground truth, with geometrical feature extraction based on multi-scale signal processing combined with machine learning. The approach in image segmentation is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application we demonstrate whole ima...
Abstract In their article, N. A. Kudryashov, M. A. Chmykhov, M. Vigdorowitsch, “Analytical featur... more Abstract In their article, N. A. Kudryashov, M. A. Chmykhov, M. Vigdorowitsch, “Analytical features of the SIR model and their applications to COVID-19”, Applied Mathematical Modelling 90 (2021) 466–473, aimed to establish the relationships among S, I and R populations, as well as to suggest a form for the exact solution of the SIR model. One of the equations given there is not correct, which leads to an error in the solution. The objective of the present letter is to present the correct parametric solution and to discuss its numerical approximation by direct quadrature.
H\"older functions represent mathematical models of nonlinear physical phenomena. This work ... more H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the exponent order. Fractional velocity is defined as the limit of the difference quotient of the function's increment and the difference of its argument raised to a fractional power. A relationship to the point-wise H\"older exponent of a function, its point-wise oscillation and the existence of fractional velocity is established. It is demonstrated that wherever the fractional velocity of non-integral order is continuous then it vanishes. The work further demonstrates the use of fractional velocity as a tool for characterization of the discontinuity set of the derivatives of functions thus providing a natural characterization of strongly non-linear local behavior. Finally the equivalence with the Kolwankar-Gangal local fractional derivativ...
The chapter introduces multiscale methods for image analysis and their applications to segmentati... more The chapter introduces multiscale methods for image analysis and their applications to segmentation of microscopic images. Specifically, it presents mathematical morphology and linear scale-space theories as overarching signal processing frameworks without excessive mathematical formalization. The chapter introduces several differential invariants, which are computed from parametrized Gaussian kernels and their derivatives. The main application of this approach is to build a multidimensional multiscale feature space, which can be subsequently used to learn characteristic fingerprints of the objects of interests. More specialized applications, such as anisotropic diffusion and detection of blob-like and fiber-like structures, are introduced for two-dimensional images, and extensions to three-dimensional images are discussed. Presented approaches are generic and thus have broad applicability to time-varying signals and to twoand three-dimensional signals, such as microscopic images. T...
Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, wh... more Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still not understood well. Recent experimental and theoretical results point out possible role of the diffusion species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries -- a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, which is derived from physically realistic assumptions using a fractional calculus approach. The derived fractional-order distribution morphs into regular order diffusion in the case of integer fractional exponents. The...
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Papers by Dimiter Prodanov