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Papers by Oleksandr Iaroshenko

Research paper thumbnail of Vortices in the Ginzburg-Landau Superconductivity Model

Research paper thumbnail of Image Compression: Sparse Coding vs. Bottleneck Autoencoders

2018 IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), 2018

Bottleneck autoencoders have been actively researched as a solution to image compression tasks. H... more Bottleneck autoencoders have been actively researched as a solution to image compression tasks. However, we observed that bottleneck autoencoders produce subjectively low quality reconstructed images. In this work, we explore the ability of sparse coding to improve reconstructed image quality for the same degree of compression. We observe that sparse image compression produces visually superior reconstructed images and yields higher values of pixel-wise measures of reconstruction quality (PSNR and SSIM) compared to bottleneck autoencoders. In addition, we find that using alternative metrics that correlate better with human perception, such as feature perceptual loss and the classification accuracy, sparse image compression scores up to 18.06% and 2.7% higher, respectively, compared to bottleneck autoencoders. Although computationally much more intensive, we find that sparse coding is otherwise superior to bottleneck autoencoders for the same degree of compression.

Research paper thumbnail of Random on-board pixel sampling (ROPS) X-ray Camera

arXiv: Instrumentation and Detectors, 2017

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-spee... more Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, an...

Research paper thumbnail of Binary Operations on Neuromorphic Hardware with Application to Linear Algebraic Operations and Stochastic Equations

Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected v... more Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses – so-called neuromorphic systems – is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement ...

Research paper thumbnail of Temporal-spatial sparse coding for X-ray image analysis and interpretation

Bulletin of the American Physical Society, 2018

Research paper thumbnail of Unsupervised learning about 4D features of microparticle motion

Review of Scientific Instruments, 2018

Material clusters of different sizes are known to exist in high-temperature plasmas due to plasma... more Material clusters of different sizes are known to exist in high-temperature plasmas due to plasma-wall interactions. The facts that these clusters, ranging from sub-microns to above mm in size, can move from one location to another quickly and that there are a lot of them make high-speed imaging and tracking one of the best, effective, and sometimes only diagnostic. An unsupervised machine learning technique based on deconvolutional neural networks is developed to analyze two-camera videos of high-temperature microparticles generated from exploding wires. The neural network utilizes a locally competitive algorithm to infer representations and optimize a dictionary composed of kernels, or basis vectors, for image analysis. Our primary goal is to use this method for feature recognition and prediction of the time-dependent three-dimensional (or "4D") microparticle motion. Features equivalent to local velocity vectors have been identified as the dictionary kernels or "building blocks" of the scene. The dictionary elements from the left and right camera views are found to be strongly correlated and satisfy the projection geometrical constraints. The results show that unsupervised machine learning techniques are promising approaches to process large sets of images for high-temperature plasmas and other scientific experiments. Machine learning techniques can be useful to handle the large amount of data and therefore aid the understanding of plasma-wall interaction.

Research paper thumbnail of On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

Journal of Differential Equations, 2018

We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number... more We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau parameter vs hole radius) is motivated by a recently dsicovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg-Landau problems in the classes of S 1-valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.

Research paper thumbnail of A compressed sensing X-ray camera with a multilayer architecture

Journal of Instrumentation, 2018

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-spee... more Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, and computational image techniques, is expected to facilitate the development and applications of high-speed X-ray camera technology.

Research paper thumbnail of The arbitrary order mixed mimetic finite difference method for the diffusion equation

ESAIM: Mathematical Modelling and Numerical Analysis, 2016

We propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximati... more We propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux and scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.

Research paper thumbnail of Vortex phase separation in mesoscopic superconductors

Scientific Reports, 2013

We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with... more We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with London penetration depth, the ground state of vortices pinned by homogeneously distributed columnar defects can form a hierarchical nested domain structure. Each domain is characterized by an average number of vortices trapped at a single pinning site within a given domain. Our study marks a radical departure from the current understanding of the ground state in disordered macroscopic systems and provides an insight into the interplay between disorder, vortex-vortex interaction, and confinement within finite system size. The observed vortex phase segregation implies the existence of the soliton solution for the vortex density in the finite superconductors and establishes a new class of nonlinear systems that exhibit the soliton phenomenon. V ortex matter in the presence of structural defects forms a wide variety of phases with specific properties depending on the relation between the vortex-vortex and vortex-defect interactions 1,2. The findings of Refs. 3, 4, which revealed significant enhancement of vortex pinning in high-temperature superconductors by ion irradiation, broke ground for a new direction in vortex physics. Heavy ions leave the tracks of the damaged amorphous material where superconductivity is suppressed. Thus the vortices penetrating the sample occupy columnar defects where the vortex energy is appreciably less than in the undamaged material. A theory of the resulting vortex Bose glass phase was developed in Refs. 5, 6, where the physics of flux lines in superconductors pinned by columnar defects was mapped onto boson localization in two dimensions. The distribution of vortices in the Bose glass state that forms in the infinite (i.e. thermodynamically large) samples, containing columnar defects, is a uniform one. A question about what happens to the Bose glass in the finite samples is most natural in view of explosively developing studies of small superconductors, i.e. superconductors with the lateral sizes R s comparable to the London screening length l or even with the coherence length j. Indeed even the samples without columnar defects reveal that the properties of the homogeneous vortex state change dramatically as R s l. The boundaries start to affect the distribution of vortices and makes it nonuniform. Experimental study of mesoscopic superconducting discs with the total vorticity L , 40 revealed formation of the concentric shells of vortices 7 in accord with the results of numerical simulations 8. The analysis of shell filling with increasing L allowed the authors of Ref. 7 to identify magic numbers corresponding to the appearance of consecutive new shells. At the same time, vortex distribution over the sample remains ''quasi-homogeneous'' with the vortex density gradually changing with the distance from the sample center. For example, the experimental and numerical studies of the samples containing a macroscopic number of vortices showed that, almost everywhere, vortices arrange themselves into a nearly perfect Abrikosov lattice, containing the few disclinations necessary to match the cylindrical symmetry of the sample. Only within a few, 2-3, shells adjacent to the surface, vortex distribution differs noticeably from that in the bulk. At the same time, theoretical consideration of the critical state in a superconducting slab containing a lattice of strong pins 9 predicted that instead of the expected in the critical state constant gradient in the vortex density a terraced piecewise vortex structure structure can form. This terraced vortex distribution, unexpected from the viewpoint of an orthodox concept of the critical state, is, formally, nothing but a standard soliton solution for the one-dimensional commensurate structures, which appeared first as a 1D model for dislocations 10,11. The physical reason for emerging such a structure is the competition between the effect of the critical current flowing uniformly through the slab and thus implying the constant gradient of the vortex density across the sample and the action of the lattice of strong pinning sites that tend to trap vortices enforcing them into a regular array with the commensurate period. As a result, a metastable structure forms, comprising vortex domains of a piecewise constant vortex density. The originally uniform current is compressed into the current filaments concentrated along the

Research paper thumbnail of Vortices in the Ginzburg-Landau Superconductivity Model

Research paper thumbnail of Image Compression: Sparse Coding vs. Bottleneck Autoencoders

2018 IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), 2018

Bottleneck autoencoders have been actively researched as a solution to image compression tasks. H... more Bottleneck autoencoders have been actively researched as a solution to image compression tasks. However, we observed that bottleneck autoencoders produce subjectively low quality reconstructed images. In this work, we explore the ability of sparse coding to improve reconstructed image quality for the same degree of compression. We observe that sparse image compression produces visually superior reconstructed images and yields higher values of pixel-wise measures of reconstruction quality (PSNR and SSIM) compared to bottleneck autoencoders. In addition, we find that using alternative metrics that correlate better with human perception, such as feature perceptual loss and the classification accuracy, sparse image compression scores up to 18.06% and 2.7% higher, respectively, compared to bottleneck autoencoders. Although computationally much more intensive, we find that sparse coding is otherwise superior to bottleneck autoencoders for the same degree of compression.

Research paper thumbnail of Random on-board pixel sampling (ROPS) X-ray Camera

arXiv: Instrumentation and Detectors, 2017

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-spee... more Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, an...

Research paper thumbnail of Binary Operations on Neuromorphic Hardware with Application to Linear Algebraic Operations and Stochastic Equations

Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected v... more Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses – so-called neuromorphic systems – is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement ...

Research paper thumbnail of Temporal-spatial sparse coding for X-ray image analysis and interpretation

Bulletin of the American Physical Society, 2018

Research paper thumbnail of Unsupervised learning about 4D features of microparticle motion

Review of Scientific Instruments, 2018

Material clusters of different sizes are known to exist in high-temperature plasmas due to plasma... more Material clusters of different sizes are known to exist in high-temperature plasmas due to plasma-wall interactions. The facts that these clusters, ranging from sub-microns to above mm in size, can move from one location to another quickly and that there are a lot of them make high-speed imaging and tracking one of the best, effective, and sometimes only diagnostic. An unsupervised machine learning technique based on deconvolutional neural networks is developed to analyze two-camera videos of high-temperature microparticles generated from exploding wires. The neural network utilizes a locally competitive algorithm to infer representations and optimize a dictionary composed of kernels, or basis vectors, for image analysis. Our primary goal is to use this method for feature recognition and prediction of the time-dependent three-dimensional (or "4D") microparticle motion. Features equivalent to local velocity vectors have been identified as the dictionary kernels or "building blocks" of the scene. The dictionary elements from the left and right camera views are found to be strongly correlated and satisfy the projection geometrical constraints. The results show that unsupervised machine learning techniques are promising approaches to process large sets of images for high-temperature plasmas and other scientific experiments. Machine learning techniques can be useful to handle the large amount of data and therefore aid the understanding of plasma-wall interaction.

Research paper thumbnail of On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

Journal of Differential Equations, 2018

We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number... more We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau parameter vs hole radius) is motivated by a recently dsicovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg-Landau problems in the classes of S 1-valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.

Research paper thumbnail of A compressed sensing X-ray camera with a multilayer architecture

Journal of Instrumentation, 2018

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-spee... more Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, and computational image techniques, is expected to facilitate the development and applications of high-speed X-ray camera technology.

Research paper thumbnail of The arbitrary order mixed mimetic finite difference method for the diffusion equation

ESAIM: Mathematical Modelling and Numerical Analysis, 2016

We propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximati... more We propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux and scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.

Research paper thumbnail of Vortex phase separation in mesoscopic superconductors

Scientific Reports, 2013

We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with... more We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with London penetration depth, the ground state of vortices pinned by homogeneously distributed columnar defects can form a hierarchical nested domain structure. Each domain is characterized by an average number of vortices trapped at a single pinning site within a given domain. Our study marks a radical departure from the current understanding of the ground state in disordered macroscopic systems and provides an insight into the interplay between disorder, vortex-vortex interaction, and confinement within finite system size. The observed vortex phase segregation implies the existence of the soliton solution for the vortex density in the finite superconductors and establishes a new class of nonlinear systems that exhibit the soliton phenomenon. V ortex matter in the presence of structural defects forms a wide variety of phases with specific properties depending on the relation between the vortex-vortex and vortex-defect interactions 1,2. The findings of Refs. 3, 4, which revealed significant enhancement of vortex pinning in high-temperature superconductors by ion irradiation, broke ground for a new direction in vortex physics. Heavy ions leave the tracks of the damaged amorphous material where superconductivity is suppressed. Thus the vortices penetrating the sample occupy columnar defects where the vortex energy is appreciably less than in the undamaged material. A theory of the resulting vortex Bose glass phase was developed in Refs. 5, 6, where the physics of flux lines in superconductors pinned by columnar defects was mapped onto boson localization in two dimensions. The distribution of vortices in the Bose glass state that forms in the infinite (i.e. thermodynamically large) samples, containing columnar defects, is a uniform one. A question about what happens to the Bose glass in the finite samples is most natural in view of explosively developing studies of small superconductors, i.e. superconductors with the lateral sizes R s comparable to the London screening length l or even with the coherence length j. Indeed even the samples without columnar defects reveal that the properties of the homogeneous vortex state change dramatically as R s l. The boundaries start to affect the distribution of vortices and makes it nonuniform. Experimental study of mesoscopic superconducting discs with the total vorticity L , 40 revealed formation of the concentric shells of vortices 7 in accord with the results of numerical simulations 8. The analysis of shell filling with increasing L allowed the authors of Ref. 7 to identify magic numbers corresponding to the appearance of consecutive new shells. At the same time, vortex distribution over the sample remains ''quasi-homogeneous'' with the vortex density gradually changing with the distance from the sample center. For example, the experimental and numerical studies of the samples containing a macroscopic number of vortices showed that, almost everywhere, vortices arrange themselves into a nearly perfect Abrikosov lattice, containing the few disclinations necessary to match the cylindrical symmetry of the sample. Only within a few, 2-3, shells adjacent to the surface, vortex distribution differs noticeably from that in the bulk. At the same time, theoretical consideration of the critical state in a superconducting slab containing a lattice of strong pins 9 predicted that instead of the expected in the critical state constant gradient in the vortex density a terraced piecewise vortex structure structure can form. This terraced vortex distribution, unexpected from the viewpoint of an orthodox concept of the critical state, is, formally, nothing but a standard soliton solution for the one-dimensional commensurate structures, which appeared first as a 1D model for dislocations 10,11. The physical reason for emerging such a structure is the competition between the effect of the critical current flowing uniformly through the slab and thus implying the constant gradient of the vortex density across the sample and the action of the lattice of strong pinning sites that tend to trap vortices enforcing them into a regular array with the commensurate period. As a result, a metastable structure forms, comprising vortex domains of a piecewise constant vortex density. The originally uniform current is compressed into the current filaments concentrated along the